%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW368+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:26:03 EDT 2023

% Result   : Theorem 143.38s 138.36s
% Output   : Proof 143.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW368+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n023.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 23:01:14 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 143.38/138.36  
% 143.38/138.36  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 143.38/138.36  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 143.38/138.36  %-----------------------------------------------------
% 143.38/138.36  ncf(matrix, plain, [(52811 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), v_G)), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))], (2 ^ _779308) ^ [_779338] : [-(_779338 = _779338)], (4 ^ _779308) ^ [_779361, _779363] : [_779363 = _779361, -(_779361 = _779363)], (10 ^ _779308) ^ [_779434, _779436, _779438] : [-(_779438 = _779434), _779438 = _779436, _779436 = _779434], (20 ^ _779308) ^ [_779571, _779573] : [-(v_wt(_779571)), _779573 = _779571, v_wt(_779573)], (30 ^ _779308) ^ [_779696, _779698, _779700, _779702] : [-(v_P(_779700, _779696)), v_P(_779702, _779698), _779702 = _779700, _779698 = _779696], (44 ^ _779308) ^ [_779889, _779891, _779893, _779895, _779897, _779899, _779901, _779903, _779905, _779907, _779909, _779911] : [-(c_Nitpick_Ofold__graph_H(_779909, _779905, _779901, _779897, _779893, _779889)), c_Nitpick_Ofold__graph_H(_779911, _779907, _779903, _779899, _779895, _779891), _779911 = _779909, _779907 = _779905, _779903 = _779901, _779899 = _779897, _779895 = _779893, _779891 = _779889], (74 ^ _779308) ^ [_780434, _780436, _780438, _780440, _780442, _780444] : [-(c_Big__Operators_Osemilattice__big(_780442, _780438, _780434)), c_Big__Operators_Osemilattice__big(_780444, _780440, _780436), _780444 = _780442, _780440 = _780438, _780436 = _780434], (92 ^ _779308) ^ [_780703, _780705, _780707, _780709, _780711, _780713, _780715, _780717, _780719, _780721] : [-(c_Big__Operators_Ocomm__monoid__big(_780719, _780715, _780711, _780707, _780703)), c_Big__Operators_Ocomm__monoid__big(_780721, _780717, _780713, _780709, _780705), _780721 = _780719, _780717 = _780715, _780713 = _780711, _780709 = _780707, _780705 = _780703], (118 ^ _779308) ^ [_781148, _781150, _781152, _781154] : [-(c_Int_Oiszero(_781152, _781148)), c_Int_Oiszero(_781154, _781150), _781154 = _781152, _781150 = _781148], (132 ^ _779308) ^ [_781341, _781343] : [-(class_Rings_Odivision__ring__inverse__zero(_781341)), _781343 = _781341, class_Rings_Odivision__ring__inverse__zero(_781343)], (142 ^ _779308) ^ [_781466, _781468] : [-(class_Rings_Odivision__ring(_781466)), _781468 = _781466, class_Rings_Odivision__ring(_781468)], (152 ^ _779308) ^ [_781591, _781593] : [-(class_Fields_Ofield__inverse__zero(_781591)), _781593 = _781591, class_Fields_Ofield__inverse__zero(_781593)], (162 ^ _779308) ^ [_781716, _781718, _781720, _781722] : [-(c_Nitpick_Orefl_H(_781720, _781716)), c_Nitpick_Orefl_H(_781722, _781718), _781722 = _781720, _781718 = _781716], (176 ^ _779308) ^ [_781909, _781911, _781913, _781915, _781917, _781919, _781921, _781923, _781925, _781927, _781929, _781931] : [-(c_Finite__Set_Ofolding__image__simple__idem(_781929, _781925, _781921, _781917, _781913, _781909)), c_Finite__Set_Ofolding__image__simple__idem(_781931, _781927, _781923, _781919, _781915, _781911), _781931 = _781929, _781927 = _781925, _781923 = _781921, _781919 = _781917, _781915 = _781913, _781911 = _781909], (206 ^ _779308) ^ [_782454, _782456] : [-(class_Fields_Ofield(_782454)), _782456 = _782454, class_Fields_Ofield(_782456)], (216 ^ _779308) ^ [_782579, _782581] : [-(c_Nat__Transfer_Ois__nat(_782579)), _782581 = _782579, c_Nat__Transfer_Ois__nat(_782581)], (226 ^ _779308) ^ [_782704, _782706] : [-(class_Fields_Olinordered__field__inverse__zero(_782704)), _782706 = _782704, class_Fields_Olinordered__field__inverse__zero(_782706)], (236 ^ _779308) ^ [_782829, _782831, _782833, _782835, _782837, _782839, _782841, _782843, _782845, _782847, _782849, _782851] : [-(c_Finite__Set_Ofolding__image__simple(_782849, _782845, _782841, _782837, _782833, _782829)), c_Finite__Set_Ofolding__image__simple(_782851, _782847, _782843, _782839, _782835, _782831), _782851 = _782849, _782847 = _782845, _782843 = _782841, _782839 = _782837, _782835 = _782833, _782831 = _782829], (266 ^ _779308) ^ [_783374, _783376, _783378, _783380] : [-(c_FunDef_Oreduction__pair(_783378, _783374)), c_FunDef_Oreduction__pair(_783380, _783376), _783380 = _783378, _783376 = _783374], (280 ^ _779308) ^ [_783567, _783569, _783571, _783573] : [-(c_Nitpick_Owf_H(_783571, _783567)), c_Nitpick_Owf_H(_783573, _783569), _783573 = _783571, _783569 = _783567], (294 ^ _779308) ^ [_783760, _783762] : [-(c_Nitpick_Ounknown(_783760)), _783762 = _783760, c_Nitpick_Ounknown(_783762)], (304 ^ _779308) ^ [_783885, _783887, _783889, _783891] : [-(c_Wellfounded_OwfP(_783889, _783885)), c_Wellfounded_OwfP(_783891, _783887), _783891 = _783889, _783887 = _783885], (318 ^ _779308) ^ [_784078, _784080, _784082, _784084, _784086, _784088, _784090, _784092] : [-(c_Finite__Set_Ofolding__idem(_784090, _784086, _784082, _784078)), c_Finite__Set_Ofolding__idem(_784092, _784088, _784084, _784080), _784092 = _784090, _784088 = _784086, _784084 = _784082, _784080 = _784078], (340 ^ _779308) ^ [_784431, _784433, _784435, _784437] : [-(c_Relation_Oirrefl(_784435, _784431)), c_Relation_Oirrefl(_784437, _784433), _784437 = _784435, _784433 = _784431], (354 ^ _779308) ^ [_784624, _784626, _784628, _784630, _784632, _784634] : [-(c_Relation_Ototal__on(_784632, _784628, _784624)), c_Relation_Ototal__on(_784634, _784630, _784626), _784634 = _784632, _784630 = _784628, _784626 = _784624], (372 ^ _779308) ^ [_784893, _784895, _784897, _784899, _784901, _784903, _784905, _784907] : [-(c_Finite__Set_Ofolding(_784905, _784901, _784897, _784893)), c_Finite__Set_Ofolding(_784907, _784903, _784899, _784895), _784907 = _784905, _784903 = _784901, _784899 = _784897, _784895 = _784893], (394 ^ _779308) ^ [_785246, _785248, _785250, _785252, _785254, _785256] : [-(c_Finite__Set_Ofolding__one__idem(_785254, _785250, _785246)), c_Finite__Set_Ofolding__one__idem(_785256, _785252, _785248), _785256 = _785254, _785252 = _785250, _785248 = _785246], (412 ^ _779308) ^ [_785515, _785517, _785519, _785521, _785523, _785525] : [-(c_Finite__Set_Ofolding__one(_785523, _785519, _785515)), c_Finite__Set_Ofolding__one(_785525, _785521, _785517), _785525 = _785523, _785521 = _785519, _785517 = _785515], (430 ^ _779308) ^ [_785784, _785786, _785788, _785790, _785792, _785794] : [-(c_Relation_Osingle__valued(_785792, _785788, _785784)), c_Relation_Osingle__valued(_785794, _785790, _785786), _785794 = _785792, _785790 = _785788, _785786 = _785784], (448 ^ _779308) ^ [_786053, _786055] : [-(class_Rings_Oinverse(_786053)), _786055 = _786053, class_Rings_Oinverse(_786055)], (458 ^ _779308) ^ [_786178, _786180, _786182, _786184, _786186, _786188] : [-(c_Nitpick_Oless__frac(_786186, _786182, _786178)), c_Nitpick_Oless__frac(_786188, _786184, _786180), _786188 = _786186, _786184 = _786182, _786180 = _786178], (476 ^ _779308) ^ [_786447, _786449, _786451, _786453, _786455, _786457] : [-(c_Nitpick_Oless__eq__frac(_786455, _786451, _786447)), c_Nitpick_Oless__eq__frac(_786457, _786453, _786449), _786457 = _786455, _786453 = _786451, _786449 = _786447], (494 ^ _779308) ^ [_786716, _786718] : [-(c_Nat__Transfer_Onat__set(_786716)), _786718 = _786716, c_Nat__Transfer_Onat__set(_786718)], (504 ^ _779308) ^ [_786841, _786843, _786845, _786847, _786849, _786851, _786853, _786855] : [-(c_List_Olistrelp(_786853, _786849, _786845, _786841)), c_List_Olistrelp(_786855, _786851, _786847, _786843), _786855 = _786853, _786851 = _786849, _786847 = _786845, _786843 = _786841], (526 ^ _779308) ^ [_787194, _787196] : [-(class_Lattices_Oab__semigroup__idem__mult(_787194)), _787196 = _787194, class_Lattices_Oab__semigroup__idem__mult(_787196)], (536 ^ _779308) ^ [_787319, _787321, _787323, _787325, _787327, _787329] : [-(c_Finite__Set_Ofun__left__comm__idem(_787327, _787323, _787319)), c_Finite__Set_Ofun__left__comm__idem(_787329, _787325, _787321), _787329 = _787327, _787325 = _787323, _787321 = _787319], (554 ^ _779308) ^ [_787588, _787590, _787592, _787594, _787596, _787598, _787600, _787602, _787604, _787606] : [-(c_Typedef_Otype__definition(_787604, _787600, _787596, _787592, _787588)), c_Typedef_Otype__definition(_787606, _787602, _787598, _787594, _787590), _787606 = _787604, _787602 = _787600, _787598 = _787596, _787594 = _787592, _787590 = _787588], (580 ^ _779308) ^ [_788033, _788035, _788037, _788039, _788041, _788043] : [-(c_Finite__Set_Ofun__left__comm(_788041, _788037, _788033)), c_Finite__Set_Ofun__left__comm(_788043, _788039, _788035), _788043 = _788041, _788039 = _788037, _788035 = _788033], (598 ^ _779308) ^ [_788302, _788304] : [-(c_List_Onat__list(_788302)), _788304 = _788302, c_List_Onat__list(_788304)], (608 ^ _779308) ^ [_788427, _788429, _788431, _788433, _788435, _788437, _788439, _788441, _788443, _788445] : [-(c_List_Olist__all2(_788443, _788439, _788435, _788431, _788427)), c_List_Olist__all2(_788445, _788441, _788437, _788433, _788429), _788445 = _788443, _788441 = _788439, _788437 = _788435, _788433 = _788431, _788429 = _788427], (634 ^ _779308) ^ [_788872, _788874, _788876, _788878] : [-(c_List_Olinorder__class_Osorted(_788876, _788872)), c_List_Olinorder__class_Osorted(_788878, _788874), _788878 = _788876, _788874 = _788872], (648 ^ _779308) ^ [_789065, _789067, _789069, _789071] : [-(c_FunDef_Ois__measure(_789069, _789065)), c_FunDef_Ois__measure(_789071, _789067), _789071 = _789069, _789067 = _789065], (662 ^ _779308) ^ [_789258, _789260, _789262, _789264, _789266, _789268, _789270, _789272] : [-(c_Nat__Transfer_Otransfer__morphism(_789270, _789266, _789262, _789258)), c_Nat__Transfer_Otransfer__morphism(_789272, _789268, _789264, _789260), _789272 = _789270, _789268 = _789266, _789264 = _789262, _789260 = _789258], (684 ^ _779308) ^ [_789611, _789613] : [-(class_Fields_Olinordered__field(_789611)), _789613 = _789611, class_Fields_Olinordered__field(_789613)], (694 ^ _779308) ^ [_789736, _789738, _789740, _789742, _789744, _789746] : [-(c_List_Olist__ex1(_789744, _789740, _789736)), c_List_Olist__ex1(_789746, _789742, _789738), _789746 = _789744, _789742 = _789740, _789738 = _789736], (712 ^ _779308) ^ [_790005, _790007, _790009, _790011, _790013, _790015] : [-(c_List_Oall__interval__int(_790013, _790009, _790005)), c_List_Oall__interval__int(_790015, _790011, _790007), _790015 = _790013, _790011 = _790009, _790007 = _790005], (730 ^ _779308) ^ [_790274, _790276, _790278, _790280] : [-(c_Predicate_Oreflp(_790278, _790274)), c_Predicate_Oreflp(_790280, _790276), _790280 = _790278, _790276 = _790274], (744 ^ _779308) ^ [_790467, _790469, _790471, _790473, _790475, _790477, _790479, _790481] : [-(c_Wellfounded_Omax__extp(_790479, _790475, _790471, _790467)), c_Wellfounded_Omax__extp(_790481, _790477, _790473, _790469), _790481 = _790479, _790477 = _790475, _790473 = _790471, _790469 = _790467], (766 ^ _779308) ^ [_790820, _790822, _790824, _790826] : [-(c_Wellfounded_Oacyclic(_790824, _790820)), c_Wellfounded_Oacyclic(_790826, _790822), _790826 = _790824, _790822 = _790820], (780 ^ _779308) ^ [_791013, _791015, _791017, _791019] : [-(c_Relation_Oantisym(_791017, _791013)), c_Relation_Oantisym(_791019, _791015), _791019 = _791017, _791015 = _791013], (794 ^ _779308) ^ [_791206, _791208, _791210, _791212] : [-(c_Relation_Otrans(_791210, _791206)), c_Relation_Otrans(_791212, _791208), _791212 = _791210, _791208 = _791206], (808 ^ _779308) ^ [_791399, _791401, _791403, _791405] : [-(c_Relation_Osym(_791403, _791399)), c_Relation_Osym(_791405, _791401), _791405 = _791403, _791401 = _791399], (822 ^ _779308) ^ [_791592, _791594, _791596, _791598] : [-(c_Predicate_Osymp(_791596, _791592)), c_Predicate_Osymp(_791598, _791594), _791598 = _791596, _791594 = _791592], (836 ^ _779308) ^ [_791785, _791787, _791789, _791791] : [-(c_Predicate_Otransp(_791789, _791785)), c_Predicate_Otransp(_791791, _791787), _791791 = _791789, _791787 = _791785], (850 ^ _779308) ^ [_791978, _791980, _791982, _791984] : [-(c_Equiv__Relations_Opart__equivp(_791982, _791978)), c_Equiv__Relations_Opart__equivp(_791984, _791980), _791984 = _791982, _791980 = _791978], (864 ^ _779308) ^ [_792171, _792173, _792175, _792177, _792179, _792181, _792183, _792185] : [-(c_Fun_Oinj__on(_792183, _792179, _792175, _792171)), c_Fun_Oinj__on(_792185, _792181, _792177, _792173), _792185 = _792183, _792181 = _792179, _792177 = _792175, _792173 = _792171], (886 ^ _779308) ^ [_792524, _792526, _792528, _792530, _792532, _792534, _792536, _792538, _792540, _792542] : [-(c_Fun_Obij__betw(_792540, _792536, _792532, _792528, _792524)), c_Fun_Obij__betw(_792542, _792538, _792534, _792530, _792526), _792542 = _792540, _792538 = _792536, _792534 = _792532, _792530 = _792528, _792526 = _792524], (912 ^ _779308) ^ [_792969, _792971, _792973, _792975, _792977, _792979] : [-(c_Relation_Orefl__on(_792977, _792973, _792969)), c_Relation_Orefl__on(_792979, _792975, _792971), _792979 = _792977, _792975 = _792973, _792971 = _792969], (930 ^ _779308) ^ [_793238, _793240, _793242, _793244] : [-(c_Equiv__Relations_Oequivp(_793242, _793238)), c_Equiv__Relations_Oequivp(_793244, _793240), _793244 = _793242, _793240 = _793238], (944 ^ _779308) ^ [_793431, _793433, _793435, _793437] : [-(c_Wellfounded_Owf(_793435, _793431)), c_Wellfounded_Owf(_793437, _793433), _793437 = _793435, _793433 = _793431], (958 ^ _779308) ^ [_793624, _793626, _793628, _793630, _793632, _793634, _793636, _793638, _793640, _793642, _793644, _793646] : [-(c_Equiv__Relations_Ocongruent2(_793644, _793640, _793636, _793632, _793628, _793624)), c_Equiv__Relations_Ocongruent2(_793646, _793642, _793638, _793634, _793630, _793626), _793646 = _793644, _793642 = _793640, _793638 = _793636, _793634 = _793632, _793630 = _793628, _793626 = _793624], (988 ^ _779308) ^ [_794169, _794171, _794173, _794175, _794177, _794179, _794181, _794183] : [-(c_Equiv__Relations_Ocongruent(_794181, _794177, _794173, _794169)), c_Equiv__Relations_Ocongruent(_794183, _794179, _794175, _794171), _794183 = _794181, _794179 = _794177, _794175 = _794173, _794171 = _794169], (1010 ^ _779308) ^ [_794522, _794524, _794526, _794528, _794530, _794532] : [-(c_List_Olist__all(_794530, _794526, _794522)), c_List_Olist__all(_794532, _794528, _794524), _794532 = _794530, _794528 = _794526, _794524 = _794522], (1028 ^ _779308) ^ [_794791, _794793, _794795, _794797, _794799, _794801] : [-(c_List_Olist__ex(_794799, _794795, _794791)), c_List_Olist__ex(_794801, _794797, _794793), _794801 = _794799, _794797 = _794795, _794793 = _794791], (1046 ^ _779308) ^ [_795060, _795062, _795064, _795066, _795068, _795070] : [-(c_List_Oall__interval__nat(_795068, _795064, _795060)), c_List_Oall__interval__nat(_795070, _795066, _795062), _795070 = _795068, _795066 = _795064, _795062 = _795060], (1064 ^ _779308) ^ [_795329, _795331, _795333, _795335, _795337, _795339, _795341, _795343, _795345, _795347] : [-(c_Finite__Set_Ofolding__image(_795345, _795341, _795337, _795333, _795329)), c_Finite__Set_Ofolding__image(_795347, _795343, _795339, _795335, _795331), _795347 = _795345, _795343 = _795341, _795339 = _795337, _795335 = _795333, _795331 = _795329], (1090 ^ _779308) ^ [_795774, _795776, _795778, _795780, _795782, _795784, _795786, _795788] : [-(c_Orderings_Oorder_Ostrict__mono(_795786, _795782, _795778, _795774)), c_Orderings_Oorder_Ostrict__mono(_795788, _795784, _795780, _795776), _795788 = _795786, _795784 = _795782, _795780 = _795778, _795776 = _795774], (1112 ^ _779308) ^ [_796127, _796129, _796131, _796133, _796135, _796137] : [-(c_Equiv__Relations_Oequiv(_796135, _796131, _796127)), c_Equiv__Relations_Oequiv(_796137, _796133, _796129), _796137 = _796135, _796133 = _796131, _796129 = _796127], (1130 ^ _779308) ^ [_796396, _796398] : [-(class_Lattices_Obounded__lattice(_796396)), _796398 = _796396, class_Lattices_Obounded__lattice(_796398)], (1140 ^ _779308) ^ [_796521, _796523] : [-(class_Rings_Olinordered__semiring__1__strict(_796521)), _796523 = _796521, class_Rings_Olinordered__semiring__1__strict(_796523)], (1150 ^ _779308) ^ [_796646, _796648] : [-(class_Groups_Oordered__ab__group__add__abs(_796646)), _796648 = _796646, class_Groups_Oordered__ab__group__add__abs(_796648)], (1160 ^ _779308) ^ [_796771, _796773] : [-(class_Groups_Olinordered__ab__group__add(_796771)), _796773 = _796771, class_Groups_Olinordered__ab__group__add(_796773)], (1170 ^ _779308) ^ [_796896, _796898] : [-(class_Rings_Oring__1__no__zero__divisors(_796896)), _796898 = _796896, class_Rings_Oring__1__no__zero__divisors(_796898)], (1180 ^ _779308) ^ [_797021, _797023] : [-(class_Rings_Olinordered__ring__strict(_797021)), _797023 = _797021, class_Rings_Olinordered__ring__strict(_797023)], (1190 ^ _779308) ^ [_797146, _797148] : [-(class_Rings_Oring__no__zero__divisors(_797146)), _797148 = _797146, class_Rings_Oring__no__zero__divisors(_797148)], (1200 ^ _779308) ^ [_797271, _797273] : [-(class_Rings_Olinordered__semiring__1(_797271)), _797273 = _797271, class_Rings_Olinordered__semiring__1(_797273)], (1210 ^ _779308) ^ [_797396, _797398] : [-(class_Groups_Oordered__ab__group__add(_797396)), _797398 = _797396, class_Groups_Oordered__ab__group__add(_797398)], (1220 ^ _779308) ^ [_797521, _797523] : [-(class_Rings_Oordered__ring__abs(_797521)), _797523 = _797521, class_Rings_Oordered__ring__abs(_797523)], (1230 ^ _779308) ^ [_797646, _797648] : [-(class_Rings_Olinordered__ring(_797646)), _797648 = _797646, class_Rings_Olinordered__ring(_797648)], (1240 ^ _779308) ^ [_797771, _797773] : [-(class_Rings_Olinordered__idom(_797771)), _797773 = _797771, class_Rings_Olinordered__idom(_797773)], (1250 ^ _779308) ^ [_797896, _797898] : [-(class_Groups_Oab__group__add(_797896)), _797898 = _797896, class_Groups_Oab__group__add(_797898)], (1260 ^ _779308) ^ [_798021, _798023] : [-(class_Rings_Oordered__ring(_798021)), _798023 = _798021, class_Rings_Oordered__ring(_798023)], (1270 ^ _779308) ^ [_798146, _798148] : [-(class_Rings_Ocomm__ring__1(_798146)), _798148 = _798146, class_Rings_Ocomm__ring__1(_798148)], (1280 ^ _779308) ^ [_798271, _798273] : [-(class_Groups_Ogroup__add(_798271)), _798273 = _798271, class_Groups_Ogroup__add(_798273)], (1290 ^ _779308) ^ [_798396, _798398] : [-(class_Divides_Oring__div(_798396)), _798398 = _798396, class_Divides_Oring__div(_798398)], (1300 ^ _779308) ^ [_798521, _798523] : [-(class_Rings_Ocomm__ring(_798521)), _798523 = _798521, class_Rings_Ocomm__ring(_798523)], (1310 ^ _779308) ^ [_798646, _798648] : [-(class_Int_Oring__char__0(_798646)), _798648 = _798646, class_Int_Oring__char__0(_798648)], (1320 ^ _779308) ^ [_798771, _798773] : [-(class_Int_Onumber__ring(_798771)), _798773 = _798771, class_Int_Onumber__ring(_798773)], (1330 ^ _779308) ^ [_798896, _798898] : [-(class_Groups_Osgn__if(_798896)), _798898 = _798896, class_Groups_Osgn__if(_798898)], (1340 ^ _779308) ^ [_799021, _799023] : [-(class_Groups_Oabs__if(_799021)), _799023 = _799021, class_Groups_Oabs__if(_799023)], (1350 ^ _779308) ^ [_799146, _799148] : [-(class_Rings_Oring__1(_799146)), _799148 = _799146, class_Rings_Oring__1(_799148)], (1360 ^ _779308) ^ [_799271, _799273] : [-(class_Rings_Oring(_799271)), _799273 = _799271, class_Rings_Oring(_799273)], (1370 ^ _779308) ^ [_799396, _799398] : [-(class_Rings_Oidom(_799396)), _799398 = _799396, class_Rings_Oidom(_799398)], (1380 ^ _779308) ^ [_799521, _799523] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799521)), _799523 = _799521, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799523)], (1390 ^ _779308) ^ [_799646, _799648] : [-(class_Orderings_Owellorder(_799646)), _799648 = _799646, class_Orderings_Owellorder(_799648)], (1400 ^ _779308) ^ [_799771, _799773] : [-(class_Complete__Lattice_Ocomplete__lattice(_799771)), _799773 = _799771, class_Complete__Lattice_Ocomplete__lattice(_799773)], (1410 ^ _779308) ^ [_799896, _799898] : [-(class_Lattices_Obounded__lattice__top(_799896)), _799898 = _799896, class_Lattices_Obounded__lattice__top(_799898)], (1420 ^ _779308) ^ [_800021, _800023] : [-(class_Lattices_Obounded__lattice__bot(_800021)), _800023 = _800021, class_Lattices_Obounded__lattice__bot(_800023)], (1430 ^ _779308) ^ [_800146, _800148] : [-(class_Lattices_Osemilattice__sup(_800146)), _800148 = _800146, class_Lattices_Osemilattice__sup(_800148)], (1440 ^ _779308) ^ [_800271, _800273] : [-(class_Lattices_Osemilattice__inf(_800271)), _800273 = _800271, class_Lattices_Osemilattice__inf(_800273)], (1450 ^ _779308) ^ [_800396, _800398] : [-(class_Lattices_Odistrib__lattice(_800396)), _800398 = _800396, class_Lattices_Odistrib__lattice(_800398)], (1460 ^ _779308) ^ [_800521, _800523] : [-(class_Lattices_Oboolean__algebra(_800521)), _800523 = _800521, class_Lattices_Oboolean__algebra(_800523)], (1470 ^ _779308) ^ [_800646, _800648] : [-(class_Lattices_Olattice(_800646)), _800648 = _800646, class_Lattices_Olattice(_800648)], (1480 ^ _779308) ^ [_800771, _800773] : [-(class_Orderings_Otop(_800771)), _800773 = _800771, class_Orderings_Otop(_800773)], (1490 ^ _779308) ^ [_800896, _800898] : [-(class_Orderings_Obot(_800896)), _800898 = _800896, class_Orderings_Obot(_800898)], (1500 ^ _779308) ^ [_801021, _801023] : [-(class_Groups_Ouminus(_801021)), _801023 = _801021, class_Groups_Ouminus(_801023)], (1510 ^ _779308) ^ [_801146, _801148] : [-(class_Lazy__Sequence_Osmall__lazy(_801146)), _801148 = _801146, class_Lazy__Sequence_Osmall__lazy(_801148)], (1520 ^ _779308) ^ [_801271, _801273] : [-(class_Finite__Set_Ofinite(_801271)), _801273 = _801271, class_Finite__Set_Ofinite(_801273)], (1530 ^ _779308) ^ [_801396, _801398] : [-(class_Enum_Oenum(_801396)), _801398 = _801396, class_Enum_Oenum(_801398)], (1540 ^ _779308) ^ [_801521, _801523] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_801521)), _801523 = _801521, class_Groups_Oordered__cancel__ab__semigroup__add(_801523)], (1550 ^ _779308) ^ [_801646, _801648] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_801646)), _801648 = _801646, class_Groups_Oordered__ab__semigroup__add__imp__le(_801648)], (1560 ^ _779308) ^ [_801771, _801773] : [-(class_Rings_Olinordered__comm__semiring__strict(_801771)), _801773 = _801771, class_Rings_Olinordered__comm__semiring__strict(_801773)], (1570 ^ _779308) ^ [_801896, _801898] : [-(class_Groups_Olinordered__ab__semigroup__add(_801896)), _801898 = _801896, class_Groups_Olinordered__ab__semigroup__add(_801898)], (1580 ^ _779308) ^ [_802021, _802023] : [-(class_Rings_Olinordered__semiring__strict(_802021)), _802023 = _802021, class_Rings_Olinordered__semiring__strict(_802023)], (1590 ^ _779308) ^ [_802146, _802148] : [-(class_Groups_Oordered__ab__semigroup__add(_802146)), _802148 = _802146, class_Groups_Oordered__ab__semigroup__add(_802148)], (1600 ^ _779308) ^ [_802271, _802273] : [-(class_Groups_Oordered__comm__monoid__add(_802271)), _802273 = _802271, class_Groups_Oordered__comm__monoid__add(_802273)], (1610 ^ _779308) ^ [_802396, _802398] : [-(class_Groups_Ocancel__ab__semigroup__add(_802396)), _802398 = _802396, class_Groups_Ocancel__ab__semigroup__add(_802398)], (1620 ^ _779308) ^ [_802521, _802523] : [-(class_Rings_Oordered__cancel__semiring(_802521)), _802523 = _802521, class_Rings_Oordered__cancel__semiring(_802523)], (1630 ^ _779308) ^ [_802646, _802648] : [-(class_Rings_Oordered__comm__semiring(_802646)), _802648 = _802646, class_Rings_Oordered__comm__semiring(_802648)], (1640 ^ _779308) ^ [_802771, _802773] : [-(class_Groups_Ocancel__semigroup__add(_802771)), _802773 = _802771, class_Groups_Ocancel__semigroup__add(_802773)], (1650 ^ _779308) ^ [_802896, _802898] : [-(class_Rings_Olinordered__semiring(_802896)), _802898 = _802896, class_Rings_Olinordered__semiring(_802898)], (1660 ^ _779308) ^ [_803021, _803023] : [-(class_Rings_Olinordered__semidom(_803021)), _803023 = _803021, class_Rings_Olinordered__semidom(_803023)], (1670 ^ _779308) ^ [_803146, _803148] : [-(class_Groups_Oab__semigroup__mult(_803146)), _803148 = _803146, class_Groups_Oab__semigroup__mult(_803148)], (1680 ^ _779308) ^ [_803271, _803273] : [-(class_Groups_Ocomm__monoid__mult(_803271)), _803273 = _803271, class_Groups_Ocomm__monoid__mult(_803273)], (1690 ^ _779308) ^ [_803396, _803398] : [-(class_Groups_Oab__semigroup__add(_803396)), _803398 = _803396, class_Groups_Oab__semigroup__add(_803398)], (1700 ^ _779308) ^ [_803521, _803523] : [-(class_Rings_Oordered__semiring(_803521)), _803523 = _803521, class_Rings_Oordered__semiring(_803523)], (1710 ^ _779308) ^ [_803646, _803648] : [-(class_Rings_Ono__zero__divisors(_803646)), _803648 = _803646, class_Rings_Ono__zero__divisors(_803648)], (1720 ^ _779308) ^ [_803771, _803773] : [-(class_Groups_Ocomm__monoid__add(_803771)), _803773 = _803771, class_Groups_Ocomm__monoid__add(_803773)], (1730 ^ _779308) ^ [_803896, _803898] : [-(class_Rings_Ocomm__semiring__1(_803896)), _803898 = _803896, class_Rings_Ocomm__semiring__1(_803898)], (1740 ^ _779308) ^ [_804021, _804023] : [-(class_Groups_Osemigroup__add(_804021)), _804023 = _804021, class_Groups_Osemigroup__add(_804023)], (1750 ^ _779308) ^ [_804146, _804148] : [-(class_Divides_Osemiring__div(_804146)), _804148 = _804146, class_Divides_Osemiring__div(_804148)], (1760 ^ _779308) ^ [_804271, _804273] : [-(class_Rings_Ocomm__semiring(_804271)), _804273 = _804271, class_Rings_Ocomm__semiring(_804273)], (1770 ^ _779308) ^ [_804396, _804398] : [-(class_Nat_Osemiring__char__0(_804396)), _804398 = _804396, class_Nat_Osemiring__char__0(_804398)], (1780 ^ _779308) ^ [_804521, _804523] : [-(class_Rings_Ozero__neq__one(_804521)), _804523 = _804521, class_Rings_Ozero__neq__one(_804523)], (1790 ^ _779308) ^ [_804646, _804648] : [-(class_Orderings_Opreorder(_804646)), _804648 = _804646, class_Orderings_Opreorder(_804648)], (1800 ^ _779308) ^ [_804771, _804773] : [-(class_Orderings_Olinorder(_804771)), _804773 = _804771, class_Orderings_Olinorder(_804773)], (1810 ^ _779308) ^ [_804896, _804898] : [-(class_Groups_Omonoid__mult(_804896)), _804898 = _804896, class_Groups_Omonoid__mult(_804898)], (1820 ^ _779308) ^ [_805021, _805023] : [-(class_Groups_Omonoid__add(_805021)), _805023 = _805021, class_Groups_Omonoid__add(_805023)], (1830 ^ _779308) ^ [_805146, _805148] : [-(class_Rings_Osemiring__1(_805146)), _805148 = _805146, class_Rings_Osemiring__1(_805148)], (1840 ^ _779308) ^ [_805271, _805273] : [-(class_Rings_Osemiring__0(_805271)), _805273 = _805271, class_Rings_Osemiring__0(_805273)], (1850 ^ _779308) ^ [_805396, _805398] : [-(class_Rings_Omult__zero(_805396)), _805398 = _805396, class_Rings_Omult__zero(_805398)], (1860 ^ _779308) ^ [_805521, _805523] : [-(class_Orderings_Oorder(_805521)), _805523 = _805521, class_Orderings_Oorder(_805523)], (1870 ^ _779308) ^ [_805646, _805648] : [-(class_Rings_Osemiring(_805646)), _805648 = _805646, class_Rings_Osemiring(_805648)], (1880 ^ _779308) ^ [_805771, _805773] : [-(class_Orderings_Oord(_805771)), _805773 = _805771, class_Orderings_Oord(_805773)], (1890 ^ _779308) ^ [_805896, _805898] : [-(class_Groups_Ominus(_805896)), _805898 = _805896, class_Groups_Ominus(_805898)], (1900 ^ _779308) ^ [_806021, _806023] : [-(class_Power_Opower(_806021)), _806023 = _806021, class_Power_Opower(_806023)], (1910 ^ _779308) ^ [_806146, _806148] : [-(class_Groups_Ozero(_806146)), _806148 = _806146, class_Groups_Ozero(_806148)], (1920 ^ _779308) ^ [_806271, _806273] : [-(class_Int_Onumber(_806271)), _806273 = _806271, class_Int_Onumber(_806273)], (1930 ^ _779308) ^ [_806396, _806398] : [-(class_Groups_Oone(_806396)), _806398 = _806396, class_Groups_Oone(_806398)], (1940 ^ _779308) ^ [_806521, _806523] : [-(class_Rings_Odvd(_806521)), _806523 = _806521, class_Rings_Odvd(_806523)], (1950 ^ _779308) ^ [_806646, _806648] : [-(class_Nat_Osize(_806646)), _806648 = _806646, class_Nat_Osize(_806648)], (1960 ^ _779308) ^ [_806767, _806769] : [-(hBOOL(_806767)), _806769 = _806767, hBOOL(_806769)], (1970 ^ _779308) ^ [_807690, _807692] : [_807692 = _807690, -(v_mgt(_807692) = v_mgt(_807690))], (1976 ^ _779308) ^ [_807775, _807777, _807779, _807781] : [-(c_Option_Othe(_807781, _807777) = c_Option_Othe(_807779, _807775)), _807781 = _807779, _807777 = _807775], (1986 ^ _779308) ^ [_807924, _807926] : [_807926 = _807924, -(c_Com_Obody(_807926) = c_Com_Obody(_807924))], (1992 ^ _779308) ^ [_808009, _808011, _808013, _808015, _808017, _808019] : [-(c_Partial__Function_Oflat__lub(_808019, _808015, _808011) = c_Partial__Function_Oflat__lub(_808017, _808013, _808009)), _808019 = _808017, _808015 = _808013, _808011 = _808009], (2006 ^ _779308) ^ [_808230, _808232, _808234, _808236, _808238, _808240, _808242, _808244, _808246, _808248] : [-(c_Nitpick_Opair__box_Opair__box__size(_808248, _808244, _808240, _808236, _808232) = c_Nitpick_Opair__box_Opair__box__size(_808246, _808242, _808238, _808234, _808230)), _808248 = _808246, _808244 = _808242, _808240 = _808238, _808236 = _808234, _808232 = _808230], (2028 ^ _779308) ^ [_808619, _808621, _808623, _808625, _808627, _808629, _808631, _808633, _808635, _808637] : [-(c_Nitpick_Opair__box_Opair__box__case(_808637, _808633, _808629, _808625, _808621) = c_Nitpick_Opair__box_Opair__box__case(_808635, _808631, _808627, _808623, _808619)), _808637 = _808635, _808633 = _808631, _808629 = _808627, _808625 = _808623, _808621 = _808619], (2050 ^ _779308) ^ [_809008, _809010, _809012, _809014, _809016, _809018, _809020, _809022, _809024, _809026] : [-(c_Nitpick_Opair__box_Opair__box__rec(_809026, _809022, _809018, _809014, _809010) = c_Nitpick_Opair__box_Opair__box__rec(_809024, _809020, _809016, _809012, _809008)), _809026 = _809024, _809022 = _809020, _809018 = _809016, _809014 = _809012, _809010 = _809008], (2072 ^ _779308) ^ [_809397, _809399, _809401, _809403, _809405, _809407, _809409, _809411] : [-(c_Nitpick_Opair__box_OPairBox(_809411, _809407, _809403, _809399) = c_Nitpick_Opair__box_OPairBox(_809409, _809405, _809401, _809397)), _809411 = _809409, _809407 = _809405, _809403 = _809401, _809399 = _809397], (2090 ^ _779308) ^ [_809698, _809700, _809702, _809704, _809706, _809708, _809710, _809712] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_809712, _809708, _809704, _809700) = c_Nat_Osemiring__1__class_Oof__nat__aux(_809710, _809706, _809702, _809698)), _809712 = _809710, _809708 = _809706, _809704 = _809702, _809700 = _809698], (2108 ^ _779308) ^ [_809999, _810001, _810003, _810005, _810007, _810009] : [-(c_Finite__Set_Ofold1Set(_810009, _810005, _810001) = c_Finite__Set_Ofold1Set(_810007, _810003, _809999)), _810009 = _810007, _810005 = _810003, _810001 = _809999], (2122 ^ _779308) ^ [_810220, _810222] : [_810222 = _810220, -(c_Nat_Osemiring__1__class_ONats(_810222) = c_Nat_Osemiring__1__class_ONats(_810220))], (2128 ^ _779308) ^ [_810305, _810307, _810309, _810311] : [-(c_Int_Onat__aux(_810311, _810307) = c_Int_Onat__aux(_810309, _810305)), _810311 = _810309, _810307 = _810305], (2138 ^ _779308) ^ [_810454, _810456, _810458, _810460, _810462, _810464] : [-(c_Nat_Onat_Onat__rec(_810464, _810460, _810456) = c_Nat_Onat_Onat__rec(_810462, _810458, _810454)), _810464 = _810462, _810460 = _810458, _810456 = _810454], (2152 ^ _779308) ^ [_810675, _810677, _810679, _810681] : [-(c_SMT_Oz3mod(_810681, _810677) = c_SMT_Oz3mod(_810679, _810675)), _810681 = _810679, _810677 = _810675], (2162 ^ _779308) ^ [_810824, _810826, _810828, _810830, _810832, _810834] : [-(c_Power_Opower_Opower(_810834, _810830, _810826) = c_Power_Opower_Opower(_810832, _810828, _810824)), _810834 = _810832, _810830 = _810828, _810826 = _810824], (2176 ^ _779308) ^ [_811045, _811047, _811049, _811051] : [-(c_SMT_Oz3div(_811051, _811047) = c_SMT_Oz3div(_811049, _811045)), _811051 = _811049, _811047 = _811045], (2186 ^ _779308) ^ [_811194, _811196] : [_811196 = _811194, -(c_Int_Osucc(_811196) = c_Int_Osucc(_811194))], (2192 ^ _779308) ^ [_811279, _811281, _811283, _811285] : [-(c_Nat__Transfer_Otsub(_811285, _811281) = c_Nat__Transfer_Otsub(_811283, _811279)), _811285 = _811283, _811281 = _811279], (2202 ^ _779308) ^ [_811428, _811430] : [_811430 = _811428, -(c_Int_Oring__1__class_OInts(_811430) = c_Int_Oring__1__class_OInts(_811428))], (2208 ^ _779308) ^ [_811513, _811515] : [_811515 = _811513, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_811515) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_811513))], (2214 ^ _779308) ^ [_811598, _811600, _811602, _811604] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_811604, _811600) = c_Code__Numeral_Odiv__mod__code__numeral(_811602, _811598)), _811604 = _811602, _811600 = _811598], (2224 ^ _779308) ^ [_811747, _811749, _811751, _811753] : [-(c_Divides_Odivmod__int__rel(_811753, _811749) = c_Divides_Odivmod__int__rel(_811751, _811747)), _811753 = _811751, _811749 = _811747], (2234 ^ _779308) ^ [_811896, _811898] : [_811898 = _811896, -(c_Divides_Oadjust(_811898) = c_Divides_Oadjust(_811896))], (2240 ^ _779308) ^ [_811981, _811983] : [_811983 = _811981, -(c_Nat_Onat_Onat__size(_811983) = c_Nat_Onat_Onat__size(_811981))], (2246 ^ _779308) ^ [_812066, _812068, _812070, _812072] : [-(c_Divides_OnegDivAlg(_812072, _812068) = c_Divides_OnegDivAlg(_812070, _812066)), _812072 = _812070, _812068 = _812066], (2256 ^ _779308) ^ [_812215, _812217, _812219, _812221, _812223, _812225, _812227, _812229, _812231, _812233] : [-(c_Product__Type_Oprod_Oprod__size(_812233, _812229, _812225, _812221, _812217) = c_Product__Type_Oprod_Oprod__size(_812231, _812227, _812223, _812219, _812215)), _812233 = _812231, _812229 = _812227, _812225 = _812223, _812221 = _812219, _812217 = _812215], (2278 ^ _779308) ^ [_812604, _812606, _812608, _812610, _812612, _812614, _812616, _812618, _812620, _812622] : [-(c_Product__Type_Oprod_Oprod__rec(_812622, _812618, _812614, _812610, _812606) = c_Product__Type_Oprod_Oprod__rec(_812620, _812616, _812612, _812608, _812604)), _812622 = _812620, _812618 = _812616, _812614 = _812612, _812610 = _812608, _812606 = _812604], (2300 ^ _779308) ^ [_812993, _812995, _812997, _812999] : [-(c_Divides_Odivmod__nat(_812999, _812995) = c_Divides_Odivmod__nat(_812997, _812993)), _812999 = _812997, _812995 = _812993], (2310 ^ _779308) ^ [_813142, _813144, _813146, _813148] : [-(c_Divides_Odivmod__nat__rel(_813148, _813144) = c_Divides_Odivmod__nat__rel(_813146, _813142)), _813148 = _813146, _813144 = _813142], (2320 ^ _779308) ^ [_813291, _813293] : [_813293 = _813291, -(c_Int_Opred(_813293) = c_Int_Opred(_813291))], (2326 ^ _779308) ^ [_813376, _813378, _813380, _813382] : [-(c_Orderings_Oord_Omax(_813382, _813378) = c_Orderings_Oord_Omax(_813380, _813376)), _813382 = _813380, _813378 = _813376], (2336 ^ _779308) ^ [_813525, _813527, _813529, _813531] : [-(c_Orderings_Oord_Omin(_813531, _813527) = c_Orderings_Oord_Omin(_813529, _813525)), _813531 = _813529, _813527 = _813525], (2346 ^ _779308) ^ [_813674, _813676, _813678, _813680] : [-(c_FunDef_Orp__inv__image(_813680, _813676) = c_FunDef_Orp__inv__image(_813678, _813674)), _813680 = _813678, _813676 = _813674], (2356 ^ _779308) ^ [_813823, _813825, _813827, _813829, _813831, _813833, _813835, _813837] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_813837, _813833, _813829, _813825) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_813835, _813831, _813827, _813823)), _813837 = _813835, _813833 = _813831, _813829 = _813827, _813825 = _813823], (2374 ^ _779308) ^ [_814124, _814126, _814128, _814130] : [-(c_Divides_Odivmod__int(_814130, _814126) = c_Divides_Odivmod__int(_814128, _814124)), _814130 = _814128, _814126 = _814124], (2384 ^ _779308) ^ [_814273, _814275, _814277, _814279] : [-(c_Groups_Osgn__class_Osgn(_814279, _814275) = c_Groups_Osgn__class_Osgn(_814277, _814273)), _814279 = _814277, _814275 = _814273], (2394 ^ _779308) ^ [_814422, _814424, _814426, _814428] : [-(c_Divides_OposDivAlg(_814428, _814424) = c_Divides_OposDivAlg(_814426, _814422)), _814428 = _814426, _814424 = _814422], (2404 ^ _779308) ^ [_814571, _814573, _814575, _814577] : [-(c_Divides_Opdivmod(_814577, _814573) = c_Divides_Opdivmod(_814575, _814571)), _814577 = _814575, _814573 = _814571], (2414 ^ _779308) ^ [_814720, _814722, _814724, _814726] : [-(c_Nitpick_Onat__gcd(_814726, _814722) = c_Nitpick_Onat__gcd(_814724, _814720)), _814726 = _814724, _814722 = _814720], (2424 ^ _779308) ^ [_814869, _814871, _814873, _814875] : [-(c_Nitpick_Onat__lcm(_814875, _814871) = c_Nitpick_Onat__lcm(_814873, _814869)), _814875 = _814873, _814871 = _814869], (2434 ^ _779308) ^ [_815018, _815020, _815022, _815024] : [-(c_Set_Othe__elem(_815024, _815020) = c_Set_Othe__elem(_815022, _815018)), _815024 = _815022, _815020 = _815018], (2444 ^ _779308) ^ [_815167, _815169, _815171, _815173, _815175, _815177, _815179, _815181] : [-(c_Sum__Type_OPlus(_815181, _815177, _815173, _815169) = c_Sum__Type_OPlus(_815179, _815175, _815171, _815167)), _815181 = _815179, _815177 = _815175, _815173 = _815171, _815169 = _815167], (2462 ^ _779308) ^ [_815468, _815470] : [_815470 = _815468, -(c_SetInterval_Oord__class_OatLeast(_815470) = c_SetInterval_Oord__class_OatLeast(_815468))], (2468 ^ _779308) ^ [_815553, _815555] : [_815555 = _815553, -(c_Int_OBit0(_815555) = c_Int_OBit0(_815553))], (2474 ^ _779308) ^ [_815638, _815640] : [_815640 = _815638, -(c_Nitpick_Ozero__frac(_815640) = c_Nitpick_Ozero__frac(_815638))], (2480 ^ _779308) ^ [_815723, _815725] : [_815725 = _815723, -(c_Nitpick_Oone__frac(_815725) = c_Nitpick_Oone__frac(_815723))], (2486 ^ _779308) ^ [_815808, _815810, _815812, _815814] : [-(c_Nitpick_Onumber__of__frac(_815814, _815810) = c_Nitpick_Onumber__of__frac(_815812, _815808)), _815814 = _815812, _815810 = _815808], (2496 ^ _779308) ^ [_815957, _815959, _815961, _815963] : [-(c_Nitpick_Onorm__frac(_815963, _815959) = c_Nitpick_Onorm__frac(_815961, _815957)), _815963 = _815961, _815959 = _815957], (2506 ^ _779308) ^ [_816106, _816108, _816110, _816112, _816114, _816116, _816118, _816120] : [-(c_Nitpick_Oprod(_816120, _816116, _816112, _816108) = c_Nitpick_Oprod(_816118, _816114, _816110, _816106)), _816120 = _816118, _816116 = _816114, _816112 = _816110, _816108 = _816106], (2524 ^ _779308) ^ [_816407, _816409] : [_816409 = _816407, -(c_Wellfounded_Omeasure(_816409) = c_Wellfounded_Omeasure(_816407))], (2530 ^ _779308) ^ [_816492, _816494, _816496, _816498] : [-(c_Wellfounded_Omin__ext(_816498, _816494) = c_Wellfounded_Omin__ext(_816496, _816492)), _816498 = _816496, _816494 = _816492], (2540 ^ _779308) ^ [_816641, _816643, _816645, _816647, _816649, _816651] : [-(c_Wellfounded_Omlex__prod(_816651, _816647, _816643) = c_Wellfounded_Omlex__prod(_816649, _816645, _816641)), _816651 = _816649, _816647 = _816645, _816643 = _816641], (2554 ^ _779308) ^ [_816862, _816864] : [_816864 = _816862, -(c_Int_Oint__ge__less__than2(_816864) = c_Int_Oint__ge__less__than2(_816862))], (2560 ^ _779308) ^ [_816947, _816949] : [_816949 = _816947, -(c_Int_Oint__ge__less__than(_816949) = c_Int_Oint__ge__less__than(_816947))], (2566 ^ _779308) ^ [_817032, _817034, _817036, _817038, _817040, _817042, _817044, _817046] : [-(c_Recdef_Osame__fst(_817046, _817042, _817038, _817034) = c_Recdef_Osame__fst(_817044, _817040, _817036, _817032)), _817046 = _817044, _817042 = _817040, _817038 = _817036, _817034 = _817032], (2584 ^ _779308) ^ [_817333, _817335, _817337, _817339, _817341, _817343] : [-(c_FunDef_Oin__rel(_817343, _817339, _817335) = c_FunDef_Oin__rel(_817341, _817337, _817333)), _817343 = _817341, _817339 = _817337, _817335 = _817333], (2598 ^ _779308) ^ [_817554, _817556, _817558, _817560] : [-(c_Predicate_OPowp(_817560, _817556) = c_Predicate_OPowp(_817558, _817554)), _817560 = _817558, _817556 = _817554], (2608 ^ _779308) ^ [_817703, _817705, _817707, _817709, _817711, _817713] : [-(c_Predicate_ODomainP(_817713, _817709, _817705) = c_Predicate_ODomainP(_817711, _817707, _817703)), _817713 = _817711, _817709 = _817707, _817705 = _817703], (2622 ^ _779308) ^ [_817924, _817926, _817928, _817930, _817932, _817934] : [-(c_Predicate_ORangeP(_817934, _817930, _817926) = c_Predicate_ORangeP(_817932, _817928, _817924)), _817934 = _817932, _817930 = _817928, _817926 = _817924], (2636 ^ _779308) ^ [_818145, _818147, _818149, _818151, _818153, _818155, _818157, _818159] : [-(c_Product__Type_Oapfst(_818159, _818155, _818151, _818147) = c_Product__Type_Oapfst(_818157, _818153, _818149, _818145)), _818159 = _818157, _818155 = _818153, _818151 = _818149, _818147 = _818145], (2654 ^ _779308) ^ [_818446, _818448, _818450, _818452, _818454, _818456, _818458, _818460] : [-(c_Product__Type_Oapsnd(_818460, _818456, _818452, _818448) = c_Product__Type_Oapsnd(_818458, _818454, _818450, _818446)), _818460 = _818458, _818456 = _818454, _818452 = _818450, _818448 = _818446], (2672 ^ _779308) ^ [_818747, _818749, _818751, _818753] : [-(c_Wellfounded_Omax__ext(_818753, _818749) = c_Wellfounded_Omax__ext(_818751, _818747)), _818753 = _818751, _818749 = _818747], (2682 ^ _779308) ^ [_818896, _818898, _818900, _818902, _818904, _818906, _818908, _818910] : [-(c_Random_Oiterate(_818910, _818906, _818902, _818898) = c_Random_Oiterate(_818908, _818904, _818900, _818896)), _818910 = _818908, _818906 = _818904, _818902 = _818900, _818898 = _818896], (2700 ^ _779308) ^ [_819197, _819199, _819201, _819203] : [-(c_Random_Olog(_819203, _819199) = c_Random_Olog(_819201, _819197)), _819203 = _819201, _819199 = _819197], (2710 ^ _779308) ^ [_819346, _819348, _819350, _819352, _819354, _819356] : [-(c_Random_Ominus__shift(_819356, _819352, _819348) = c_Random_Ominus__shift(_819354, _819350, _819346)), _819356 = _819354, _819352 = _819350, _819348 = _819346], (2724 ^ _779308) ^ [_819567, _819569, _819571, _819573] : [-(c_Random_Oinc__shift(_819573, _819569) = c_Random_Oinc__shift(_819571, _819567)), _819573 = _819571, _819569 = _819567], (2734 ^ _779308) ^ [_819716, _819718] : [_819718 = _819716, -(c_Nat_Ofunpow(_819718) = c_Nat_Ofunpow(_819716))], (2740 ^ _779308) ^ [_819801, _819803] : [_819803 = _819801, -(c_Set_OBall(_819803) = c_Set_OBall(_819801))], (2746 ^ _779308) ^ [_819886, _819888] : [_819888 = _819886, -(c_SetInterval_Oord__class_OgreaterThan(_819888) = c_SetInterval_Oord__class_OgreaterThan(_819886))], (2752 ^ _779308) ^ [_819971, _819973] : [_819973 = _819971, -(c_Relation_OField(_819973) = c_Relation_OField(_819971))], (2758 ^ _779308) ^ [_820056, _820058, _820060, _820062] : [-(c_Relation_ORange(_820062, _820058) = c_Relation_ORange(_820060, _820056)), _820062 = _820060, _820058 = _820056], (2768 ^ _779308) ^ [_820205, _820207, _820209, _820211] : [-(c_Relation_ODomain(_820211, _820207) = c_Relation_ODomain(_820209, _820205)), _820211 = _820209, _820207 = _820205], (2778 ^ _779308) ^ [_820354, _820356] : [_820356 = _820354, -(c_HOL_OAll(_820356) = c_HOL_OAll(_820354))], (2784 ^ _779308) ^ [_820439, _820441, _820443, _820445, _820447, _820449, _820451, _820453, _820455, _820457] : [-(c_Finite__Set_Ofold__graph(_820457, _820453, _820449, _820445, _820441) = c_Finite__Set_Ofold__graph(_820455, _820451, _820447, _820443, _820439)), _820457 = _820455, _820453 = _820451, _820449 = _820447, _820445 = _820443, _820441 = _820439], (2806 ^ _779308) ^ [_820828, _820830, _820832, _820834] : [-(c_Nitpick_Oint__lcm(_820834, _820830) = c_Nitpick_Oint__lcm(_820832, _820828)), _820834 = _820832, _820830 = _820828], (2816 ^ _779308) ^ [_820977, _820979, _820981, _820983, _820985, _820987] : [-(c_Nitpick_Otimes__frac(_820987, _820983, _820979) = c_Nitpick_Otimes__frac(_820985, _820981, _820977)), _820987 = _820985, _820983 = _820981, _820979 = _820977], (2830 ^ _779308) ^ [_821198, _821200, _821202, _821204, _821206, _821208] : [-(c_Nitpick_Oof__frac(_821208, _821204, _821200) = c_Nitpick_Oof__frac(_821206, _821202, _821198)), _821208 = _821206, _821204 = _821202, _821200 = _821198], (2844 ^ _779308) ^ [_821419, _821421] : [_821421 = _821419, -(c_Rings_Oinverse__class_Odivide(_821421) = c_Rings_Oinverse__class_Odivide(_821419))], (2850 ^ _779308) ^ [_821504, _821506] : [_821506 = _821504, -(c_Int_Oring__1__class_Oof__int(_821506) = c_Int_Oring__1__class_Oof__int(_821504))], (2856 ^ _779308) ^ [_821589, _821591, _821593, _821595] : [-(c_Nitpick_Oinverse__frac(_821595, _821591) = c_Nitpick_Oinverse__frac(_821593, _821589)), _821595 = _821593, _821591 = _821589], (2866 ^ _779308) ^ [_821738, _821740] : [_821740 = _821738, -(c_Nitpick_Ofrac(_821740) = c_Nitpick_Ofrac(_821738))], (2872 ^ _779308) ^ [_821823, _821825, _821827, _821829] : [-(c_Nitpick_OAbs__Frac(_821829, _821825) = c_Nitpick_OAbs__Frac(_821827, _821823)), _821829 = _821827, _821825 = _821823], (2882 ^ _779308) ^ [_821972, _821974, _821976, _821978, _821980, _821982] : [-(c_Nitpick_Oplus__frac(_821982, _821978, _821974) = c_Nitpick_Oplus__frac(_821980, _821976, _821972)), _821982 = _821980, _821978 = _821976, _821974 = _821972], (2896 ^ _779308) ^ [_822193, _822195, _822197, _822199] : [-(c_Nitpick_Ouminus__frac(_822199, _822195) = c_Nitpick_Ouminus__frac(_822197, _822193)), _822199 = _822197, _822195 = _822193], (2906 ^ _779308) ^ [_822342, _822344] : [_822344 = _822342, -(c_Nitpick_Odenom(_822344) = c_Nitpick_Odenom(_822342))], (2912 ^ _779308) ^ [_822427, _822429] : [_822429 = _822427, -(c_Nitpick_Onum(_822429) = c_Nitpick_Onum(_822427))], (2918 ^ _779308) ^ [_822512, _822514] : [_822514 = _822512, -(c_Nitpick_ORep__Frac(_822514) = c_Nitpick_ORep__Frac(_822512))], (2924 ^ _779308) ^ [_822597, _822599, _822601, _822603, _822605, _822607] : [-(c_Product__Type_Ointernal__split(_822607, _822603, _822599) = c_Product__Type_Ointernal__split(_822605, _822601, _822597)), _822607 = _822605, _822603 = _822601, _822599 = _822597], (2938 ^ _779308) ^ [_822818, _822820] : [_822820 = _822818, -(c_HOL_Obool_Obool__size(_822820) = c_HOL_Obool_Obool__size(_822818))], (2944 ^ _779308) ^ [_822903, _822905, _822907, _822909] : [-(c_List_Olenlex(_822909, _822905) = c_List_Olenlex(_822907, _822903)), _822909 = _822907, _822905 = _822903], (2954 ^ _779308) ^ [_823052, _823054, _823056, _823058, _823060, _823062, _823064, _823066, _823068, _823070, _823072, _823074] : [-(c_Product__Type_Omap__pair(_823074, _823070, _823066, _823062, _823058, _823054) = c_Product__Type_Omap__pair(_823072, _823068, _823064, _823060, _823056, _823052)), _823074 = _823072, _823070 = _823068, _823066 = _823064, _823062 = _823060, _823058 = _823056, _823054 = _823052], (2980 ^ _779308) ^ [_823537, _823539, _823541, _823543] : [-(c_List_Olexn(_823543, _823539) = c_List_Olexn(_823541, _823537)), _823543 = _823541, _823539 = _823537], (2990 ^ _779308) ^ [_823686, _823688, _823690, _823692] : [-(c_Wellfounded_Oacc(_823692, _823688) = c_Wellfounded_Oacc(_823690, _823686)), _823692 = _823690, _823688 = _823686], (3000 ^ _779308) ^ [_823835, _823837, _823839, _823841] : [-(c_Nitpick_Ocard_H(_823841, _823837) = c_Nitpick_Ocard_H(_823839, _823835)), _823841 = _823839, _823837 = _823835], (3010 ^ _779308) ^ [_823984, _823986, _823988, _823990, _823992, _823994] : [-(c_List_Oset__Cons(_823994, _823990, _823986) = c_List_Oset__Cons(_823992, _823988, _823984)), _823994 = _823992, _823990 = _823988, _823986 = _823984], (3024 ^ _779308) ^ [_824205, _824207, _824209, _824211] : [-(c_List_Olistset(_824211, _824207) = c_List_Olistset(_824209, _824205)), _824211 = _824209, _824207 = _824205], (3034 ^ _779308) ^ [_824354, _824356, _824358, _824360] : [-(c_List_Olistrel1(_824360, _824356) = c_List_Olistrel1(_824358, _824354)), _824360 = _824358, _824356 = _824354], (3044 ^ _779308) ^ [_824503, _824505, _824507, _824509, _824511, _824513, _824515, _824517] : [-(c_Nat_Onat_Onat__case(_824517, _824513, _824509, _824505) = c_Nat_Onat_Onat__case(_824515, _824511, _824507, _824503)), _824517 = _824515, _824513 = _824511, _824509 = _824507, _824505 = _824503], (3062 ^ _779308) ^ [_824804, _824806, _824808, _824810] : [-(c_Nat_Ocompow(_824810, _824806) = c_Nat_Ocompow(_824808, _824804)), _824810 = _824808, _824806 = _824804], (3072 ^ _779308) ^ [_824953, _824955] : [_824955 = _824953, -(c_List_Orotate1(_824955) = c_List_Orotate1(_824953))], (3078 ^ _779308) ^ [_825038, _825040, _825042, _825044] : [-(c_Finite__Set_Ofold1(_825044, _825040) = c_Finite__Set_Ofold1(_825042, _825038)), _825044 = _825042, _825040 = _825038], (3088 ^ _779308) ^ [_825187, _825189, _825191, _825193] : [-(c_Big__Operators_Olattice__class_OSup__fin(_825193, _825189) = c_Big__Operators_Olattice__class_OSup__fin(_825191, _825187)), _825193 = _825191, _825189 = _825187], (3098 ^ _779308) ^ [_825336, _825338, _825340, _825342] : [-(c_Big__Operators_Olattice__class_OInf__fin(_825342, _825338) = c_Big__Operators_Olattice__class_OInf__fin(_825340, _825336)), _825342 = _825340, _825338 = _825336], (3108 ^ _779308) ^ [_825485, _825487, _825489, _825491] : [-(c_Big__Operators_Olinorder__class_OMin(_825491, _825487) = c_Big__Operators_Olinorder__class_OMin(_825489, _825485)), _825491 = _825489, _825487 = _825485], (3118 ^ _779308) ^ [_825634, _825636, _825638, _825640] : [-(c_Big__Operators_Olinorder__class_OMax(_825640, _825636) = c_Big__Operators_Olinorder__class_OMax(_825638, _825634)), _825640 = _825638, _825636 = _825634], (3128 ^ _779308) ^ [_825783, _825785, _825787, _825789, _825791, _825793] : [-(c_Big__Operators_Olattice_OInf__fin(_825793, _825789, _825785) = c_Big__Operators_Olattice_OInf__fin(_825791, _825787, _825783)), _825793 = _825791, _825789 = _825787, _825785 = _825783], (3142 ^ _779308) ^ [_826004, _826006, _826008, _826010, _826012, _826014] : [-(c_Big__Operators_Olattice_OSup__fin(_826014, _826010, _826006) = c_Big__Operators_Olattice_OSup__fin(_826012, _826008, _826004)), _826014 = _826012, _826010 = _826008, _826006 = _826004], (3156 ^ _779308) ^ [_826225, _826227, _826229, _826231, _826233, _826235, _826237, _826239, _826241, _826243] : [-(c_Fun_Ofun__upd(_826243, _826239, _826235, _826231, _826227) = c_Fun_Ofun__upd(_826241, _826237, _826233, _826229, _826225)), _826243 = _826241, _826239 = _826237, _826235 = _826233, _826231 = _826229, _826227 = _826225], (3178 ^ _779308) ^ [_826614, _826616, _826618, _826620, _826622, _826624, _826626, _826628] : [-(c_Nitpick_Osetsum_H(_826628, _826624, _826620, _826616) = c_Nitpick_Osetsum_H(_826626, _826622, _826618, _826614)), _826628 = _826626, _826624 = _826622, _826620 = _826618, _826616 = _826614], (3196 ^ _779308) ^ [_826915, _826917, _826919, _826921, _826923, _826925] : [-(c_List_Olist_Olist__size(_826925, _826921, _826917) = c_List_Olist_Olist__size(_826923, _826919, _826915)), _826925 = _826923, _826921 = _826919, _826917 = _826915], (3210 ^ _779308) ^ [_827136, _827138, _827140, _827142] : [-(c_Random_Oselect(_827142, _827138) = c_Random_Oselect(_827140, _827136)), _827142 = _827140, _827138 = _827136], (3220 ^ _779308) ^ [_827285, _827287] : [_827287 = _827285, -(c_Random_Orange(_827287) = c_Random_Orange(_827285))], (3226 ^ _779308) ^ [_827370, _827372, _827374, _827376] : [-(c_Code__Numeral_Onat__of__aux(_827376, _827372) = c_Code__Numeral_Onat__of__aux(_827374, _827370)), _827376 = _827374, _827372 = _827370], (3236 ^ _779308) ^ [_827519, _827521] : [_827521 = _827519, -(c_Lazy__Sequence_Ohb__not__seq(_827521) = c_Lazy__Sequence_Ohb__not__seq(_827519))], (3242 ^ _779308) ^ [_827604, _827606] : [_827606 = _827604, -(c_Int_OBit1(_827606) = c_Int_OBit1(_827604))], (3248 ^ _779308) ^ [_827689, _827691, _827693, _827695] : [-(c_List_Olists(_827695, _827691) = c_List_Olists(_827693, _827689)), _827695 = _827693, _827691 = _827689], (3258 ^ _779308) ^ [_827838, _827840, _827842, _827844] : [-(c_List_Olistsp(_827844, _827840) = c_List_Olistsp(_827842, _827838)), _827844 = _827842, _827840 = _827838], (3268 ^ _779308) ^ [_827987, _827989, _827991, _827993, _827995, _827997, _827999, _828001] : [-(c_Enum_Oproduct(_828001, _827997, _827993, _827989) = c_Enum_Oproduct(_827999, _827995, _827991, _827987)), _828001 = _827999, _827997 = _827995, _827993 = _827991, _827989 = _827987], (3286 ^ _779308) ^ [_828288, _828290, _828292, _828294] : [-(c_Product__Type_OSigma(_828294, _828290) = c_Product__Type_OSigma(_828292, _828288)), _828294 = _828292, _828290 = _828288], (3296 ^ _779308) ^ [_828437, _828439] : [_828439 = _828437, -(c_Set_OPow(_828439) = c_Set_OPow(_828437))], (3302 ^ _779308) ^ [_828522, _828524, _828526, _828528] : [-(c_HOL_OLet(_828528, _828524) = c_HOL_OLet(_828526, _828522)), _828528 = _828526, _828524 = _828522], (3312 ^ _779308) ^ [_828671, _828673, _828675, _828677] : [-(c_Enum_Osublists(_828677, _828673) = c_Enum_Osublists(_828675, _828671)), _828677 = _828675, _828673 = _828671], (3322 ^ _779308) ^ [_828820, _828822, _828824, _828826] : [-(c_Enum_Oenum__the(_828826, _828822) = c_Enum_Oenum__the(_828824, _828820)), _828826 = _828824, _828822 = _828820], (3332 ^ _779308) ^ [_828969, _828971, _828973, _828975, _828977, _828979] : [-(c_Finite__Set_Ofold(_828979, _828975, _828971) = c_Finite__Set_Ofold(_828977, _828973, _828969)), _828979 = _828977, _828975 = _828973, _828971 = _828969], (3346 ^ _779308) ^ [_829190, _829192, _829194, _829196, _829198, _829200] : [-(c_Enum_On__lists(_829200, _829196, _829192) = c_Enum_On__lists(_829198, _829194, _829190)), _829200 = _829198, _829196 = _829194, _829192 = _829190], (3360 ^ _779308) ^ [_829411, _829413, _829415, _829417, _829419, _829421] : [-(c_List_Opartition(_829421, _829417, _829413) = c_List_Opartition(_829419, _829415, _829411)), _829421 = _829419, _829417 = _829415, _829413 = _829411], (3374 ^ _779308) ^ [_829632, _829634, _829636, _829638] : [-(c_List_OremoveAll(_829638, _829634) = c_List_OremoveAll(_829636, _829632)), _829638 = _829636, _829634 = _829632], (3384 ^ _779308) ^ [_829781, _829783, _829785, _829787, _829789, _829791, _829793, _829795] : [-(c_List_Olist_Olist__case(_829795, _829791, _829787, _829783) = c_List_Olist_Olist__case(_829793, _829789, _829785, _829781)), _829795 = _829793, _829791 = _829789, _829787 = _829785, _829783 = _829781], (3402 ^ _779308) ^ [_830082, _830084, _830086, _830088] : [-(c_Random_Oselect__weight(_830088, _830084) = c_Random_Oselect__weight(_830086, _830082)), _830088 = _830086, _830084 = _830082], (3412 ^ _779308) ^ [_830231, _830233, _830235, _830237] : [-(c_Random_Opick(_830237, _830233) = c_Random_Opick(_830235, _830231)), _830237 = _830235, _830233 = _830231], (3422 ^ _779308) ^ [_830380, _830382] : [_830382 = _830380, -(c_List_Otranspose__rel(_830382) = c_List_Otranspose__rel(_830380))], (3428 ^ _779308) ^ [_830465, _830467, _830469, _830471, _830473, _830475] : [-(c_List_Osublist(_830475, _830471, _830467) = c_List_Osublist(_830473, _830469, _830465)), _830475 = _830473, _830471 = _830469, _830467 = _830465], (3442 ^ _779308) ^ [_830686, _830688] : [_830688 = _830686, -(c_SetInterval_Oord__class_OlessThan(_830688) = c_SetInterval_Oord__class_OlessThan(_830686))], (3448 ^ _779308) ^ [_830771, _830773, _830775, _830777, _830779, _830781] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_830781, _830777, _830773) = c_SetInterval_Oord__class_OgreaterThanAtMost(_830779, _830775, _830771)), _830781 = _830779, _830777 = _830775, _830773 = _830771], (3462 ^ _779308) ^ [_830992, _830994, _830996, _830998, _831000, _831002] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_831002, _830998, _830994) = c_SetInterval_Oord__class_OgreaterThanLessThan(_831000, _830996, _830992)), _831002 = _831000, _830998 = _830996, _830994 = _830992], (3476 ^ _779308) ^ [_831213, _831215] : [_831215 = _831213, -(c_SetInterval_Oord__class_OatMost(_831215) = c_SetInterval_Oord__class_OatMost(_831213))], (3482 ^ _779308) ^ [_831298, _831300, _831302, _831304, _831306, _831308, _831310, _831312] : [-(c_List_Olinorder__class_Osort__key(_831312, _831308, _831304, _831300) = c_List_Olinorder__class_Osort__key(_831310, _831306, _831302, _831298)), _831312 = _831310, _831308 = _831306, _831304 = _831302, _831300 = _831298], (3500 ^ _779308) ^ [_831599, _831601, _831603, _831605, _831607, _831609, _831611, _831613, _831615, _831617] : [-(c_List_Olinorder__class_Oinsort__insert__key(_831617, _831613, _831609, _831605, _831601) = c_List_Olinorder__class_Oinsort__insert__key(_831615, _831611, _831607, _831603, _831599)), _831617 = _831615, _831613 = _831611, _831609 = _831607, _831605 = _831603, _831601 = _831599], (3522 ^ _779308) ^ [_831988, _831990, _831992, _831994] : [-(c_List_Olinorder__class_Osorted__list__of__set(_831994, _831990) = c_List_Olinorder__class_Osorted__list__of__set(_831992, _831988)), _831994 = _831992, _831990 = _831988], (3532 ^ _779308) ^ [_832137, _832139, _832141, _832143, _832145, _832147] : [-(c_List_Oremove1(_832147, _832143, _832139) = c_List_Oremove1(_832145, _832141, _832137)), _832147 = _832145, _832143 = _832141, _832139 = _832137], (3546 ^ _779308) ^ [_832358, _832360, _832362, _832364] : [-(c_List_Orotate(_832364, _832360) = c_List_Orotate(_832362, _832358)), _832364 = _832362, _832360 = _832358], (3556 ^ _779308) ^ [_832507, _832509, _832511, _832513] : [-(c_List_Olist__update(_832513, _832509) = c_List_Olist__update(_832511, _832507)), _832513 = _832511, _832509 = _832507], (3566 ^ _779308) ^ [_832656, _832658, _832660, _832662, _832664, _832666, _832668, _832670, _832672, _832674] : [-(c_List_Ofoldr(_832674, _832670, _832666, _832662, _832658) = c_List_Ofoldr(_832672, _832668, _832664, _832660, _832656)), _832674 = _832672, _832670 = _832668, _832666 = _832664, _832662 = _832660, _832658 = _832656], (3588 ^ _779308) ^ [_833045, _833047] : [_833047 = _833045, -(c_Orderings_Oord__class_Omax(_833047) = c_Orderings_Oord__class_Omax(_833045))], (3594 ^ _779308) ^ [_833130, _833132, _833134, _833136] : [-(c_List_Otranspose(_833136, _833132) = c_List_Otranspose(_833134, _833130)), _833136 = _833134, _833132 = _833130], (3604 ^ _779308) ^ [_833279, _833281, _833283, _833285] : [-(c_List_Obutlast(_833285, _833281) = c_List_Obutlast(_833283, _833279)), _833285 = _833283, _833281 = _833279], (3614 ^ _779308) ^ [_833428, _833430] : [_833430 = _833428, -(c_List_Oreturn__list(_833430) = c_List_Oreturn__list(_833428))], (3620 ^ _779308) ^ [_833513, _833515] : [_833515 = _833513, -(c_List_Oembed__list(_833515) = c_List_Oembed__list(_833513))], (3626 ^ _779308) ^ [_833598, _833600] : [_833600 = _833598, -(c_List_Omonoid__add__class_Olistsum(_833600) = c_List_Omonoid__add__class_Olistsum(_833598))], (3632 ^ _779308) ^ [_833683, _833685, _833687, _833689] : [-(c_List_Oremdups(_833689, _833685) = c_List_Oremdups(_833687, _833683)), _833689 = _833687, _833685 = _833683], (3642 ^ _779308) ^ [_833832, _833834, _833836, _833838, _833840, _833842] : [-(c_List_Oinsert(_833842, _833838, _833834) = c_List_Oinsert(_833840, _833836, _833832)), _833842 = _833840, _833838 = _833836, _833834 = _833832], (3656 ^ _779308) ^ [_834053, _834055, _834057, _834059, _834061, _834063, _834065, _834067] : [-(c_List_Omaps(_834067, _834063, _834059, _834055) = c_List_Omaps(_834065, _834061, _834057, _834053)), _834067 = _834065, _834063 = _834061, _834059 = _834057, _834055 = _834053], (3674 ^ _779308) ^ [_834354, _834356, _834358, _834360] : [-(c_List_Olex(_834360, _834356) = c_List_Olex(_834358, _834354)), _834360 = _834358, _834356 = _834354], (3684 ^ _779308) ^ [_834503, _834505, _834507, _834509] : [-(c_List_Omeasures(_834509, _834505) = c_List_Omeasures(_834507, _834503)), _834509 = _834507, _834505 = _834503], (3694 ^ _779308) ^ [_834652, _834654, _834656, _834658, _834660, _834662, _834664, _834666] : [-(c_List_Ofoldl(_834666, _834662, _834658, _834654) = c_List_Ofoldl(_834664, _834660, _834656, _834652)), _834666 = _834664, _834662 = _834660, _834658 = _834656, _834654 = _834652], (3712 ^ _779308) ^ [_834953, _834955] : [_834955 = _834953, -(c_Enum_Oenum__class_Oenum__ex(_834955) = c_Enum_Oenum__class_Oenum__ex(_834953))], (3718 ^ _779308) ^ [_835038, _835040, _835042, _835044, _835046, _835048, _835050, _835052] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_835052, _835048, _835044, _835040) = c_New__Random__Sequence_Opos__not__random__dseq(_835050, _835046, _835042, _835038)), _835052 = _835050, _835048 = _835046, _835044 = _835042, _835040 = _835038], (3736 ^ _779308) ^ [_835339, _835341] : [_835341 = _835339, -(c_New__DSequence_Opos__not__seq(_835341) = c_New__DSequence_Opos__not__seq(_835339))], (3742 ^ _779308) ^ [_835424, _835426, _835428, _835430, _835432, _835434] : [-(c_List_OdropWhile(_835434, _835430, _835426) = c_List_OdropWhile(_835432, _835428, _835424)), _835434 = _835432, _835430 = _835428, _835426 = _835424], (3756 ^ _779308) ^ [_835645, _835647] : [_835647 = _835645, -(c_List_Odistinct(_835647) = c_List_Odistinct(_835645))], (3762 ^ _779308) ^ [_835730, _835732, _835734, _835736, _835738, _835740] : [-(c_List_OtakeWhile(_835740, _835736, _835732) = c_List_OtakeWhile(_835738, _835734, _835730)), _835740 = _835738, _835736 = _835734, _835732 = _835730], (3776 ^ _779308) ^ [_835951, _835953, _835955, _835957, _835959, _835961] : [-(c_List_Olinorder__class_Oinsort__key(_835961, _835957, _835953) = c_List_Olinorder__class_Oinsort__key(_835959, _835955, _835951)), _835961 = _835959, _835957 = _835955, _835953 = _835951], (3790 ^ _779308) ^ [_836172, _836174] : [_836174 = _836172, -(c_Enum_Oenum__class_Oenum__all(_836174) = c_Enum_Oenum__class_Oenum__all(_836172))], (3796 ^ _779308) ^ [_836257, _836259] : [_836259 = _836257, -(c_Nat_Osemiring__1__class_Oof__nat(_836259) = c_Nat_Osemiring__1__class_Oof__nat(_836257))], (3802 ^ _779308) ^ [_836342, _836344] : [_836344 = _836342, -(c_Lazy__Sequence_Ohit__bound(_836344) = c_Lazy__Sequence_Ohit__bound(_836342))], (3808 ^ _779308) ^ [_836427, _836429, _836431, _836433, _836435, _836437, _836439, _836441, _836443, _836445, _836447, _836449, _836451, _836453] : [-(c_New__Random__Sequence_Oneg__decr__bind(_836453, _836449, _836445, _836441, _836437, _836433, _836429) = c_New__Random__Sequence_Oneg__decr__bind(_836451, _836447, _836443, _836439, _836435, _836431, _836427)), _836453 = _836451, _836449 = _836447, _836445 = _836443, _836441 = _836439, _836437 = _836435, _836433 = _836431, _836429 = _836427], (3838 ^ _779308) ^ [_837016, _837018, _837020, _837022, _837024, _837026, _837028, _837030] : [-(c_New__DSequence_Oneg__decr__bind(_837030, _837026, _837022, _837018) = c_New__DSequence_Oneg__decr__bind(_837028, _837024, _837020, _837016)), _837030 = _837028, _837026 = _837024, _837022 = _837020, _837018 = _837016], (3856 ^ _779308) ^ [_837317, _837319, _837321, _837323, _837325, _837327, _837329, _837331, _837333, _837335, _837337, _837339, _837341, _837343] : [-(c_New__Random__Sequence_Opos__decr__bind(_837343, _837339, _837335, _837331, _837327, _837323, _837319) = c_New__Random__Sequence_Opos__decr__bind(_837341, _837337, _837333, _837329, _837325, _837321, _837317)), _837343 = _837341, _837339 = _837337, _837335 = _837333, _837331 = _837329, _837327 = _837325, _837323 = _837321, _837319 = _837317], (3886 ^ _779308) ^ [_837906, _837908, _837910, _837912, _837914, _837916, _837918, _837920] : [-(c_New__DSequence_Opos__decr__bind(_837920, _837916, _837912, _837908) = c_New__DSequence_Opos__decr__bind(_837918, _837914, _837910, _837906)), _837920 = _837918, _837916 = _837914, _837912 = _837910, _837908 = _837906], (3904 ^ _779308) ^ [_838207, _838209, _838211, _838213, _838215, _838217, _838219, _838221] : [-(c_Lazy__Sequence_Ohb__bind(_838221, _838217, _838213, _838209) = c_Lazy__Sequence_Ohb__bind(_838219, _838215, _838211, _838207)), _838221 = _838219, _838217 = _838215, _838213 = _838211, _838209 = _838207], (3922 ^ _779308) ^ [_838508, _838510, _838512, _838514, _838516, _838518, _838520, _838522] : [-(c_New__Random__Sequence_Opos__empty(_838522, _838518, _838514, _838510) = c_New__Random__Sequence_Opos__empty(_838520, _838516, _838512, _838508)), _838522 = _838520, _838518 = _838516, _838514 = _838512, _838510 = _838508], (3940 ^ _779308) ^ [_838809, _838811] : [_838811 = _838809, -(c_New__DSequence_Opos__empty(_838811) = c_New__DSequence_Opos__empty(_838809))], (3946 ^ _779308) ^ [_838894, _838896, _838898, _838900, _838902, _838904, _838906, _838908] : [-(c_New__DSequence_Oneg__bind(_838908, _838904, _838900, _838896) = c_New__DSequence_Oneg__bind(_838906, _838902, _838898, _838894)), _838908 = _838906, _838904 = _838902, _838900 = _838898, _838896 = _838894], (3964 ^ _779308) ^ [_839195, _839197, _839199, _839201, _839203, _839205, _839207, _839209] : [-(c_New__Random__Sequence_Oneg__map(_839209, _839205, _839201, _839197) = c_New__Random__Sequence_Oneg__map(_839207, _839203, _839199, _839195)), _839209 = _839207, _839205 = _839203, _839201 = _839199, _839197 = _839195], (3982 ^ _779308) ^ [_839496, _839498, _839500, _839502, _839504, _839506, _839508, _839510] : [-(c_New__Random__Sequence_Oneg__bind(_839510, _839506, _839502, _839498) = c_New__Random__Sequence_Oneg__bind(_839508, _839504, _839500, _839496)), _839510 = _839508, _839506 = _839504, _839502 = _839500, _839498 = _839496], (4000 ^ _779308) ^ [_839797, _839799] : [_839799 = _839797, -(c_New__Random__Sequence_Oneg__single(_839799) = c_New__Random__Sequence_Oneg__single(_839797))], (4006 ^ _779308) ^ [_839882, _839884, _839886, _839888, _839890, _839892, _839894, _839896] : [-(c_New__DSequence_Opos__bind(_839896, _839892, _839888, _839884) = c_New__DSequence_Opos__bind(_839894, _839890, _839886, _839882)), _839896 = _839894, _839892 = _839890, _839888 = _839886, _839884 = _839882], (4024 ^ _779308) ^ [_840183, _840185, _840187, _840189] : [-(c_New__DSequence_Oneg__single(_840189, _840185) = c_New__DSequence_Oneg__single(_840187, _840183)), _840189 = _840187, _840185 = _840183], (4034 ^ _779308) ^ [_840332, _840334, _840336, _840338] : [-(c_Lazy__Sequence_Ohb__single(_840338, _840334) = c_Lazy__Sequence_Ohb__single(_840336, _840332)), _840338 = _840336, _840334 = _840332], (4044 ^ _779308) ^ [_840481, _840483, _840485, _840487, _840489, _840491, _840493, _840495] : [-(c_New__Random__Sequence_Opos__map(_840495, _840491, _840487, _840483) = c_New__Random__Sequence_Opos__map(_840493, _840489, _840485, _840481)), _840495 = _840493, _840491 = _840489, _840487 = _840485, _840483 = _840481], (4062 ^ _779308) ^ [_840782, _840784, _840786, _840788, _840790, _840792, _840794, _840796] : [-(c_New__Random__Sequence_Opos__bind(_840796, _840792, _840788, _840784) = c_New__Random__Sequence_Opos__bind(_840794, _840790, _840786, _840782)), _840796 = _840794, _840792 = _840790, _840788 = _840786, _840784 = _840782], (4080 ^ _779308) ^ [_841083, _841085] : [_841085 = _841083, -(c_New__Random__Sequence_Opos__single(_841085) = c_New__Random__Sequence_Opos__single(_841083))], (4086 ^ _779308) ^ [_841168, _841170, _841172, _841174, _841176, _841178] : [-(c_List_Osplice(_841178, _841174, _841170) = c_List_Osplice(_841176, _841172, _841168)), _841178 = _841176, _841174 = _841172, _841170 = _841168], (4100 ^ _779308) ^ [_841389, _841391, _841393, _841395] : [-(c_New__DSequence_Opos__single(_841395, _841391) = c_New__DSequence_Opos__single(_841393, _841389)), _841395 = _841393, _841391 = _841389], (4110 ^ _779308) ^ [_841538, _841540, _841542, _841544, _841546, _841548] : [-(c_Predicate_Oconversep(_841548, _841544, _841540) = c_Predicate_Oconversep(_841546, _841542, _841538)), _841548 = _841546, _841544 = _841542, _841540 = _841538], (4124 ^ _779308) ^ [_841759, _841761] : [_841761 = _841759, -(c_List_Otl(_841761) = c_List_Otl(_841759))], (4130 ^ _779308) ^ [_841844, _841846] : [_841846 = _841844, -(c_List_Orev(_841846) = c_List_Orev(_841844))], (4136 ^ _779308) ^ [_841929, _841931] : [_841931 = _841929, -(c_List_Odrop(_841931) = c_List_Odrop(_841929))], (4142 ^ _779308) ^ [_842014, _842016] : [_842016 = _842014, -(c_List_Ohd(_842016) = c_List_Ohd(_842014))], (4148 ^ _779308) ^ [_842099, _842101, _842103, _842105] : [-(c_List_Olast(_842105, _842101) = c_List_Olast(_842103, _842099)), _842105 = _842103, _842101 = _842099], (4158 ^ _779308) ^ [_842248, _842250] : [_842250 = _842248, -(c_List_Otake(_842250) = c_List_Otake(_842248))], (4164 ^ _779308) ^ [_842333, _842335, _842337, _842339] : [-(c_List_Ozip(_842339, _842335) = c_List_Ozip(_842337, _842333)), _842339 = _842337, _842335 = _842333], (4174 ^ _779308) ^ [_842482, _842484] : [_842484 = _842482, -(c_Orderings_Oord__class_Omin(_842484) = c_Orderings_Oord__class_Omin(_842482))], (4180 ^ _779308) ^ [_842567, _842569] : [_842569 = _842567, -(c_List_Onth(_842569) = c_List_Onth(_842567))], (4186 ^ _779308) ^ [_842652, _842654, _842656, _842658] : [-(c_List_Ofilter(_842658, _842654) = c_List_Ofilter(_842656, _842652)), _842658 = _842656, _842654 = _842652], (4196 ^ _779308) ^ [_842801, _842803, _842805, _842807] : [-(c_List_Oconcat(_842807, _842803) = c_List_Oconcat(_842805, _842801)), _842807 = _842805, _842803 = _842801], (4206 ^ _779308) ^ [_842950, _842952] : [_842952 = _842950, -(c_List_Oappend(_842952) = c_List_Oappend(_842950))], (4212 ^ _779308) ^ [_843035, _843037, _843039, _843041] : [-(c_List_Omap(_843041, _843037) = c_List_Omap(_843039, _843035)), _843041 = _843039, _843037 = _843035], (4222 ^ _779308) ^ [_843184, _843186, _843188, _843190, _843192, _843194] : [-(c_List_Oreplicate(_843194, _843190, _843186) = c_List_Oreplicate(_843192, _843188, _843184)), _843194 = _843192, _843190 = _843188, _843186 = _843184], (4236 ^ _779308) ^ [_843405, _843407] : [_843407 = _843405, -(c_If(_843407) = c_If(_843405))], (4242 ^ _779308) ^ [_843490, _843492, _843494, _843496, _843498, _843500, _843502, _843504, _843506, _843508] : [-(c_Predicate_Opred__comp(_843508, _843504, _843500, _843496, _843492) = c_Predicate_Opred__comp(_843506, _843502, _843498, _843494, _843490)), _843508 = _843506, _843504 = _843502, _843500 = _843498, _843496 = _843494, _843492 = _843490], (4264 ^ _779308) ^ [_843879, _843881, _843883, _843885, _843887, _843889, _843891, _843893] : [-(c_Lazy__Sequence_Oproduct(_843893, _843889, _843885, _843881) = c_Lazy__Sequence_Oproduct(_843891, _843887, _843883, _843879)), _843893 = _843891, _843889 = _843887, _843885 = _843883, _843881 = _843879], (4282 ^ _779308) ^ [_844180, _844182, _844184, _844186, _844188, _844190, _844192, _844194, _844196, _844198, _844200, _844202] : [-(c_New__Random__Sequence_Opos__union(_844202, _844198, _844194, _844190, _844186, _844182) = c_New__Random__Sequence_Opos__union(_844200, _844196, _844192, _844188, _844184, _844180)), _844202 = _844200, _844198 = _844196, _844194 = _844192, _844190 = _844188, _844186 = _844184, _844182 = _844180], (4308 ^ _779308) ^ [_844665, _844667, _844669, _844671, _844673, _844675] : [-(c_New__DSequence_Opos__union(_844675, _844671, _844667) = c_New__DSequence_Opos__union(_844673, _844669, _844665)), _844675 = _844673, _844671 = _844669, _844667 = _844665], (4322 ^ _779308) ^ [_844886, _844888, _844890, _844892] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_844892, _844888) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_844890, _844886)), _844892 = _844890, _844888 = _844886], (4332 ^ _779308) ^ [_845035, _845037] : [_845037 = _845035, -(c_Lazy__Sequence_Oempty(_845037) = c_Lazy__Sequence_Oempty(_845035))], (4338 ^ _779308) ^ [_845120, _845122] : [_845122 = _845120, -(c_Lazy__Sequence_Osingle(_845122) = c_Lazy__Sequence_Osingle(_845120))], (4344 ^ _779308) ^ [_845205, _845207, _845209, _845211] : [-(c_Lazy__Sequence_Osmall__lazy_H(_845211, _845207) = c_Lazy__Sequence_Osmall__lazy_H(_845209, _845205)), _845211 = _845209, _845207 = _845205], (4354 ^ _779308) ^ [_845354, _845356, _845358, _845360] : [-(c_Wellfounded_Oaccp(_845360, _845356) = c_Wellfounded_Oaccp(_845358, _845354)), _845360 = _845358, _845356 = _845354], (4364 ^ _779308) ^ [_845503, _845505, _845507, _845509, _845511, _845513, _845515, _845517, _845519, _845521] : [-(c_Option_Ooption_Ooption__case(_845521, _845517, _845513, _845509, _845505) = c_Option_Ooption_Ooption__case(_845519, _845515, _845511, _845507, _845503)), _845521 = _845519, _845517 = _845515, _845513 = _845511, _845509 = _845507, _845505 = _845503], (4386 ^ _779308) ^ [_845892, _845894] : [_845894 = _845892, -(c_Lazy__Sequence_Oyieldn(_845894) = c_Lazy__Sequence_Oyieldn(_845892))], (4392 ^ _779308) ^ [_845977, _845979, _845981, _845983, _845985, _845987] : [-(c_Lazy__Sequence_Oanamorph(_845987, _845983, _845979) = c_Lazy__Sequence_Oanamorph(_845985, _845981, _845977)), _845987 = _845985, _845983 = _845981, _845979 = _845977], (4406 ^ _779308) ^ [_846198, _846200] : [_846200 = _846198, -(c_Lazy__Sequence_Oyield(_846200) = c_Lazy__Sequence_Oyield(_846198))], (4412 ^ _779308) ^ [_846283, _846285] : [_846285 = _846283, -(c_List_Olist_OCons(_846285) = c_List_Olist_OCons(_846283))], (4418 ^ _779308) ^ [_846368, _846370] : [_846370 = _846368, -(c_List_Olist_ONil(_846370) = c_List_Olist_ONil(_846368))], (4424 ^ _779308) ^ [_846453, _846455] : [_846455 = _846453, -(c_List_Omember(_846455) = c_List_Omember(_846453))], (4430 ^ _779308) ^ [_846538, _846540, _846542, _846544] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846544, _846540) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846542, _846538)), _846544 = _846542, _846540 = _846538], (4440 ^ _779308) ^ [_846687, _846689, _846691, _846693] : [-(c_HOL_OThe(_846693, _846689) = c_HOL_OThe(_846691, _846687)), _846693 = _846691, _846689 = _846687], (4450 ^ _779308) ^ [_846836, _846838, _846840, _846842, _846844, _846846] : [-(c_FunDef_OTHE__default(_846846, _846842, _846838) = c_FunDef_OTHE__default(_846844, _846840, _846836)), _846846 = _846844, _846842 = _846840, _846838 = _846836], (4464 ^ _779308) ^ [_847057, _847059, _847061, _847063] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_847063, _847059) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_847061, _847057)), _847063 = _847061, _847059 = _847057], (4474 ^ _779308) ^ [_847206, _847208] : [_847208 = _847206, -(c_Nat_Osize__class_Osize(_847208) = c_Nat_Osize__class_Osize(_847206))], (4480 ^ _779308) ^ [_847291, _847293, _847295, _847297, _847299, _847301, _847303, _847305, _847307, _847309] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_847309, _847305, _847301, _847297, _847293) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_847307, _847303, _847299, _847295, _847291)), _847309 = _847307, _847305 = _847303, _847301 = _847299, _847297 = _847295, _847293 = _847291], (4502 ^ _779308) ^ [_847680, _847682, _847684, _847686] : [-(c_List_Oupto(_847686, _847682) = c_List_Oupto(_847684, _847680)), _847686 = _847684, _847682 = _847680], (4512 ^ _779308) ^ [_847829, _847831] : [_847831 = _847829, -(c_Code__Numeral_OSuc__code__numeral(_847831) = c_Code__Numeral_OSuc__code__numeral(_847829))], (4518 ^ _779308) ^ [_847914, _847916, _847918, _847920, _847922, _847924, _847926, _847928] : [-(c_Product__Type_Oscomp(_847928, _847924, _847920, _847916) = c_Product__Type_Oscomp(_847926, _847922, _847918, _847914)), _847928 = _847926, _847924 = _847922, _847920 = _847918, _847916 = _847914], (4536 ^ _779308) ^ [_848215, _848217, _848219, _848221, _848223, _848225, _848227, _848229] : [-(c_Random__Sequence_ORandom(_848229, _848225, _848221, _848217) = c_Random__Sequence_ORandom(_848227, _848223, _848219, _848215)), _848229 = _848227, _848225 = _848223, _848221 = _848219, _848217 = _848215], (4554 ^ _779308) ^ [_848516, _848518] : [_848518 = _848516, -(c_DSequence_Ounion(_848518) = c_DSequence_Ounion(_848516))], (4560 ^ _779308) ^ [_848601, _848603, _848605, _848607, _848609, _848611, _848613, _848615] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_848615, _848611, _848607, _848603) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_848613, _848609, _848605, _848601)), _848615 = _848613, _848611 = _848609, _848607 = _848605, _848603 = _848601], (4578 ^ _779308) ^ [_848902, _848904, _848906, _848908, _848910, _848912] : [-(c_Random__Sequence_Oempty(_848912, _848908, _848904) = c_Random__Sequence_Oempty(_848910, _848906, _848902)), _848912 = _848910, _848908 = _848906, _848904 = _848902], (4592 ^ _779308) ^ [_849123, _849125] : [_849125 = _849123, -(c_DSequence_Oempty(_849125) = c_DSequence_Oempty(_849123))], (4598 ^ _779308) ^ [_849208, _849210] : [_849210 = _849208, -(c_DSequence_Osingle(_849210) = c_DSequence_Osingle(_849208))], (4604 ^ _779308) ^ [_849293, _849295, _849297, _849299, _849301, _849303, _849305, _849307] : [-(c_Random__Sequence_Omap(_849307, _849303, _849299, _849295) = c_Random__Sequence_Omap(_849305, _849301, _849297, _849293)), _849307 = _849305, _849303 = _849301, _849299 = _849297, _849295 = _849293], (4622 ^ _779308) ^ [_849594, _849596, _849598, _849600, _849602, _849604, _849606, _849608] : [-(c_Random__Sequence_Obind(_849608, _849604, _849600, _849596) = c_Random__Sequence_Obind(_849606, _849602, _849598, _849594)), _849608 = _849606, _849604 = _849602, _849600 = _849598, _849596 = _849594], (4640 ^ _779308) ^ [_849895, _849897] : [_849897 = _849895, -(c_Random__Sequence_Osingle(_849897) = c_Random__Sequence_Osingle(_849895))], (4646 ^ _779308) ^ [_849980, _849982, _849984, _849986] : [-(c_Product__Type_Osnd(_849986, _849982) = c_Product__Type_Osnd(_849984, _849980)), _849986 = _849984, _849982 = _849980], (4656 ^ _779308) ^ [_850129, _850131, _850133, _850135] : [-(c_Product__Type_Ofst(_850135, _850131) = c_Product__Type_Ofst(_850133, _850129)), _850135 = _850133, _850131 = _850129], (4666 ^ _779308) ^ [_850278, _850280, _850282, _850284, _850286, _850288] : [-(c_Relation_OImage(_850288, _850284, _850280) = c_Relation_OImage(_850286, _850282, _850278)), _850288 = _850286, _850284 = _850282, _850280 = _850278], (4680 ^ _779308) ^ [_850499, _850501, _850503, _850505, _850507, _850509, _850511, _850513] : [-(c_Wellfounded_Olex__prod(_850513, _850509, _850505, _850501) = c_Wellfounded_Olex__prod(_850511, _850507, _850503, _850499)), _850513 = _850511, _850509 = _850507, _850505 = _850503, _850501 = _850499], (4698 ^ _779308) ^ [_850800, _850802] : [_850802 = _850800, -(c_Set_OBex(_850802) = c_Set_OBex(_850800))], (4704 ^ _779308) ^ [_850885, _850887, _850889, _850891] : [-(c_List_Olexord(_850891, _850887) = c_List_Olexord(_850889, _850885)), _850891 = _850889, _850887 = _850885], (4714 ^ _779308) ^ [_851034, _851036] : [_851036 = _851034, -(c_Wellfounded_Ofinite__psubset(_851036) = c_Wellfounded_Ofinite__psubset(_851034))], (4720 ^ _779308) ^ [_851119, _851121] : [_851121 = _851119, -(c_List_Oset(_851121) = c_List_Oset(_851119))], (4726 ^ _779308) ^ [_851204, _851206, _851208, _851210] : [-(c_Complete__Lattice_OSup__class_OSup(_851210, _851206) = c_Complete__Lattice_OSup__class_OSup(_851208, _851204)), _851210 = _851208, _851206 = _851204], (4736 ^ _779308) ^ [_851353, _851355, _851357, _851359] : [-(c_Complete__Lattice_OInf__class_OInf(_851359, _851355) = c_Complete__Lattice_OInf__class_OInf(_851357, _851353)), _851359 = _851357, _851355 = _851353], (4746 ^ _779308) ^ [_851502, _851504, _851506, _851508, _851510, _851512, _851514, _851516, _851518, _851520, _851522, _851524] : [-(c_Partial__Function_Ofun__lub(_851524, _851520, _851516, _851512, _851508, _851504) = c_Partial__Function_Ofun__lub(_851522, _851518, _851514, _851510, _851506, _851502)), _851524 = _851522, _851520 = _851518, _851516 = _851514, _851512 = _851510, _851508 = _851506, _851504 = _851502], (4772 ^ _779308) ^ [_851987, _851989, _851991, _851993, _851995, _851997] : [-(c_Relation_Orel__comp(_851997, _851993, _851989) = c_Relation_Orel__comp(_851995, _851991, _851987)), _851997 = _851995, _851993 = _851991, _851989 = _851987], (4786 ^ _779308) ^ [_852208, _852210, _852212, _852214] : [-(c_Relation_Oinv__image(_852214, _852210) = c_Relation_Oinv__image(_852212, _852208)), _852214 = _852212, _852210 = _852208], (4796 ^ _779308) ^ [_852357, _852359, _852361, _852363] : [-(c_List_Olistrel(_852363, _852359) = c_List_Olistrel(_852361, _852357)), _852363 = _852361, _852359 = _852357], (4806 ^ _779308) ^ [_852506, _852508] : [_852508 = _852506, -(c_Relation_OId(_852508) = c_Relation_OId(_852506))], (4812 ^ _779308) ^ [_852591, _852593, _852595, _852597] : [-(c_Relation_OId__on(_852597, _852593) = c_Relation_OId__on(_852595, _852591)), _852597 = _852595, _852593 = _852591], (4822 ^ _779308) ^ [_852740, _852742, _852744, _852746] : [-(c_Relation_Oconverse(_852746, _852742) = c_Relation_Oconverse(_852744, _852740)), _852746 = _852744, _852742 = _852740], (4832 ^ _779308) ^ [_852889, _852891] : [_852891 = _852889, -(c_HOL_OEx(_852891) = c_HOL_OEx(_852889))], (4838 ^ _779308) ^ [_852974, _852976, _852978, _852980] : [-(c_Hilbert__Choice_OEps(_852980, _852976) = c_Hilbert__Choice_OEps(_852978, _852974)), _852980 = _852978, _852976 = _852974], (4848 ^ _779308) ^ [_853123, _853125, _853127, _853129, _853131, _853133] : [-(c_Finite__Set_Ofold__image(_853133, _853129, _853125) = c_Finite__Set_Ofold__image(_853131, _853127, _853123)), _853133 = _853131, _853129 = _853127, _853125 = _853123], (4862 ^ _779308) ^ [_853344, _853346, _853348, _853350] : [-(c_Quickcheck_Obeyond(_853350, _853346) = c_Quickcheck_Obeyond(_853348, _853344)), _853350 = _853348, _853346 = _853344], (4872 ^ _779308) ^ [_853493, _853495, _853497, _853499, _853501, _853503, _853505, _853507, _853509, _853511] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_853511, _853507, _853503, _853499, _853495) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_853509, _853505, _853501, _853497, _853493)), _853511 = _853509, _853507 = _853505, _853503 = _853501, _853499 = _853497, _853495 = _853493], (4894 ^ _779308) ^ [_853882, _853884] : [_853884 = _853882, -(c_Set_OCollect(_853884) = c_Set_OCollect(_853882))], (4900 ^ _779308) ^ [_853967, _853969] : [_853969 = _853967, -(c_Lattices_Osemilattice__inf__class_Oinf(_853969) = c_Lattices_Osemilattice__inf__class_Oinf(_853967))], (4906 ^ _779308) ^ [_854052, _854054] : [_854054 = _854052, -(c_Lattices_Osemilattice__sup__class_Osup(_854054) = c_Lattices_Osemilattice__sup__class_Osup(_854052))], (4912 ^ _779308) ^ [_854137, _854139] : [_854139 = _854137, -(c_Fun_Oid(_854139) = c_Fun_Oid(_854137))], (4918 ^ _779308) ^ [_854222, _854224, _854226, _854228, _854230, _854232, _854234, _854236] : [-(c_Fun_Othe__inv__into(_854236, _854232, _854228, _854224) = c_Fun_Othe__inv__into(_854234, _854230, _854226, _854222)), _854236 = _854234, _854232 = _854230, _854228 = _854226, _854224 = _854222], (4936 ^ _779308) ^ [_854523, _854525, _854527, _854529, _854531, _854533] : [-(c_Product__Type_Oprod_Oprod__case(_854533, _854529, _854525) = c_Product__Type_Oprod_Oprod__case(_854531, _854527, _854523)), _854533 = _854531, _854529 = _854527, _854525 = _854523], (4950 ^ _779308) ^ [_854744, _854746, _854748, _854750, _854752, _854754, _854756, _854758] : [-(c_Product__Type_Ocurry(_854758, _854754, _854750, _854746) = c_Product__Type_Ocurry(_854756, _854752, _854748, _854744)), _854758 = _854756, _854754 = _854752, _854750 = _854748, _854746 = _854744], (4968 ^ _779308) ^ [_855045, _855047, _855049, _855051, _855053, _855055] : [-(c_Set_Ovimage(_855055, _855051, _855047) = c_Set_Ovimage(_855053, _855049, _855045)), _855055 = _855053, _855051 = _855049, _855047 = _855045], (4982 ^ _779308) ^ [_855266, _855268, _855270, _855272, _855274, _855276, _855278, _855280] : [-(c_Hilbert__Choice_Oinv__into(_855280, _855276, _855272, _855268) = c_Hilbert__Choice_Oinv__into(_855278, _855274, _855270, _855266)), _855280 = _855278, _855276 = _855274, _855272 = _855270, _855268 = _855266], (5000 ^ _779308) ^ [_855567, _855569] : [_855569 = _855567, -(c_Orderings_Otop__class_Otop(_855569) = c_Orderings_Otop__class_Otop(_855567))], (5006 ^ _779308) ^ [_855652, _855654, _855656, _855658, _855660, _855662] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_855662, _855658, _855654) = c_SetInterval_Oord__class_OatLeastAtMost(_855660, _855656, _855652)), _855662 = _855660, _855658 = _855656, _855654 = _855652], (5020 ^ _779308) ^ [_855873, _855875, _855877, _855879] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855879, _855875) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855877, _855873)), _855879 = _855877, _855875 = _855873], (5030 ^ _779308) ^ [_856022, _856024, _856026, _856028] : [-(c_Quotient_ORespects(_856028, _856024) = c_Quotient_ORespects(_856026, _856022)), _856028 = _856026, _856024 = _856022], (5040 ^ _779308) ^ [_856171, _856173, _856175, _856177, _856179, _856181, _856183, _856185] : [-(c_Quotient_OBabs(_856185, _856181, _856177, _856173) = c_Quotient_OBabs(_856183, _856179, _856175, _856171)), _856185 = _856183, _856181 = _856179, _856177 = _856175, _856173 = _856171], (5058 ^ _779308) ^ [_856472, _856474, _856476, _856478] : [-(c_Transitive__Closure_Otrancl(_856478, _856474) = c_Transitive__Closure_Otrancl(_856476, _856472)), _856478 = _856476, _856474 = _856472], (5068 ^ _779308) ^ [_856621, _856623, _856625, _856627] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856627, _856623) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856625, _856621)), _856627 = _856625, _856623 = _856621], (5078 ^ _779308) ^ [_856770, _856772, _856774, _856776] : [-(c_Transitive__Closure_Ortrancl(_856776, _856772) = c_Transitive__Closure_Ortrancl(_856774, _856770)), _856776 = _856774, _856772 = _856770], (5088 ^ _779308) ^ [_856919, _856921, _856923, _856925] : [-(c_Product__Type_OPair(_856925, _856921) = c_Product__Type_OPair(_856923, _856919)), _856925 = _856923, _856921 = _856919], (5098 ^ _779308) ^ [_857068, _857070, _857072, _857074, _857076, _857078] : [-(c_Lazy__Sequence_Oappend(_857078, _857074, _857070) = c_Lazy__Sequence_Oappend(_857076, _857072, _857068)), _857078 = _857076, _857074 = _857072, _857070 = _857068], (5112 ^ _779308) ^ [_857289, _857291, _857293, _857295] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_857295, _857291) = c_SetInterval_Oord__class_OatLeastLessThan(_857293, _857289)), _857295 = _857293, _857291 = _857289], (5122 ^ _779308) ^ [_857438, _857440, _857442, _857444] : [-(c_List_Oupt(_857444, _857440) = c_List_Oupt(_857442, _857438)), _857444 = _857442, _857440 = _857438], (5132 ^ _779308) ^ [_857587, _857589, _857591, _857593, _857595, _857597, _857599, _857601] : [-(c_Fun_Ocomp(_857601, _857597, _857593, _857589) = c_Fun_Ocomp(_857599, _857595, _857591, _857587)), _857601 = _857599, _857597 = _857595, _857593 = _857591, _857589 = _857587], (5150 ^ _779308) ^ [_857888, _857890, _857892, _857894, _857896, _857898] : [-(c_Lazy__Sequence_Obind(_857898, _857894, _857890) = c_Lazy__Sequence_Obind(_857896, _857892, _857888)), _857898 = _857896, _857894 = _857892, _857890 = _857888], (5164 ^ _779308) ^ [_858109, _858111, _858113, _858115] : [-(c_Lazy__Sequence_Oflat(_858115, _858111) = c_Lazy__Sequence_Oflat(_858113, _858109)), _858115 = _858113, _858111 = _858109], (5174 ^ _779308) ^ [_858258, _858260, _858262, _858264, _858266, _858268] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_858268, _858264, _858260) = c_Lazy__Sequence_Olazy__sequence_OInsert(_858266, _858262, _858258)), _858268 = _858266, _858264 = _858262, _858260 = _858258], (5188 ^ _779308) ^ [_858479, _858481] : [_858481 = _858479, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_858481) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_858479))], (5194 ^ _779308) ^ [_858564, _858566, _858568, _858570, _858572, _858574, _858576, _858578, _858580, _858582] : [-(c_New__DSequence_Opos__map(_858582, _858578, _858574, _858570, _858566) = c_New__DSequence_Opos__map(_858580, _858576, _858572, _858568, _858564)), _858582 = _858580, _858578 = _858576, _858574 = _858572, _858570 = _858568, _858566 = _858564], (5216 ^ _779308) ^ [_858953, _858955, _858957, _858959, _858961, _858963, _858965, _858967] : [-(c_Lazy__Sequence_Omap(_858967, _858963, _858959, _858955) = c_Lazy__Sequence_Omap(_858965, _858961, _858957, _858953)), _858967 = _858965, _858963 = _858961, _858959 = _858957, _858955 = _858953], (5234 ^ _779308) ^ [_859254, _859256] : [_859256 = _859254, -(c_Int_Onumber__class_Onumber__of(_859256) = c_Int_Onumber__class_Onumber__of(_859254))], (5240 ^ _779308) ^ [_859339, _859341, _859343, _859345, _859347, _859349] : [-(c_SetInterval_Oord_OatLeast(_859349, _859345, _859341) = c_SetInterval_Oord_OatLeast(_859347, _859343, _859339)), _859349 = _859347, _859345 = _859343, _859341 = _859339], (5254 ^ _779308) ^ [_859560, _859562, _859564, _859566, _859568, _859570] : [-(c_SetInterval_Oord_OatMost(_859570, _859566, _859562) = c_SetInterval_Oord_OatMost(_859568, _859564, _859560)), _859570 = _859568, _859566 = _859564, _859562 = _859560], (5268 ^ _779308) ^ [_859781, _859783, _859785, _859787, _859789, _859791] : [-(c_SetInterval_Oord_OlessThan(_859791, _859787, _859783) = c_SetInterval_Oord_OlessThan(_859789, _859785, _859781)), _859791 = _859789, _859787 = _859785, _859783 = _859781], (5282 ^ _779308) ^ [_860002, _860004, _860006, _860008, _860010, _860012] : [-(c_SetInterval_Oord_OgreaterThan(_860012, _860008, _860004) = c_SetInterval_Oord_OgreaterThan(_860010, _860006, _860002)), _860012 = _860010, _860008 = _860006, _860004 = _860002], (5296 ^ _779308) ^ [_860223, _860225] : [_860225 = _860223, -(c_Groups_Oabs__class_Oabs(_860225) = c_Groups_Oabs__class_Oabs(_860223))], (5302 ^ _779308) ^ [_860308, _860310, _860312, _860314, _860316, _860318] : [-(c_Divides_Odiv__class_Omod(_860318, _860314, _860310) = c_Divides_Odiv__class_Omod(_860316, _860312, _860308)), _860318 = _860316, _860314 = _860312, _860310 = _860308], (5316 ^ _779308) ^ [_860529, _860531] : [_860531 = _860529, -(c_Groups_Ouminus__class_Ouminus(_860531) = c_Groups_Ouminus__class_Ouminus(_860529))], (5322 ^ _779308) ^ [_860614, _860616, _860618, _860620, _860622, _860624, _860626, _860628] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_860628, _860624, _860620, _860616) = c_SetInterval_Oord_OgreaterThanLessThan(_860626, _860622, _860618, _860614)), _860628 = _860626, _860624 = _860622, _860620 = _860618, _860616 = _860614], (5340 ^ _779308) ^ [_860915, _860917, _860919, _860921, _860923, _860925, _860927, _860929, _860931, _860933] : [-(c_SetInterval_Oord_OatLeastLessThan(_860933, _860929, _860925, _860921, _860917) = c_SetInterval_Oord_OatLeastLessThan(_860931, _860927, _860923, _860919, _860915)), _860933 = _860931, _860929 = _860927, _860925 = _860923, _860921 = _860919, _860917 = _860915], (5362 ^ _779308) ^ [_861304, _861306, _861308, _861310, _861312, _861314, _861316, _861318, _861320, _861322] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_861322, _861318, _861314, _861310, _861306) = c_SetInterval_Oord_OgreaterThanAtMost(_861320, _861316, _861312, _861308, _861304)), _861322 = _861320, _861318 = _861316, _861314 = _861312, _861310 = _861308, _861306 = _861304], (5384 ^ _779308) ^ [_861693, _861695, _861697, _861699, _861701, _861703, _861705, _861707] : [-(c_SetInterval_Oord_OatLeastAtMost(_861707, _861703, _861699, _861695) = c_SetInterval_Oord_OatLeastAtMost(_861705, _861701, _861697, _861693)), _861707 = _861705, _861703 = _861701, _861699 = _861697, _861695 = _861693], (5402 ^ _779308) ^ [_861994, _861996] : [_861996 = _861994, -(c_Orderings_Obot__class_Obot(_861996) = c_Orderings_Obot__class_Obot(_861994))], (5408 ^ _779308) ^ [_862079, _862081] : [_862081 = _862079, -(c_Divides_Odiv__class_Odiv(_862081) = c_Divides_Odiv__class_Odiv(_862079))], (5414 ^ _779308) ^ [_862164, _862166] : [_862166 = _862164, -(c_Groups_Oplus__class_Oplus(_862166) = c_Groups_Oplus__class_Oplus(_862164))], (5420 ^ _779308) ^ [_862249, _862251, _862253, _862255] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862255, _862251) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862253, _862249)), _862255 = _862253, _862251 = _862249], (5430 ^ _779308) ^ [_862398, _862400] : [_862400 = _862398, -(c_Power_Opower__class_Opower(_862400) = c_Power_Opower__class_Opower(_862398))], (5436 ^ _779308) ^ [_862483, _862485] : [_862485 = _862483, -(c_Groups_Otimes__class_Otimes(_862485) = c_Groups_Otimes__class_Otimes(_862483))], (5442 ^ _779308) ^ [_862568, _862570] : [_862570 = _862568, -(c_Groups_Oone__class_Oone(_862570) = c_Groups_Oone__class_Oone(_862568))], (5448 ^ _779308) ^ [_862653, _862655] : [_862655 = _862653, -(c_Equiv__Relations_Oquotient(_862655) = c_Equiv__Relations_Oquotient(_862653))], (5454 ^ _779308) ^ [_862738, _862740] : [_862740 = _862738, -(c_Orderings_Oord__class_Oless(_862740) = c_Orderings_Oord__class_Oless(_862738))], (5460 ^ _779308) ^ [_862823, _862825] : [_862825 = _862823, -(c_Groups_Ozero__class_Ozero(_862825) = c_Groups_Ozero__class_Ozero(_862823))], (5466 ^ _779308) ^ [_862908, _862910] : [_862910 = _862908, -(c_Rings_Odvd__class_Odvd(_862910) = c_Rings_Odvd__class_Odvd(_862908))], (5472 ^ _779308) ^ [_862993, _862995] : [_862995 = _862993, -(tc_List_Olist(_862995) = tc_List_Olist(_862993))], (5478 ^ _779308) ^ [_863078, _863080, _863082, _863084] : [-(tc_sum(_863084, _863080) = tc_sum(_863082, _863078)), _863084 = _863082, _863080 = _863078], (5488 ^ _779308) ^ [_863227, _863229] : [_863229 = _863227, -(tc_Option_Ooption(_863229) = tc_Option_Ooption(_863227))], (5494 ^ _779308) ^ [_863312, _863314, _863316, _863318] : [-(tc_Nitpick_Opair__box(_863318, _863314) = tc_Nitpick_Opair__box(_863316, _863312)), _863318 = _863316, _863314 = _863312], (5504 ^ _779308) ^ [_863461, _863463, _863465, _863467] : [-(tc_prod(_863467, _863463) = tc_prod(_863465, _863461)), _863467 = _863465, _863463 = _863461], (5514 ^ _779308) ^ [_863610, _863612] : [_863612 = _863610, -(tc_Lazy__Sequence_Olazy__sequence(_863612) = tc_Lazy__Sequence_Olazy__sequence(_863610))], (5520 ^ _779308) ^ [_863695, _863697] : [_863697 = _863695, -(c_COMBI(_863697) = c_COMBI(_863695))], (5526 ^ _779308) ^ [_863780, _863782, _863784, _863786] : [-(c_COMBK(_863786, _863782) = c_COMBK(_863784, _863780)), _863786 = _863784, _863782 = _863780], (5536 ^ _779308) ^ [_863929, _863931, _863933, _863935, _863937, _863939] : [-(c_COMBB(_863939, _863935, _863931) = c_COMBB(_863937, _863933, _863929)), _863939 = _863937, _863935 = _863933, _863931 = _863929], (5550 ^ _779308) ^ [_864150, _864152, _864154, _864156, _864158, _864160] : [-(c_COMBC(_864160, _864156, _864152) = c_COMBC(_864158, _864154, _864150)), _864160 = _864158, _864156 = _864154, _864152 = _864150], (5564 ^ _779308) ^ [_864371, _864373, _864375, _864377, _864379, _864381] : [-(c_COMBS(_864381, _864377, _864373) = c_COMBS(_864379, _864375, _864371)), _864381 = _864379, _864377 = _864375, _864373 = _864371], (5578 ^ _779308) ^ [_864592, _864594] : [_864594 = _864592, -(c_Finite__Set_Ofinite(_864594) = c_Finite__Set_Ofinite(_864592))], (5584 ^ _779308) ^ [_864677, _864679] : [_864679 = _864677, -(c_Groups_Ominus__class_Ominus(_864679) = c_Groups_Ominus__class_Ominus(_864677))], (5590 ^ _779308) ^ [_864762, _864764] : [_864764 = _864762, -(c_Finite__Set_Ocard(_864764) = c_Finite__Set_Ocard(_864762))], (5596 ^ _779308) ^ [_864847, _864849] : [_864849 = _864847, -(c_member(_864849) = c_member(_864847))], (5602 ^ _779308) ^ [_864932, _864934] : [_864934 = _864932, -(c_Orderings_Oord__class_Oless__eq(_864934) = c_Orderings_Oord__class_Oless__eq(_864932))], (5608 ^ _779308) ^ [_865017, _865019, _865021, _865023] : [-(tc_fun(_865023, _865019) = tc_fun(_865021, _865017)), _865023 = _865021, _865019 = _865017], (5618 ^ _779308) ^ [_865166, _865168] : [_865168 = _865166, -(c_Set_Oinsert(_865168) = c_Set_Oinsert(_865166))], (5624 ^ _779308) ^ [_865251, _865253, _865255, _865257] : [-(hAPP(_865257, _865253) = hAPP(_865255, _865251)), _865257 = _865255, _865253 = _865251], (5634 ^ _779308) ^ [_865396, _865398, _865400, _865402, _865404, _865406] : [-(c_Set_Oimage(_865406, _865402, _865398) = c_Set_Oimage(_865404, _865400, _865396)), _865406 = _865404, _865402 = _865400, _865398 = _865396], (5648 ^ _779308) ^ [_868386, _868388] : [hAPP(_868386, 5649 ^ [_868386, _868388]) = hAPP(_868388, 5649 ^ [_868386, _868388]), -(_868386 = _868388)], (5655 ^ _779308) ^ [_868512, _868514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), _868512), _868514)), -(v_P(_868514, _868512))], (5661 ^ _779308) ^ [_868599, _868601, _868603, _868605] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_868599), _868601)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_868603), hAPP(c_Set_Oimage(_868599, _868603, _868605), _868601))))], (5667 ^ _779308) ^ [_868710, _868712, _868714] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_868710), _868712)), 5670 ^ _779308 : [(5671 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_868710), _868714), _868712)), -(hAPP(c_Finite__Set_Ocard(_868710), hAPP(hAPP(c_Set_Oinsert(_868710), _868714), _868712)) = hAPP(c_Finite__Set_Ocard(_868710), _868712))], (5677 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_868710), _868714), _868712))), -(hAPP(c_Finite__Set_Ocard(_868710), hAPP(hAPP(c_Set_Oinsert(_868710), _868714), _868712)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_868710), _868712)))]]], (5683 ^ _779308) ^ [_869004, _869006, _869008] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_869004), _869006)), -(hBOOL(hAPP(hAPP(c_member(_869004), _869008), _869006))), -(hAPP(c_Finite__Set_Ocard(_869004), hAPP(hAPP(c_Set_Oinsert(_869004), _869008), _869006)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_869004), _869006)))], (5693 ^ _779308) ^ [_869162, _869164, _869166] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_869162), _869164)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_869162), hAPP(hAPP(c_Set_Oinsert(_869162), _869166), _869164))))], (5699 ^ _779308) ^ [_869273, _869275, _869277, _869279, _869281, _869283] : [_869273 = hAPP(_869275, _869277), hBOOL(hAPP(hAPP(c_member(_869279), _869277), _869281)), -(hBOOL(hAPP(hAPP(c_member(_869283), _869273), hAPP(c_Set_Oimage(_869279, _869283, _869275), _869281))))], (5709 ^ _779308) ^ [_869466, _869468, _869470, _869472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869466, tc_HOL_Obool)), _869468), _869470)), hBOOL(hAPP(hAPP(c_member(_869466), _869472), _869468)), -(hBOOL(hAPP(hAPP(c_member(_869466), _869472), _869470)))], (5719 ^ _779308) ^ [_869651, _869653, _869655, _869657] : [hBOOL(hAPP(hAPP(c_member(_869651), _869653), hAPP(hAPP(c_Set_Oinsert(_869651), _869655), _869657))), -(_869653 = _869655), -(hBOOL(hAPP(hAPP(c_member(_869651), _869653), _869657)))], (5729 ^ _779308) ^ [_869791, _869793, _869795, _869797] : [5730 ^ _779308 : [(5731 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_869791), _869793), _869795))], (5733 ^ _779308) ^ [] : [_869793 = _869797]], -(hBOOL(hAPP(hAPP(c_member(_869791), _869793), hAPP(hAPP(c_Set_Oinsert(_869791), _869797), _869795))))], (5737 ^ _779308) ^ [_869956, _869958, _869960, _869962] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_869956), _869958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_869960), hAPP(c_Set_Oimage(_869956, _869960, _869962), _869958))), hAPP(c_Finite__Set_Ocard(_869956), _869958))))], (5743 ^ _779308) ^ [_870089, _870091, _870093] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_870089), _870091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870089, tc_HOL_Obool)), _870093), _870091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_870089), _870093)), hAPP(c_Finite__Set_Ocard(_870089), _870091))))], (5753 ^ _779308) ^ [_870280, _870282, _870284] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_870280), _870282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870280, tc_HOL_Obool)), _870284), _870282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_870280), _870282)), hAPP(c_Finite__Set_Ocard(_870280), _870284))), -(_870284 = _870282)], (5767 ^ _779308) ^ [_870525, _870527, _870529, _870531] : [_870525 = _870527, 5772 ^ _779308 : [(5773 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_870529), _870531), _870525)))], (5775 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_870529), _870531), _870527)))]], 5776 ^ _779308 : [(5777 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870529), _870531), _870525))], (5779 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870529), _870531), _870527))]]], (5781 ^ _779308) ^ [_870788, _870790, _870792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870788, tc_HOL_Obool)), _870790), _870792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870788, tc_HOL_Obool)), _870792), _870790)), -(_870790 = _870792)], (5791 ^ _779308) ^ [_870961, _870963, _870965, _870967] : [_870961 = _870963, hBOOL(hAPP(hAPP(c_member(_870965), _870963), _870967)), -(hBOOL(hAPP(hAPP(c_member(_870965), _870961), _870967)))], (5801 ^ _779308) ^ [_871126, _871128, _871130, _871132] : [_871126 = _871128, 5804 ^ _779308 : [(5805 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_871130), _871126), _871132)), -(hBOOL(hAPP(hAPP(c_member(_871130), _871128), _871132)))], (5811 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_871130), _871128), _871132)), -(hBOOL(hAPP(hAPP(c_member(_871130), _871126), _871132)))]]], (5817 ^ _779308) ^ [_871387, _871389, _871391, _871393] : [_871387 = _871389, 5820 ^ _779308 : [(5821 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_871391), _871393), _871387)), -(hBOOL(hAPP(hAPP(c_member(_871391), _871393), _871389)))], (5827 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_871391), _871393), _871389)), -(hBOOL(hAPP(hAPP(c_member(_871391), _871393), _871387)))]]], (5833 ^ _779308) ^ [_871666, _871668, _871670] : [hBOOL(hAPP(hAPP(c_member(_871666), _871668), _871670)), -(hBOOL(hAPP(_871670, _871668)))], (5839 ^ _779308) ^ [_871759, _871761, _871763] : [hBOOL(hAPP(_871763, _871761)), -(hBOOL(hAPP(hAPP(c_member(_871759), _871761), _871763)))], (5845 ^ _779308) ^ [_871858, _871860] : [class_Finite__Set_Ofinite(_871858), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_871858), _871860)))], (5851 ^ _779308) ^ [_871941, _871943] : [class_Finite__Set_Ofinite(_871941), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_871941), _871943)))], (5867 ^ _779308) ^ [_872159, _872161, _872163, _872165] : [5868 ^ _779308 : [(5869 ^ _779308) ^ [] : [_872161 = _872165], (5871 ^ _779308) ^ [] : [hBOOL(hAPP(_872163, _872165))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_872159), _872161), _872163), _872165)))], (5857 ^ _779308) ^ [_872045, _872047, _872049, _872051] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_872045), _872047), _872049), _872051)), -(_872047 = _872051), -(hBOOL(hAPP(_872049, _872051)))], (5875 ^ _779308) ^ [_872304, _872306, _872308, _872310] : [-(hAPP(hAPP(c_Set_Oinsert(_872304), _872306), hAPP(hAPP(c_Set_Oinsert(_872304), _872308), _872310)) = hAPP(hAPP(c_Set_Oinsert(_872304), _872308), hAPP(hAPP(c_Set_Oinsert(_872304), _872306), _872310)))], (5877 ^ _779308) ^ [_872365, _872367, _872369] : [-(hAPP(hAPP(c_Set_Oinsert(_872365), _872367), hAPP(hAPP(c_Set_Oinsert(_872365), _872367), _872369)) = hAPP(hAPP(c_Set_Oinsert(_872365), _872367), _872369))], (5879 ^ _779308) ^ [_872416, _872418, _872420] : [_872416 = _872418, 5882 ^ _779308 : [(5883 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872420, tc_HOL_Obool)), _872416), _872418)))], (5885 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872420, tc_HOL_Obool)), _872418), _872416)))]]], (5887 ^ _779308) ^ [_872565, _872567, _872569, _872571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872565, tc_HOL_Obool)), _872567), _872569)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872565, tc_HOL_Obool)), _872569), _872571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872565, tc_HOL_Obool)), _872567), _872571)))], (5897 ^ _779308) ^ [_872762, _872764, _872766] : [_872762 = _872764, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872766, tc_HOL_Obool)), _872764), _872762)))], (5903 ^ _779308) ^ [_872861, _872863, _872865] : [_872861 = _872863, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872865, tc_HOL_Obool)), _872861), _872863)))], (5909 ^ _779308) ^ [_872978, _872980, _872982] : [_872978 = _872980, 5912 ^ _779308 : [(5913 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872982, tc_HOL_Obool)), _872978), _872980)))], (5915 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872982, tc_HOL_Obool)), _872980), _872978)))]]], (5917 ^ _779308) ^ [_873119, _873121, _873123] : [-(_873119 = _873121), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873123, tc_HOL_Obool)), _873119), _873121)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873123, tc_HOL_Obool)), _873121), _873119))], (5927 ^ _779308) ^ [_873294, _873296] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873294, tc_HOL_Obool)), _873296), _873296)))], (5929 ^ _779308) ^ [_873329, _873331, _873333, _873335, _873337, _873339] : [-(hAPP(c_Set_Oimage(_873329, _873331, _873333), hAPP(c_Set_Oimage(_873335, _873329, _873337), _873339)) = hAPP(c_Set_Oimage(_873335, _873331, hAPP(hAPP(c_COMBB(_873329, _873331, _873335), _873333), _873337)), _873339))], (5931 ^ _779308) ^ [_873393, _873395, _873397] : [hBOOL(hAPP(hAPP(c_member(_873393), _873395), _873397)), -(hAPP(hAPP(c_Set_Oinsert(_873393), _873395), _873397) = _873397)], (5937 ^ _779308) ^ [_873502, _873504, _873506, _873508] : [hBOOL(hAPP(hAPP(c_member(_873502), _873504), _873506)), -(hBOOL(hAPP(hAPP(c_member(_873502), _873504), hAPP(hAPP(c_Set_Oinsert(_873502), _873508), _873506))))], (5943 ^ _779308) ^ [_873626, _873628, _873630, _873632] : [-(hBOOL(hAPP(hAPP(c_member(_873626), _873628), _873630))), -(hBOOL(hAPP(hAPP(c_member(_873626), _873628), _873632))), 5950 ^ _779308 : [(5951 ^ _779308) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_873626), _873628), _873630) = hAPP(hAPP(c_Set_Oinsert(_873626), _873628), _873632), -(_873630 = _873632)], (5957 ^ _779308) ^ [] : [_873630 = _873632, -(hAPP(hAPP(c_Set_Oinsert(_873626), _873628), _873630) = hAPP(hAPP(c_Set_Oinsert(_873626), _873628), _873632))]]], (5973 ^ _779308) ^ [_874126, _874128, _874130, _874132] : [5974 ^ _779308 : [(5975 ^ _779308) ^ [] : [_874128 = _874130], (5977 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874126), _874128), _874132))]], -(hBOOL(hAPP(hAPP(c_member(_874126), _874128), hAPP(hAPP(c_Set_Oinsert(_874126), _874130), _874132))))], (5963 ^ _779308) ^ [_873992, _873994, _873996, _873998] : [hBOOL(hAPP(hAPP(c_member(_873992), _873994), hAPP(hAPP(c_Set_Oinsert(_873992), _873996), _873998))), -(_873994 = _873996), -(hBOOL(hAPP(hAPP(c_member(_873992), _873994), _873998)))], (5981 ^ _779308) ^ [_874291, _874293, _874295] : [-(hBOOL(hAPP(hAPP(c_member(_874291), _874293), hAPP(hAPP(c_Set_Oinsert(_874291), _874293), _874295))))], (5983 ^ _779308) ^ [_874333, _874335, _874337, _874339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874333, tc_HOL_Obool)), _874335), _874337)), hBOOL(hAPP(hAPP(c_member(_874333), _874339), _874335)), -(hBOOL(hAPP(hAPP(c_member(_874333), _874339), _874337)))], (5993 ^ _779308) ^ [_874518, _874520, _874522, _874524] : [hBOOL(hAPP(hAPP(c_member(_874518), _874520), _874522)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874518, tc_HOL_Obool)), _874522), _874524)), -(hBOOL(hAPP(hAPP(c_member(_874518), _874520), _874524)))], (6003 ^ _779308) ^ [_874703, _874705, _874707, _874709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874703, tc_HOL_Obool)), _874705), _874707)), hBOOL(hAPP(hAPP(c_member(_874703), _874709), _874705)), -(hBOOL(hAPP(hAPP(c_member(_874703), _874709), _874707)))], (6013 ^ _779308) ^ [_874888, _874890, _874892, _874894, _874896, _874898] : [hBOOL(hAPP(hAPP(c_member(_874888), _874890), _874892)), _874894 = hAPP(_874896, _874890), -(hBOOL(hAPP(hAPP(c_member(_874898), _874894), hAPP(c_Set_Oimage(_874888, _874898, _874896), _874892))))], (6023 ^ _779308) ^ [_875081, _875083, _875085, _875087, _875089] : [hBOOL(hAPP(hAPP(c_member(_875081), _875083), _875085)), -(hBOOL(hAPP(hAPP(c_member(_875087), hAPP(_875089, _875083)), hAPP(c_Set_Oimage(_875081, _875087, _875089), _875085))))], (6029 ^ _779308) ^ [_875236, _875238, _875240, _875242, _875244] : [hBOOL(hAPP(hAPP(c_member(_875236), _875238), hAPP(c_Set_Oimage(_875240, _875236, _875242), _875244))), 6033 ^ _779308 : [(6034 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_875240), 6032 ^ [_875236, _875238, _875240, _875242, _875244]), _875244)))], (6036 ^ _779308) ^ [] : [-(_875238 = hAPP(_875242, 6032 ^ [_875236, _875238, _875240, _875242, _875244]))]]], (6038 ^ _779308) ^ [_875420, _875422, _875424, _875426, _875428] : [-(hBOOL(hAPP(hAPP(c_member(_875420), _875422), hAPP(c_Set_Oimage(_875424, _875420, _875426), _875428)))), 6039 ^ _779308 : [(6040 ^ _779308) ^ [_875490] : [hBOOL(hAPP(hAPP(c_member(_875424), _875490), _875428)), _875422 = hAPP(_875426, _875490)]]], (6048 ^ _779308) ^ [_875656, _875658, _875660] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_875656), hAPP(hAPP(c_Set_Oinsert(_875656), _875658), _875660))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_875656), _875660)))], (6054 ^ _779308) ^ [_875763, _875765, _875767] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_875763), _875767)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_875763), hAPP(hAPP(c_Set_Oinsert(_875763), _875765), _875767))))], (6060 ^ _779308) ^ [_875876, _875878, _875880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875876, tc_HOL_Obool)), _875878), _875880)), hBOOL(hAPP(c_Finite__Set_Ofinite(_875876), _875880)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_875876), _875878)))], (6070 ^ _779308) ^ [_876045, _876047, _876049] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_876045), _876047)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876045, tc_HOL_Obool)), _876049), _876047)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_876045), _876049)))], (6080 ^ _779308) ^ [_876214, _876216, _876218, _876220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876214, tc_HOL_Obool)), _876216), _876218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876214, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_876214), _876220), _876216)), hAPP(hAPP(c_Set_Oinsert(_876214), _876220), _876218))))], (6086 ^ _779308) ^ [_876367, _876369, _876371, _876373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876367, tc_HOL_Obool)), _876369), _876371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876367, tc_HOL_Obool)), _876369), hAPP(hAPP(c_Set_Oinsert(_876367), _876373), _876371))))], (6092 ^ _779308) ^ [_876504, _876506, _876508] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876504, tc_HOL_Obool)), _876506), hAPP(hAPP(c_Set_Oinsert(_876504), _876508), _876506))))], (6094 ^ _779308) ^ [_876549, _876551, _876553, _876555, _876557] : [-(hAPP(c_Set_Oimage(_876549, _876551, _876553), hAPP(hAPP(c_Set_Oinsert(_876549), _876555), _876557)) = hAPP(hAPP(c_Set_Oinsert(_876551), hAPP(_876553, _876555)), hAPP(c_Set_Oimage(_876549, _876551, _876553), _876557)))], (6096 ^ _779308) ^ [_876613, _876615, _876617, _876619, _876621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876613, tc_HOL_Obool)), _876615), _876617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876619, tc_HOL_Obool)), hAPP(c_Set_Oimage(_876613, _876619, _876621), _876615)), hAPP(c_Set_Oimage(_876613, _876619, _876621), _876617))))], (6102 ^ _779308) ^ [_876788, _876790, _876792, _876794, _876796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876788, tc_HOL_Obool)), _876790), hAPP(c_Set_Oimage(_876792, _876788, _876794), _876796))), 6106 ^ _779308 : [(6107 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876792, tc_HOL_Obool)), 6105 ^ [_876788, _876790, _876792, _876794, _876796]), _876796)))], (6109 ^ _779308) ^ [] : [-(_876790 = hAPP(c_Set_Oimage(_876792, _876788, _876794), 6105 ^ [_876788, _876790, _876792, _876794, _876796]))]]], (6111 ^ _779308) ^ [_876992, _876994, _876996, _876998, _877000] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876992, tc_HOL_Obool)), _876994), hAPP(c_Set_Oimage(_876996, _876992, _876998), _877000)))), 6112 ^ _779308 : [(6113 ^ _779308) ^ [_877072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876996, tc_HOL_Obool)), _877072), _877000)), _876994 = hAPP(c_Set_Oimage(_876996, _876992, _876998), _877072)]]], (6121 ^ _779308) ^ [_877236, _877238, _877240, _877242] : [-(hBOOL(hAPP(hAPP(c_member(_877236), _877238), _877240))), 6124 ^ _779308 : [(6125 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877236, tc_HOL_Obool)), _877240), hAPP(hAPP(c_Set_Oinsert(_877236), _877238), _877242))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877236, tc_HOL_Obool)), _877240), _877242)))], (6131 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877236, tc_HOL_Obool)), _877240), _877242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877236, tc_HOL_Obool)), _877240), hAPP(hAPP(c_Set_Oinsert(_877236), _877238), _877242))))]]], (6137 ^ _779308) ^ [_877565, _877567, _877569, _877571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877565, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_877565), _877567), _877569)), _877571)), 6140 ^ _779308 : [(6141 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877565), _877567), _877571)))], (6143 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877565, tc_HOL_Obool)), _877569), _877571)))]]], (6145 ^ _779308) ^ [_877738, _877740, _877742, _877744] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877738, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_877738), _877740), _877742)), _877744))), hBOOL(hAPP(hAPP(c_member(_877738), _877740), _877744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877738, tc_HOL_Obool)), _877742), _877744))], (6155 ^ _779308) ^ [_877947, _877949, _877951, _877953, _877955] : [hBOOL(hAPP(hAPP(c_member(_877947), _877949), _877951)), -(hAPP(hAPP(c_Set_Oinsert(_877953), hAPP(_877955, _877949)), hAPP(c_Set_Oimage(_877947, _877953, _877955), _877951)) = hAPP(c_Set_Oimage(_877947, _877953, _877955), _877951))], (6161 ^ _779308) ^ [_878094, _878096, _878098, _878100, _878102] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_878094), _878096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878098, tc_HOL_Obool)), _878100), hAPP(c_Set_Oimage(_878094, _878098, _878102), _878096))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_878098), _878100)))], (6171 ^ _779308) ^ [_878285, _878287, _878289] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_878285), _878287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_878285), _878287)), hAPP(c_Finite__Set_Ocard(_878285), hAPP(hAPP(c_Set_Oinsert(_878285), _878289), _878287)))))], (6177 ^ _779308) ^ [_878418, _878420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _878418), _878420)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _878420)), _878418) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _878420), _878418)))], (6183 ^ _779308) ^ [_878541, _878543] : [class_Orderings_Opreorder(_878541), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878541), _878543), _878543)))], (6189 ^ _779308) ^ [_878648, _878650, _878652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878648, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_878648, tc_fun(_878648, tc_HOL_Obool), tc_HOL_Obool), c_member(_878648)), _878650)), hAPP(hAPP(c_COMBC(_878648, tc_fun(_878648, tc_HOL_Obool), tc_HOL_Obool), c_member(_878648)), _878652))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878648, tc_HOL_Obool)), _878650), _878652)))], (6195 ^ _779308) ^ [_878823, _878825, _878827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878823, tc_HOL_Obool)), _878825), _878827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878823, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_878823, tc_fun(_878823, tc_HOL_Obool), tc_HOL_Obool), c_member(_878823)), _878825)), hAPP(hAPP(c_COMBC(_878823, tc_fun(_878823, tc_HOL_Obool), tc_HOL_Obool), c_member(_878823)), _878827))))], (6201 ^ _779308) ^ [_879004, _879006, _879008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _879004), _879006)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _879004), _879008)), 6208 ^ _779308 : [(6209 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879006), _879004)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879008), _879004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _879006), _879008)))], (6215 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _879006), _879008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879006), _879004)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879008), _879004))))]]], (6221 ^ _779308) ^ [_879357, _879359, _879361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _879357), _879359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _879357), _879361)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879359), _879357)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879361), _879357)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879359), _879361))], (6231 ^ _779308) ^ [_879558, _879560, _879562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _879558), _879560)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _879558), _879562)), 6238 ^ _779308 : [(6239 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879560), _879558) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879562), _879558), -(_879560 = _879562)], (6245 ^ _779308) ^ [] : [_879560 = _879562, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879560), _879558) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879562), _879558))]]], (6251 ^ _779308) ^ [_879881, _879883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _879881), _879883)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879883), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879883), _879881)) = _879881)], (6257 ^ _779308) ^ [_879992, _879994, _879996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _879992), _879994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879992), _879996)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _879994), _879996))))], (6263 ^ _779308) ^ [_880115, _880117, _880119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _880115), _880117)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _880119), _880117)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _880119), _880115))))], (6269 ^ _779308) ^ [_880238, _880240] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _880238), _880240)), _880238)))], (6271 ^ _779308) ^ [_880274, _880276, _880278] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _880274)), _880276)), hAPP(c_Nat_OSuc, _880278)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _880274), _880276)), _880278))], (6273 ^ _779308) ^ [_880331, _880333, _880335] : [class_Orderings_Olinorder(_880331), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880331), _880333), _880335))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880331), _880335), _880333)))], (6283 ^ _779308) ^ [_880449, _880451, _880453] : [class_Orderings_Oorder(_880449), 6286 ^ _779308 : [(6287 ^ _779308) ^ [] : [_880451 = _880453, 6290 ^ _779308 : [(6291 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880449), _880451), _880453)))], (6293 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880449), _880453), _880451)))]]], (6295 ^ _779308) ^ [] : [-(_880451 = _880453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880449), _880451), _880453)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880449), _880453), _880451))]]], (6305 ^ _779308) ^ [_880776, _880778, _880780] : [class_Orderings_Opreorder(_880776), _880778 = _880780, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880776), _880778), _880780)))], (6315 ^ _779308) ^ [_880921, _880923, _880925] : [class_Orderings_Oorder(_880921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880921), _880923), _880925)), 6322 ^ _779308 : [(6323 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880921), _880925), _880923)), -(_880925 = _880923)], (6329 ^ _779308) ^ [] : [_880925 = _880923, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880921), _880925), _880923)))]]], (6335 ^ _779308) ^ [_881221, _881223, _881225, _881227] : [class_Orderings_Oord(_881221), _881223 = _881225, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881221), _881225), _881227)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881221), _881223), _881227)))], (6349 ^ _779308) ^ [_881440, _881442, _881444, _881446] : [class_Orderings_Oorder(_881440), _881442 = _881444, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881440), _881446), _881444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881440), _881446), _881442)))], (6363 ^ _779308) ^ [_881659, _881661, _881663, _881665] : [class_Orderings_Oord(_881659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881659), _881661), _881663)), _881663 = _881665, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881659), _881661), _881665)))], (6377 ^ _779308) ^ [_881878, _881880, _881882, _881884] : [class_Orderings_Oorder(_881878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881878), _881880), _881882)), _881880 = _881884, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881878), _881884), _881882)))], (6391 ^ _779308) ^ [_882097, _882099, _882101] : [class_Orderings_Oorder(_882097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882097), _882099), _882101)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882097), _882101), _882099)), -(_882099 = _882101)], (6405 ^ _779308) ^ [_882310, _882312, _882314, _882316] : [class_Orderings_Opreorder(_882310), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882310), _882312), _882314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882310), _882314), _882316)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882310), _882312), _882316)))], (6419 ^ _779308) ^ [_882543, _882545, _882547] : [class_Orderings_Oorder(_882543), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882543), _882545), _882547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882543), _882547), _882545)), -(_882547 = _882545)], (6433 ^ _779308) ^ [_882756, _882758, _882760, _882762] : [class_Orderings_Oorder(_882756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882756), _882758), _882760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882756), _882762), _882758)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882756), _882762), _882760)))], (6447 ^ _779308) ^ [_882989, _882991, _882993] : [class_Orderings_Olinorder(_882989), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882989), _882991), _882993))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882989), _882993), _882991)))], (6457 ^ _779308) ^ [_883127, _883129, _883131] : [hBOOL(hAPP(hAPP(c_member(_883127), _883129), hAPP(c_fequal, _883131))), -(_883129 = _883131)], (6463 ^ _779308) ^ [_883222, _883224, _883226] : [_883224 = _883226, -(hBOOL(hAPP(hAPP(c_member(_883222), _883224), hAPP(c_fequal, _883226))))], (6469 ^ _779308) ^ [_883332] : [_883332 = hAPP(c_Nat_OSuc, _883332)], (6471 ^ _779308) ^ [_883367] : [hAPP(c_Nat_OSuc, _883367) = _883367], (6473 ^ _779308) ^ [_883408, _883410] : [hAPP(c_Nat_OSuc, _883408) = hAPP(c_Nat_OSuc, _883410), -(_883408 = _883410)], (6479 ^ _779308) ^ [_883493, _883495] : [_883493 = _883495, -(hAPP(c_Nat_OSuc, _883493) = hAPP(c_Nat_OSuc, _883495))], (6485 ^ _779308) ^ [_883584, _883586] : [hAPP(c_Nat_OSuc, _883584) = hAPP(c_Nat_OSuc, _883586), -(_883584 = _883586)], (6491 ^ _779308) ^ [_883673, _883675, _883677, _883679] : [hBOOL(hAPP(_883673, _883675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883677, tc_HOL_Obool)), _883673), _883679)), -(hBOOL(hAPP(_883679, _883675)))], (6501 ^ _779308) ^ [_883838, _883840, _883842, _883844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883838, tc_HOL_Obool)), _883840), _883842)), hBOOL(hAPP(_883840, _883844)), -(hBOOL(hAPP(_883842, _883844)))], (6511 ^ _779308) ^ [_884003] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _884003), _884003)))], (6513 ^ _779308) ^ [_884027, _884029] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _884027), _884029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _884029), _884027)))], (6519 ^ _779308) ^ [_884073, _884075] : [_884073 = _884075, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _884073), _884075)))], (6525 ^ _779308) ^ [_884160, _884162, _884164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _884160), _884162)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _884162), _884164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _884160), _884164)))], (6535 ^ _779308) ^ [_884323, _884325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _884323), _884325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _884325), _884323)), -(_884323 = _884325)], (6545 ^ _779308) ^ [_884472, _884474, _884476] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _884472), _884474)), _884476) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _884472), _884476)), _884474))], (6547 ^ _779308) ^ [_884541, _884543, _884545] : [hAPP(hAPP(c_COMBC(_884541, tc_fun(_884541, tc_HOL_Obool), tc_HOL_Obool), c_member(_884541)), _884543) = hAPP(hAPP(c_COMBC(_884541, tc_fun(_884541, tc_HOL_Obool), tc_HOL_Obool), c_member(_884541)), _884545), -(_884543 = _884545)], (6553 ^ _779308) ^ [_884676, _884678, _884680] : [_884678 = _884680, -(hAPP(hAPP(c_COMBC(_884676, tc_fun(_884676, tc_HOL_Obool), tc_HOL_Obool), c_member(_884676)), _884678) = hAPP(hAPP(c_COMBC(_884676, tc_fun(_884676, tc_HOL_Obool), tc_HOL_Obool), c_member(_884676)), _884680))], (6559 ^ _779308) ^ [_884817, _884819, _884821, _884823] : [class_Orderings_Oord(_884817), 6562 ^ _779308 : [(6563 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884819, _884817)), _884821), _884823)), 6566 ^ _779308 : [(6567 ^ _779308) ^ [_884974] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884817), hAPP(_884821, _884974)), hAPP(_884823, _884974))))]]], (6569 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884817), hAPP(_884821, 6570 ^ [_884817, _884819, _884821, _884823])), hAPP(_884823, 6570 ^ [_884817, _884819, _884821, _884823]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884819, _884817)), _884821), _884823)))]]], (6576 ^ _779308) ^ [_885163, _885165, _885167, _885169, _885171] : [class_Orderings_Oord(_885163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885165, _885163)), _885167), _885169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885163), hAPP(_885167, _885171)), hAPP(_885169, _885171))))], (6586 ^ _779308) ^ [_885348, _885350, _885352, _885354, _885356] : [class_Orderings_Oord(_885348), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885350, _885348)), _885352), _885354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885348), hAPP(_885352, _885356)), hAPP(_885354, _885356))))], (6596 ^ _779308) ^ [_885542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _885542)), _885542))], (6598 ^ _779308) ^ [_885582, _885584] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _885582), _885584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _885584)), _885582)))], (6604 ^ _779308) ^ [_885627, _885629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _885629)), _885627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _885627), _885629))], (6620 ^ _779308) ^ [_885866, _885868] : [6621 ^ _779308 : [(6622 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _885866), _885868))], (6624 ^ _779308) ^ [] : [_885866 = hAPP(c_Nat_OSuc, _885868)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _885866), hAPP(c_Nat_OSuc, _885868))))], (6610 ^ _779308) ^ [_885748, _885750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _885748), hAPP(c_Nat_OSuc, _885750))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _885748), _885750))), -(_885748 = hAPP(c_Nat_OSuc, _885750))], (6628 ^ _779308) ^ [_886030, _886032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _886030)), hAPP(c_Nat_OSuc, _886032))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _886030), _886032)))], (6634 ^ _779308) ^ [_886135, _886137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _886135), _886137)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _886135)), hAPP(c_Nat_OSuc, _886137))))], (6640 ^ _779308) ^ [_886246, _886248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _886246), _886248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _886246), hAPP(c_Nat_OSuc, _886248))))], (6646 ^ _779308) ^ [_886349, _886351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _886349), hAPP(c_Nat_OSuc, _886351))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _886349), _886351))), -(_886349 = hAPP(c_Nat_OSuc, _886351))], (6656 ^ _779308) ^ [_886473, _886475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _886473)), _886475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _886473), _886475)))], (6662 ^ _779308) ^ [_886576, _886578] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _886576)), hAPP(c_Nat_OSuc, _886578)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _886576), _886578))], (6664 ^ _779308) ^ [_886619, _886621, _886623, _886625, _886627] : [class_Groups_Oordered__ab__group__add(_886619), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_886619), _886621), _886623) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_886619), _886625), _886627), 6671 ^ _779308 : [(6672 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886619), _886621), _886623)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886619), _886625), _886627)))], (6678 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886619), _886625), _886627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886619), _886621), _886623)))]]], (6684 ^ _779308) ^ [_886974, _886976, _886978, _886980, _886982, _886984, _886986, _886988] : [c_Finite__Set_Ofolding__image__simple(_886974, _886976, _886978, _886980, _886982, _886984), hBOOL(hAPP(c_Finite__Set_Ofinite(_886976), _886986)), -(hBOOL(hAPP(hAPP(c_member(_886976), _886988), _886986))), -(hAPP(_886984, hAPP(hAPP(c_Set_Oinsert(_886976), _886988), _886986)) = hAPP(hAPP(_886978, hAPP(_886982, _886988)), hAPP(_886984, _886986)))], (6698 ^ _779308) ^ [_887233, _887235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _887233)), _887235)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _887233), _887235)))], (6704 ^ _779308) ^ [_887336, _887338] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _887336), _887338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _887336)), _887338)))], (6710 ^ _779308) ^ [_887445, _887447] : [v_wt(_887445), 6716 ^ _779308 : [(6717 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), 6715 ^ [_887445, _887447]), v_U)))], (6719 ^ _779308) ^ [] : [v_P(_887447, hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, 6715 ^ [_887445, _887447])), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))))]], -(v_P(_887447, hAPP(hAPP(c_Set_Oinsert(t_a), v_mgt(_887445)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))))], (6723 ^ _779308) ^ [_887688, _887690, _887692, _887694, _887696, _887698, _887700, _887702] : [c_Finite__Set_Ofolding__image__simple__idem(_887688, _887690, _887692, _887694, _887696, _887698), hBOOL(hAPP(c_Finite__Set_Ofinite(_887690), _887700)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887690, tc_HOL_Obool)), _887702), _887700)), -(hAPP(hAPP(_887692, hAPP(_887698, _887702)), hAPP(_887698, _887700)) = hAPP(_887698, _887700))], (6737 ^ _779308) ^ [_887971, _887973, _887975, _887977, _887979, _887981, _887983, _887985] : [c_Finite__Set_Ofolding__image__simple__idem(_887971, _887973, _887975, _887977, _887979, _887981), hBOOL(hAPP(c_Finite__Set_Ofinite(_887973), _887983)), -(hAPP(_887981, hAPP(hAPP(c_Set_Oinsert(_887973), _887985), _887983)) = hAPP(hAPP(_887975, hAPP(_887979, _887985)), hAPP(_887981, _887983)))], (6747 ^ _779308) ^ [_888186, _888188, _888190, _888192, _888194, _888196, _888198, _888200] : [c_Finite__Set_Ofolding__image__simple__idem(_888186, _888188, _888190, _888192, _888194, _888196), hBOOL(hAPP(c_Finite__Set_Ofinite(_888188), _888198)), hBOOL(hAPP(hAPP(c_member(_888188), _888200), _888198)), -(hAPP(hAPP(_888190, hAPP(_888194, _888200)), hAPP(_888196, _888198)) = hAPP(_888196, _888198))], (6761 ^ _779308) ^ [_888463, _888465] : [-(hAPP(c_Set_Oimage(_888463, _888463, c_COMBI(_888463)), _888465) = _888465)], (6763 ^ _779308) ^ [_888497, _888499, _888501, _888503, _888505] : [class_Groups_Ominus(_888497), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888499, _888497)), _888501), _888503), _888505) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_888497), hAPP(_888501, _888505)), hAPP(_888503, _888505)))], (6769 ^ _779308) ^ [_888634, _888636, _888638, _888640, _888642] : [c_Fun_Oinj__on(_888634, _888636, _888638, _888640), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888636, tc_HOL_Obool)), hAPP(c_Set_Oimage(_888634, _888636, _888638), _888640)), _888642)), hBOOL(hAPP(c_Finite__Set_Ofinite(_888636), _888642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_888634), _888640)), hAPP(c_Finite__Set_Ocard(_888636), _888642))))], (6783 ^ _779308) ^ [_888909, _888911, _888913, _888915, _888917] : [c_Finite__Set_Ofolding__one__idem(_888909, _888911, _888913), hBOOL(hAPP(c_Finite__Set_Ofinite(_888909), _888915)), hBOOL(hAPP(hAPP(c_member(_888909), _888917), _888915)), -(hAPP(hAPP(_888911, _888917), hAPP(_888913, _888915)) = hAPP(_888913, _888915))], (6797 ^ _779308) ^ [_889156] : [hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _889156), v_U)), -(v_wt(c_Option_Othe(tc_Com_Ocom, c_Com_Obody(_889156))))], (6803 ^ _779308) ^ [_889249, _889251, _889253, _889255] : [hBOOL(hAPP(hAPP(c_member(_889249), _889251), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889249, tc_HOL_Obool)), _889253), _889255))), 6806 ^ _779308 : [(6807 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889249), _889251), _889253)))], (6809 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889249), _889251), _889255))]]], (6811 ^ _779308) ^ [_889428, _889430, _889432, _889434] : [hBOOL(hAPP(hAPP(c_member(_889428), _889430), _889432)), -(hBOOL(hAPP(hAPP(c_member(_889428), _889430), _889434))), -(hBOOL(hAPP(hAPP(c_member(_889428), _889430), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889428, tc_HOL_Obool)), _889432), _889434))))], (6821 ^ _779308) ^ [_889588, _889590, _889592] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_889588), _889590)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_889588), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889588, tc_HOL_Obool)), _889590), _889592))))], (6827 ^ _779308) ^ [_889717, _889719] : [hBOOL(hAPP(hAPP(c_member(_889717), _889719), c_Orderings_Obot__class_Obot(tc_fun(_889717, tc_HOL_Obool))))], (6829 ^ _779308) ^ [_889754] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_889754), c_Orderings_Obot__class_Obot(tc_fun(_889754, tc_HOL_Obool)))))], (6831 ^ _779308) ^ [_889786, _889788] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889786, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_889786, tc_HOL_Obool))), _889788)))], (6833 ^ _779308) ^ [_889826, _889828, _889830] : [-(c_Fun_Oinj__on(_889826, _889828, _889830, c_Orderings_Obot__class_Obot(tc_fun(_889826, tc_HOL_Obool))))], (6835 ^ _779308) ^ [_889860, _889862] : [v_P(hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, _889860)), _889862), hAPP(hAPP(c_Set_Oinsert(t_a), v_mgt(c_Option_Othe(tc_Com_Ocom, c_Com_Obody(_889860)))), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), -(v_P(_889862, hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, _889860)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))))], (6841 ^ _779308) ^ [_889999, _890001, _890003] : [class_Orderings_Obot(_889999), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_890001, _889999)), _890003) = c_Orderings_Obot__class_Obot(_889999))], (6847 ^ _779308) ^ [_890096, _890098, _890100] : [class_Orderings_Obot(_890096), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_890098, _890096)), _890100) = c_Orderings_Obot__class_Obot(_890096))], (6853 ^ _779308) ^ [_890193, _890195] : [-(c_Fun_Oinj__on(_890193, _890193, c_COMBI(_890193), _890195))], (6873 ^ _779308) ^ [_890628, _890630, _890632, _890634] : [6875 ^ _779308 : [(6876 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_890628), 6874 ^ [_890628, _890630, _890632, _890634]), _890634)))], (6879 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_890628), 6877 ^ [_890628, _890630, _890632, _890634]), _890634)))], (6881 ^ _779308) ^ [] : [-(hAPP(_890632, 6874 ^ [_890628, _890630, _890632, _890634]) = hAPP(_890632, 6877 ^ [_890628, _890630, _890632, _890634]))], (6883 ^ _779308) ^ [] : [6874 ^ [_890628, _890630, _890632, _890634] = 6877 ^ [_890628, _890630, _890632, _890634]]], -(c_Fun_Oinj__on(_890628, _890630, _890632, _890634))], (6855 ^ _779308) ^ [_890243, _890245, _890247, _890249] : [c_Fun_Oinj__on(_890243, _890245, _890247, _890249), 6858 ^ _779308 : [(6859 ^ _779308) ^ [_890351] : [hBOOL(hAPP(hAPP(c_member(_890243), _890351), _890249)), 6862 ^ _779308 : [(6863 ^ _779308) ^ [_890453] : [hBOOL(hAPP(hAPP(c_member(_890243), _890453), _890249)), hAPP(_890247, _890351) = hAPP(_890247, _890453), -(_890351 = _890453)]]]]], (6887 ^ _779308) ^ [_891020, _891022, _891024, _891026, _891028] : [c_Fun_Oinj__on(_891020, _891022, _891024, _891026), -(c_Fun_Oinj__on(_891020, _891022, _891024, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891020, tc_HOL_Obool)), _891026), _891028)))], (6893 ^ _779308) ^ [_891133, _891135, _891137, _891139, _891141, _891143] : [c_Finite__Set_Ofolding__image__simple(_891133, _891135, _891137, _891139, _891141, _891143), -(hAPP(_891143, c_Orderings_Obot__class_Obot(tc_fun(_891135, tc_HOL_Obool))) = _891139)], (6899 ^ _779308) ^ [_891242, _891244] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891242, tc_HOL_Obool)), _891244), _891244) = c_Orderings_Obot__class_Obot(tc_fun(_891242, tc_HOL_Obool)))], (6901 ^ _779308) ^ [_891283, _891285] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891283, tc_HOL_Obool)), _891285), c_Orderings_Obot__class_Obot(tc_fun(_891283, tc_HOL_Obool))) = _891285)], (6903 ^ _779308) ^ [_891324, _891326] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891324, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_891324, tc_HOL_Obool))), _891326) = c_Orderings_Obot__class_Obot(tc_fun(_891324, tc_HOL_Obool)))], (6905 ^ _779308) ^ [_891370, _891372, _891374, _891376, _891378, _891380] : [c_Fun_Oinj__on(_891370, _891372, _891374, _891376), hAPP(_891374, _891378) = hAPP(_891374, _891380), hBOOL(hAPP(hAPP(c_member(_891370), _891378), _891376)), hBOOL(hAPP(hAPP(c_member(_891370), _891380), _891376)), -(_891378 = _891380)], (6923 ^ _779308) ^ [_891679, _891681, _891683, _891685, _891687, _891689] : [c_Fun_Oinj__on(_891679, _891681, _891683, _891685), hBOOL(hAPP(hAPP(c_member(_891679), _891687), _891685)), hBOOL(hAPP(hAPP(c_member(_891679), _891689), _891685)), 6934 ^ _779308 : [(6935 ^ _779308) ^ [] : [hAPP(_891683, _891687) = hAPP(_891683, _891689), -(_891687 = _891689)], (6941 ^ _779308) ^ [] : [_891687 = _891689, -(hAPP(_891683, _891687) = hAPP(_891683, _891689))]]], (6947 ^ _779308) ^ [_892080, _892082, _892084, _892086, _892088, _892090] : [c_Fun_Oinj__on(_892080, _892082, _892084, _892086), -(_892088 = _892090), hBOOL(hAPP(hAPP(c_member(_892080), _892088), _892086)), hBOOL(hAPP(hAPP(c_member(_892080), _892090), _892086)), hAPP(_892084, _892088) = hAPP(_892084, _892090)], (6965 ^ _779308) ^ [_892393, _892395, _892397, _892399] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892393, tc_HOL_Obool)), _892395), hAPP(hAPP(c_Set_Oinsert(_892393), _892397), _892399)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892393, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892393, tc_HOL_Obool)), _892395), _892399)), hAPP(hAPP(c_Set_Oinsert(_892393), _892397), c_Orderings_Obot__class_Obot(tc_fun(_892393, tc_HOL_Obool)))))], (6967 ^ _779308) ^ [_892476, _892478, _892480, _892482] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892476, tc_HOL_Obool)), _892478), hAPP(hAPP(c_Set_Oinsert(_892476), _892480), _892482)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892476, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892476, tc_HOL_Obool)), _892478), hAPP(hAPP(c_Set_Oinsert(_892476), _892480), c_Orderings_Obot__class_Obot(tc_fun(_892476, tc_HOL_Obool))))), _892482))], (6969 ^ _779308) ^ [_892559, _892561, _892563] : [-(hAPP(hAPP(c_Set_Oinsert(_892559), _892561), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892559, tc_HOL_Obool)), _892563), hAPP(hAPP(c_Set_Oinsert(_892559), _892561), c_Orderings_Obot__class_Obot(tc_fun(_892559, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_892559), _892561), _892563))], (6971 ^ _779308) ^ [_892626, _892628, _892630, _892632, _892634] : [c_Fun_Oinj__on(_892626, _892628, _892630, _892632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892626, tc_HOL_Obool)), _892634), _892632)), -(c_Fun_Oinj__on(_892626, _892628, _892630, _892634))], (6981 ^ _779308) ^ [_892795, _892797, _892799, _892801] : [c_Finite__Set_Ofolding__one__idem(_892795, _892797, _892799), -(hAPP(hAPP(_892797, _892801), _892801) = _892801)], (6987 ^ _779308) ^ [_892890, _892892, _892894, _892896, _892898, _892900] : [c_Fun_Oinj__on(_892890, _892892, _892894, _892896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892890, tc_HOL_Obool)), _892898), _892896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892890, tc_HOL_Obool)), _892900), _892896)), -(hAPP(c_Set_Oimage(_892890, _892892, _892894), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892890, tc_HOL_Obool)), _892898), _892900)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892892, tc_HOL_Obool)), hAPP(c_Set_Oimage(_892890, _892892, _892894), _892898)), hAPP(c_Set_Oimage(_892890, _892892, _892894), _892900)))], (7001 ^ _779308) ^ [_893225, _893227, _893229, _893231, _893233, _893235, _893237] : [c_Finite__Set_Ofolding__image__simple__idem(_893225, _893227, _893229, _893231, _893233, _893235), -(hAPP(hAPP(_893229, _893237), _893237) = _893237)], (7007 ^ _779308) ^ [_893356, _893358, _893360, _893362, _893364] : [c_Fun_Oinj__on(_893356, _893358, _893360, hAPP(hAPP(c_Set_Oinsert(_893356), _893362), _893364)), 7010 ^ _779308 : [(7011 ^ _779308) ^ [] : [-(c_Fun_Oinj__on(_893356, _893358, _893360, _893364))], (7013 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_893358), hAPP(_893360, _893362)), hAPP(c_Set_Oimage(_893356, _893358, _893360), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893356, tc_HOL_Obool)), _893364), hAPP(hAPP(c_Set_Oinsert(_893356), _893362), c_Orderings_Obot__class_Obot(tc_fun(_893356, tc_HOL_Obool)))))))]]], (7015 ^ _779308) ^ [_893575, _893577, _893579, _893581, _893583] : [-(c_Fun_Oinj__on(_893575, _893577, _893579, hAPP(hAPP(c_Set_Oinsert(_893575), _893581), _893583))), c_Fun_Oinj__on(_893575, _893577, _893579, _893583), -(hBOOL(hAPP(hAPP(c_member(_893577), hAPP(_893579, _893581)), hAPP(c_Set_Oimage(_893575, _893577, _893579), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893575, tc_HOL_Obool)), _893583), hAPP(hAPP(c_Set_Oinsert(_893575), _893581), c_Orderings_Obot__class_Obot(tc_fun(_893575, tc_HOL_Obool))))))))], (7025 ^ _779308) ^ [_893827, _893829, _893831, _893833, _893835, _893837, _893839, _893841] : [c_Finite__Set_Ofolding__image__simple(_893827, _893829, _893831, _893833, _893835, _893837), hBOOL(hAPP(c_Finite__Set_Ofinite(_893829), _893839)), -(hAPP(_893837, hAPP(hAPP(c_Set_Oinsert(_893829), _893841), _893839)) = hAPP(hAPP(_893831, hAPP(_893835, _893841)), hAPP(_893837, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893829, tc_HOL_Obool)), _893839), hAPP(hAPP(c_Set_Oinsert(_893829), _893841), c_Orderings_Obot__class_Obot(tc_fun(_893829, tc_HOL_Obool)))))))], (7035 ^ _779308) ^ [_894090, _894092, _894094] : [hBOOL(hAPP(hAPP(c_member(_894090), _894092), _894094)), -(hAPP(hAPP(c_Set_Oinsert(_894090), _894092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894090, tc_HOL_Obool)), _894094), hAPP(hAPP(c_Set_Oinsert(_894090), _894092), c_Orderings_Obot__class_Obot(tc_fun(_894090, tc_HOL_Obool))))) = _894094)], (7041 ^ _779308) ^ [_894243, _894245, _894247] : [-(hBOOL(hAPP(hAPP(c_member(_894243), _894245), _894247))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894243, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_894243), _894245), _894247)), hAPP(hAPP(c_Set_Oinsert(_894243), _894245), c_Orderings_Obot__class_Obot(tc_fun(_894243, tc_HOL_Obool)))) = _894247)], (7047 ^ _779308) ^ [_894320] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _894320))], (7049 ^ _779308) ^ [_894345, _894347, _894349, _894351, _894353, _894355, _894357, _894359] : [c_Finite__Set_Ofolding__image__simple(_894345, _894347, _894349, _894351, _894353, _894355), hBOOL(hAPP(c_Finite__Set_Ofinite(_894347), _894357)), hBOOL(hAPP(hAPP(c_member(_894347), _894359), _894357)), -(hAPP(_894355, _894357) = hAPP(hAPP(_894349, hAPP(_894353, _894359)), hAPP(_894355, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894347, tc_HOL_Obool)), _894357), hAPP(hAPP(c_Set_Oinsert(_894347), _894359), c_Orderings_Obot__class_Obot(tc_fun(_894347, tc_HOL_Obool)))))))], (7063 ^ _779308) ^ [_894670, _894672, _894674, _894676] : [hBOOL(hAPP(hAPP(c_member(_894670), _894672), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894670, tc_HOL_Obool)), _894674), _894676))), hBOOL(hAPP(hAPP(c_member(_894670), _894672), _894676))], (7069 ^ _779308) ^ [_894802, _894804, _894806, _894808] : [hBOOL(hAPP(hAPP(c_member(_894802), _894804), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894802, tc_HOL_Obool)), _894806), _894808))), -(hBOOL(hAPP(hAPP(c_member(_894802), _894804), _894806)))], (7075 ^ _779308) ^ [_894954, _894956, _894958, _894960] : [hBOOL(hAPP(hAPP(c_member(_894954), _894956), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894954, tc_HOL_Obool)), _894958), _894960))), 7078 ^ _779308 : [(7079 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894954), _894956), _894958)))], (7081 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_894954), _894956), _894960))]]], (7083 ^ _779308) ^ [_895129, _895131, _895133, _895135] : [-(hBOOL(hAPP(hAPP(c_member(_895129), _895131), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895129, tc_HOL_Obool)), _895133), _895135)))), hBOOL(hAPP(hAPP(c_member(_895129), _895131), _895133)), -(hBOOL(hAPP(hAPP(c_member(_895129), _895131), _895135)))], (7093 ^ _779308) ^ [_895335, _895337, _895339] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895335), _895337)), 7096 ^ _779308 : [(7097 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895335), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895335, tc_HOL_Obool)), _895339), _895337))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_895335), _895339)))], (7103 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895335), _895339)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_895335), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895335, tc_HOL_Obool)), _895339), _895337))))]]], (7109 ^ _779308) ^ [_895613, _895615, _895617, _895619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895613, tc_HOL_Obool)), _895615), _895617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895613, tc_HOL_Obool)), _895617), _895619)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895613, tc_HOL_Obool)), _895617), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895613, tc_HOL_Obool)), _895619), _895615)) = _895615)], (7119 ^ _779308) ^ [_895834, _895836, _895838, _895840, _895842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895834, tc_HOL_Obool)), _895836), _895838)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895834, tc_HOL_Obool)), _895840), _895842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895834, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895834, tc_HOL_Obool)), _895836), _895842)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895834, tc_HOL_Obool)), _895838), _895840))))], (7129 ^ _779308) ^ [_896079, _896081, _896083] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896079, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896079, tc_HOL_Obool)), _896081), _896083)), _896081)))], (7131 ^ _779308) ^ [_896127, _896129, _896131] : [_896127 = c_Orderings_Obot__class_Obot(tc_fun(_896129, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_896129), _896131), _896127))], (7137 ^ _779308) ^ [_896243, _896245] : [hBOOL(hAPP(hAPP(c_member(_896243), _896245), c_Orderings_Obot__class_Obot(tc_fun(_896243, tc_HOL_Obool))))], (7139 ^ _779308) ^ [_896295, _896297] : [7140 ^ _779308 : [(7141 ^ _779308) ^ [_896348] : [hBOOL(hAPP(hAPP(c_member(_896295), _896348), _896297))]], _896297 = c_Orderings_Obot__class_Obot(tc_fun(_896295, tc_HOL_Obool))], (7145 ^ _779308) ^ [_896404, _896406] : [-(_896406 = c_Orderings_Obot__class_Obot(tc_fun(_896404, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_896404), 7148 ^ [_896404, _896406]), _896406)))], (7152 ^ _779308) ^ [_896470, _896472] : [-(hBOOL(hAPP(hAPP(c_member(_896470), 7153 ^ [_896470, _896472]), _896472))), -(_896472 = c_Orderings_Obot__class_Obot(tc_fun(_896470, tc_HOL_Obool)))], (7159 ^ _779308) ^ [_896521, _896523] : [_896523 = c_Orderings_Obot__class_Obot(tc_fun(_896521, tc_HOL_Obool)), 7162 ^ _779308 : [(7163 ^ _779308) ^ [_896601] : [hBOOL(hAPP(hAPP(c_member(_896521), _896601), _896523))]]], (7165 ^ _779308) ^ [_896637] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_896637), c_Orderings_Obot__class_Obot(tc_fun(_896637, tc_HOL_Obool)))))], (7167 ^ _779308) ^ [_896669, _896671, _896673] : [hAPP(hAPP(c_Set_Oinsert(_896669), _896671), c_Orderings_Obot__class_Obot(tc_fun(_896669, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_896669), _896673), c_Orderings_Obot__class_Obot(tc_fun(_896669, tc_HOL_Obool))), -(_896671 = _896673)], (7173 ^ _779308) ^ [_896824, _896826, _896828, _896830, _896832] : [hAPP(hAPP(c_Set_Oinsert(_896824), _896826), hAPP(hAPP(c_Set_Oinsert(_896824), _896828), c_Orderings_Obot__class_Obot(tc_fun(_896824, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_896824), _896830), hAPP(hAPP(c_Set_Oinsert(_896824), _896832), c_Orderings_Obot__class_Obot(tc_fun(_896824, tc_HOL_Obool)))), 7178 ^ _779308 : [(7179 ^ _779308) ^ [] : [-(_896826 = _896830)], (7181 ^ _779308) ^ [] : [-(_896828 = _896832)]], 7182 ^ _779308 : [(7183 ^ _779308) ^ [] : [-(_896826 = _896832)], (7185 ^ _779308) ^ [] : [-(_896828 = _896830)]]], (7187 ^ _779308) ^ [_897086, _897088, _897090, _897092, _897094] : [-(hAPP(hAPP(c_Set_Oinsert(_897086), _897088), hAPP(hAPP(c_Set_Oinsert(_897086), _897090), c_Orderings_Obot__class_Obot(tc_fun(_897086, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_897086), _897092), hAPP(hAPP(c_Set_Oinsert(_897086), _897094), c_Orderings_Obot__class_Obot(tc_fun(_897086, tc_HOL_Obool))))), 7188 ^ _779308 : [(7189 ^ _779308) ^ [] : [_897088 = _897092, _897090 = _897094], (7195 ^ _779308) ^ [] : [_897088 = _897094, _897090 = _897092]]], (7203 ^ _779308) ^ [_897417, _897419, _897421] : [hAPP(hAPP(c_Set_Oinsert(_897417), _897419), _897421) = c_Orderings_Obot__class_Obot(tc_fun(_897417, tc_HOL_Obool))], (7205 ^ _779308) ^ [_897472, _897474, _897476] : [c_Orderings_Obot__class_Obot(tc_fun(_897472, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_897472), _897474), _897476)], (7207 ^ _779308) ^ [_897527, _897529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897527, tc_HOL_Obool)), _897529), c_Orderings_Obot__class_Obot(tc_fun(_897527, tc_HOL_Obool)))), -(_897529 = c_Orderings_Obot__class_Obot(tc_fun(_897527, tc_HOL_Obool)))], (7213 ^ _779308) ^ [_897640, _897642] : [_897642 = c_Orderings_Obot__class_Obot(tc_fun(_897640, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897640, tc_HOL_Obool)), _897642), c_Orderings_Obot__class_Obot(tc_fun(_897640, tc_HOL_Obool)))))], (7219 ^ _779308) ^ [_897780, _897782, _897784, _897786] : [hAPP(c_Set_Oimage(_897780, _897782, _897784), _897786) = c_Orderings_Obot__class_Obot(tc_fun(_897782, tc_HOL_Obool)), -(_897786 = c_Orderings_Obot__class_Obot(tc_fun(_897780, tc_HOL_Obool)))], (7225 ^ _779308) ^ [_897891, _897893, _897895, _897897] : [_897897 = c_Orderings_Obot__class_Obot(tc_fun(_897891, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_897891, _897893, _897895), _897897) = c_Orderings_Obot__class_Obot(tc_fun(_897893, tc_HOL_Obool)))], (7231 ^ _779308) ^ [_898008, _898010, _898012] : [-(hAPP(c_Set_Oimage(_898008, _898010, _898012), c_Orderings_Obot__class_Obot(tc_fun(_898008, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_898010, tc_HOL_Obool)))], (7233 ^ _779308) ^ [_898073, _898075, _898077, _898079] : [c_Orderings_Obot__class_Obot(tc_fun(_898073, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_898075, _898073, _898077), _898079), -(_898079 = c_Orderings_Obot__class_Obot(tc_fun(_898075, tc_HOL_Obool)))], (7239 ^ _779308) ^ [_898184, _898186, _898188, _898190] : [_898190 = c_Orderings_Obot__class_Obot(tc_fun(_898186, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_898184, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_898186, _898184, _898188), _898190))], (7245 ^ _779308) ^ [_898301, _898303, _898305, _898307, _898309] : [c_Finite__Set_Ofolding__one__idem(_898301, _898303, _898305), hBOOL(hAPP(c_Finite__Set_Ofinite(_898301), _898307)), -(_898307 = c_Orderings_Obot__class_Obot(tc_fun(_898301, tc_HOL_Obool))), -(hAPP(_898305, hAPP(hAPP(c_Set_Oinsert(_898301), _898309), _898307)) = hAPP(hAPP(_898303, _898309), hAPP(_898305, _898307)))], (7259 ^ _779308) ^ [_898517, _898519, _898521, _898523, _898525] : [c_Finite__Set_Ofolding__one__idem(_898517, _898519, _898521), hBOOL(hAPP(c_Finite__Set_Ofinite(_898517), _898523)), -(_898525 = c_Orderings_Obot__class_Obot(tc_fun(_898517, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898517, tc_HOL_Obool)), _898525), _898523)), -(hAPP(hAPP(_898519, hAPP(_898521, _898525)), hAPP(_898521, _898523)) = hAPP(_898521, _898523))], (7277 ^ _779308) ^ [_898847, _898849, _898851, _898853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898847, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898847, tc_HOL_Obool)), _898849), hAPP(hAPP(c_Set_Oinsert(_898847), _898851), c_Orderings_Obot__class_Obot(tc_fun(_898847, tc_HOL_Obool))))), _898853)), hBOOL(hAPP(hAPP(c_member(_898847), _898851), _898849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898847, tc_HOL_Obool)), _898849), hAPP(hAPP(c_Set_Oinsert(_898847), _898851), _898853))))], (7303 ^ _779308) ^ [_899455, _899457, _899459, _899461] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899455, tc_HOL_Obool)), _899457), hAPP(hAPP(c_Set_Oinsert(_899455), _899459), _899461)))), 7306 ^ _779308 : [(7307 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899455), _899459), _899457)))], (7309 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899455, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899455, tc_HOL_Obool)), _899457), hAPP(hAPP(c_Set_Oinsert(_899455), _899459), c_Orderings_Obot__class_Obot(tc_fun(_899455, tc_HOL_Obool))))), _899461))]], 7310 ^ _779308 : [(7311 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899455), _899459), _899457))], (7313 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899455, tc_HOL_Obool)), _899457), _899461))]]], (7287 ^ _779308) ^ [_899123, _899125, _899127, _899129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899123, tc_HOL_Obool)), _899125), hAPP(hAPP(c_Set_Oinsert(_899123), _899127), _899129))), 7290 ^ _779308 : [(7291 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_899123), _899127), _899125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899123, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_899123, tc_HOL_Obool)), _899125), hAPP(hAPP(c_Set_Oinsert(_899123), _899127), c_Orderings_Obot__class_Obot(tc_fun(_899123, tc_HOL_Obool))))), _899129)))], (7297 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_899123), _899127), _899125))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_899123, tc_HOL_Obool)), _899125), _899129)))]]], (7317 ^ _779308) ^ [_899834, _899836] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_899834, tc_HOL_Obool)), _899836)), -(hBOOL(hAPP(hAPP(c_member(_899834), _899836), c_Orderings_Obot__class_Obot(tc_fun(_899834, tc_HOL_Obool)))))], (7323 ^ _779308) ^ [_899945, _899947] : [hBOOL(hAPP(hAPP(c_member(_899945), _899947), c_Orderings_Obot__class_Obot(tc_fun(_899945, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_899945, tc_HOL_Obool)), _899947)))], (7329 ^ _779308) ^ [_900062, _900064] : [class_Orderings_Obot(_900062), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900062), c_Orderings_Obot__class_Obot(_900062)), _900064)))], (7335 ^ _779308) ^ [_900155, _900157, _900159, _900161] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_900155), hAPP(c_Set_Oimage(_900157, _900155, _900159), _900161))), c_Fun_Oinj__on(_900157, _900155, _900159, _900161), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_900157), _900161)))], (7345 ^ _779308) ^ [_900326, _900328, _900330, _900332] : [c_Fun_Oinj__on(_900326, _900328, _900330, _900332), -(hAPP(c_Finite__Set_Ocard(_900328), hAPP(c_Set_Oimage(_900326, _900328, _900330), _900332)) = hAPP(c_Finite__Set_Ocard(_900326), _900332))], (7351 ^ _779308) ^ [_900445, _900447, _900449] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_900445), _900447)), -(hAPP(c_Finite__Set_Ocard(_900445), hAPP(hAPP(c_Set_Oinsert(_900445), _900449), _900447)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_900445), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900445, tc_HOL_Obool)), _900447), hAPP(hAPP(c_Set_Oinsert(_900445), _900449), c_Orderings_Obot__class_Obot(tc_fun(_900445, tc_HOL_Obool)))))))], (7357 ^ _779308) ^ [_900622, _900624, _900626] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_900622), _900624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_900622), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900622, tc_HOL_Obool)), _900624), hAPP(hAPP(c_Set_Oinsert(_900622), _900626), c_Orderings_Obot__class_Obot(tc_fun(_900622, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_900622), _900624))))], (7363 ^ _779308) ^ [_900787, _900789, _900791, _900793] : [hBOOL(hAPP(hAPP(c_member(_900787), _900789), _900791)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900787, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_900787), _900789), _900793)), _900791) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900787, tc_HOL_Obool)), _900793), _900791))], (7369 ^ _779308) ^ [_900957, _900959, _900961, _900963] : [hBOOL(hAPP(hAPP(c_member(_900957), _900959), _900961)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900957, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_900957), _900959), _900963)), _900961) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_900957, tc_HOL_Obool)), _900963), _900961))], (7375 ^ _779308) ^ [_901106, _901108, _901110, _901112] : [-(hBOOL(hAPP(hAPP(c_member(_901106), _901108), _901110))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901106, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_901106), _901108), _901112)), _901110) = hAPP(hAPP(c_Set_Oinsert(_901106), _901108), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901106, tc_HOL_Obool)), _901112), _901110)))], (7381 ^ _779308) ^ [_901214, _901216, _901218, _901220] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_901214), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901214, tc_HOL_Obool)), _901216), hAPP(hAPP(c_Set_Oinsert(_901214), _901218), _901220)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_901214), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901214, tc_HOL_Obool)), _901216), _901220))))], (7387 ^ _779308) ^ [_901367, _901369, _901371, _901373] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_901367), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901367, tc_HOL_Obool)), _901369), _901373))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_901367), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901367, tc_HOL_Obool)), _901369), hAPP(hAPP(c_Set_Oinsert(_901367), _901371), _901373)))))], (7393 ^ _779308) ^ [_901526, _901528, _901530, _901532, _901534] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901526, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901526, tc_HOL_Obool)), hAPP(c_Set_Oimage(_901528, _901526, _901530), _901532)), hAPP(c_Set_Oimage(_901528, _901526, _901530), _901534))), hAPP(c_Set_Oimage(_901528, _901526, _901530), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_901528, tc_HOL_Obool)), _901532), _901534)))))], (7395 ^ _779308) ^ [_901610, _901612, _901614] : [hBOOL(hAPP(hAPP(c_member(_901610), _901612), hAPP(hAPP(c_Set_Oinsert(_901610), _901614), c_Orderings_Obot__class_Obot(tc_fun(_901610, tc_HOL_Obool))))), -(_901612 = _901614)], (7401 ^ _779308) ^ [_901747, _901749, _901751] : [hBOOL(hAPP(hAPP(c_member(_901747), _901749), hAPP(hAPP(c_Set_Oinsert(_901747), _901751), c_Orderings_Obot__class_Obot(tc_fun(_901747, tc_HOL_Obool))))), -(_901749 = _901751)], (7407 ^ _779308) ^ [_901862, _901864, _901866] : [_901864 = _901866, -(hBOOL(hAPP(hAPP(c_member(_901862), _901864), hAPP(hAPP(c_Set_Oinsert(_901862), _901866), c_Orderings_Obot__class_Obot(tc_fun(_901862, tc_HOL_Obool))))))], (7413 ^ _779308) ^ [_901983, _901985, _901987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901983, tc_HOL_Obool)), _901985), hAPP(hAPP(c_Set_Oinsert(_901983), _901987), c_Orderings_Obot__class_Obot(tc_fun(_901983, tc_HOL_Obool))))), -(_901985 = c_Orderings_Obot__class_Obot(tc_fun(_901983, tc_HOL_Obool))), -(_901985 = hAPP(hAPP(c_Set_Oinsert(_901983), _901987), c_Orderings_Obot__class_Obot(tc_fun(_901983, tc_HOL_Obool))))], (7423 ^ _779308) ^ [_902157, _902159, _902161] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902157), _902159)), hBOOL(hAPP(hAPP(c_member(_902157), _902161), _902159)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_902157), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_902157, tc_HOL_Obool)), _902159), hAPP(hAPP(c_Set_Oinsert(_902157), _902161), c_Orderings_Obot__class_Obot(tc_fun(_902157, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_902157), _902159))], (7433 ^ _779308) ^ [_902386, _902388, _902390, _902392] : [-(c_Nat_Onat_Onat__case(_902386, _902388, _902390, hAPP(c_Nat_OSuc, _902392)) = hAPP(_902390, _902392))], (7435 ^ _779308) ^ [_902441, _902443, _902445, _902447] : [_902441 = c_Orderings_Obot__class_Obot(tc_fun(_902443, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_902443, _902445, hAPP(c_COMBK(_902445, _902443), _902447)), _902441) = c_Orderings_Obot__class_Obot(tc_fun(_902445, tc_HOL_Obool)))], (7441 ^ _779308) ^ [_902562, _902564, _902566, _902568] : [-(_902562 = c_Orderings_Obot__class_Obot(tc_fun(_902564, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_902564, _902566, hAPP(c_COMBK(_902566, _902564), _902568)), _902562) = hAPP(hAPP(c_Set_Oinsert(_902566), _902568), c_Orderings_Obot__class_Obot(tc_fun(_902566, tc_HOL_Obool))))], (7447 ^ _779308) ^ [_902635, _902637, _902639] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902635), _902637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902635, tc_HOL_Obool)), hAPP(c_Set_Oimage(_902635, _902635, _902639), _902637)), _902637)), c_Fun_Oinj__on(_902635, _902635, _902639, _902637), -(hAPP(c_Set_Oimage(_902635, _902635, _902639), _902637) = _902637)], (7461 ^ _779308) ^ [_902882, _902884, _902886] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902882), _902884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902882, tc_HOL_Obool)), _902884), hAPP(c_Set_Oimage(_902882, _902882, _902886), _902884))), -(c_Fun_Oinj__on(_902882, _902882, _902886, _902884))], (7471 ^ _779308) ^ [_903061, _903063, _903065, _903067] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_903061), _903063)), hAPP(c_Finite__Set_Ocard(_903065), hAPP(c_Set_Oimage(_903061, _903065, _903067), _903063)) = hAPP(c_Finite__Set_Ocard(_903061), _903063), -(c_Fun_Oinj__on(_903061, _903065, _903067, _903063))], (7481 ^ _779308) ^ [_903244, _903246, _903248, _903250] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_903244), _903246)), 7484 ^ _779308 : [(7485 ^ _779308) ^ [] : [c_Fun_Oinj__on(_903244, _903248, _903250, _903246), -(hAPP(c_Finite__Set_Ocard(_903248), hAPP(c_Set_Oimage(_903244, _903248, _903250), _903246)) = hAPP(c_Finite__Set_Ocard(_903244), _903246))], (7491 ^ _779308) ^ [] : [hAPP(c_Finite__Set_Ocard(_903248), hAPP(c_Set_Oimage(_903244, _903248, _903250), _903246)) = hAPP(c_Finite__Set_Ocard(_903244), _903246), -(c_Fun_Oinj__on(_903244, _903248, _903250, _903246))]]], (7497 ^ _779308) ^ [_903528, _903530, _903532, _903534, _903536] : [class_Groups_Oab__group__add(_903528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_903528), _903530), _903532) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_903528), _903534), _903536), 7504 ^ _779308 : [(7505 ^ _779308) ^ [] : [_903530 = _903532, -(_903534 = _903536)], (7511 ^ _779308) ^ [] : [_903534 = _903536, -(_903530 = _903532)]]], (7517 ^ _779308) ^ [_903841, _903843, _903845, _903847, _903849] : [class_Groups_Ominus(_903841), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_903843, _903841)), _903845), _903847), _903849) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_903841), hAPP(_903845, _903849)), hAPP(_903847, _903849)))], (7523 ^ _779308) ^ [_903978, _903980, _903982, _903984, _903986] : [hBOOL(hAPP(hAPP(c_member(_903978), _903980), _903982)), -(hAPP(c_Set_Oimage(_903978, _903984, hAPP(c_COMBK(_903984, _903978), _903986)), _903982) = hAPP(hAPP(c_Set_Oinsert(_903984), _903986), c_Orderings_Obot__class_Obot(tc_fun(_903984, tc_HOL_Obool))))], (7529 ^ _779308) ^ [_904127, _904129, _904131, _904133, _904135, _904137] : [c_Fun_Oinj__on(_904127, _904129, _904131, _904133), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904129, tc_HOL_Obool)), hAPP(c_Set_Oimage(_904127, _904129, _904131), _904133)), _904135)), c_Fun_Oinj__on(_904129, _904127, _904137, _904135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904127, tc_HOL_Obool)), hAPP(c_Set_Oimage(_904129, _904127, _904137), _904135)), _904133)), hBOOL(hAPP(c_Finite__Set_Ofinite(_904127), _904133)), hBOOL(hAPP(c_Finite__Set_Ofinite(_904129), _904135)), -(hAPP(c_Finite__Set_Ocard(_904127), _904133) = hAPP(c_Finite__Set_Ocard(_904129), _904135))], (7555 ^ _779308) ^ [_904624, _904626, _904628] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_904624), _904626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904624, tc_HOL_Obool)), _904626), _904628)), -(hAPP(c_Finite__Set_Ocard(_904624), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904624, tc_HOL_Obool)), _904628), _904626)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_904624), _904628)), hAPP(c_Finite__Set_Ocard(_904624), _904626)))], (7565 ^ _779308) ^ [_904849, _904851, _904853] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_904849), _904851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_904849), _904853)), hAPP(c_Finite__Set_Ocard(_904849), _904851))), hAPP(c_Finite__Set_Ocard(_904849), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904849, tc_HOL_Obool)), _904853), _904851)))))], (7571 ^ _779308) ^ [_905010, _905012, _905014, _905016] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_905010), _905012)), hBOOL(hAPP(c_Finite__Set_Ofinite(_905014), _905016)), 7578 ^ _779308 : [(7589 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_905010), _905012)), hAPP(c_Finite__Set_Ocard(_905014), _905016))), 7593 ^ _779308 : [(7594 ^ _779308) ^ [] : [-(c_Fun_Oinj__on(_905010, _905014, 7592 ^ [_905010, _905012, _905014, _905016], _905012))], (7596 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905014, tc_HOL_Obool)), hAPP(c_Set_Oimage(_905010, _905014, 7592 ^ [_905010, _905012, _905014, _905016]), _905012)), _905016)))]]], (7579 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_905010), _905012)), hAPP(c_Finite__Set_Ocard(_905014), _905016)))), 7580 ^ _779308 : [(7581 ^ _779308) ^ [_905221] : [c_Fun_Oinj__on(_905010, _905014, _905221, _905012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905014, tc_HOL_Obool)), hAPP(c_Set_Oimage(_905010, _905014, _905221), _905012)), _905016))]]]]], (7598 ^ _779308) ^ [_905536, _905538, _905540, _905542] : [-(_905536 = c_Orderings_Obot__class_Obot(tc_fun(_905538, tc_HOL_Obool))), 7601 ^ _779308 : [(7613 ^ _779308) ^ [] : [7614 ^ _779308 : [(7615 ^ _779308) ^ [_905869] : [hAPP(c_Set_Oimage(_905540, _905538, _905869), _905542) = _905536]], 7617 ^ _779308 : [(7618 ^ _779308) ^ [] : [-(c_Fun_Oinj__on(_905538, _905540, 7616 ^ [_905536, _905538, _905540, _905542], _905536))], (7620 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905540, tc_HOL_Obool)), hAPP(c_Set_Oimage(_905538, _905540, 7616 ^ [_905536, _905538, _905540, _905542]), _905536)), _905542)))]]], (7602 ^ _779308) ^ [] : [-(hAPP(c_Set_Oimage(_905540, _905538, 7609 ^ [_905536, _905538, _905540, _905542]), _905542) = _905536), 7603 ^ _779308 : [(7604 ^ _779308) ^ [_905677] : [c_Fun_Oinj__on(_905538, _905540, _905677, _905536), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905540, tc_HOL_Obool)), hAPP(c_Set_Oimage(_905538, _905540, _905677), _905536)), _905542))]]]]], (7622 ^ _779308) ^ [_905994, _905996] : [-(c_Set_Othe__elem(_905994, hAPP(hAPP(c_Set_Oinsert(_905994), _905996), c_Orderings_Obot__class_Obot(tc_fun(_905994, tc_HOL_Obool)))) = _905996)], (7624 ^ _779308) ^ [_906035, _906037, _906039, _906041, _906043] : [c_Finite__Set_Ofolding__one(_906035, _906037, _906039), hBOOL(hAPP(c_Finite__Set_Ofinite(_906035), _906041)), hBOOL(hAPP(hAPP(c_member(_906035), _906043), _906041)), 7635 ^ _779308 : [(7636 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906035, tc_HOL_Obool)), _906041), hAPP(hAPP(c_Set_Oinsert(_906035), _906043), c_Orderings_Obot__class_Obot(tc_fun(_906035, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_906035, tc_HOL_Obool)), -(hAPP(_906039, _906041) = _906043)], (7642 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906035, tc_HOL_Obool)), _906041), hAPP(hAPP(c_Set_Oinsert(_906035), _906043), c_Orderings_Obot__class_Obot(tc_fun(_906035, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_906035, tc_HOL_Obool))), -(hAPP(_906039, _906041) = hAPP(hAPP(_906037, _906043), hAPP(_906039, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_906035, tc_HOL_Obool)), _906041), hAPP(hAPP(c_Set_Oinsert(_906035), _906043), c_Orderings_Obot__class_Obot(tc_fun(_906035, tc_HOL_Obool)))))))]]], (7648 ^ _779308) ^ [_906557, _906559, _906561, _906563, _906565] : [c_Finite__Set_Ofolding__one(_906557, _906559, _906561), hBOOL(hAPP(c_Finite__Set_Ofinite(_906557), _906563)), -(hBOOL(hAPP(hAPP(c_member(_906557), _906565), _906563))), -(_906563 = c_Orderings_Obot__class_Obot(tc_fun(_906557, tc_HOL_Obool))), -(hAPP(_906561, hAPP(hAPP(c_Set_Oinsert(_906557), _906565), _906563)) = hAPP(hAPP(_906559, _906565), hAPP(_906561, _906563)))], (7666 ^ _779308) ^ [_906802, _906804, _906806, _906808, _906810, _906812] : [c_Fun_Oinj__on(_906802, _906804, _906806, _906808), hBOOL(hAPP(hAPP(c_member(_906804), _906810), hAPP(c_Set_Oimage(_906802, _906804, _906806), _906808))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_906802, tc_HOL_Obool)), _906808), _906812)), -(hBOOL(hAPP(hAPP(c_member(_906802), hAPP(c_Fun_Othe__inv__into(_906802, _906804, _906808, _906806), _906810)), _906812)))], (7680 ^ _779308) ^ [_907089, _907091, _907093] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_907089), _907091)), hBOOL(hAPP(hAPP(c_member(_907089), _907093), _907091)), -(hAPP(c_Finite__Set_Ocard(_907089), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907089, tc_HOL_Obool)), _907091), hAPP(hAPP(c_Set_Oinsert(_907089), _907093), c_Orderings_Obot__class_Obot(tc_fun(_907089, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_907089), _907091)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7690 ^ _779308) ^ [_907324, _907326, _907328] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_907324), _907326)), 7693 ^ _779308 : [(7694 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_907324), _907328), _907326)), -(hAPP(c_Finite__Set_Ocard(_907324), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907324, tc_HOL_Obool)), _907326), hAPP(hAPP(c_Set_Oinsert(_907324), _907328), c_Orderings_Obot__class_Obot(tc_fun(_907324, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_907324), _907326)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7700 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_907324), _907328), _907326))), -(hAPP(c_Finite__Set_Ocard(_907324), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907324, tc_HOL_Obool)), _907326), hAPP(hAPP(c_Set_Oinsert(_907324), _907328), c_Orderings_Obot__class_Obot(tc_fun(_907324, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_907324), _907326))]]], (7706 ^ _779308) ^ [_907688, _907690, _907692, _907694] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_907688), _907690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907688, tc_HOL_Obool)), _907690), _907692)), hBOOL(hAPP(_907694, c_Orderings_Obot__class_Obot(tc_fun(_907688, tc_HOL_Obool)))), 7721 ^ _779308 : [(7722 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_907688), 7720 ^ [_907688, _907690, _907692, _907694])))], (7724 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_907688), 7719 ^ [_907688, _907690, _907692, _907694]), _907692)))], (7726 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_907688), 7719 ^ [_907688, _907690, _907692, _907694]), 7720 ^ [_907688, _907690, _907692, _907694]))], (7728 ^ _779308) ^ [] : [-(hBOOL(hAPP(_907694, 7720 ^ [_907688, _907690, _907692, _907694])))], (7730 ^ _779308) ^ [] : [hBOOL(hAPP(_907694, hAPP(hAPP(c_Set_Oinsert(_907688), 7719 ^ [_907688, _907690, _907692, _907694]), 7720 ^ [_907688, _907690, _907692, _907694])))]], -(hBOOL(hAPP(_907694, _907690)))], (7734 ^ _779308) ^ [_908353, _908355, _908357, _908359, _908361] : [c_Finite__Set_Ofolding__one__idem(_908353, _908355, _908357), hAPP(_908359, hAPP(hAPP(_908355, 7739 ^ [_908353, _908355, _908357, _908359, _908361]), 7740 ^ [_908353, _908355, _908357, _908359, _908361])) = hAPP(hAPP(_908355, hAPP(_908359, 7739 ^ [_908353, _908355, _908357, _908359, _908361])), hAPP(_908359, 7740 ^ [_908353, _908355, _908357, _908359, _908361])), hBOOL(hAPP(c_Finite__Set_Ofinite(_908353), _908361)), -(_908361 = c_Orderings_Obot__class_Obot(tc_fun(_908353, tc_HOL_Obool))), -(hAPP(_908359, hAPP(_908357, _908361)) = hAPP(_908357, hAPP(c_Set_Oimage(_908353, _908353, _908359), _908361)))], (7754 ^ _779308) ^ [_908788, _908790, _908792, _908794, _908796] : [c_Finite__Set_Ofolding__one(_908788, _908790, _908792), hBOOL(hAPP(c_Finite__Set_Ofinite(_908788), _908794)), 7761 ^ _779308 : [(7762 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908788, tc_HOL_Obool)), _908794), hAPP(hAPP(c_Set_Oinsert(_908788), _908796), c_Orderings_Obot__class_Obot(tc_fun(_908788, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_908788, tc_HOL_Obool)), -(hAPP(_908792, hAPP(hAPP(c_Set_Oinsert(_908788), _908796), _908794)) = _908796)], (7768 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908788, tc_HOL_Obool)), _908794), hAPP(hAPP(c_Set_Oinsert(_908788), _908796), c_Orderings_Obot__class_Obot(tc_fun(_908788, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_908788, tc_HOL_Obool))), -(hAPP(_908792, hAPP(hAPP(c_Set_Oinsert(_908788), _908796), _908794)) = hAPP(hAPP(_908790, _908796), hAPP(_908792, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_908788, tc_HOL_Obool)), _908794), hAPP(hAPP(c_Set_Oinsert(_908788), _908796), c_Orderings_Obot__class_Obot(tc_fun(_908788, tc_HOL_Obool)))))))]]], (7774 ^ _779308) ^ [_909270, _909272] : [class_Groups_Oone(_909270), 7777 ^ _779308 : [(7778 ^ _779308) ^ [] : [c_Groups_Oone__class_Oone(_909270) = _909272, -(_909272 = c_Groups_Oone__class_Oone(_909270))], (7784 ^ _779308) ^ [] : [_909272 = c_Groups_Oone__class_Oone(_909270), -(c_Groups_Oone__class_Oone(_909270) = _909272)]]], (7790 ^ _779308) ^ [_909487, _909489, _909491] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909487, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909487, tc_HOL_Obool)), _909489), _909491)), _909491) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909487, tc_HOL_Obool)), _909489), _909491))], (7792 ^ _779308) ^ [_909547, _909549] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _909547), hAPP(c_Nat_OSuc, _909549)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _909547), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _909549))], (7794 ^ _779308) ^ [_909593] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _909593)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _909593)], (7796 ^ _779308) ^ [_909625, _909627, _909629, _909631, _909633] : [c_Fun_Oinj__on(_909625, _909627, _909629, _909631), hBOOL(hAPP(hAPP(c_member(_909625), _909633), _909631)), -(hAPP(c_Fun_Othe__inv__into(_909625, _909627, _909631, _909629), hAPP(_909629, _909633)) = _909633)], (7806 ^ _779308) ^ [_909806, _909808, _909810, _909812, _909814, _909816] : [c_Fun_Oinj__on(_909806, _909808, _909810, _909812), hAPP(_909810, _909814) = _909816, hBOOL(hAPP(hAPP(c_member(_909806), _909814), _909812)), -(hAPP(c_Fun_Othe__inv__into(_909806, _909808, _909812, _909810), _909816) = _909814)], (7831 ^ _779308) ^ [_910250] : [7833 ^ _779308 : [(7834 ^ _779308) ^ [_910326] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 7832 ^ [_910250, _910326]), _910250)))], (7836 ^ _779308) ^ [_910360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 7832 ^ [_910250, _910360]), _910360))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _910250)))], (7820 ^ _779308) ^ [_910063] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _910063)), 7824 ^ _779308 : [(7825 ^ _779308) ^ [_910143] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _910143), _910063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _910143), 7823 ^ [_910063])))]]], (7840 ^ _779308) ^ [_910429, _910431, _910433, _910435] : [c_Fun_Oinj__on(_910429, _910431, _910433, _910435), -(c_Fun_Oinj__on(_910431, _910429, c_Fun_Othe__inv__into(_910429, _910431, _910435, _910433), hAPP(c_Set_Oimage(_910429, _910431, _910433), _910435)))], (7846 ^ _779308) ^ [_910542, _910544, _910546, _910548] : [c_Fun_Oinj__on(_910542, _910544, _910546, _910548), -(hAPP(c_Set_Oimage(_910544, _910542, c_Fun_Othe__inv__into(_910542, _910544, _910548, _910546)), hAPP(c_Set_Oimage(_910542, _910544, _910546), _910548)) = _910548)], (7852 ^ _779308) ^ [_910665, _910667, _910669, _910671] : [c_Finite__Set_Ofolding__one(_910665, _910667, _910669), -(hAPP(_910669, hAPP(hAPP(c_Set_Oinsert(_910665), _910671), c_Orderings_Obot__class_Obot(tc_fun(_910665, tc_HOL_Obool)))) = _910671)], (7858 ^ _779308) ^ [_910780, _910782, _910784, _910786, _910788] : [c_Fun_Oinj__on(_910780, _910782, _910784, _910786), hBOOL(hAPP(hAPP(c_member(_910782), _910788), hAPP(c_Set_Oimage(_910780, _910782, _910784), _910786))), -(hAPP(_910784, hAPP(c_Fun_Othe__inv__into(_910780, _910782, _910786, _910784), _910788)) = _910788)], (7868 ^ _779308) ^ [_910975, _910977, _910979, _910981] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_910975), _910977)), hBOOL(hAPP(hAPP(c_member(_910975), _910979), _910977)), -(hBOOL(hAPP(hAPP(c_member(_910975), _910979), _910981))), -(hAPP(c_Finite__Set_Ocard(_910975), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910975, tc_HOL_Obool)), _910977), hAPP(hAPP(c_Set_Oinsert(_910975), _910979), _910981))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_910975), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910975, tc_HOL_Obool)), _910977), _910981))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7882 ^ _779308) ^ [_911276, _911278, _911280, _911282] : [hBOOL(hAPP(hAPP(c_member(_911276), _911278), c_SetInterval_Oord_OatMost(_911276, _911280, _911282))), -(hBOOL(hAPP(hAPP(_911280, _911278), _911282)))], (7888 ^ _779308) ^ [_911385, _911387, _911389, _911391] : [hBOOL(hAPP(hAPP(_911389, _911387), _911391)), -(hBOOL(hAPP(hAPP(c_member(_911385), _911387), c_SetInterval_Oord_OatMost(_911385, _911389, _911391))))], (7894 ^ _779308) ^ [_911521, _911523, _911525, _911527] : [hBOOL(hAPP(hAPP(c_member(_911521), _911523), c_SetInterval_Oord_OatLeast(_911521, _911525, _911527))), -(hBOOL(hAPP(hAPP(_911525, _911527), _911523)))], (7900 ^ _779308) ^ [_911630, _911632, _911634, _911636] : [hBOOL(hAPP(hAPP(_911634, _911636), _911632)), -(hBOOL(hAPP(hAPP(c_member(_911630), _911632), c_SetInterval_Oord_OatLeast(_911630, _911634, _911636))))], (7906 ^ _779308) ^ [_911766, _911768, _911770, _911772] : [hBOOL(hAPP(hAPP(c_member(_911766), _911768), c_SetInterval_Oord_OlessThan(_911766, _911770, _911772))), -(hBOOL(hAPP(hAPP(_911770, _911768), _911772)))], (7912 ^ _779308) ^ [_911875, _911877, _911879, _911881] : [hBOOL(hAPP(hAPP(_911879, _911877), _911881)), -(hBOOL(hAPP(hAPP(c_member(_911875), _911877), c_SetInterval_Oord_OlessThan(_911875, _911879, _911881))))], (7918 ^ _779308) ^ [_912011, _912013, _912015, _912017] : [hBOOL(hAPP(hAPP(c_member(_912011), _912013), c_SetInterval_Oord_OgreaterThan(_912011, _912015, _912017))), -(hBOOL(hAPP(hAPP(_912015, _912017), _912013)))], (7924 ^ _779308) ^ [_912120, _912122, _912124, _912126] : [hBOOL(hAPP(hAPP(_912124, _912126), _912122)), -(hBOOL(hAPP(hAPP(c_member(_912120), _912122), c_SetInterval_Oord_OgreaterThan(_912120, _912124, _912126))))], (7930 ^ _779308) ^ [_912259, _912261, _912263, _912265, _912267] : [hBOOL(hAPP(hAPP(c_member(_912259), _912261), c_SetInterval_Oord_OatLeastAtMost(_912259, _912263, _912265, _912267))), 7933 ^ _779308 : [(7934 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_912263, _912265), _912261)))], (7936 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_912263, _912261), _912267)))]]], (7938 ^ _779308) ^ [_912408, _912410, _912412, _912414, _912416] : [-(hBOOL(hAPP(hAPP(c_member(_912408), _912410), c_SetInterval_Oord_OatLeastAtMost(_912408, _912412, _912414, _912416)))), hBOOL(hAPP(hAPP(_912412, _912414), _912410)), hBOOL(hAPP(hAPP(_912412, _912410), _912416))], (7948 ^ _779308) ^ [_912619, _912621, _912623, _912625, _912627] : [hBOOL(hAPP(hAPP(c_member(_912619), _912621), c_SetInterval_Oord_OgreaterThanLessThan(_912619, _912623, _912625, _912627))), 7951 ^ _779308 : [(7952 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_912623, _912625), _912621)))], (7954 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_912623, _912621), _912627)))]]], (7956 ^ _779308) ^ [_912768, _912770, _912772, _912774, _912776] : [-(hBOOL(hAPP(hAPP(c_member(_912768), _912770), c_SetInterval_Oord_OgreaterThanLessThan(_912768, _912772, _912774, _912776)))), hBOOL(hAPP(hAPP(_912772, _912774), _912770)), hBOOL(hAPP(hAPP(_912772, _912770), _912776))], (7966 ^ _779308) ^ [_912982, _912984, _912986, _912988, _912990, _912992] : [hBOOL(hAPP(hAPP(c_member(_912982), _912984), c_SetInterval_Oord_OatLeastLessThan(_912982, _912986, _912988, _912990, _912992))), 7969 ^ _779308 : [(7970 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_912986, _912990), _912984)))], (7972 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_912988, _912984), _912992)))]]], (7974 ^ _779308) ^ [_913135, _913137, _913139, _913141, _913143, _913145] : [-(hBOOL(hAPP(hAPP(c_member(_913135), _913137), c_SetInterval_Oord_OatLeastLessThan(_913135, _913139, _913141, _913143, _913145)))), hBOOL(hAPP(hAPP(_913139, _913143), _913137)), hBOOL(hAPP(hAPP(_913141, _913137), _913145))], (7984 ^ _779308) ^ [_913355, _913357, _913359, _913361, _913363, _913365] : [hBOOL(hAPP(hAPP(c_member(_913355), _913357), c_SetInterval_Oord_OgreaterThanAtMost(_913355, _913359, _913361, _913363, _913365))), 7987 ^ _779308 : [(7988 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_913361, _913363), _913357)))], (7990 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_913359, _913357), _913365)))]]], (7992 ^ _779308) ^ [_913508, _913510, _913512, _913514, _913516, _913518] : [-(hBOOL(hAPP(hAPP(c_member(_913508), _913510), c_SetInterval_Oord_OgreaterThanAtMost(_913508, _913512, _913514, _913516, _913518)))), hBOOL(hAPP(hAPP(_913514, _913516), _913510)), hBOOL(hAPP(hAPP(_913512, _913510), _913518))], (8002 ^ _779308) ^ [_913701, _913703, _913705] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_913701), _913703)), hBOOL(hAPP(hAPP(c_member(_913701), _913705), _913703)), -(hAPP(c_Finite__Set_Ocard(_913701), _913703) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_913701), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913701, tc_HOL_Obool)), _913703), hAPP(hAPP(c_Set_Oinsert(_913701), _913705), c_Orderings_Obot__class_Obot(tc_fun(_913701, tc_HOL_Obool)))))))], (8012 ^ _779308) ^ [_913930, _913932, _913934, _913936] : [c_Finite__Set_Ofolding__one(_913930, _913932, _913934), hBOOL(hAPP(c_Finite__Set_Ofinite(_913930), _913936)), -(_913936 = c_Orderings_Obot__class_Obot(tc_fun(_913930, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_913930), hAPP(hAPP(_913932, 8025 ^ [_913930, _913932, _913934, _913936]), 8026 ^ [_913930, _913932, _913934, _913936])), hAPP(hAPP(c_Set_Oinsert(_913930), 8025 ^ [_913930, _913932, _913934, _913936]), hAPP(hAPP(c_Set_Oinsert(_913930), 8026 ^ [_913930, _913932, _913934, _913936]), c_Orderings_Obot__class_Obot(tc_fun(_913930, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_913930), hAPP(_913934, _913936)), _913936)))], (8032 ^ _779308) ^ [_914437, _914439, _914441, _914443, _914445, _914447] : [hBOOL(hAPP(hAPP(c_member(_914437), _914439), _914441)), -(hAPP(c_Set_Oimage(_914437, _914443, c_Fun_Ofun__upd(_914437, _914443, _914445, _914439, _914447)), _914441) = hAPP(hAPP(c_Set_Oinsert(_914443), _914447), hAPP(c_Set_Oimage(_914437, _914443, _914445), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914437, tc_HOL_Obool)), _914441), hAPP(hAPP(c_Set_Oinsert(_914437), _914439), c_Orderings_Obot__class_Obot(tc_fun(_914437, tc_HOL_Obool)))))))], (8038 ^ _779308) ^ [_914634, _914636, _914638, _914640, _914642, _914644] : [-(hBOOL(hAPP(hAPP(c_member(_914634), _914636), _914638))), -(hAPP(c_Set_Oimage(_914634, _914640, c_Fun_Ofun__upd(_914634, _914640, _914642, _914636, _914644)), _914638) = hAPP(c_Set_Oimage(_914634, _914640, _914642), _914638))], (8044 ^ _779308) ^ [_914707, _914709, _914711, _914713] : [-(c_Fun_Ofun__upd(_914707, _914709, _914711, _914713, hAPP(_914711, _914713)) = _914711)], (8046 ^ _779308) ^ [_914763, _914765, _914767] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914763), _914765) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914767), _914765), -(_914763 = _914767)], (8052 ^ _779308) ^ [_914862, _914864, _914866] : [_914862 = _914866, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914862), _914864) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914866), _914864))], (8058 ^ _779308) ^ [_914985, _914987, _914989] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914985), _914987) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _914985), _914989), -(_914987 = _914989)], (8064 ^ _779308) ^ [_915084, _915086, _915088] : [_915086 = _915088, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915084), _915086) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915084), _915088))], (8070 ^ _779308) ^ [_915189, _915191, _915193] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915189), _915191)), _915193) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915189), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915191), _915193)))], (8072 ^ _779308) ^ [_915240, _915242, _915244] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915240), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915242), _915244)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915240), _915244)))], (8074 ^ _779308) ^ [_915291, _915293] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915291), _915293) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _915293), _915291))], (8076 ^ _779308) ^ [_915328, _915330, _915332, _915334] : [class_Groups_Ocancel__semigroup__add(_915328), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_915328), _915330), _915332) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_915328), _915334), _915332), -(_915330 = _915334)], (8086 ^ _779308) ^ [_915495, _915497, _915499, _915501] : [class_Groups_Ocancel__ab__semigroup__add(_915495), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_915495), _915497), _915499) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_915495), _915497), _915501), -(_915499 = _915501)], (8096 ^ _779308) ^ [_915662, _915664, _915666, _915668] : [class_Groups_Ocancel__semigroup__add(_915662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_915662), _915664), _915666) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_915662), _915664), _915668), -(_915666 = _915668)], (8106 ^ _779308) ^ [_915829, _915831, _915833, _915835, _915837] : [hAPP(_915829, _915831) = _915833, -(c_Fun_Ofun__upd(_915835, _915837, _915829, _915831, _915833) = _915829)], (8112 ^ _779308) ^ [_915926, _915928, _915930, _915932, _915934, _915936] : [-(_915926 = _915928), -(hAPP(c_Fun_Ofun__upd(_915930, _915932, _915934, _915928, _915936), _915926) = hAPP(_915934, _915926))], (8118 ^ _779308) ^ [_915978, _915980, _915982, _915984, _915986, _915988, _915990] : [-(_915978 = _915980), -(c_Fun_Ofun__upd(_915982, _915984, c_Fun_Ofun__upd(_915982, _915984, _915986, _915978, _915988), _915980, _915990) = c_Fun_Ofun__upd(_915982, _915984, c_Fun_Ofun__upd(_915982, _915984, _915986, _915980, _915990), _915978, _915988))], (8124 ^ _779308) ^ [_916069, _916071, _916073, _916075, _916077, _916079] : [_916069 = _916071, -(hAPP(c_Fun_Ofun__upd(_916073, _916075, _916077, _916071, _916079), _916069) = _916079)], (8130 ^ _779308) ^ [_916166, _916168, _916170, _916172, _916174, _916176] : [-(_916166 = _916168), -(hAPP(c_Fun_Ofun__upd(_916170, _916172, _916174, _916168, _916176), _916166) = hAPP(_916174, _916166))], (8136 ^ _779308) ^ [_916224, _916226, _916228, _916230, _916232] : [-(hAPP(c_Fun_Ofun__upd(_916224, _916226, _916228, _916230, _916232), _916230) = _916232)], (8138 ^ _779308) ^ [_916264, _916266, _916268, _916270, _916272, _916274] : [-(c_Fun_Ofun__upd(_916264, _916266, c_Fun_Ofun__upd(_916264, _916266, _916268, _916270, _916272), _916270, _916274) = c_Fun_Ofun__upd(_916264, _916266, _916268, _916270, _916274))], (8140 ^ _779308) ^ [_916339, _916341, _916343, _916345, _916347] : [c_Fun_Ofun__upd(_916339, _916341, _916343, _916345, _916347) = _916343, -(hAPP(_916343, _916345) = _916347)], (8146 ^ _779308) ^ [_916436, _916438, _916440, _916442, _916444] : [hAPP(_916440, _916442) = _916444, -(c_Fun_Ofun__upd(_916436, _916438, _916440, _916442, _916444) = _916440)], (8152 ^ _779308) ^ [_916539, _916541, _916543, _916545] : [class_Groups_Ocancel__semigroup__add(_916539), 8155 ^ _779308 : [(8156 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916539), _916541), _916543) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916539), _916545), _916543), -(_916541 = _916545)], (8162 ^ _779308) ^ [] : [_916541 = _916545, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916539), _916541), _916543) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916539), _916545), _916543))]]], (8168 ^ _779308) ^ [_916804, _916806, _916808, _916810] : [class_Groups_Ocancel__semigroup__add(_916804), 8171 ^ _779308 : [(8172 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916804), _916806), _916808) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916804), _916806), _916810), -(_916808 = _916810)], (8178 ^ _779308) ^ [] : [_916808 = _916810, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916804), _916806), _916808) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_916804), _916806), _916810))]]], (8184 ^ _779308) ^ [_917069, _917071, _917073, _917075] : [class_Groups_Oab__semigroup__add(_917069), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917069), _917071), _917073)), _917075) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917069), _917071), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917069), _917073), _917075)))], (8190 ^ _779308) ^ [_917233, _917235, _917237, _917239, _917241, _917243] : [_917233 = _917235, -(hAPP(c_Fun_Ofun__upd(_917237, _917239, _917241, _917235, _917243), _917233) = _917243)], (8196 ^ _779308) ^ [_917330, _917332, _917334, _917336, _917338, _917340] : [-(_917330 = _917332), -(hAPP(c_Fun_Ofun__upd(_917334, _917336, _917338, _917332, _917340), _917330) = hAPP(_917338, _917330))], (8202 ^ _779308) ^ [_917388, _917390, _917392, _917394] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_917388), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917388), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917388), _917390), _917392)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917388), _917390), _917394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917388), _917392), _917394)))], (8212 ^ _779308) ^ [_917583, _917585, _917587, _917589] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_917583), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917583), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917583), _917585), _917587)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917583), _917589), _917587))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917583), _917585), _917589)))], (8222 ^ _779308) ^ [_917778, _917780, _917782, _917784, _917786] : [class_Groups_Oordered__ab__semigroup__add(_917778), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917778), _917780), _917782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917778), _917784), _917786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917778), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917778), _917780), _917784)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_917778), _917782), _917786))))], (8236 ^ _779308) ^ [_918049, _918051, _918053, _918055] : [class_Groups_Oordered__ab__semigroup__add(_918049), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918049), _918051), _918053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918049), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918049), _918055), _918051)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918049), _918055), _918053))))], (8246 ^ _779308) ^ [_918244, _918246, _918248, _918250] : [class_Groups_Oordered__ab__semigroup__add(_918244), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918244), _918246), _918248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918244), _918246), _918250)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918244), _918248), _918250))))], (8256 ^ _779308) ^ [_918439, _918441, _918443, _918445] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_918439), 8259 ^ _779308 : [(8260 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918439), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918439), _918441), _918443)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918439), _918441), _918445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918439), _918443), _918445)))], (8266 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918439), _918443), _918445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918439), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918439), _918441), _918443)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918439), _918441), _918445))))]]], (8272 ^ _779308) ^ [_918746, _918748, _918750, _918752] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_918746), 8275 ^ _779308 : [(8276 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918746), _918748), _918750)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918746), _918752), _918750))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918746), _918748), _918752)))], (8282 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918746), _918748), _918752)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918746), _918748), _918750)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918746), _918752), _918750))))]]], (8288 ^ _779308) ^ [_919053, _919055, _919057] : [class_Groups_Ogroup__add(_919053), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_919053), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919053), _919055), _919057)), _919057) = _919055)], (8294 ^ _779308) ^ [_919162, _919164, _919166] : [class_Groups_Ogroup__add(_919162), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919162), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_919162), _919164), _919166)), _919166) = _919164)], (8300 ^ _779308) ^ [_919271, _919273] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _919271)), _919273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919271), hAPP(c_Nat_OSuc, _919273)))], (8302 ^ _779308) ^ [_919314, _919316] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _919314)), _919316) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919314), _919316)))], (8304 ^ _779308) ^ [_919357, _919359] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919357), hAPP(c_Nat_OSuc, _919359)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919357), _919359)))], (8306 ^ _779308) ^ [_919400, _919402, _919404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919400), _919402)), _919404)), 8309 ^ _779308 : [(8310 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919400), _919404)))], (8312 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919402), _919404)))]]], (8314 ^ _779308) ^ [_919551, _919553, _919555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919551), _919553)), _919555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919551), _919555)))], (8320 ^ _779308) ^ [_919662, _919664, _919666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919662), _919664)), _919666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919664), _919666)))], (8326 ^ _779308) ^ [_919773, _919775, _919777, _919779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919773), _919775)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919777), _919779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919773), _919777)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919775), _919779))))], (8336 ^ _779308) ^ [_919964, _919966, _919968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _919964), _919966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919964), _919968)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _919966), _919968))))], (8342 ^ _779308) ^ [_920087, _920089, _920091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _920087), _920089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _920087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920091), _920089))))], (8348 ^ _779308) ^ [_920198, _920200, _920202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _920198), _920200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _920198), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920200), _920202))))], (8354 ^ _779308) ^ [_920327, _920329, _920331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920327), _920329)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920327), _920331))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _920329), _920331)))], (8360 ^ _779308) ^ [_920446, _920448, _920450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _920448), _920450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920446), _920448)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920446), _920450))))], (8366 ^ _779308) ^ [_920586, _920588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _920586), _920588)), -(_920588 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920586), 8369 ^ [_920586, _920588]))], (8373 ^ _779308) ^ [_920693, _920695] : [8374 ^ _779308 : [(8375 ^ _779308) ^ [_920743] : [_920695 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920693), _920743)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _920693), _920695)))], (8379 ^ _779308) ^ [_920807, _920809] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _920807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920807), _920809))))], (8381 ^ _779308) ^ [_920843, _920845] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _920843), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920845), _920843))))], (8383 ^ _779308) ^ [_920879, _920881, _920883] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920879), _920881)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920883), _920881)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _920879), _920883))], (8385 ^ _779308) ^ [_920930, _920932, _920934] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920930), _920932)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920930), _920934)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _920932), _920934))], (8387 ^ _779308) ^ [_920981, _920983, _920985] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _920981), _920983)), _920985) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _920981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _920983), _920985)))], (8389 ^ _779308) ^ [_921032, _921034] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _921032), _921034)), _921032) = _921034)], (8391 ^ _779308) ^ [_921069, _921071] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _921069), _921071)), _921071) = _921069)], (8393 ^ _779308) ^ [_921106, _921108, _921110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _921106), _921108)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _921108), _921110)), _921106) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _921108), _921106)), _921110))], (8399 ^ _779308) ^ [_921243, _921245, _921247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _921243), _921245)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _921245), _921243)), _921247) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _921245), _921247)), _921243))], (8405 ^ _779308) ^ [_921380, _921382, _921384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _921380), _921382)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _921384), _921382)), _921380) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _921384), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _921382), _921380)))], (8411 ^ _779308) ^ [_921517, _921519, _921521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _921517), _921519)), 8414 ^ _779308 : [(8415 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _921519), _921517) = _921521, -(_921519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _921521), _921517))], (8421 ^ _779308) ^ [] : [_921519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _921521), _921517), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _921519), _921517) = _921521)]]], (8427 ^ _779308) ^ [_921776, _921778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _921776), _921778)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _921778), _921776)), _921776) = _921778)], (8433 ^ _779308) ^ [_921887, _921889, _921891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _921887), _921889)), 8436 ^ _779308 : [(8437 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _921891), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _921889), _921887))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _921891), _921887)), _921889)))], (8443 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _921891), _921887)), _921889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _921891), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _921889), _921887))))]]], (8449 ^ _779308) ^ [_922176, _922178, _922180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _922176), _922178)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _922180), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _922178), _922176)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _922180), _922178)), _922176))], (8455 ^ _779308) ^ [_922313, _922315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _922313), _922315)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _922313), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _922315), _922313)) = _922315)], (8461 ^ _779308) ^ [_922424, _922426, _922428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _922424), _922426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _922428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _922426), _922428)), _922424))))], (8467 ^ _779308) ^ [_922565, _922567, _922569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _922565), _922567)), _922569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _922565), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _922569), _922567))))], (8473 ^ _779308) ^ [_922684, _922686, _922688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _922684), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _922688), _922686))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _922684), _922686)), _922688)))], (8479 ^ _779308) ^ [_922809, _922811, _922813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _922809), _922811)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _922813), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _922811), _922809)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _922813), _922809)), _922811))], (8485 ^ _779308) ^ [_922946] : [-(hAPP(c_Nat_OSuc, _922946) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _922946))], (8487 ^ _779308) ^ [_922975] : [-(hAPP(c_Nat_OSuc, _922975) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _922975), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8489 ^ _779308) ^ [_923007, _923009] : [-(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)), _923007), _923009))], (8491 ^ _779308) ^ [_923037, _923039, _923041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _923037), _923039)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _923039), _923037))), _923041) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _923039)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923037), _923041)))], (8497 ^ _779308) ^ [_923186, _923188, _923190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _923186), _923188)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _923190), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _923188), _923186))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923190), _923186)), hAPP(c_Nat_OSuc, _923188)))], (8503 ^ _779308) ^ [_923335, _923337, _923339, _923341, _923343, _923345] : [c_Fun_Oinj__on(_923335, _923337, _923339, _923341), -(hBOOL(hAPP(hAPP(c_member(_923337), _923343), hAPP(c_Set_Oimage(_923335, _923337, _923339), _923341)))), -(c_Fun_Oinj__on(_923335, _923337, c_Fun_Ofun__upd(_923335, _923337, _923339, _923345, _923343), _923341))], (8513 ^ _779308) ^ [_923483, _923485, _923487] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_923483), _923485)), -(hBOOL(hAPP(hAPP(c_member(_923483), _923487), _923485))), -(hAPP(c_Finite__Set_Ocard(_923483), hAPP(hAPP(c_Set_Oinsert(_923483), _923487), _923485)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_923483), _923485)))], (8523 ^ _779308) ^ [_923641, _923643, _923645] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_923641), _923643)), -(hAPP(c_Finite__Set_Ocard(_923641), hAPP(hAPP(c_Set_Oinsert(_923641), _923645), _923643)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_923641), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923641, tc_HOL_Obool)), _923643), hAPP(hAPP(c_Set_Oinsert(_923641), _923645), c_Orderings_Obot__class_Obot(tc_fun(_923641, tc_HOL_Obool)))))))], (8529 ^ _779308) ^ [_923818, _923820, _923822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _923818), _923820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _923818), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923822), _923820))))], (8535 ^ _779308) ^ [_923929, _923931, _923933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _923929), _923931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _923929), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _923931), _923933))))], (8541 ^ _779308) ^ [_924040, _924042, _924044, _924046] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_924040), _924042)), hBOOL(hAPP(hAPP(c_member(_924040), _924044), _924042)), hBOOL(hAPP(hAPP(c_member(_924040), _924046), _924042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_924040), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924040, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924040, tc_HOL_Obool)), _924042), hAPP(hAPP(c_Set_Oinsert(_924040), _924044), c_Orderings_Obot__class_Obot(tc_fun(_924040, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_924040), _924046), c_Orderings_Obot__class_Obot(tc_fun(_924040, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_924040), _924042))))], (8555 ^ _779308) ^ [_924395, _924397, _924399] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_924395), _924397)), hBOOL(hAPP(hAPP(c_member(_924395), _924399), _924397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_924395), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924395, tc_HOL_Obool)), _924397), hAPP(hAPP(c_Set_Oinsert(_924395), _924399), c_Orderings_Obot__class_Obot(tc_fun(_924395, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_924395), _924397))))], (8565 ^ _779308) ^ [_924628, _924630, _924632] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_924628), _924630)), hBOOL(hAPP(_924632, _924630)), 8576 ^ _779308 : [(8577 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_924628), 8575 ^ [_924628, _924630, _924632])))], (8579 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_924628), 8574 ^ [_924628, _924630, _924632]), 8575 ^ [_924628, _924630, _924632])))], (8581 ^ _779308) ^ [] : [-(hBOOL(hAPP(_924632, 8575 ^ [_924628, _924630, _924632])))], (8583 ^ _779308) ^ [] : [hBOOL(hAPP(_924632, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924628, tc_HOL_Obool)), 8575 ^ [_924628, _924630, _924632]), hAPP(hAPP(c_Set_Oinsert(_924628), 8574 ^ [_924628, _924630, _924632]), c_Orderings_Obot__class_Obot(tc_fun(_924628, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_924632, c_Orderings_Obot__class_Obot(tc_fun(_924628, tc_HOL_Obool)))))], (8587 ^ _779308) ^ [_925153, _925155] : [-(c_Set_Othe__elem(_925153, _925155) = c_HOL_OThe(_925153, hAPP(hAPP(c_COMBB(tc_fun(_925153, tc_HOL_Obool), tc_HOL_Obool, _925153), hAPP(c_fequal, _925155)), hAPP(hAPP(c_COMBC(_925153, tc_fun(_925153, tc_HOL_Obool), tc_fun(_925153, tc_HOL_Obool)), c_Set_Oinsert(_925153)), c_Orderings_Obot__class_Obot(tc_fun(_925153, tc_HOL_Obool))))))], (8589 ^ _779308) ^ [_925223] : [-(c_Finite__Set_Ofun__left__comm__idem(_925223, tc_fun(_925223, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_925223, tc_HOL_Obool), tc_fun(tc_fun(_925223, tc_HOL_Obool), tc_fun(_925223, tc_HOL_Obool)), _925223), hAPP(c_COMBC(tc_fun(_925223, tc_HOL_Obool), tc_fun(_925223, tc_HOL_Obool), tc_fun(_925223, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_925223, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_925223, tc_fun(_925223, tc_HOL_Obool), tc_fun(_925223, tc_HOL_Obool)), c_Set_Oinsert(_925223)), c_Orderings_Obot__class_Obot(tc_fun(_925223, tc_HOL_Obool))))))], (8591 ^ _779308) ^ [_925316, _925318] : [8593 ^ _779308 : [(8594 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 8592 ^ [_925316, _925318]), _925316)))], (8596 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _925318), 8592 ^ [_925316, _925318]))]], -(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), _925318), _925316))], (8600 ^ _779308) ^ [_925491, _925493, _925495, _925497] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_925491), _925493)), hBOOL(hAPP(c_Finite__Set_Ofinite(_925495), _925497)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_925491, _925495)), c_Sum__Type_OPlus(_925491, _925495, _925493, _925497)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_925491), _925493)), hAPP(c_Finite__Set_Ocard(_925495), _925497)))], (8636 ^ _779308) ^ [_926250, _926252, _926254, _926256] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926250, tc_HOL_Obool)), _926252), hAPP(hAPP(c_Set_Oinsert(_926250), _926254), _926256)))), 8639 ^ _779308 : [(8640 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926250), _926254), _926256)))], (8642 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926250, tc_HOL_Obool)), _926252), _926256))]], 8643 ^ _779308 : [(8644 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_926250), _926254), _926256))], (8646 ^ _779308) ^ [] : [8647 ^ _779308 : [(8648 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926250), _926254), _926252)))], (8650 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926250, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_926250, tc_HOL_Obool)), _926252), hAPP(hAPP(c_Set_Oinsert(_926250), _926254), c_Orderings_Obot__class_Obot(tc_fun(_926250, tc_HOL_Obool))))), _926256))]], 8651 ^ _779308 : [(8652 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_926250), _926254), _926252))], (8654 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_926250, tc_HOL_Obool)), _926252), _926256))]]]]], (8610 ^ _779308) ^ [_925723, _925725, _925727, _925729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_925723, tc_HOL_Obool)), _925725), hAPP(hAPP(c_Set_Oinsert(_925723), _925727), _925729))), 8613 ^ _779308 : [(8614 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_925723), _925727), _925729)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_925723, tc_HOL_Obool)), _925725), _925729)))], (8620 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_925723), _925727), _925729))), 8623 ^ _779308 : [(8624 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_925723), _925727), _925725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_925723, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925723, tc_HOL_Obool)), _925725), hAPP(hAPP(c_Set_Oinsert(_925723), _925727), c_Orderings_Obot__class_Obot(tc_fun(_925723, tc_HOL_Obool))))), _925729)))], (8630 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_925723), _925727), _925725))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925723, tc_HOL_Obool)), _925725), _925729)))]]]]], (8658 ^ _779308) ^ [_926789, _926791, _926793] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_926789), _926791)), hBOOL(hAPP(_926793, c_Orderings_Obot__class_Obot(tc_fun(_926789, tc_HOL_Obool)))), 8669 ^ _779308 : [(8670 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_926789), 8668 ^ [_926789, _926791, _926793])))], (8672 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_926789), 8667 ^ [_926789, _926791, _926793]), 8668 ^ [_926789, _926791, _926793]))], (8674 ^ _779308) ^ [] : [-(hBOOL(hAPP(_926793, 8668 ^ [_926789, _926791, _926793])))], (8676 ^ _779308) ^ [] : [hBOOL(hAPP(_926793, hAPP(hAPP(c_Set_Oinsert(_926789), 8667 ^ [_926789, _926791, _926793]), 8668 ^ [_926789, _926791, _926793])))]], -(hBOOL(hAPP(_926793, _926791)))], (8680 ^ _779308) ^ [_927276] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _927276), hAPP(c_Nat_OSuc, _927276))))], (8682 ^ _779308) ^ [_927307, _927309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _927307), _927309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _927307)), hAPP(c_Nat_OSuc, _927309))))], (8688 ^ _779308) ^ [_927416, _927418, _927420, _927422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927416, tc_HOL_Obool)), _927418), _927420)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927416, tc_HOL_Obool)), _927420), _927422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_927416, tc_HOL_Obool)), _927418), _927422)))], (8698 ^ _779308) ^ [_927622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _927622), _927622))], (8700 ^ _779308) ^ [_927650, _927652] : [class_Orderings_Opreorder(_927650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927650), _927652), _927652))], (8716 ^ _779308) ^ [_927798, _927800] : [8717 ^ _779308 : [(8718 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _927798), _927800))], (8720 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _927800), _927798))]], _927798 = _927800], (8706 ^ _779308) ^ [_927749, _927751] : [-(_927749 = _927751), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _927749), _927751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _927751), _927749)))], (8724 ^ _779308) ^ [_927936, _927938, _927940] : [class_Orderings_Olinorder(_927936), 8727 ^ _779308 : [(8738 ^ _779308) ^ [] : [8739 ^ _779308 : [(8740 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927936), _927938), _927940))], (8742 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927936), _927940), _927938))]], _927938 = _927940], (8728 ^ _779308) ^ [] : [-(_927938 = _927940), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927936), _927938), _927940))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927936), _927940), _927938)))]]], (8746 ^ _779308) ^ [_928190, _928192, _928194] : [class_Orderings_Olinorder(_928190), 8749 ^ _779308 : [(8760 ^ _779308) ^ [] : [8761 ^ _779308 : [(8762 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928190), _928194), _928192))], (8764 ^ _779308) ^ [] : [_928192 = _928194]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928190), _928192), _928194))], (8750 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928190), _928192), _928194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928190), _928194), _928192))), -(_928192 = _928194)]]], (8768 ^ _779308) ^ [_928444, _928446, _928448] : [class_Orderings_Olinorder(_928444), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928444), _928446), _928448))), -(_928446 = _928448), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928444), _928448), _928446)))], (8782 ^ _779308) ^ [_928575, _928577, _928579] : [class_Orderings_Olinorder(_928575), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928575), _928577), _928579))), 8789 ^ _779308 : [(8790 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928575), _928579), _928577))), -(_928579 = _928577)], (8796 ^ _779308) ^ [] : [_928579 = _928577, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928575), _928579), _928577))]]], (8802 ^ _779308) ^ [_928834, _928836, _928838] : [class_Orderings_Olinorder(_928834), -(_928836 = _928838), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928834), _928836), _928838))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928834), _928838), _928836)))], (8816 ^ _779308) ^ [_928965, _928967] : [-(_928965 = _928967), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928965), _928967))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _928967), _928965)))], (8826 ^ _779308) ^ [_929027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _929027), _929027))], (8828 ^ _779308) ^ [_929055, _929057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _929055), _929057)), _929057 = _929055], (8834 ^ _779308) ^ [_929143, _929145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _929143), _929145)), _929143 = _929145], (8840 ^ _779308) ^ [_929231, _929233, _929235] : [class_Orderings_Oorder(_929231), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929231), _929233), _929235)), _929233 = _929235], (8850 ^ _779308) ^ [_929377, _929379, _929381] : [class_Orderings_Opreorder(_929377), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929377), _929379), _929381)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929377), _929381), _929379))], (8860 ^ _779308) ^ [_929537, _929539, _929541] : [class_Orderings_Opreorder(_929537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929537), _929539), _929541)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929537), _929541), _929539))], (8870 ^ _779308) ^ [_929697, _929699, _929701] : [class_Orderings_Oorder(_929697), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929697), _929699), _929701)), _929699 = _929701], (8880 ^ _779308) ^ [_929843, _929845, _929847] : [class_Orderings_Oorder(_929843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929843), _929845), _929847)), _929847 = _929845], (8890 ^ _779308) ^ [_929989, _929991, _929993] : [class_Orderings_Opreorder(_929989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929989), _929991), _929993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929989), _929993), _929991))], (8900 ^ _779308) ^ [_930149, _930151, _930153] : [class_Orderings_Oorder(_930149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930149), _930151), _930153)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930149), _930153), _930151))], (8910 ^ _779308) ^ [_930309, _930311, _930313, _930315] : [class_Orderings_Oord(_930309), _930311 = _930313, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930309), _930313), _930315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930309), _930311), _930315)))], (8924 ^ _779308) ^ [_930528, _930530, _930532, _930534] : [class_Orderings_Oorder(_930528), _930530 = _930532, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930528), _930534), _930532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930528), _930534), _930530)))], (8938 ^ _779308) ^ [_930747, _930749, _930751, _930753] : [class_Orderings_Oord(_930747), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930747), _930749), _930751)), _930751 = _930753, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930747), _930749), _930753)))], (8952 ^ _779308) ^ [_930966, _930968, _930970, _930972] : [class_Orderings_Oorder(_930966), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930966), _930968), _930970)), _930968 = _930972, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930966), _930972), _930970)))], (8966 ^ _779308) ^ [_931185, _931187, _931189, _931191] : [class_Orderings_Opreorder(_931185), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931185), _931187), _931189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931185), _931189), _931191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931185), _931187), _931191)))], (8980 ^ _779308) ^ [_931418, _931420, _931422, _931424] : [class_Orderings_Oorder(_931418), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931418), _931420), _931422)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931418), _931424), _931420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931418), _931424), _931422)))], (8994 ^ _779308) ^ [_931651, _931653, _931655] : [class_Orderings_Opreorder(_931651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931651), _931653), _931655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931651), _931655), _931653))], (9004 ^ _779308) ^ [_931811, _931813, _931815] : [class_Orderings_Olinorder(_931811), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931811), _931813), _931815))), -(_931813 = _931815), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931811), _931815), _931813)))], (9018 ^ _779308) ^ [_931946, _931948, _931950] : [9019 ^ _779308 : [(9020 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931946), _931948)))], (9022 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_931950, _931948), _931946))]], 9025 ^ _779308 : [(9026 ^ _779308) ^ [] : [-(_931946 = _931948)], (9028 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_931950, _931948), _931946))]], 9031 ^ _779308 : [(9032 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _931948), _931946)))], (9034 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_931950, _931948), _931946))]], -(hBOOL(hAPP(hAPP(_931950, _931948), _931946)))], (9038 ^ _779308) ^ [_932292, _932294, _932296, _932298, _932300] : [c_Finite__Set_Ofun__left__comm__idem(_932292, _932294, _932296), -(hAPP(hAPP(_932296, _932298), hAPP(hAPP(_932296, _932298), _932300)) = hAPP(hAPP(_932296, _932298), _932300))], (9044 ^ _779308) ^ [_932413, _932415, _932417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _932413), _932415)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _932413), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _932417), _932415))))], (9050 ^ _779308) ^ [_932524, _932526, _932528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _932524), _932526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _932524), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _932526), _932528))))], (9056 ^ _779308) ^ [_932635, _932637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _932635), _932637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _932635), _932637)))], (9062 ^ _779308) ^ [_932732, _932734, _932736] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_932732), _932734)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_932732, tc_HOL_Obool)), _932736), _932734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_932732), _932736)), hAPP(c_Finite__Set_Ocard(_932732), _932734))))], (9072 ^ _779308) ^ [_932923, _932925, _932927, _932929, _932931] : [c_Finite__Set_Ofun__left__comm__idem(_932923, _932925, _932927), -(c_Finite__Set_Ofun__left__comm__idem(_932929, _932925, hAPP(hAPP(c_COMBB(_932923, tc_fun(_932925, _932925), _932929), _932927), _932931)))], (9078 ^ _779308) ^ [_933036, _933038, _933040, _933042] : [class_Orderings_Oord(_933036), 9081 ^ _779308 : [(9082 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_933038, _933036)), _933040), _933042)), 9085 ^ _779308 : [(9086 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933038, _933036)), _933040), _933042)))], (9088 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933038, _933036)), _933042), _933040))]]], (9090 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_933038, _933036)), _933040), _933042))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933038, _933036)), _933040), _933042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933038, _933036)), _933042), _933040)))]]], (9100 ^ _779308) ^ [_933428, _933430, _933432] : [class_Orderings_Olinorder(_933428), 9103 ^ _779308 : [(9104 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933428), _933430), _933432))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933428), _933432), _933430)))], (9110 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933428), _933432), _933430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933428), _933430), _933432))]]], (9116 ^ _779308) ^ [_933637, _933639, _933641] : [class_Orderings_Olinorder(_933637), 9119 ^ _779308 : [(9120 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933637), _933639), _933641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933637), _933641), _933639)))], (9126 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933637), _933641), _933639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933637), _933639), _933641))]]], (9132 ^ _779308) ^ [_933846, _933848, _933850] : [class_Orderings_Olinorder(_933846), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933846), _933848), _933850))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933846), _933850), _933848)))], (9142 ^ _779308) ^ [_933964, _933966, _933968] : [class_Orderings_Oorder(_933964), 9145 ^ _779308 : [(9146 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933964), _933966), _933968)), 9149 ^ _779308 : [(9150 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933964), _933966), _933968)))], (9152 ^ _779308) ^ [] : [_933966 = _933968]]], (9154 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933964), _933966), _933968))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933964), _933966), _933968)), -(_933966 = _933968)]]], (9164 ^ _779308) ^ [_934300, _934302, _934304] : [class_Orderings_Opreorder(_934300), 9167 ^ _779308 : [(9168 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934300), _934302), _934304)), 9171 ^ _779308 : [(9172 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934300), _934302), _934304)))], (9174 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934300), _934304), _934302))]]], (9176 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934300), _934302), _934304))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934300), _934302), _934304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934300), _934304), _934302)))]]], (9186 ^ _779308) ^ [_934657, _934659, _934661] : [class_Orderings_Oorder(_934657), 9189 ^ _779308 : [(9200 ^ _779308) ^ [] : [9201 ^ _779308 : [(9202 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934657), _934659), _934661))], (9204 ^ _779308) ^ [] : [_934659 = _934661]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934657), _934659), _934661)))], (9190 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934657), _934659), _934661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934657), _934659), _934661))), -(_934659 = _934661)]]], (9208 ^ _779308) ^ [_934955, _934957, _934959] : [class_Orderings_Olinorder(_934955), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934955), _934957), _934959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934955), _934959), _934957)))], (9218 ^ _779308) ^ [_935075, _935077, _935079] : [class_Orderings_Olinorder(_935075), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935075), _935077), _935079))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935075), _935079), _935077)))], (9228 ^ _779308) ^ [_935195, _935197, _935199] : [class_Orderings_Olinorder(_935195), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935195), _935197), _935199))), 9235 ^ _779308 : [(9236 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935195), _935197), _935199)), -(_935197 = _935199)], (9242 ^ _779308) ^ [] : [_935197 = _935199, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935195), _935197), _935199)))]]], (9248 ^ _779308) ^ [_935498, _935500, _935502] : [class_Orderings_Oorder(_935498), -(_935500 = _935502), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935498), _935500), _935502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935498), _935500), _935502)))], (9262 ^ _779308) ^ [_935714, _935716, _935718] : [class_Orderings_Oorder(_935714), -(_935716 = _935718), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935714), _935718), _935716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935714), _935718), _935716)))], (9276 ^ _779308) ^ [_935930, _935932, _935934] : [class_Orderings_Olinorder(_935930), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935930), _935932), _935934)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935930), _935934), _935932))], (9286 ^ _779308) ^ [_936090, _936092, _936094] : [class_Orderings_Opreorder(_936090), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936090), _936092), _936094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936090), _936092), _936094)))], (9296 ^ _779308) ^ [_936249, _936251, _936253] : [class_Orderings_Olinorder(_936249), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936249), _936251), _936253)), 9303 ^ _779308 : [(9304 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936249), _936251), _936253))), -(_936251 = _936253)], (9310 ^ _779308) ^ [] : [_936251 = _936253, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936249), _936251), _936253))]]], (9316 ^ _779308) ^ [_936505, _936507, _936509] : [class_Orderings_Oorder(_936505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936505), _936507), _936509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936505), _936507), _936509))), -(_936507 = _936509)], (9330 ^ _779308) ^ [_936677, _936679, _936681] : [class_Orderings_Oorder(_936677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936677), _936679), _936681)), -(_936679 = _936681), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936677), _936679), _936681)))], (9344 ^ _779308) ^ [_936851, _936853, _936855] : [class_Orderings_Oorder(_936851), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936851), _936853), _936855)), -(_936855 = _936853), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936851), _936853), _936855)))], (9358 ^ _779308) ^ [_937025, _937027, _937029, _937031] : [class_Orderings_Opreorder(_937025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937025), _937027), _937029)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937025), _937029), _937031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937025), _937027), _937031)))], (9372 ^ _779308) ^ [_937258, _937260, _937262, _937264] : [class_Orderings_Oorder(_937258), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937258), _937260), _937262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937258), _937264), _937260)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937258), _937264), _937262)))], (9386 ^ _779308) ^ [_937491, _937493, _937495, _937497] : [class_Orderings_Opreorder(_937491), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937491), _937493), _937495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937491), _937495), _937497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937491), _937493), _937497)))], (9400 ^ _779308) ^ [_937724, _937726, _937728, _937730] : [class_Orderings_Oorder(_937724), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937724), _937726), _937728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937724), _937730), _937726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937724), _937730), _937728)))], (9414 ^ _779308) ^ [_937957, _937959, _937961, _937963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_937957, tc_HOL_Obool)), _937959), _937961)), hBOOL(hAPP(hAPP(c_member(_937957), _937963), _937959)), -(hBOOL(hAPP(hAPP(c_member(_937957), _937963), _937961)))], (9424 ^ _779308) ^ [_938142, _938144, _938146, _938148] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_938142), 9427 ^ _779308 : [(9428 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938142), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938142), _938144), _938146)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938142), _938148), _938146))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938142), _938144), _938148)))], (9434 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938142), _938144), _938148)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938142), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938142), _938144), _938146)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938142), _938148), _938146))))]]], (9440 ^ _779308) ^ [_938449, _938451, _938453, _938455] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_938449), 9443 ^ _779308 : [(9444 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938449), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938449), _938451), _938453)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938449), _938451), _938455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938449), _938453), _938455)))], (9450 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938449), _938453), _938455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938449), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938449), _938451), _938453)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938449), _938451), _938455))))]]], (9456 ^ _779308) ^ [_938756, _938758, _938760, _938762] : [class_Groups_Oordered__cancel__ab__semigroup__add(_938756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938756), _938758), _938760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938756), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938756), _938758), _938762)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938756), _938760), _938762))))], (9466 ^ _779308) ^ [_938951, _938953, _938955, _938957] : [class_Groups_Oordered__cancel__ab__semigroup__add(_938951), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938951), _938953), _938955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938951), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938951), _938957), _938953)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_938951), _938957), _938955))))], (9476 ^ _779308) ^ [_939146, _939148, _939150, _939152, _939154] : [class_Groups_Oordered__cancel__ab__semigroup__add(_939146), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939146), _939148), _939150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939146), _939152), _939154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939146), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939146), _939148), _939152)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939146), _939150), _939154))))], (9490 ^ _779308) ^ [_939417, _939419, _939421, _939423] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_939417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939417), _939419), _939421)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939417), _939423), _939421))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939417), _939419), _939423)))], (9500 ^ _779308) ^ [_939612, _939614, _939616, _939618] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_939612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939612), _939614), _939616)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_939612), _939614), _939618))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939612), _939616), _939618)))], (9510 ^ _779308) ^ [_939819, _939821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_939819, tc_HOL_Obool)), _939821), c_Orderings_Obot__class_Obot(tc_fun(_939819, tc_HOL_Obool))))], (9512 ^ _779308) ^ [_939859, _939861, _939863, _939865, _939867] : [class_Groups_Oordered__ab__group__add(_939859), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_939859), _939861), _939863) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_939859), _939865), _939867), 9519 ^ _779308 : [(9520 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939859), _939861), _939863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939859), _939865), _939867)))], (9526 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939859), _939865), _939867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939859), _939861), _939863)))]]], (9532 ^ _779308) ^ [_940232, _940234, _940236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940232, tc_HOL_Obool)), _940234), _940236)), 9535 ^ _779308 : [(9536 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940232, tc_HOL_Obool)), _940234), _940236)))], (9538 ^ _779308) ^ [] : [_940234 = _940236]]], (9540 ^ _779308) ^ [_940381, _940383, _940385] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940381, tc_HOL_Obool)), _940383), _940385))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940381, tc_HOL_Obool)), _940383), _940385)), -(_940383 = _940385)], (9560 ^ _779308) ^ [_940705, _940707, _940709] : [9561 ^ _779308 : [(9562 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940705, tc_HOL_Obool)), _940707), _940709))], (9564 ^ _779308) ^ [] : [_940707 = _940709]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940705, tc_HOL_Obool)), _940707), _940709)))], (9550 ^ _779308) ^ [_940577, _940579, _940581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940577, tc_HOL_Obool)), _940579), _940581)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940577, tc_HOL_Obool)), _940579), _940581))), -(_940579 = _940581)], (9568 ^ _779308) ^ [_940864, _940866, _940868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940864, tc_HOL_Obool)), _940866), _940868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940864, tc_HOL_Obool)), _940866), _940868)))], (9574 ^ _779308) ^ [_940983, _940985, _940987, _940989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940983, tc_HOL_Obool)), _940985), _940987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940983, tc_HOL_Obool)), _940987), _940989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940983, tc_HOL_Obool)), _940985), _940989)))], (9584 ^ _779308) ^ [_941180, _941182, _941184, _941186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941180, tc_HOL_Obool)), _941182), _941184)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_941180, tc_HOL_Obool)), _941184), _941186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_941180, tc_HOL_Obool)), _941182), _941186)))], (9594 ^ _779308) ^ [_941386, _941388] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941386), _941388))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941388), hAPP(c_Nat_OSuc, _941386))))], (9600 ^ _779308) ^ [_941431, _941433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941433), hAPP(c_Nat_OSuc, _941431))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941431), _941433))], (9616 ^ _779308) ^ [_941664, _941666] : [9617 ^ _779308 : [(9618 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941664), _941666))], (9620 ^ _779308) ^ [] : [_941664 = _941666]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941664), hAPP(c_Nat_OSuc, _941666))))], (9606 ^ _779308) ^ [_941552, _941554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941552), hAPP(c_Nat_OSuc, _941554))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941552), _941554))), -(_941552 = _941554)], (9624 ^ _779308) ^ [_941822, _941824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _941822)), hAPP(c_Nat_OSuc, _941824))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941822), _941824)))], (9630 ^ _779308) ^ [_941927, _941929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _941927), _941929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _941927)), hAPP(c_Nat_OSuc, _941929))))], (9636 ^ _779308) ^ [_942037, _942039] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942037), _942039))), 9639 ^ _779308 : [(9640 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942037), hAPP(c_Nat_OSuc, _942039))), -(_942037 = _942039)], (9646 ^ _779308) ^ [] : [_942037 = _942039, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942037), hAPP(c_Nat_OSuc, _942039))))]]], (9652 ^ _779308) ^ [_942270, _942272] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942270), _942272))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942270), hAPP(c_Nat_OSuc, _942272))), -(_942272 = _942270)], (9662 ^ _779308) ^ [_942418, _942420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942418), _942420)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942418), hAPP(c_Nat_OSuc, _942420))))], (9668 ^ _779308) ^ [_942521, _942523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942521), _942523)), -(hAPP(c_Nat_OSuc, _942521) = _942523), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _942521)), _942523)))], (9678 ^ _779308) ^ [_942645, _942647, _942649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942645), _942647)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942647), _942649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _942645)), _942649)))], (9688 ^ _779308) ^ [_942814, _942816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942814), hAPP(c_Nat_OSuc, _942816))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942814), _942816))), -(_942814 = _942816)], (9698 ^ _779308) ^ [_942932, _942934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _942932)), _942934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _942932), _942934)))], (9704 ^ _779308) ^ [_943035, _943037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _943035)), hAPP(c_Nat_OSuc, _943037))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943035), _943037)))], (9710 ^ _779308) ^ [_943156, _943158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943156), _943158)), _943156))], (9712 ^ _779308) ^ [_943204, _943206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943204), _943206)), _943206))], (9714 ^ _779308) ^ [_943258, _943260, _943262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943258), _943260)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943258), _943262))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943260), _943262)))], (9720 ^ _779308) ^ [_943377, _943379, _943381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943379), _943381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943377), _943379)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943377), _943381))))], (9726 ^ _779308) ^ [_943502, _943504, _943506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943502), _943504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943502), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943504), _943506))))], (9732 ^ _779308) ^ [_943613, _943615, _943617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943613), _943615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943613), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943617), _943615))))], (9738 ^ _779308) ^ [_943724, _943726, _943728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943724), _943726)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943724), _943728)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943726), _943728))))], (9744 ^ _779308) ^ [_943847, _943849, _943851, _943853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943847), _943849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943851), _943853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943847), _943851)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943849), _943853))))], (9754 ^ _779308) ^ [_944038, _944040, _944042, _944044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944038), _944040)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _944042), _944040) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _944038), _944044), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944042), _944044)))], (9764 ^ _779308) ^ [_944219, _944221, _944223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _944219), _944221)), _944223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944219), _944223)))], (9770 ^ _779308) ^ [_944345, _944347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944345), _944347)), 9773 ^ _779308 : [(9774 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944345), _944347)))], (9776 ^ _779308) ^ [] : [_944345 = _944347]]], (9778 ^ _779308) ^ [_944472, _944474] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944472), _944474))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944472), _944474)), -(_944472 = _944474)], (9798 ^ _779308) ^ [_944747, _944749] : [9799 ^ _779308 : [(9800 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944747), _944749))], (9802 ^ _779308) ^ [] : [_944747 = _944749]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944747), _944749)))], (9788 ^ _779308) ^ [_944641, _944643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944641), _944643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944641), _944643))), -(_944641 = _944643)], (9806 ^ _779308) ^ [_944884, _944886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944884), _944886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944884), _944886)))], (9812 ^ _779308) ^ [_944981, _944983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _944981), _944983)), -(_944981 = _944983), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944981), _944983)))], (9822 ^ _779308) ^ [_945093, _945095] : [9823 ^ _779308 : [(9824 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945093), _945095))], (9826 ^ _779308) ^ [] : [_945093 = _945095]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945093), _945095)))], (9830 ^ _779308) ^ [_945228, _945230, _945232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945228), _945230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _945228), _945232)), _945230)))], (9836 ^ _779308) ^ [_945339, _945341, _945343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945339), _945341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945339), _945343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _945343), _945341)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _945343), _945339))))], (9857 ^ _779308) ^ [_945725] : [9859 ^ _779308 : [(9860 ^ _779308) ^ [_945801] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 9858 ^ [_945725, _945801]), _945725)))], (9862 ^ _779308) ^ [_945835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 9858 ^ [_945725, _945835]), _945835))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _945725)))], (9846 ^ _779308) ^ [_945538] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _945538)), 9850 ^ _779308 : [(9851 ^ _779308) ^ [_945618] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _945618), _945538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945618), 9849 ^ [_945538])))]]], (9866 ^ _779308) ^ [_945904, _945906, _945908] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_945904), _945906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945904, tc_HOL_Obool)), _945908), _945906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_945904), _945908)), hAPP(c_Finite__Set_Ocard(_945904), _945906))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_945904, tc_HOL_Obool)), _945908), _945906)))], (9880 ^ _779308) ^ [_946169] : [-(c_Finite__Set_Ofun__left__comm__idem(_946169, tc_fun(_946169, tc_HOL_Obool), c_Set_Oinsert(_946169)))], (9882 ^ _779308) ^ [_946219, _946221, _946223, _946225] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_946219, _946221)), c_Sum__Type_OPlus(_946219, _946221, _946223, _946225))), 9885 ^ _779308 : [(9886 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_946219), _946223)))], (9888 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_946221), _946225)))]]], (9890 ^ _779308) ^ [_946362, _946364, _946366, _946368] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_946362, _946364)), c_Sum__Type_OPlus(_946362, _946364, _946366, _946368)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_946362), _946366)), hBOOL(hAPP(c_Finite__Set_Ofinite(_946364), _946368))], (9900 ^ _779308) ^ [_946541, _946543, _946545, _946547] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_946541), _946543)), hBOOL(hAPP(c_Finite__Set_Ofinite(_946545), _946547)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_946541, _946545)), c_Sum__Type_OPlus(_946541, _946545, _946543, _946547))))], (9910 ^ _779308) ^ [_946718, _946720, _946722, _946724] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_946718, _946720)), c_Sum__Type_OPlus(_946718, _946720, _946722, _946724))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_946718), _946722)))], (9916 ^ _779308) ^ [_946831, _946833, _946835, _946837] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_946831, _946833)), c_Sum__Type_OPlus(_946831, _946833, _946835, _946837))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_946833), _946837)))], (9922 ^ _779308) ^ [_946944, _946946, _946948, _946950, _946952] : [class_Groups_Oordered__cancel__ab__semigroup__add(_946944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_946944), _946946), _946948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946944), _946950), _946952)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946944), _946946), _946950)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946944), _946948), _946952))))], (9936 ^ _779308) ^ [_947215, _947217, _947219, _947221, _947223] : [class_Groups_Oordered__cancel__ab__semigroup__add(_947215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947215), _947217), _947219)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947215), _947221), _947223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_947215), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947215), _947217), _947221)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947215), _947219), _947223))))], (9950 ^ _779308) ^ [_947501, _947503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947501), _947503)), -(_947503 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947501), 9953 ^ [_947501, _947503])))], (9957 ^ _779308) ^ [_947614, _947616] : [9958 ^ _779308 : [(9959 ^ _779308) ^ [_947667] : [_947616 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947614), _947667))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947614), _947616)))], (9963 ^ _779308) ^ [_947734, _947736] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947734), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947736), _947734)))))], (9965 ^ _779308) ^ [_947773, _947775] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947773), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _947773), _947775)))))], (9967 ^ _779308) ^ [_947812, _947814, _947816, _947818, _947820] : [c_Fun_Oinj__on(_947812, _947814, _947816, _947818), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_947812, tc_HOL_Obool)), _947820), _947818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_947814, tc_HOL_Obool)), hAPP(c_Set_Oimage(_947812, _947814, _947816), _947820)), hAPP(c_Set_Oimage(_947812, _947814, _947816), _947818))))], (9977 ^ _779308) ^ [_948040, _948042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948040), _948042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _948040)), _948042)))], (9983 ^ _779308) ^ [_948139, _948141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _948139)), _948141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948139), _948141)))], (9989 ^ _779308) ^ [_948259, _948261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948259), hAPP(c_Nat_OSuc, _948261))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _948259), _948261)))], (9995 ^ _779308) ^ [_948358, _948360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _948358), _948360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948358), hAPP(c_Nat_OSuc, _948360))))], (10001 ^ _779308) ^ [_948478, _948480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _948478)), _948480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948478), _948480)))], (10007 ^ _779308) ^ [_948577, _948579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948577), _948579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _948577)), _948579)))], (10013 ^ _779308) ^ [_948682, _948684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _948682), _948684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948682), hAPP(c_Nat_OSuc, _948684))))], (10019 ^ _779308) ^ [_948785, _948787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948785), _948787)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _948785)), _948787)))], (10025 ^ _779308) ^ [_948888, _948890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _948888), _948890)), 10028 ^ _779308 : [(10029 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948890), hAPP(c_Nat_OSuc, _948888))), -(_948890 = _948888)], (10035 ^ _779308) ^ [] : [_948890 = _948888, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948890), hAPP(c_Nat_OSuc, _948888))))]]], (10041 ^ _779308) ^ [_949129, _949131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _949129)), _949131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949129), _949131)))], (10047 ^ _779308) ^ [_949232, _949234] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949232), _949234)), hAPP(c_Nat_OSuc, _949232))))], (10049 ^ _779308) ^ [_949267, _949269] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949267), _949269))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _949269), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949267), _949269)) = _949267)], (10055 ^ _779308) ^ [_949338, _949340, _949342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949338), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949340), _949342))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _949338), _949342)), _949340)))], (10061 ^ _779308) ^ [_949457, _949459, _949461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _949457), _949461)), _949459)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949457), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949459), _949461))))], (10067 ^ _779308) ^ [_949582, _949584, _949586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949582), _949584)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949586), _949582)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949582), _949586)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949584), _949586))))], (10077 ^ _779308) ^ [_949769, _949771, _949773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949769), _949771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949769), _949773)), 10084 ^ _779308 : [(10085 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949771), _949769)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949773), _949769))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949771), _949773)))], (10091 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _949771), _949773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949771), _949769)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949773), _949769))))]]], (10097 ^ _779308) ^ [_950122] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _950122) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _950122)))], (10099 ^ _779308) ^ [_950154, _950156, _950158, _950160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_950154), hAPP(c_Set_Oimage(_950156, _950154, _950158), _950160))), hAPP(c_Finite__Set_Ocard(_950156), _950160))), c_Fun_Oinj__on(_950156, _950154, _950158, _950160)], (10105 ^ _779308) ^ [_950284, _950286, _950288, _950290, _950292] : [-(hAPP(c_Fun_Othe__inv__into(_950284, _950286, _950288, _950290), _950292) = c_HOL_OThe(_950284, hAPP(hAPP(c_COMBS(_950284, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _950284), c_fconj), hAPP(hAPP(c_COMBC(_950284, tc_fun(_950284, tc_HOL_Obool), tc_HOL_Obool), c_member(_950284)), _950288))), hAPP(hAPP(c_COMBC(_950284, _950286, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_950286, tc_fun(_950286, tc_HOL_Obool), _950284), c_fequal), _950290)), _950292))))], (10107 ^ _779308) ^ [_950384, _950386] : [class_Rings_Olinordered__semidom(_950384), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950384), _950386), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950384), _950386), c_Groups_Oone__class_Oone(_950384)))))], (10113 ^ _779308) ^ [_950505, _950507, _950509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950505, tc_HOL_Obool)), _950507), hAPP(hAPP(c_Set_Oinsert(_950505), _950509), c_Orderings_Obot__class_Obot(tc_fun(_950505, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_950505, _950509, _950507) = _950509)], (10119 ^ _779308) ^ [_950632, _950634, _950636] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950632, tc_HOL_Obool)), _950634), hAPP(hAPP(c_Set_Oinsert(_950632), _950636), c_Orderings_Obot__class_Obot(tc_fun(_950632, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_950632, _950636, _950634) = c_HOL_OThe(_950632, hAPP(hAPP(c_COMBC(_950632, tc_fun(_950632, tc_HOL_Obool), tc_HOL_Obool), c_member(_950632)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_950632, tc_HOL_Obool)), _950634), hAPP(hAPP(c_Set_Oinsert(_950632), _950636), c_Orderings_Obot__class_Obot(tc_fun(_950632, tc_HOL_Obool)))))))], (10125 ^ _779308) ^ [_950762, _950764, _950766, _950768] : [c_Sum__Type_OPlus(_950762, _950764, _950766, _950768) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_950762, _950764), tc_HOL_Obool)), 10128 ^ _779308 : [(10129 ^ _779308) ^ [] : [-(_950766 = c_Orderings_Obot__class_Obot(tc_fun(_950762, tc_HOL_Obool)))], (10131 ^ _779308) ^ [] : [-(_950768 = c_Orderings_Obot__class_Obot(tc_fun(_950764, tc_HOL_Obool)))]]], (10133 ^ _779308) ^ [_950911, _950913, _950915, _950917] : [-(c_Sum__Type_OPlus(_950911, _950913, _950915, _950917) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_950911, _950913), tc_HOL_Obool))), _950915 = c_Orderings_Obot__class_Obot(tc_fun(_950911, tc_HOL_Obool)), _950917 = c_Orderings_Obot__class_Obot(tc_fun(_950913, tc_HOL_Obool))], (10153 ^ _779308) ^ [_951316, _951318, _951320, _951322] : [10154 ^ _779308 : [(10155 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_951316), _951318)))], (10157 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_951320), _951322)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_951316, _951320)), c_Sum__Type_OPlus(_951316, _951320, _951318, _951322)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10143 ^ _779308) ^ [_951111, _951113, _951115, _951117] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_951111, _951115)), c_Sum__Type_OPlus(_951111, _951115, _951113, _951117)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_951111), _951113)), hAPP(c_Finite__Set_Ocard(_951115), _951117))), hBOOL(hAPP(c_Finite__Set_Ofinite(_951111), _951113)), hBOOL(hAPP(c_Finite__Set_Ofinite(_951115), _951117))], (10161 ^ _779308) ^ [_951416, _951418] : [-(c_HOL_OThe(_951416, hAPP(hAPP(c_COMBC(_951416, _951416, tc_HOL_Obool), c_fequal), _951418)) = _951418)], (10163 ^ _779308) ^ [_951454, _951456] : [-(c_HOL_OThe(_951454, hAPP(c_fequal, _951456)) = _951456)], (10165 ^ _779308) ^ [_951485, _951487, _951489, _951491, _951493, _951495, _951497] : [hBOOL(hAPP(hAPP(c_member(_951485), _951487), _951489)), c_Nitpick_Ofold__graph_H(_951485, _951491, _951493, _951495, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_951485, tc_HOL_Obool)), _951489), hAPP(hAPP(c_Set_Oinsert(_951485), _951487), c_Orderings_Obot__class_Obot(tc_fun(_951485, tc_HOL_Obool)))), _951497), -(c_Nitpick_Ofold__graph_H(_951485, _951491, _951493, _951495, _951489, hAPP(hAPP(_951493, _951487), _951497)))], (10175 ^ _779308) ^ [_951724, _951726, _951728, _951730, _951732, _951734, _951736] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_951724, _951726, _951728, _951730, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_951724, tc_HOL_Obool)), _951732), hAPP(hAPP(c_Set_Oinsert(_951724), _951734), c_Orderings_Obot__class_Obot(tc_fun(_951724, tc_HOL_Obool))))), _951736)), hBOOL(hAPP(hAPP(c_member(_951724), _951734), _951732)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_951724, _951726, _951728, _951730, _951732), hAPP(hAPP(_951728, _951734), _951736))))], (10185 ^ _779308) ^ [_951988, _951990] : [_951988 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951988), _951990) = _951990)], (10191 ^ _779308) ^ [_952071, _952073] : [-(_952071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _952071), _952073) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _952071), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _952073)))], (10197 ^ _779308) ^ [_952130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _952130)), -(_952130 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _952130), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (10203 ^ _779308) ^ [_952236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _952236), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10205 ^ _779308) ^ [_952264] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _952264)))], (10207 ^ _779308) ^ [_952289] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _952289))))], (10209 ^ _779308) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10211 ^ _779308) ^ [_952335, _952337] : [class_Groups_Ozero(_952335), 10214 ^ _779308 : [(10215 ^ _779308) ^ [] : [c_Groups_Ozero__class_Ozero(_952335) = _952337, -(_952337 = c_Groups_Ozero__class_Ozero(_952335))], (10221 ^ _779308) ^ [] : [_952337 = c_Groups_Ozero__class_Ozero(_952335), -(c_Groups_Ozero__class_Ozero(_952335) = _952337)]]], (10227 ^ _779308) ^ [_952552] : [class_Rings_Ozero__neq__one(_952552), c_Groups_Oone__class_Oone(_952552) = c_Groups_Ozero__class_Ozero(_952552)], (10233 ^ _779308) ^ [_952634] : [class_Rings_Ozero__neq__one(_952634), c_Groups_Ozero__class_Ozero(_952634) = c_Groups_Oone__class_Oone(_952634)], (10239 ^ _779308) ^ [_952716, _952718, _952720, _952722] : [-(c_Nitpick_Ofold__graph_H(_952716, _952718, _952720, _952722, c_Orderings_Obot__class_Obot(tc_fun(_952716, tc_HOL_Obool)), _952722))], (10241 ^ _779308) ^ [_952754, _952756, _952758, _952760] : [-(c_Nitpick_Ofold__graph_H(_952754, _952756, _952758, _952760, c_Orderings_Obot__class_Obot(tc_fun(_952754, tc_HOL_Obool)), _952760))], (10243 ^ _779308) ^ [_952792, _952794] : [class_Groups_Ocomm__monoid__add(_952792), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952792), _952794), c_Groups_Ozero__class_Ozero(_952792)) = _952794)], (10249 ^ _779308) ^ [_952887, _952889] : [class_Groups_Omonoid__add(_952887), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952887), _952889), c_Groups_Ozero__class_Ozero(_952887)) = _952889)], (10255 ^ _779308) ^ [_952982, _952984] : [class_Groups_Olinordered__ab__group__add(_952982), 10258 ^ _779308 : [(10259 ^ _779308) ^ [] : [c_Groups_Ozero__class_Ozero(_952982) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952982), _952984), _952984), -(_952984 = c_Groups_Ozero__class_Ozero(_952982))], (10265 ^ _779308) ^ [] : [_952984 = c_Groups_Ozero__class_Ozero(_952982), -(c_Groups_Ozero__class_Ozero(_952982) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952982), _952984), _952984))]]], (10271 ^ _779308) ^ [_953223, _953225] : [class_Groups_Ocomm__monoid__add(_953223), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953223), c_Groups_Ozero__class_Ozero(_953223)), _953225) = _953225)], (10277 ^ _779308) ^ [_953318, _953320] : [class_Groups_Omonoid__add(_953318), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953318), c_Groups_Ozero__class_Ozero(_953318)), _953320) = _953320)], (10283 ^ _779308) ^ [_953413, _953415, _953417] : [class_Groups_Ogroup__add(_953413), 10286 ^ _779308 : [(10287 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_953413), _953415), _953417) = c_Groups_Ozero__class_Ozero(_953413), -(_953415 = _953417)], (10293 ^ _779308) ^ [] : [_953415 = _953417, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_953413), _953415), _953417) = c_Groups_Ozero__class_Ozero(_953413))]]], (10299 ^ _779308) ^ [_953654, _953656, _953658] : [class_Groups_Oab__group__add(_953654), 10302 ^ _779308 : [(10303 ^ _779308) ^ [] : [_953656 = _953658, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_953654), _953656), _953658) = c_Groups_Ozero__class_Ozero(_953654))], (10309 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_953654), _953656), _953658) = c_Groups_Ozero__class_Ozero(_953654), -(_953656 = _953658)]]], (10315 ^ _779308) ^ [_953895, _953897] : [class_Groups_Ogroup__add(_953895), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_953895), _953897), _953897) = c_Groups_Ozero__class_Ozero(_953895))], (10321 ^ _779308) ^ [_953990, _953992] : [class_Groups_Ogroup__add(_953990), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_953990), _953992), c_Groups_Ozero__class_Ozero(_953990)) = _953992)], (10327 ^ _779308) ^ [_954094] : [hAPP(c_Nat_OSuc, _954094) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10329 ^ _779308) ^ [_954129] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _954129)], (10331 ^ _779308) ^ [_954164] : [hAPP(c_Nat_OSuc, _954164) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10333 ^ _779308) ^ [_954199] : [hAPP(c_Nat_OSuc, _954199) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10335 ^ _779308) ^ [_954234] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _954234)], (10337 ^ _779308) ^ [_954269] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _954269)], (10339 ^ _779308) ^ [_954291] : [-(_954291 = 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)), _954291)))], (10345 ^ _779308) ^ [_954327, _954329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _954327), _954329)), _954329 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10351 ^ _779308) ^ [_954424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _954424), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10353 ^ _779308) ^ [_954458] : [-(_954458 = 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)), _954458)))], (10359 ^ _779308) ^ [_954490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _954490)), _954490 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10365 ^ _779308) ^ [_954581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _954581), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10367 ^ _779308) ^ [_954609, _954611] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954609), _954611) = _954609, -(_954611 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10373 ^ _779308) ^ [_954713, _954715] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954713), _954715) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 10376 ^ _779308 : [(10377 ^ _779308) ^ [] : [-(_954713 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10379 ^ _779308) ^ [] : [-(_954715 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (10381 ^ _779308) ^ [_954824, _954826] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954824), _954826) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _954824 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _954826 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10391 ^ _779308) ^ [_954967] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _954967), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _954967)], (10393 ^ _779308) ^ [_954996] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _954996) = _954996)], (10395 ^ _779308) ^ [_955034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955034), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_955034 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10401 ^ _779308) ^ [_955115] : [_955115 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955115), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10407 ^ _779308) ^ [_955202] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _955202)))], (10409 ^ _779308) ^ [_955227, _955229] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _955227), _955229) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _955229), _955227) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_955227 = _955229)], (10419 ^ _779308) ^ [_955380] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _955380), _955380) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10421 ^ _779308) ^ [_955409] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _955409), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _955409)], (10423 ^ _779308) ^ [_955438] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _955438) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10425 ^ _779308) ^ [_955464, _955466, _955468, _955470] : [class_Rings_Olinordered__semidom(_955464), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955464), c_Groups_Ozero__class_Ozero(_955464)), _955466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955464), _955468), _955470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_955464), _955468), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955464), _955466), _955470))))], (10439 ^ _779308) ^ [_955717, _955719, _955721, _955723, _955725] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_955717, _955719, _955721, _955723, c_Orderings_Obot__class_Obot(tc_fun(_955717, tc_HOL_Obool))), _955725)), -(_955725 = _955723)], (10445 ^ _779308) ^ [_955826, _955828, _955830, _955832] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_955826, _955828, _955830, _955832, c_Orderings_Obot__class_Obot(tc_fun(_955826, tc_HOL_Obool))), _955832)))], (10447 ^ _779308) ^ [_955868, _955870, _955872, _955874] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_955868, _955870, _955872, _955874, c_Orderings_Obot__class_Obot(tc_fun(_955868, tc_HOL_Obool))), _955874)))], (10449 ^ _779308) ^ [_955910, _955912, _955914, _955916, _955918, _955920] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_955910, _955912, _955914, _955916, _955918), _955920)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_955910), _955918)))], (10455 ^ _779308) ^ [_956019] : [class_Rings_Olinordered__semidom(_956019), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956019), c_Groups_Ozero__class_Ozero(_956019)), c_Groups_Oone__class_Oone(_956019))))], (10461 ^ _779308) ^ [_956114] : [class_Rings_Olinordered__semidom(_956114), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956114), c_Groups_Oone__class_Oone(_956114)), c_Groups_Ozero__class_Ozero(_956114)))], (10467 ^ _779308) ^ [_956210] : [class_Rings_Olinordered__semidom(_956210), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956210), c_Groups_Oone__class_Oone(_956210)), c_Groups_Ozero__class_Ozero(_956210)))], (10473 ^ _779308) ^ [_956306] : [class_Rings_Olinordered__semidom(_956306), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956306), c_Groups_Ozero__class_Ozero(_956306)), c_Groups_Oone__class_Oone(_956306))))], (10479 ^ _779308) ^ [_956401, _956403, _956405] : [-(c_Nat_Onat_Onat__case(_956401, _956403, _956405, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _956403)], (10481 ^ _779308) ^ [_956433] : [class_Rings_Olinordered__semidom(_956433), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_956433), c_Groups_Ozero__class_Ozero(_956433)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956433), c_Groups_Oone__class_Oone(_956433)), c_Groups_Oone__class_Oone(_956433)))))], (10487 ^ _779308) ^ [_956548, _956550] : [class_Groups_Olinordered__ab__group__add(_956548), 10490 ^ _779308 : [(10491 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956548), c_Groups_Ozero__class_Ozero(_956548)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956548), _956550), _956550))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956548), c_Groups_Ozero__class_Ozero(_956548)), _956550)))], (10497 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956548), c_Groups_Ozero__class_Ozero(_956548)), _956550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956548), c_Groups_Ozero__class_Ozero(_956548)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956548), _956550), _956550))))]]], (10503 ^ _779308) ^ [_956831, _956833] : [class_Groups_Olinordered__ab__group__add(_956831), 10506 ^ _779308 : [(10507 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956831), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956831), _956833), _956833)), c_Groups_Ozero__class_Ozero(_956831))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956831), _956833), c_Groups_Ozero__class_Ozero(_956831))))], (10513 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956831), _956833), c_Groups_Ozero__class_Ozero(_956831))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956831), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956831), _956833), _956833)), c_Groups_Ozero__class_Ozero(_956831))))]]], (10519 ^ _779308) ^ [_957114, _957116, _957118] : [class_Groups_Oordered__comm__monoid__add(_957114), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957114), c_Groups_Ozero__class_Ozero(_957114)), _957116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957114), c_Groups_Ozero__class_Ozero(_957114)), _957118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957114), c_Groups_Ozero__class_Ozero(_957114)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957114), _957116), _957118))))], (10533 ^ _779308) ^ [_957369, _957371, _957373] : [class_Groups_Oordered__comm__monoid__add(_957369), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957369), c_Groups_Ozero__class_Ozero(_957369)), _957371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957369), c_Groups_Ozero__class_Ozero(_957369)), _957373)), 10544 ^ _779308 : [(10545 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957369), _957371), _957373) = c_Groups_Ozero__class_Ozero(_957369), 10548 ^ _779308 : [(10549 ^ _779308) ^ [] : [-(_957371 = c_Groups_Ozero__class_Ozero(_957369))], (10551 ^ _779308) ^ [] : [-(_957373 = c_Groups_Ozero__class_Ozero(_957369))]]], (10553 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957369), _957371), _957373) = c_Groups_Ozero__class_Ozero(_957369)), _957371 = c_Groups_Ozero__class_Ozero(_957369), _957373 = c_Groups_Ozero__class_Ozero(_957369)]]], (10563 ^ _779308) ^ [_957840, _957842, _957844, _957846] : [class_Groups_Oordered__comm__monoid__add(_957840), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957840), c_Groups_Ozero__class_Ozero(_957840)), _957842)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957840), _957844), _957846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957840), _957844), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957840), _957842), _957846))))], (10577 ^ _779308) ^ [_958093, _958095, _958097, _958099] : [class_Groups_Oordered__comm__monoid__add(_958093), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958093), c_Groups_Ozero__class_Ozero(_958093)), _958095)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958093), _958097), _958099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958093), _958097), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958093), _958099), _958095))))], (10591 ^ _779308) ^ [_958346, _958348, _958350] : [class_Groups_Oordered__comm__monoid__add(_958346), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958346), _958348), c_Groups_Ozero__class_Ozero(_958346))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958346), _958350), c_Groups_Ozero__class_Ozero(_958346))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_958346), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958346), _958348), _958350)), c_Groups_Ozero__class_Ozero(_958346))))], (10605 ^ _779308) ^ [_958601, _958603, _958605] : [class_Groups_Oordered__comm__monoid__add(_958601), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958601), _958603), c_Groups_Ozero__class_Ozero(_958601))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958601), _958605), c_Groups_Ozero__class_Ozero(_958601))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958601), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958601), _958603), _958605)), c_Groups_Ozero__class_Ozero(_958601))))], (10619 ^ _779308) ^ [_958856, _958858, _958860] : [class_Groups_Oordered__comm__monoid__add(_958856), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958856), c_Groups_Ozero__class_Ozero(_958856)), _958858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958856), c_Groups_Ozero__class_Ozero(_958856)), _958860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_958856), c_Groups_Ozero__class_Ozero(_958856)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958856), _958858), _958860))))], (10633 ^ _779308) ^ [_959111, _959113] : [class_Groups_Olinordered__ab__group__add(_959111), 10636 ^ _779308 : [(10637 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959111), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959111), _959113), _959113)), c_Groups_Ozero__class_Ozero(_959111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959111), _959113), c_Groups_Ozero__class_Ozero(_959111))))], (10643 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959111), _959113), c_Groups_Ozero__class_Ozero(_959111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959111), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959111), _959113), _959113)), c_Groups_Ozero__class_Ozero(_959111))))]]], (10649 ^ _779308) ^ [_959394, _959396] : [class_Groups_Olinordered__ab__group__add(_959394), 10652 ^ _779308 : [(10653 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959394), c_Groups_Ozero__class_Ozero(_959394)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959394), _959396), _959396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959394), c_Groups_Ozero__class_Ozero(_959394)), _959396)))], (10659 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959394), c_Groups_Ozero__class_Ozero(_959394)), _959396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959394), c_Groups_Ozero__class_Ozero(_959394)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959394), _959396), _959396))))]]], (10665 ^ _779308) ^ [_959677, _959679, _959681] : [class_Groups_Oordered__ab__group__add(_959677), 10668 ^ _779308 : [(10669 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959677), _959679), _959681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959677), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959677), _959679), _959681)), c_Groups_Ozero__class_Ozero(_959677))))], (10675 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959677), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959677), _959679), _959681)), c_Groups_Ozero__class_Ozero(_959677))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_959677), _959679), _959681)))]]], (10681 ^ _779308) ^ [_959960, _959962, _959964] : [class_Groups_Oordered__ab__group__add(_959960), 10684 ^ _779308 : [(10685 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959960), _959962), _959964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959960), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959960), _959962), _959964)), c_Groups_Ozero__class_Ozero(_959960))))], (10691 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959960), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959960), _959962), _959964)), c_Groups_Ozero__class_Ozero(_959960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_959960), _959962), _959964)))]]], (10697 ^ _779308) ^ [_960255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _960255)), -(_960255 = hAPP(c_Nat_OSuc, 10700 ^ [_960255]))], (10704 ^ _779308) ^ [_960346] : [10705 ^ _779308 : [(10706 ^ _779308) ^ [_960388] : [_960346 = hAPP(c_Nat_OSuc, _960388)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _960346)))], (10710 ^ _779308) ^ [_960458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960458), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_960458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10716 ^ _779308) ^ [_960539] : [_960539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960539), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (10722 ^ _779308) ^ [_960641, _960643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960641), hAPP(c_Nat_OSuc, _960643))), -(_960641 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10730 ^ _779308 : [(10731 ^ _779308) ^ [] : [-(_960641 = hAPP(c_Nat_OSuc, 10729 ^ [_960641, _960643]))], (10733 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 10729 ^ [_960641, _960643]), _960643)))]]], (10735 ^ _779308) ^ [_960821, _960823] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960821), hAPP(c_Nat_OSuc, _960823)))), 10736 ^ _779308 : [(10737 ^ _779308) ^ [] : [_960821 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10739 ^ _779308) ^ [_960909] : [_960821 = hAPP(c_Nat_OSuc, _960909), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _960909), _960823))]]], (10747 ^ _779308) ^ [_961058, _961060] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _961058), _961060), 10752 ^ _779308 : [(10753 ^ _779308) ^ [] : [-(_961058 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10755 ^ _779308) ^ [] : [-(_961060 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 10756 ^ _779308 : [(10757 ^ _779308) ^ [] : [-(_961058 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10759 ^ _779308) ^ [] : [-(_961060 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10761 ^ _779308) ^ [_961242, _961244] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _961242), _961244)), 10762 ^ _779308 : [(10763 ^ _779308) ^ [] : [_961242 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _961244 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10769 ^ _779308) ^ [] : [_961242 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _961244 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (10777 ^ _779308) ^ [_961483, _961485] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _961483), _961485) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10782 ^ _779308 : [(10783 ^ _779308) ^ [] : [-(_961483 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10785 ^ _779308) ^ [] : [-(_961485 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 10786 ^ _779308 : [(10787 ^ _779308) ^ [] : [-(_961483 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10789 ^ _779308) ^ [] : [-(_961485 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10791 ^ _779308) ^ [_961667, _961669] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _961667), _961669) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 10792 ^ _779308 : [(10793 ^ _779308) ^ [] : [_961667 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _961669 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10799 ^ _779308) ^ [] : [_961667 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _961669 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (10817 ^ _779308) ^ [_962018, _962020] : [10818 ^ _779308 : [(10819 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962018))], (10821 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962020))]], -(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), _962018), _962020))))], (10807 ^ _779308) ^ [_961908, _961910] : [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), _961908), _961910))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _961908))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _961910)))], (10825 ^ _779308) ^ [_962159] : [-(hAPP(c_Finite__Set_Ocard(_962159), c_Orderings_Obot__class_Obot(tc_fun(_962159, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10827 ^ _779308) ^ [_962188, _962190] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_962188), _962190))), -(hAPP(c_Finite__Set_Ocard(_962188), _962190) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10833 ^ _779308) ^ [_962248, _962250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962248), _962250))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962250), _962248)))], (10839 ^ _779308) ^ [_962347, _962349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _962349), _962347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962347), _962349))))], (10845 ^ _779308) ^ [_962452, _962454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962452)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _962454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962454), _962452)), _962454)))], (10855 ^ _779308) ^ [_962611, _962613] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962611), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _962611), _962613)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10857 ^ _779308) ^ [_962648, _962650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962648), _962650)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962648), _962650) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10863 ^ _779308) ^ [_962762, _962764] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962762), _962764) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962762), _962764)))], (10869 ^ _779308) ^ [_962857, _962859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _962857), _962859)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _962857), _962859) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10875 ^ _779308) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10877 ^ _779308) ^ [_962975, _962977, _962979, _962981, _962983, _962985, _962987] : [-(hBOOL(hAPP(hAPP(c_member(_962975), _962977), _962979))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_962975, _962981, _962983, _962985, _962979), _962987)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_962975, _962981, _962983, _962985, hAPP(hAPP(c_Set_Oinsert(_962975), _962977), _962979)), hAPP(hAPP(_962983, _962977), _962987))))], (10887 ^ _779308) ^ [_963189, _963191] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963189), hAPP(c_Nat_OSuc, _963191)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_COMBI(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963189), _963191)))], (10889 ^ _779308) ^ [_963234, _963236, _963238] : [class_Groups_Oordered__comm__monoid__add(_963234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963234), _963236), c_Groups_Ozero__class_Ozero(_963234))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963234), _963238), c_Groups_Ozero__class_Ozero(_963234))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963234), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963234), _963236), _963238)), c_Groups_Ozero__class_Ozero(_963234))))], (10903 ^ _779308) ^ [_963489, _963491, _963493] : [class_Groups_Oordered__comm__monoid__add(_963489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963489), _963491), c_Groups_Ozero__class_Ozero(_963489))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963489), _963493), c_Groups_Ozero__class_Ozero(_963489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963489), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963489), _963491), _963493)), c_Groups_Ozero__class_Ozero(_963489))))], (10917 ^ _779308) ^ [_963744, _963746, _963748, _963750] : [class_Groups_Oordered__comm__monoid__add(_963744), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963744), c_Groups_Ozero__class_Ozero(_963744)), _963746)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963744), _963748), _963750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963744), _963748), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963744), _963746), _963750))))], (10931 ^ _779308) ^ [_963997, _963999, _964001, _964003] : [class_Groups_Oordered__comm__monoid__add(_963997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963997), c_Groups_Ozero__class_Ozero(_963997)), _963999)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963997), _964001), _964003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963997), _964001), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963997), _963999), _964003))))], (10945 ^ _779308) ^ [_964250, _964252, _964254] : [class_Groups_Oordered__comm__monoid__add(_964250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964250), c_Groups_Ozero__class_Ozero(_964250)), _964252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964250), c_Groups_Ozero__class_Ozero(_964250)), _964254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964250), c_Groups_Ozero__class_Ozero(_964250)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964250), _964252), _964254))))], (10959 ^ _779308) ^ [_964505, _964507, _964509] : [class_Groups_Oordered__comm__monoid__add(_964505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964505), c_Groups_Ozero__class_Ozero(_964505)), _964507)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964505), c_Groups_Ozero__class_Ozero(_964505)), _964509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964505), c_Groups_Ozero__class_Ozero(_964505)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_964505), _964507), _964509))))], (10973 ^ _779308) ^ [_964760, _964762, _964764] : [class_Rings_Olinordered__idom(_964760), -(_964762 = _964764), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964760), _964762), _964764))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_964760), _964764), _964762)))], (10997 ^ _779308) ^ [_965065, _965067] : [10998 ^ _779308 : [(10999 ^ _779308) ^ [] : [_965067 = c_Orderings_Obot__class_Obot(tc_fun(_965065, tc_HOL_Obool))], (11001 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_965065), _965067)))]], -(hAPP(c_Finite__Set_Ocard(_965065), _965067) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10987 ^ _779308) ^ [_964910, _964912] : [hAPP(c_Finite__Set_Ocard(_964910), _964912) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_964912 = c_Orderings_Obot__class_Obot(tc_fun(_964910, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_964910), _964912))], (11005 ^ _779308) ^ [_965209, _965211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_965209), _965211))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_965209), _965211)))], (11011 ^ _779308) ^ [_965308, _965310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965308), hAPP(c_Nat_OSuc, _965310))), _965308)))], (11017 ^ _779308) ^ [_965417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _965417)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965417), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _965417)], (11039 ^ _779308) ^ [_965816, _965818, _965820] : [-(hBOOL(hAPP(_965816, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965818), _965820)))), 11042 ^ _779308 : [(11043 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965818), _965820)))], (11045 ^ _779308) ^ [] : [hBOOL(hAPP(_965816, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 11047 ^ _779308 : [(11048 ^ _779308) ^ [] : [-(_965818 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _965820), 11046 ^ [_965816, _965818, _965820]))], (11050 ^ _779308) ^ [] : [hBOOL(hAPP(_965816, 11046 ^ [_965816, _965818, _965820]))]]], (11023 ^ _779308) ^ [_965532, _965534, _965536] : [hBOOL(hAPP(_965532, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _965534), _965536))), 11026 ^ _779308 : [(11027 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965534), _965536)), -(hBOOL(hAPP(_965532, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11033 ^ _779308) ^ [_965717] : [_965534 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _965536), _965717), -(hBOOL(hAPP(_965532, _965717)))]]], (11070 ^ _779308) ^ [_966411, _966413, _966415] : [-(hBOOL(hAPP(_966411, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966413), _966415)))), 11073 ^ _779308 : [(11074 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _966413), _966415)))], (11076 ^ _779308) ^ [] : [hBOOL(hAPP(_966411, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 11078 ^ _779308 : [(11079 ^ _779308) ^ [] : [-(_966413 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _966415), 11077 ^ [_966411, _966413, _966415]))], (11081 ^ _779308) ^ [] : [hBOOL(hAPP(_966411, 11077 ^ [_966411, _966413, _966415]))]]], (11054 ^ _779308) ^ [_966119, _966121, _966123] : [hBOOL(hAPP(_966119, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _966121), _966123))), 11057 ^ _779308 : [(11058 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _966121), _966123)), -(hBOOL(hAPP(_966119, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11064 ^ _779308) ^ [_966310] : [_966121 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _966123), _966310), -(hBOOL(hAPP(_966119, _966310)))]]], (11085 ^ _779308) ^ [_966719, _966721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_966719), _966721))), 11088 ^ _779308 : [(11089 ^ _779308) ^ [] : [_966721 = c_Orderings_Obot__class_Obot(tc_fun(_966719, tc_HOL_Obool))], (11091 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_966719), _966721)))]]], (11093 ^ _779308) ^ [_966860, _966862] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_966860), _966862)))), -(_966862 = c_Orderings_Obot__class_Obot(tc_fun(_966860, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_966860), _966862))], (11103 ^ _779308) ^ [_967026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _967026)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _967026), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _967026)], (11109 ^ _779308) ^ [_967123, _967125] : [class_Rings_Olinordered__idom(_967123), 11112 ^ _779308 : [(11113 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967123), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967123), _967125), _967125)), c_Groups_Ozero__class_Ozero(_967123))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967123), _967125), c_Groups_Ozero__class_Ozero(_967123))))], (11119 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967123), _967125), c_Groups_Ozero__class_Ozero(_967123))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_967123), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967123), _967125), _967125)), c_Groups_Ozero__class_Ozero(_967123))))]]], (11125 ^ _779308) ^ [_967406, _967408, _967410, _967412, _967414] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_967406, _967406, _967408, _967410, _967412), _967414)), -(hBOOL(hAPP(hAPP(c_member(_967406), _967410), _967412))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_967406, _967408, hAPP(hAPP(c_Set_Oinsert(_967406), _967410), _967412)), _967414)))], (11135 ^ _779308) ^ [_967580, _967582, _967584] : [hAPP(c_Finite__Set_Ocard(_967580), _967582) = hAPP(c_Nat_OSuc, _967584), 11140 ^ _779308 : [(11141 ^ _779308) ^ [] : [-(_967582 = hAPP(hAPP(c_Set_Oinsert(_967580), 11138 ^ [_967580, _967582, _967584]), 11139 ^ [_967580, _967582, _967584]))], (11143 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_967580), 11138 ^ [_967580, _967582, _967584]), 11139 ^ [_967580, _967582, _967584]))], (11145 ^ _779308) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_967580), 11139 ^ [_967580, _967582, _967584]) = _967584)], (11147 ^ _779308) ^ [] : [_967584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(11139 ^ [_967580, _967582, _967584] = c_Orderings_Obot__class_Obot(tc_fun(_967580, tc_HOL_Obool)))]]], (11153 ^ _779308) ^ [_967998, _968000, _968002] : [-(hAPP(c_Finite__Set_Ocard(_967998), _968000) = hAPP(c_Nat_OSuc, _968002)), 11154 ^ _779308 : [(11155 ^ _779308) ^ [_968098, _968100] : [_968000 = hAPP(hAPP(c_Set_Oinsert(_967998), _968100), _968098), -(hBOOL(hAPP(hAPP(c_member(_967998), _968100), _968098))), hAPP(c_Finite__Set_Ocard(_967998), _968098) = _968002, 11166 ^ _779308 : [(11167 ^ _779308) ^ [] : [-(_968002 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11169 ^ _779308) ^ [] : [_968098 = c_Orderings_Obot__class_Obot(tc_fun(_967998, tc_HOL_Obool))]]]]], (11173 ^ _779308) ^ [_968450, _968452, _968454, _968456, _968458, _968460, _968462] : [c_Nitpick_Ofold__graph_H(_968450, _968452, _968454, _968456, _968458, hAPP(hAPP(_968454, _968460), _968462)), 11178 ^ _779308 : [(11179 ^ _779308) ^ [] : [-(_968458 = c_Orderings_Obot__class_Obot(tc_fun(_968450, tc_HOL_Obool)))], (11181 ^ _779308) ^ [] : [-(hAPP(hAPP(_968454, _968460), _968462) = _968456)]], 11184 ^ _779308 : [(11185 ^ _779308) ^ [] : [-(hAPP(hAPP(_968454, _968460), _968462) = hAPP(hAPP(_968454, 11182 ^ [_968450, _968452, _968454, _968456, _968458, _968460, _968462]), 11183 ^ [_968450, _968452, _968454, _968456, _968458, _968460, _968462]))], (11187 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_968450), 11182 ^ [_968450, _968452, _968454, _968456, _968458, _968460, _968462]), _968458)))], (11189 ^ _779308) ^ [] : [-(c_Nitpick_Ofold__graph_H(_968450, _968452, _968454, _968456, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968450, tc_HOL_Obool)), _968458), hAPP(hAPP(c_Set_Oinsert(_968450), 11182 ^ [_968450, _968452, _968454, _968456, _968458, _968460, _968462]), c_Orderings_Obot__class_Obot(tc_fun(_968450, tc_HOL_Obool)))), 11183 ^ [_968450, _968452, _968454, _968456, _968458, _968460, _968462]))]]], (11191 ^ _779308) ^ [_968887, _968889, _968891, _968893, _968895, _968897, _968899] : [-(c_Nitpick_Ofold__graph_H(_968887, _968889, _968891, _968893, _968895, hAPP(hAPP(_968891, _968897), _968899))), 11192 ^ _779308 : [(11193 ^ _779308) ^ [] : [_968895 = c_Orderings_Obot__class_Obot(tc_fun(_968887, tc_HOL_Obool)), hAPP(hAPP(_968891, _968897), _968899) = _968893], (11199 ^ _779308) ^ [_969116, _969118] : [hAPP(hAPP(_968891, _968897), _968899) = hAPP(hAPP(_968891, _969118), _969116), hBOOL(hAPP(hAPP(c_member(_968887), _969118), _968895)), c_Nitpick_Ofold__graph_H(_968887, _968889, _968891, _968893, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968887, tc_HOL_Obool)), _968895), hAPP(hAPP(c_Set_Oinsert(_968887), _969118), c_Orderings_Obot__class_Obot(tc_fun(_968887, tc_HOL_Obool)))), _969116)]]], (11211 ^ _779308) ^ [_969408, _969410] : [class_Rings_Ocomm__semiring__1(_969408), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969408), c_Groups_Ozero__class_Ozero(_969408)), _969410) = _969410)], (11217 ^ _779308) ^ [_969503, _969505] : [class_Rings_Ocomm__semiring__1(_969503), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969503), _969505), c_Groups_Ozero__class_Ozero(_969503)) = _969505)], (11223 ^ _779308) ^ [_969598, _969600, _969602] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_969598), 11226 ^ _779308 : [(11227 ^ _779308) ^ [] : [_969600 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969598), _969600), _969602), -(_969602 = c_Groups_Ozero__class_Ozero(_969598))], (11233 ^ _779308) ^ [] : [_969602 = c_Groups_Ozero__class_Ozero(_969598), -(_969600 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969598), _969600), _969602))]]], (11239 ^ _779308) ^ [_969839, _969841] : [class_Groups_Olinordered__ab__group__add(_969839), 11242 ^ _779308 : [(11243 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969839), _969841), _969841) = c_Groups_Ozero__class_Ozero(_969839), -(_969841 = c_Groups_Ozero__class_Ozero(_969839))], (11249 ^ _779308) ^ [] : [_969841 = c_Groups_Ozero__class_Ozero(_969839), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969839), _969841), _969841) = c_Groups_Ozero__class_Ozero(_969839))]]], (11255 ^ _779308) ^ [_970079, _970081] : [-(hBOOL(hAPP(_970079, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_970079, _970081)), 11263 ^ _779308 : [(11264 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 11262 ^ [_970079, _970081]), _970081)))], (11272 ^ _779308) ^ [] : [-(hBOOL(hAPP(_970079, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 11262 ^ [_970079, _970081]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (11266 ^ _779308) ^ [_970317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _970317), 11262 ^ [_970079, _970081])), hBOOL(hAPP(_970079, _970317))]]], (11274 ^ _779308) ^ [_970469, _970471] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_970469), _970471)), -(hAPP(c_Finite__Set_Ocard(_970469), _970471) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _970469, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _970469), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970471))], (11280 ^ _779308) ^ [_970602, _970604, _970606, _970608, _970610] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_970602, _970604, _970606), _970608), _970610), c_Orderings_Obot__class_Obot(tc_fun(_970604, tc_HOL_Obool))) = _970610)], (11282 ^ _779308) ^ [_970666, _970668, _970670] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_970666, _970668, c_Orderings_Obot__class_Obot(tc_fun(_970666, tc_HOL_Obool))), _970670))], (11284 ^ _779308) ^ [_970704, _970706, _970708, _970710] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_970704, _970706, _970708), _970710)), _970708 = c_Orderings_Obot__class_Obot(tc_fun(_970704, tc_HOL_Obool))], (11290 ^ _779308) ^ [_970808, _970810, _970812, _970814, _970816, _970818, _970820] : [c_Finite__Set_Ofolding__image__simple(_970808, _970810, _970812, _970814, _970816, _970818), hBOOL(hAPP(c_Finite__Set_Ofinite(_970810), _970820)), -(hAPP(_970818, _970820) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_970808, _970810, _970812), _970816), _970814), _970820))], (11300 ^ _779308) ^ [_971005, _971007, _971009, _971011, _971013] : [class_Rings_Ocomm__semiring__1(_971005), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971005), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971005), _971007), _971009)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971005), _971011), _971013)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971005), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971005), _971007), _971011)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971005), _971009), _971013)))], (11306 ^ _779308) ^ [_971182, _971184, _971186, _971188] : [class_Rings_Ocomm__semiring__1(_971182), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971182), _971184), _971186)), _971188) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971182), _971184), _971188)), _971186))], (11312 ^ _779308) ^ [_971325, _971327, _971329, _971331] : [class_Rings_Ocomm__semiring__1(_971325), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971325), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971325), _971327), _971329)), _971331) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971325), _971327), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971325), _971329), _971331)))], (11318 ^ _779308) ^ [_971468, _971470, _971472, _971474] : [class_Rings_Ocomm__semiring__1(_971468), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971468), _971470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971468), _971472), _971474)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971468), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971468), _971470), _971472)), _971474))], (11324 ^ _779308) ^ [_971611, _971613, _971615, _971617] : [class_Rings_Ocomm__semiring__1(_971611), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971611), _971613), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971611), _971615), _971617)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971611), _971615), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971611), _971613), _971617)))], (11330 ^ _779308) ^ [_971754, _971756, _971758] : [class_Rings_Ocomm__semiring__1(_971754), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971754), _971756), _971758) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971754), _971758), _971756))], (11336 ^ _779308) ^ [_971884, _971886, _971888, _971890] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_971884, _971886, hAPP(hAPP(c_Set_Oinsert(_971884), _971888), c_Orderings_Obot__class_Obot(tc_fun(_971884, tc_HOL_Obool)))), _971890)), -(_971888 = _971890)], (11342 ^ _779308) ^ [_971999, _972001, _972003, _972005] : [_972003 = _972005, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_971999, _972001, hAPP(hAPP(c_Set_Oinsert(_971999), _972003), c_Orderings_Obot__class_Obot(tc_fun(_971999, tc_HOL_Obool)))), _972005)))], (11348 ^ _779308) ^ [_972129, _972131] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_972129), _972131)), -(hAPP(c_Finite__Set_Ocard(_972129), _972131) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _972129, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _972129), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _972131))], (11354 ^ _779308) ^ [_972256, _972258] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_972256), _972258))), -(hAPP(c_Finite__Set_Ocard(_972256), _972258) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11360 ^ _779308) ^ [_972303, _972305] : [class_Rings_Olinordered__idom(_972303), hBOOL(hAPP(hAPP(c_member(_972303), _972305), c_Int_Oring__1__class_OInts(_972303))), 11367 ^ _779308 : [(11368 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972303), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972303), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972303), c_Groups_Oone__class_Oone(_972303)), _972305)), _972305)), c_Groups_Ozero__class_Ozero(_972303))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972303), _972305), c_Groups_Ozero__class_Ozero(_972303))))], (11374 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972303), _972305), c_Groups_Ozero__class_Ozero(_972303))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972303), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972303), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972303), c_Groups_Oone__class_Oone(_972303)), _972305)), _972305)), c_Groups_Ozero__class_Ozero(_972303))))]]], (11380 ^ _779308) ^ [_972710, _972712, _972714, _972716, _972718] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_972710, _972712, hAPP(hAPP(c_Set_Oinsert(_972710), _972714), _972716)), _972718)), 11385 ^ _779308 : [(11386 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_972710), _972714), _972716) = hAPP(hAPP(c_Set_Oinsert(_972710), 11383 ^ [_972710, _972712, _972714, _972716, _972718]), 11384 ^ [_972710, _972712, _972714, _972716, _972718]))], (11388 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_972710, _972710, _972712, 11383 ^ [_972710, _972712, _972714, _972716, _972718], 11384 ^ [_972710, _972712, _972714, _972716, _972718]), _972718)))], (11390 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_972710), 11383 ^ [_972710, _972712, _972714, _972716, _972718]), 11384 ^ [_972710, _972712, _972714, _972716, _972718]))]]], (11392 ^ _779308) ^ [_973101, _973103, _973105, _973107, _973109] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_973101, _973103, hAPP(hAPP(c_Set_Oinsert(_973101), _973105), _973107)), _973109))), 11393 ^ _779308 : [(11394 ^ _779308) ^ [_973205, _973207] : [hAPP(hAPP(c_Set_Oinsert(_973101), _973105), _973107) = hAPP(hAPP(c_Set_Oinsert(_973101), _973207), _973205), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_973101, _973101, _973103, _973207, _973205), _973109)), -(hBOOL(hAPP(hAPP(c_member(_973101), _973207), _973205)))]]], (11406 ^ _779308) ^ [_973462, _973464, _973466, _973468, _973470] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_973462, _973464, hAPP(hAPP(c_Set_Oinsert(_973462), _973466), _973468)), _973470)), 11411 ^ _779308 : [(11412 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_973462), _973466), _973468) = hAPP(hAPP(c_Set_Oinsert(_973462), 11409 ^ [_973462, _973464, _973466, _973468, _973470]), 11410 ^ [_973462, _973464, _973466, _973468, _973470]))], (11414 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_973462, _973462, _973464, 11409 ^ [_973462, _973464, _973466, _973468, _973470], 11410 ^ [_973462, _973464, _973466, _973468, _973470]), _973470)))], (11416 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_973462), 11409 ^ [_973462, _973464, _973466, _973468, _973470]), 11410 ^ [_973462, _973464, _973466, _973468, _973470]))]]], (11418 ^ _779308) ^ [_973855, _973857] : [class_Int_Oring__char__0(_973855), hBOOL(hAPP(hAPP(c_member(_973855), _973857), c_Int_Oring__1__class_OInts(_973855))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973855), c_Groups_Oone__class_Oone(_973855)), _973857)), _973857) = c_Groups_Ozero__class_Ozero(_973855)], (11428 ^ _779308) ^ [_974041, _974043, _974045, _974047, _974049] : [class_Groups_Oab__semigroup__mult(_974041), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_974041, _974041, c_Groups_Otimes__class_Otimes(_974041), _974043, _974045), _974047)), hBOOL(hAPP(hAPP(c_member(_974041), _974049), _974045)), -(hBOOL(hAPP(hAPP(c_member(_974041), _974043), _974045))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_974041, _974041, c_Groups_Otimes__class_Otimes(_974041), _974049, hAPP(hAPP(c_Set_Oinsert(_974041), _974043), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_974041, tc_HOL_Obool)), _974045), hAPP(hAPP(c_Set_Oinsert(_974041), _974049), c_Orderings_Obot__class_Obot(tc_fun(_974041, tc_HOL_Obool)))))), _974047)))], (11446 ^ _779308) ^ [_974385, _974387] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_974385), _974387)), 11452 ^ _779308 : [(11453 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_974385), 11451 ^ [_974385, _974387]), _974387)))], (11455 ^ _779308) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_974385), _974387) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11459 ^ _779308) ^ [_974585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _974585))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _974585) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _974585)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (11465 ^ _779308) ^ [_974700, _974702, _974704, _974706, _974708, _974710] : [class_Rings_Olinordered__semiring__1__strict(_974700), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974700), _974702), _974704)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974700), _974706), _974704)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974700), c_Groups_Ozero__class_Ozero(_974700)), _974708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974700), c_Groups_Ozero__class_Ozero(_974700)), _974710)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974700), _974708), _974710) = c_Groups_Oone__class_Oone(_974700), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974700), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974700), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974700), _974708), _974702)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974700), _974710), _974706))), _974704)))], (11491 ^ _779308) ^ [_975229, _975231, _975233, _975235, _975237, _975239] : [-(c_Nitpick_Opair__box_Opair__box__size(_975229, _975231, _975233, _975235, c_Nitpick_Opair__box_OPairBox(_975229, _975231, _975237, _975239)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_975233, _975237)), hAPP(_975235, _975239))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11493 ^ _779308) ^ [_975291, _975293] : [class_Int_Onumber__ring(_975291), -(hBOOL(hAPP(hAPP(c_member(_975291), hAPP(c_Int_Onumber__class_Onumber__of(_975291), _975293)), c_Int_Oring__1__class_OInts(_975291))))], (11499 ^ _779308) ^ [_975394, _975396, _975398, _975400, _975402] : [class_Rings_Ocomm__semiring__1(_975394), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975394), _975396), _975398)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975394), _975400), _975402)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975394), _975396), _975400)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975394), _975398), _975402)))], (11505 ^ _779308) ^ [_975571, _975573, _975575, _975577, _975579] : [class_Rings_Ocomm__semiring__1(_975571), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975571), _975573), _975575)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975571), _975577), _975579)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975571), _975577), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975571), _975573), _975575)), _975579)))], (11511 ^ _779308) ^ [_975748, _975750, _975752, _975754, _975756] : [class_Rings_Ocomm__semiring__1(_975748), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975748), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975748), _975750), _975752)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975748), _975754), _975756)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975748), _975750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975748), _975752), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975748), _975754), _975756))))], (11517 ^ _779308) ^ [_975925, _975927, _975929, _975931] : [class_Rings_Ocomm__semiring__1(_975925), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975925), _975927), _975929)), _975931) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975925), _975927), _975931)), _975929))], (11523 ^ _779308) ^ [_976068, _976070, _976072, _976074] : [class_Rings_Ocomm__semiring__1(_976068), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976068), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976068), _976070), _976072)), _976074) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976068), _976070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976068), _976072), _976074)))], (11529 ^ _779308) ^ [_976211, _976213, _976215, _976217] : [class_Int_Onumber__ring(_976211), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976211), hAPP(c_Int_Onumber__class_Onumber__of(_976211), _976213)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976211), hAPP(c_Int_Onumber__class_Onumber__of(_976211), _976215)), _976217)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976211), hAPP(c_Int_Onumber__class_Onumber__of(_976211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _976213), _976215))), _976217))], (11535 ^ _779308) ^ [_976380, _976382, _976384] : [class_Int_Onumber__ring(_976380), class_Int_Oring__char__0(_976380), 11542 ^ _779308 : [(11543 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_976380), _976382) = hAPP(c_Int_Onumber__class_Onumber__of(_976380), _976384), -(_976382 = _976384)], (11549 ^ _779308) ^ [] : [_976382 = _976384, -(hAPP(c_Int_Onumber__class_Onumber__of(_976380), _976382) = hAPP(c_Int_Onumber__class_Onumber__of(_976380), _976384))]]], (11555 ^ _779308) ^ [_976675, _976677, _976679] : [class_Int_Onumber__ring(_976675), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976675), hAPP(c_Int_Onumber__class_Onumber__of(_976675), _976677)), hAPP(c_Int_Onumber__class_Onumber__of(_976675), _976679)) = hAPP(c_Int_Onumber__class_Onumber__of(_976675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _976677), _976679)))], (11561 ^ _779308) ^ [_976810, _976812, _976814] : [class_Int_Onumber(_976810), 11564 ^ _779308 : [(11565 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_976810), _976812) = _976814, -(_976814 = hAPP(c_Int_Onumber__class_Onumber__of(_976810), _976812))], (11571 ^ _779308) ^ [] : [_976814 = hAPP(c_Int_Onumber__class_Onumber__of(_976810), _976812), -(hAPP(c_Int_Onumber__class_Onumber__of(_976810), _976812) = _976814)]]], (11577 ^ _779308) ^ [_977051, _977053, _977055, _977057] : [class_Rings_Ocomm__semiring__1(_977051), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977051), _977053), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977051), _977055), _977057)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977051), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977051), _977053), _977055)), _977057))], (11583 ^ _779308) ^ [_977194, _977196, _977198, _977200] : [class_Rings_Ocomm__semiring__1(_977194), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977194), _977196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977194), _977198), _977200)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977194), _977198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977194), _977196), _977200)))], (11589 ^ _779308) ^ [_977337, _977339, _977341] : [class_Rings_Ocomm__semiring__1(_977337), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977337), _977339), _977341) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977337), _977341), _977339))], (11595 ^ _779308) ^ [_977446, _977448, _977450] : [class_Int_Onumber__ring(_977446), -(hAPP(c_Int_Onumber__class_Onumber__of(_977446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _977448), _977450)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977446), hAPP(c_Int_Onumber__class_Onumber__of(_977446), _977448)), hAPP(c_Int_Onumber__class_Onumber__of(_977446), _977450)))], (11601 ^ _779308) ^ [_977581, _977583, _977585, _977587] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977581), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_977581), _977583), _977585)), hAPP(c_Int_Onumber__class_Onumber__of(_977581), _977587)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_977581), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977581), _977583), hAPP(c_Int_Onumber__class_Onumber__of(_977581), _977587))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977581), _977585), hAPP(c_Int_Onumber__class_Onumber__of(_977581), _977587)))), class_Int_Onumber(_977581), class_Rings_Oring(_977581)], (11611 ^ _779308) ^ [_977824, _977826, _977828, _977830] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977824), hAPP(c_Int_Onumber__class_Onumber__of(_977824), _977826)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_977824), _977828), _977830)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_977824), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977824), hAPP(c_Int_Onumber__class_Onumber__of(_977824), _977826)), _977828)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977824), hAPP(c_Int_Onumber__class_Onumber__of(_977824), _977826)), _977830))), class_Int_Onumber(_977824), class_Rings_Oring(_977824)], (11621 ^ _779308) ^ [_978067, _978069, _978071, _978073] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978067), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978067), _978069), _978071)), hAPP(c_Int_Onumber__class_Onumber__of(_978067), _978073)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978067), _978069), hAPP(c_Int_Onumber__class_Onumber__of(_978067), _978073))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978067), _978071), hAPP(c_Int_Onumber__class_Onumber__of(_978067), _978073)))), class_Int_Onumber(_978067), class_Rings_Osemiring(_978067)], (11631 ^ _779308) ^ [_978310, _978312, _978314, _978316] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978310), hAPP(c_Int_Onumber__class_Onumber__of(_978310), _978312)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978310), _978314), _978316)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978310), hAPP(c_Int_Onumber__class_Onumber__of(_978310), _978312)), _978314)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978310), hAPP(c_Int_Onumber__class_Onumber__of(_978310), _978312)), _978316))), class_Int_Onumber(_978310), class_Rings_Osemiring(_978310)], (11641 ^ _779308) ^ [_978553, _978555, _978557, _978559] : [class_Groups_Oab__semigroup__mult(_978553), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978553), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978553), _978555), _978557)), _978559) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978553), _978555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978553), _978557), _978559)))], (11647 ^ _779308) ^ [_978696, _978698, _978700] : [class_Lattices_Oab__semigroup__idem__mult(_978696), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978696), _978698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978696), _978698), _978700)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978696), _978698), _978700))], (11653 ^ _779308) ^ [_978821, _978823] : [class_Lattices_Oab__semigroup__idem__mult(_978821), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978821), _978823), _978823) = _978823)], (11659 ^ _779308) ^ [_978912, _978914] : [class_Lattices_Oab__semigroup__idem__mult(_978912), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978912), _978914), _978914) = _978914)], (11665 ^ _779308) ^ [_979030, _979032, _979034, _979036, _979038, _979040] : [c_Nitpick_Opair__box_OPairBox(_979030, _979032, _979034, _979036) = c_Nitpick_Opair__box_OPairBox(_979030, _979032, _979038, _979040), 11668 ^ _779308 : [(11669 ^ _779308) ^ [] : [-(_979034 = _979038)], (11671 ^ _779308) ^ [] : [-(_979036 = _979040)]]], (11673 ^ _779308) ^ [_979157, _979159, _979161, _979163, _979165, _979167] : [-(c_Nitpick_Opair__box_OPairBox(_979157, _979159, _979161, _979163) = c_Nitpick_Opair__box_OPairBox(_979157, _979159, _979165, _979167)), _979161 = _979165, _979163 = _979167], (11683 ^ _779308) ^ [_979324, _979326, _979328] : [class_Rings_Oring__1(_979324), hBOOL(hAPP(hAPP(c_member(_979324), _979326), c_Int_Oring__1__class_OInts(_979324))), hBOOL(hAPP(hAPP(c_member(_979324), _979328), c_Int_Oring__1__class_OInts(_979324))), -(hBOOL(hAPP(hAPP(c_member(_979324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979324), _979326), _979328)), c_Int_Oring__1__class_OInts(_979324))))], (11697 ^ _779308) ^ [_979579, _979581, _979583] : [class_Int_Onumber__ring(_979579), class_Rings_Olinordered__idom(_979579), 11704 ^ _779308 : [(11705 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979579), hAPP(c_Int_Onumber__class_Onumber__of(_979579), _979581)), hAPP(c_Int_Onumber__class_Onumber__of(_979579), _979583))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _979581), _979583)))], (11711 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _979581), _979583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979579), hAPP(c_Int_Onumber__class_Onumber__of(_979579), _979581)), hAPP(c_Int_Onumber__class_Onumber__of(_979579), _979583))))]]], (11717 ^ _779308) ^ [_979910, _979912, _979914] : [class_Int_Onumber__ring(_979910), class_Rings_Olinordered__idom(_979910), 11724 ^ _779308 : [(11725 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979910), hAPP(c_Int_Onumber__class_Onumber__of(_979910), _979912)), hAPP(c_Int_Onumber__class_Onumber__of(_979910), _979914))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _979912), _979914)))], (11731 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _979912), _979914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979910), hAPP(c_Int_Onumber__class_Onumber__of(_979910), _979912)), hAPP(c_Int_Onumber__class_Onumber__of(_979910), _979914))))]]], (11737 ^ _779308) ^ [_980241, _980243, _980245] : [class_Int_Onumber__ring(_980241), -(hAPP(c_Int_Onumber__class_Onumber__of(_980241), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _980243), _980245)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980241), hAPP(c_Int_Onumber__class_Onumber__of(_980241), _980243)), hAPP(c_Int_Onumber__class_Onumber__of(_980241), _980245)))], (11743 ^ _779308) ^ [_980376, _980378, _980380] : [class_Int_Onumber__ring(_980376), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980376), hAPP(c_Int_Onumber__class_Onumber__of(_980376), _980378)), hAPP(c_Int_Onumber__class_Onumber__of(_980376), _980380)) = hAPP(c_Int_Onumber__class_Onumber__of(_980376), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _980378), _980380)))], (11749 ^ _779308) ^ [_980511, _980513, _980515, _980517] : [class_Int_Onumber__ring(_980511), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980511), hAPP(c_Int_Onumber__class_Onumber__of(_980511), _980513)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980511), hAPP(c_Int_Onumber__class_Onumber__of(_980511), _980515)), _980517)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980511), hAPP(c_Int_Onumber__class_Onumber__of(_980511), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _980513), _980515))), _980517))], (11755 ^ _779308) ^ [_980680, _980682, _980684] : [class_Int_Onumber__ring(_980680), -(hAPP(c_Int_Onumber__class_Onumber__of(_980680), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _980682), _980684)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_980680), hAPP(c_Int_Onumber__class_Onumber__of(_980680), _980682)), hAPP(c_Int_Onumber__class_Onumber__of(_980680), _980684)))], (11761 ^ _779308) ^ [_980815, _980817] : [class_Rings_Omult__zero(_980815), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980815), c_Groups_Ozero__class_Ozero(_980815)), _980817) = c_Groups_Ozero__class_Ozero(_980815))], (11767 ^ _779308) ^ [_980914, _980916] : [class_Rings_Omult__zero(_980914), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980914), _980916), c_Groups_Ozero__class_Ozero(_980914)) = c_Groups_Ozero__class_Ozero(_980914))], (11773 ^ _779308) ^ [_981013, _981015, _981017] : [class_Rings_Oring__no__zero__divisors(_981013), 11776 ^ _779308 : [(11787 ^ _779308) ^ [] : [11788 ^ _779308 : [(11789 ^ _779308) ^ [] : [_981015 = c_Groups_Ozero__class_Ozero(_981013)], (11791 ^ _779308) ^ [] : [_981017 = c_Groups_Ozero__class_Ozero(_981013)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981013), _981015), _981017) = c_Groups_Ozero__class_Ozero(_981013))], (11777 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981013), _981015), _981017) = c_Groups_Ozero__class_Ozero(_981013), -(_981015 = c_Groups_Ozero__class_Ozero(_981013)), -(_981017 = c_Groups_Ozero__class_Ozero(_981013))]]], (11795 ^ _779308) ^ [_981311, _981313, _981315] : [class_Rings_Ono__zero__divisors(_981311), -(_981313 = c_Groups_Ozero__class_Ozero(_981311)), -(_981315 = c_Groups_Ozero__class_Ozero(_981311)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981311), _981313), _981315) = c_Groups_Ozero__class_Ozero(_981311)], (11809 ^ _779308) ^ [_981531, _981533, _981535] : [class_Rings_Ono__zero__divisors(_981531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981531), _981533), _981535) = c_Groups_Ozero__class_Ozero(_981531), -(_981533 = c_Groups_Ozero__class_Ozero(_981531)), -(_981535 = c_Groups_Ozero__class_Ozero(_981531))], (11823 ^ _779308) ^ [_981703, _981705] : [class_Rings_Ocomm__semiring__1(_981703), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981703), c_Groups_Ozero__class_Ozero(_981703)), _981705) = c_Groups_Ozero__class_Ozero(_981703))], (11829 ^ _779308) ^ [_981802, _981804] : [class_Rings_Ocomm__semiring__1(_981802), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981802), _981804), c_Groups_Ozero__class_Ozero(_981802)) = c_Groups_Ozero__class_Ozero(_981802))], (11835 ^ _779308) ^ [_981901, _981903, _981905, _981907] : [class_Rings_Ocomm__semiring(_981901), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981901), _981903), _981905)), _981907) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981901), _981903), _981907)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981901), _981905), _981907)))], (11841 ^ _779308) ^ [_982060, _982062, _982064, _982066, _982068] : [class_Rings_Osemiring(_982060), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982060), _982062), _982064)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982060), _982066), _982064)), _982068)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982060), _982062), _982066)), _982064)), _982068))], (11847 ^ _779308) ^ [_982253, _982255, _982257, _982259] : [class_Rings_Ocomm__semiring__1(_982253), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982253), _982255), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982253), _982257), _982259)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982253), _982255), _982257)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982253), _982255), _982259)))], (11853 ^ _779308) ^ [_982412, _982414, _982416, _982418, _982420] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_982412), 11856 ^ _779308 : [(11867 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982412), _982414), _982418)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982412), _982416), _982420)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982412), _982414), _982420)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982412), _982416), _982418))), 11870 ^ _779308 : [(11871 ^ _779308) ^ [] : [_982414 = _982416], (11873 ^ _779308) ^ [] : [_982418 = _982420]]], (11857 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982412), _982414), _982418)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982412), _982416), _982420)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982412), _982414), _982420)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982412), _982416), _982418)), -(_982414 = _982416), -(_982418 = _982420)]]], (11875 ^ _779308) ^ [_982830, _982832, _982834, _982836] : [class_Rings_Ocomm__semiring__1(_982830), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982830), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982830), _982832), _982834)), _982836) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982830), _982832), _982836)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982830), _982834), _982836)))], (11881 ^ _779308) ^ [_982989, _982991, _982993, _982995] : [class_Rings_Ocomm__semiring__1(_982989), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982989), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982989), _982991), _982993)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982989), _982995), _982993)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982989), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982989), _982991), _982995)), _982993))], (11887 ^ _779308) ^ [_983148, _983150, _983152, _983154, _983156] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_983148), 11890 ^ _779308 : [(11901 ^ _779308) ^ [] : [11902 ^ _779308 : [(11903 ^ _779308) ^ [] : [_983150 = _983154], (11905 ^ _779308) ^ [] : [_983152 = _983156]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983148), _983150), _983152)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983148), _983154), _983156)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983148), _983150), _983156)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983148), _983154), _983152)))], (11891 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983148), _983150), _983152)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983148), _983154), _983156)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_983148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983148), _983150), _983156)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983148), _983154), _983152)), -(_983150 = _983154), -(_983152 = _983156)]]], (11909 ^ _779308) ^ [_983560, _983562] : [class_Groups_Ocomm__monoid__mult(_983560), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983560), _983562), c_Groups_Oone__class_Oone(_983560)) = _983562)], (11915 ^ _779308) ^ [_983655, _983657] : [class_Groups_Omonoid__mult(_983655), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983655), _983657), c_Groups_Oone__class_Oone(_983655)) = _983657)], (11921 ^ _779308) ^ [_983750, _983752] : [class_Groups_Ocomm__monoid__mult(_983750), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983750), c_Groups_Oone__class_Oone(_983750)), _983752) = _983752)], (11927 ^ _779308) ^ [_983845, _983847] : [class_Groups_Omonoid__mult(_983845), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983845), c_Groups_Oone__class_Oone(_983845)), _983847) = _983847)], (11933 ^ _779308) ^ [_983940, _983942] : [class_Rings_Ocomm__semiring__1(_983940), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983940), c_Groups_Oone__class_Oone(_983940)), _983942) = _983942)], (11939 ^ _779308) ^ [_984035, _984037] : [class_Rings_Ocomm__semiring__1(_984035), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984035), _984037), c_Groups_Oone__class_Oone(_984035)) = _984037)], (11955 ^ _779308) ^ [_984260, _984262, _984264] : [11956 ^ _779308 : [(11957 ^ _779308) ^ [] : [_984260 = _984264], (11959 ^ _779308) ^ [] : [_984262 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984260), _984262) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984264), _984262))], (11945 ^ _779308) ^ [_984148, _984150, _984152] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984148), _984150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984152), _984150), -(_984148 = _984152), -(_984150 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11973 ^ _779308) ^ [_984533, _984535, _984537] : [11974 ^ _779308 : [(11975 ^ _779308) ^ [] : [_984535 = _984537], (11977 ^ _779308) ^ [] : [_984533 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984533), _984535) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984533), _984537))], (11963 ^ _779308) ^ [_984421, _984423, _984425] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984421), _984423) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984421), _984425), -(_984423 = _984425), -(_984421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11991 ^ _779308) ^ [_984789, _984791] : [11992 ^ _779308 : [(11993 ^ _779308) ^ [] : [_984789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11995 ^ _779308) ^ [] : [_984791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984789), _984791) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11981 ^ _779308) ^ [_984691, _984693] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984691), _984693) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_984691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_984693 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11999 ^ _779308) ^ [_984918] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _984918), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12001 ^ _779308) ^ [_984947] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _984947) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12003 ^ _779308) ^ [_984991, _984993, _984995] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _984991)), _984993) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _984991)), _984995), -(_984993 = _984995)], (12009 ^ _779308) ^ [_985102, _985104, _985106] : [_985104 = _985106, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985102)), _985104) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _985102)), _985106))], (12015 ^ _779308) ^ [_985219, _985221, _985223] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985219), _985221)), _985223) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985219), _985223)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985221), _985223)))], (12017 ^ _779308) ^ [_985276, _985278, _985280] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985276), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _985278), _985280)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985276), _985278)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985276), _985280)))], (12019 ^ _779308) ^ [_985333, _985335, _985337, _985339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985333), _985335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985337), _985339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985333), _985337)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985335), _985339))))], (12029 ^ _779308) ^ [_985524, _985526, _985528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985524), _985526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985528), _985524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985528), _985526))))], (12035 ^ _779308) ^ [_985647, _985649, _985651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985647), _985649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985647), _985651)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985649), _985651))))], (12041 ^ _779308) ^ [_985770] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985770), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985770), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985770), _985770)))))], (12043 ^ _779308) ^ [_985810] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _985810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985810), _985810))))], (12045 ^ _779308) ^ [_985844, _985846, _985848] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _985844), _985846)), _985848) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985844), _985848)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985846), _985848)))], (12047 ^ _779308) ^ [_985901, _985903, _985905] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985901), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _985903), _985905)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985901), _985903)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985901), _985905)))], (12049 ^ _779308) ^ [_985973, _985975] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _985973), _985975) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 12052 ^ _779308 : [(12053 ^ _779308) ^ [] : [-(_985973 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12055 ^ _779308) ^ [] : [-(_985975 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (12057 ^ _779308) ^ [_986084, _986086] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986084), _986086) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _986084 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _986086 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12067 ^ _779308) ^ [_986227] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986227), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _986227)], (12069 ^ _779308) ^ [_986271, _986273] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986271), _986273), 12072 ^ _779308 : [(12073 ^ _779308) ^ [] : [-(_986271 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (12075 ^ _779308) ^ [] : [-(_986273 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (12077 ^ _779308) ^ [_986382, _986384] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _986382), _986384)), _986382 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _986384 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (12087 ^ _779308) ^ [_986525] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _986525) = _986525)], (12089 ^ _779308) ^ [_986551] : [class_Lattices_Oab__semigroup__idem__mult(_986551), -(c_Finite__Set_Ofun__left__comm__idem(_986551, _986551, c_Groups_Otimes__class_Otimes(_986551)))], (12095 ^ _779308) ^ [_986630, _986632, _986634] : [class_Int_Onumber(_986630), class_Orderings_Olinorder(_986630), 12102 ^ _779308 : [(12103 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986630), hAPP(c_Int_Onumber__class_Onumber__of(_986630), _986632)), hAPP(c_Int_Onumber__class_Onumber__of(_986630), _986634))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986630), hAPP(c_Int_Onumber__class_Onumber__of(_986630), _986634)), hAPP(c_Int_Onumber__class_Onumber__of(_986630), _986632)))], (12109 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986630), hAPP(c_Int_Onumber__class_Onumber__of(_986630), _986634)), hAPP(c_Int_Onumber__class_Onumber__of(_986630), _986632)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_986630), hAPP(c_Int_Onumber__class_Onumber__of(_986630), _986632)), hAPP(c_Int_Onumber__class_Onumber__of(_986630), _986634))))]]], (12115 ^ _779308) ^ [_986957, _986959, _986961, _986963] : [class_Int_Onumber__ring(_986957), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_986957), hAPP(c_Int_Onumber__class_Onumber__of(_986957), _986959)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_986957), hAPP(c_Int_Onumber__class_Onumber__of(_986957), _986961)), _986963)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_986957), hAPP(c_Int_Onumber__class_Onumber__of(_986957), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _986959), _986961))), _986963))], (12121 ^ _779308) ^ [_987126, _987128, _987130] : [class_Rings_Oordered__cancel__semiring(_987126), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987126), _987128), _987130)), c_Groups_Ozero__class_Ozero(_987126)))), 12126 ^ _779308 : [(12127 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987126), c_Groups_Ozero__class_Ozero(_987126)), _987128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987126), _987130), c_Groups_Ozero__class_Ozero(_987126)))], (12133 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987126), _987128), c_Groups_Ozero__class_Ozero(_987126))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987126), c_Groups_Ozero__class_Ozero(_987126)), _987130))]]], (12141 ^ _779308) ^ [_987502, _987504, _987506] : [class_Rings_Oordered__ring(_987502), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987502), c_Groups_Ozero__class_Ozero(_987502)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987502), _987504), _987506)))), 12146 ^ _779308 : [(12147 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987502), c_Groups_Ozero__class_Ozero(_987502)), _987504)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987502), c_Groups_Ozero__class_Ozero(_987502)), _987506))], (12153 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987502), _987504), c_Groups_Ozero__class_Ozero(_987502))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987502), _987506), c_Groups_Ozero__class_Ozero(_987502)))]]], (12161 ^ _779308) ^ [_987878, _987880, _987882, _987884, _987886] : [class_Rings_Oordered__semiring(_987878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987878), _987880), _987882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987878), _987884), _987886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987878), c_Groups_Ozero__class_Ozero(_987878)), _987882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987878), c_Groups_Ozero__class_Ozero(_987878)), _987884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987878), _987880), _987884)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987878), _987882), _987886))))], (12183 ^ _779308) ^ [_988301, _988303, _988305, _988307, _988309] : [class_Rings_Oordered__semiring(_988301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988301), _988303), _988305)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988301), _988307), _988309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988301), c_Groups_Ozero__class_Ozero(_988301)), _988303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988301), c_Groups_Ozero__class_Ozero(_988301)), _988307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988301), _988303), _988307)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988301), _988305), _988309))))], (12205 ^ _779308) ^ [_988724, _988726, _988728, _988730] : [class_Rings_Oordered__ring(_988724), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988724), _988726), _988728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988724), _988730), c_Groups_Ozero__class_Ozero(_988724))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988724), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988724), _988730), _988728)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988724), _988730), _988726))))], (12219 ^ _779308) ^ [_988993, _988995, _988997, _988999] : [class_Rings_Oordered__ring(_988993), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988993), _988995), _988997)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988993), _988999), c_Groups_Ozero__class_Ozero(_988993))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988993), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988993), _988997), _988999)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_988993), _988995), _988999))))], (12233 ^ _779308) ^ [_989262, _989264, _989266, _989268] : [class_Rings_Oordered__comm__semiring(_989262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989262), _989264), _989266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989262), c_Groups_Ozero__class_Ozero(_989262)), _989268)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989262), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989262), _989268), _989264)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989262), _989268), _989266))))], (12247 ^ _779308) ^ [_989531, _989533, _989535, _989537] : [class_Rings_Oordered__semiring(_989531), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989531), _989533), _989535)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989531), c_Groups_Ozero__class_Ozero(_989531)), _989537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989531), _989537), _989533)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989531), _989537), _989535))))], (12261 ^ _779308) ^ [_989800, _989802, _989804, _989806] : [class_Rings_Oordered__semiring(_989800), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989800), _989802), _989804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989800), c_Groups_Ozero__class_Ozero(_989800)), _989806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989800), _989802), _989806)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_989800), _989804), _989806))))], (12275 ^ _779308) ^ [_990069, _990071, _990073] : 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996525), _996527), _996531)))), 12646 ^ _779308 : [(12647 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996525), c_Groups_Ozero__class_Ozero(_996525)), _996527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996525), _996529), _996531))], (12653 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996525), _996527), c_Groups_Ozero__class_Ozero(_996525))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996525), _996531), _996529))]]]]], (12661 ^ _779308) ^ [_997131, _997133, _997135, _997137] : [class_Rings_Olinordered__ring__strict(_997131), 12664 ^ _779308 : [(12665 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997131), _997133), _997135)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997131), _997137), _997135))), 12670 ^ _779308 : [(12671 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997131), c_Groups_Ozero__class_Ozero(_997131)), _997135)))], (12673 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997131), _997133), _997137)))]], 12674 ^ _779308 : [(12675 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997131), _997135), c_Groups_Ozero__class_Ozero(_997131))))], (12677 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997131), _997137), _997133)))]]], (12679 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997131), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997131), _997133), _997135)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997131), _997137), _997135)))), 12680 ^ _779308 : [(12681 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997131), c_Groups_Ozero__class_Ozero(_997131)), _997135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997131), _997133), _997137))], (12687 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997131), _997135), c_Groups_Ozero__class_Ozero(_997131))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997131), _997137), _997133))]]]]], (12695 ^ _779308) ^ [_997737, _997739] : [class_Rings_Olinordered__ring(_997737), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997737), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997737), _997739), _997739)), c_Groups_Ozero__class_Ozero(_997737)))], (12701 ^ _779308) ^ [_997847, _997849, _997851] : [class_Rings_Olinordered__ring__strict(_997847), 12704 ^ _779308 : [(12705 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997847), _997849), _997849)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997847), _997851), _997851)) = c_Groups_Ozero__class_Ozero(_997847), 12708 ^ _779308 : [(12709 ^ _779308) ^ [] : [-(_997849 = c_Groups_Ozero__class_Ozero(_997847))], (12711 ^ _779308) ^ [] : [-(_997851 = c_Groups_Ozero__class_Ozero(_997847))]]], (12713 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997847), _997849), _997849)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997847), _997851), _997851)) = c_Groups_Ozero__class_Ozero(_997847)), _997849 = c_Groups_Ozero__class_Ozero(_997847), _997851 = c_Groups_Ozero__class_Ozero(_997847)]]], (12723 ^ _779308) ^ [_998222, _998224, _998226, _998228, _998230, _998232] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_998222), -(_998224 = c_Groups_Ozero__class_Ozero(_998222)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998222), _998226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998222), _998224), _998230)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998222), _998228), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998222), _998224), _998232)), _998226 = _998228, -(_998230 = _998232)], (12741 ^ _779308) ^ [_998560, _998562, _998564] : [class_Rings_Olinordered__semidom(_998560), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998560), c_Groups_Oone__class_Oone(_998560)), _998562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998560), c_Groups_Oone__class_Oone(_998560)), _998564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998560), c_Groups_Oone__class_Oone(_998560)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998560), _998562), _998564))))], (12755 ^ _779308) ^ [_998815, _998817, _998819, _998821, _998823, _998825] : [class_Rings_Oring(_998815), 12758 ^ _779308 : [(12759 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998815), _998817), _998819)), _998821) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998815), _998823), _998819)), _998825), -(_998821 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998815), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_998815), _998823), _998817)), _998819)), _998825))], (12765 ^ _779308) ^ [] : [_998821 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998815), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_998815), _998823), _998817)), _998819)), _998825), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998815), _998817), _998819)), _998821) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998815), _998823), _998819)), _998825))]]], (12771 ^ _779308) ^ [_999212, _999214, _999216, _999218, _999220, _999222] : [class_Rings_Oring(_999212), 12774 ^ _779308 : [(12775 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999212), _999214), _999216)), _999218) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999212), _999220), _999216)), _999222), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999212), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_999212), _999214), _999220)), _999216)), _999218) = _999222)], (12781 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999212), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_999212), _999214), _999220)), _999216)), _999218) = _999222, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999212), _999214), _999216)), _999218) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999212), _999220), _999216)), _999222))]]], (12787 ^ _779308) ^ [_999609, _999611, _999613] : [class_Rings_Ocomm__semiring__1(_999609), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999609), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999609), _999611), _999613)), _999613) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999609), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999609), _999611), c_Groups_Oone__class_Oone(_999609))), _999613))], (12793 ^ _779308) ^ [_999754, _999756, _999758] : [class_Rings_Ocomm__semiring__1(_999754), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999754), _999756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999754), _999758), _999756)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999754), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999754), _999758), c_Groups_Oone__class_Oone(_999754))), _999756))], (12799 ^ _779308) ^ [_999899, _999901] : [class_Rings_Ocomm__semiring__1(_999899), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999899), _999901), _999901) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999899), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999899), c_Groups_Oone__class_Oone(_999899)), c_Groups_Oone__class_Oone(_999899))), _999901))], (12805 ^ _779308) ^ [_1000045, _1000047] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000045), _1000047) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 12808 ^ _779308 : [(12809 ^ _779308) ^ [] : [-(_1000045 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12811 ^ _779308) ^ [] : [-(_1000047 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (12813 ^ _779308) ^ [_1000156, _1000158] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000156), _1000158) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1000156 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1000158 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12823 ^ _779308) ^ [_1000299, _1000301, _1000303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000299), _1000301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1000303)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000303), _1000299)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000303), _1000301))))], (12833 ^ _779308) ^ [_1000480, _1000482, _1000484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000480), _1000482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1000484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000480), _1000484)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000482), _1000484))))], (12843 ^ _779308) ^ [_1000679, _1000681, _1000683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000679), _1000681)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000683), _1000681))), 12846 ^ _779308 : [(12847 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1000681)))], (12849 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000679), _1000683)))]]], (12851 ^ _779308) ^ [_1000828, _1000830, _1000832] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000828), _1000830)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1000832), _1000830)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1000830)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000828), _1000832))], (12861 ^ _779308) ^ [_1001029, _1001031, _1001033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001029), _1001031)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001029), _1001033))), 12864 ^ _779308 : [(12865 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1001029)))], (12867 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1001031), _1001033)))]]], (12869 ^ _779308) ^ [_1001178, _1001180, _1001182] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001178), _1001180)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001178), _1001182)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1001178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1001180), _1001182))], (12879 ^ _779308) ^ [_1001376, _1001378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001376), _1001378))), 12882 ^ _779308 : [(12883 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1001376)))], (12885 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1001378)))]]], (12887 ^ _779308) ^ [_1001499, _1001501] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001499), _1001501)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1001499)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1001501))], (12897 ^ _779308) ^ [_1001672, _1001674, _1001676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1001672)), _1001674)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1001672)), _1001676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1001674), _1001676)))], (12903 ^ _779308) ^ [_1001803, _1001805, _1001807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1001805), _1001807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1001803)), _1001805)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1001803)), _1001807))))], (12909 ^ _779308) ^ [_1001940, _1001942] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001940), hAPP(c_Nat_OSuc, _1001942)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1001940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001940), _1001942)))], (12911 ^ _779308) ^ [_1001986, _1001988] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1001986)), _1001988) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1001988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1001986), _1001988)))], (12913 ^ _779308) ^ [_1002050, _1002052, _1002054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1002050)), _1002052)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1002050)), _1002054))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1002052), _1002054)))], (12919 ^ _779308) ^ [_1002181, _1002183, _1002185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1002183), _1002185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1002181)), _1002183)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1002181)), _1002185))))], (12925 ^ _779308) ^ [_1002318, _1002320] : [_1002318 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1002318), _1002320), -(_1002320 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1002318 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12935 ^ _779308) ^ [_1002420] : [class_Rings_Oring__1(_1002420), -(hBOOL(hAPP(hAPP(c_member(_1002420), c_Groups_Ozero__class_Ozero(_1002420)), c_Int_Oring__1__class_OInts(_1002420))))], (12941 ^ _779308) ^ [_1002515, _1002517, _1002519] : [class_Rings_Oring__1(_1002515), hBOOL(hAPP(hAPP(c_member(_1002515), _1002517), c_Int_Oring__1__class_OInts(_1002515))), hBOOL(hAPP(hAPP(c_member(_1002515), _1002519), c_Int_Oring__1__class_OInts(_1002515))), -(hBOOL(hAPP(hAPP(c_member(_1002515), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002515), _1002517), _1002519)), c_Int_Oring__1__class_OInts(_1002515))))], (12955 ^ _779308) ^ [_1002770, _1002772, _1002774] : [class_Rings_Oring__1(_1002770), hBOOL(hAPP(hAPP(c_member(_1002770), _1002772), c_Int_Oring__1__class_OInts(_1002770))), hBOOL(hAPP(hAPP(c_member(_1002770), _1002774), c_Int_Oring__1__class_OInts(_1002770))), -(hBOOL(hAPP(hAPP(c_member(_1002770), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1002770), _1002772), _1002774)), c_Int_Oring__1__class_OInts(_1002770))))], (12969 ^ _779308) ^ [_1003025, _1003027, _1003029, _1003031] : [class_Rings_Olinordered__semiring__strict(_1003025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1003025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003025), _1003027), _1003029)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003025), _1003027), _1003031))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003025), c_Groups_Ozero__class_Ozero(_1003025)), _1003027)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1003025), _1003029), _1003031)))], (12983 ^ _779308) ^ [_1003294, _1003296, _1003298, _1003300] : [class_Rings_Olinordered__semiring__strict(_1003294), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1003294), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003294), _1003296), _1003298)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003294), _1003300), _1003298))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003294), c_Groups_Ozero__class_Ozero(_1003294)), _1003298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1003294), _1003296), _1003300)))], (12997 ^ _779308) ^ [_1003563, _1003565, _1003567, _1003569] : [class_Rings_Olinordered__semiring__strict(_1003563), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003563), _1003565), _1003567)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003563), _1003565), _1003569))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1003563), c_Groups_Ozero__class_Ozero(_1003563)), _1003565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003563), _1003567), _1003569)))], (13011 ^ _779308) ^ [_1003832, _1003834, _1003836, _1003838] : [class_Rings_Olinordered__semiring(_1003832), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003832), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003832), _1003834), _1003836)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1003832), _1003834), _1003838))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1003832), c_Groups_Ozero__class_Ozero(_1003832)), _1003834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003832), _1003836), _1003838)))], (13025 ^ _779308) ^ [_1004101, _1004103, _1004105, _1004107] : [class_Rings_Olinordered__semiring__strict(_1004101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004101), _1004103), _1004105)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004101), _1004107), _1004105))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004101), c_Groups_Ozero__class_Ozero(_1004101)), _1004105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004101), _1004103), _1004107)))], (13039 ^ _779308) ^ [_1004370, _1004372, _1004374, _1004376] : [class_Rings_Olinordered__semiring(_1004370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004370), _1004372), _1004374)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1004370), _1004376), _1004374))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1004370), c_Groups_Ozero__class_Ozero(_1004370)), _1004374)), 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hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1010209), _1010211), _1010217)), _1010213)), _1010215)), _1010219)))], (13337 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010209), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010209), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1010209), _1010211), _1010217)), _1010213)), _1010215)), _1010219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010209), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010209), _1010211), _1010213)), _1010215)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010209), _1010217), _1010213)), _1010219))))]]], (13343 ^ _779308) ^ [_1010648, _1010650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1010648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1010650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010650), _1010648))))], (13353 ^ _779308) ^ [_1010801, _1010803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1010801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1010803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1010801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010801), _1010803))))], (13363 ^ _779308) ^ [_1010960, _1010962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1010960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1010962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1010960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1010962), _1010960))))], (13373 ^ _779308) ^ [_1011134, _1011136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011134), _1011136))), 13376 ^ _779308 : [(13377 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1011134)))], (13379 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1011136)))]]], (13381 ^ _779308) ^ [_1011257, _1011259] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011257), _1011259)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1011257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1011259))], (13401 ^ _779308) ^ [_1011607, _1011609, _1011611] : [13402 ^ _779308 : [(13403 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011609)))], (13405 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1011607), _1011611))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011607), _1011609)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011611), _1011609))))], (13391 ^ _779308) ^ [_1011430, _1011432, _1011434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011430), _1011432)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011434), _1011432))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1011430), _1011434)))], (13419 ^ _779308) ^ [_1011964, _1011966, _1011968] : [13420 ^ _779308 : [(13421 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011964)))], (13423 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1011966), _1011968))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011964), _1011966)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011964), _1011968))))], (13409 ^ _779308) ^ [_1011787, _1011789, _1011791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011787), _1011789)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1011787), _1011791))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1011787)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1011789), _1011791)))], (13427 ^ _779308) ^ [_1012126, _1012128, _1012130, _1012132, _1012134] : [class_Groups_Oab__semigroup__mult(_1012126), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1012126, _1012126, c_Groups_Otimes__class_Otimes(_1012126), _1012128, _1012130), _1012132)), -(hBOOL(hAPP(hAPP(c_member(_1012126), _1012128), _1012130))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1012126, _1012126, c_Groups_Otimes__class_Otimes(_1012126), _1012134, hAPP(hAPP(c_Set_Oinsert(_1012126), _1012128), _1012130)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012126), _1012134), _1012132))))], (13441 ^ _779308) ^ [_1012366, _1012368, _1012370, _1012372, _1012374] : [class_Groups_Ocomm__monoid__mult(_1012366), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012368), _1012370)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1012366, _1012368, c_Groups_Otimes__class_Otimes(_1012366)), hAPP(hAPP(c_COMBS(_1012368, _1012366, _1012366), hAPP(hAPP(c_COMBB(_1012366, tc_fun(_1012366, _1012366), _1012368), c_Groups_Otimes__class_Otimes(_1012366)), _1012372)), _1012374)), c_Groups_Oone__class_Oone(_1012366)), _1012370) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012366), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1012366, _1012368, c_Groups_Otimes__class_Otimes(_1012366)), _1012372), c_Groups_Oone__class_Oone(_1012366)), _1012370)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1012366, _1012368, c_Groups_Otimes__class_Otimes(_1012366)), _1012374), c_Groups_Oone__class_Oone(_1012366)), _1012370)))], (13451 ^ _779308) ^ [_1012681, _1012683, _1012685, _1012687, _1012689, _1012691] : [class_Rings_Olinordered__semiring__1(_1012681), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012681), _1012683), _1012685)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012681), _1012687), _1012685)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012681), c_Groups_Ozero__class_Ozero(_1012681)), _1012689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012681), c_Groups_Ozero__class_Ozero(_1012681)), _1012691)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012681), _1012689), _1012691) = c_Groups_Oone__class_Oone(_1012681), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012681), _1012689), _1012683)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012681), _1012691), _1012687))), _1012685)))], (13477 ^ _779308) ^ [_1013210, _1013212, _1013214, _1013216, _1013218, _1013220] : [class_Groups_Oab__semigroup__mult(_1013210), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013212), _1013214)), -(hBOOL(hAPP(hAPP(c_member(_1013212), _1013216), _1013214))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1013210, _1013212, c_Groups_Otimes__class_Otimes(_1013210)), _1013218), _1013220), hAPP(hAPP(c_Set_Oinsert(_1013212), _1013216), _1013214)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1013210), hAPP(_1013218, _1013216)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1013210, _1013212, c_Groups_Otimes__class_Otimes(_1013210)), _1013218), _1013220), _1013214)))], (13491 ^ _779308) ^ [_1013497, _1013499] : [_1013497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013497), _1013499) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13497 ^ _779308) ^ [_1013580, _1013582] : [-(_1013580 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013580), _1013582) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013582), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1013580), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1013582)))], (13503 ^ _779308) ^ [_1013642, _1013644] : [class_Int_Oring__char__0(_1013642), hBOOL(hAPP(hAPP(c_member(_1013642), _1013644), c_Int_Oring__1__class_OInts(_1013642))), 13510 ^ _779308 : [(13511 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013642), _1013644), _1013644) = c_Groups_Ozero__class_Ozero(_1013642), -(_1013644 = c_Groups_Ozero__class_Ozero(_1013642))], (13517 ^ _779308) ^ [] : [_1013644 = c_Groups_Ozero__class_Ozero(_1013642), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013642), _1013644), _1013644) = c_Groups_Ozero__class_Ozero(_1013642))]]], (13523 ^ _779308) ^ [_1013953, _1013955, _1013957, _1013959, _1013961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1013953), _1013955)), 13526 ^ _779308 : [(13527 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013953), _1013957)), _1013959)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013955), _1013957)), _1013961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013959), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1013955), _1013953)), _1013957)), _1013961))))], (13533 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1013959), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1013955), _1013953)), _1013957)), _1013961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013953), _1013957)), _1013959)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013955), _1013957)), _1013961))))]]], (13539 ^ _779308) ^ [_1014344, _1014346, _1014348, _1014350, _1014352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014344), _1014346)), 13542 ^ _779308 : [(13543 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014346), _1014348)), _1014350)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014344), _1014348)), _1014352))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014346), _1014344)), _1014348)), _1014350)), _1014352)))], (13549 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014346), _1014344)), _1014348)), _1014350)), _1014352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014346), _1014348)), _1014350)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014344), _1014348)), _1014352))))]]], (13555 ^ _779308) ^ [_1014735, _1014737, _1014739, _1014741, _1014743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014735), _1014737)), 13558 ^ _779308 : [(13559 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014737), _1014739)), _1014741)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014735), _1014739)), _1014743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014737), _1014735)), _1014739)), _1014741)), _1014743)))], (13565 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1014737), _1014735)), _1014739)), _1014741)), _1014743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014737), _1014739)), _1014741)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014735), _1014739)), _1014743))))]]], (13571 ^ _779308) ^ [_1015126, _1015128, _1015130, _1015132, _1015134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015126), _1015128)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015128), _1015130)), _1015132)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015126), _1015130)), _1015134)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015128), _1015126)), _1015130)), _1015132)), _1015134))], (13577 ^ _779308) ^ [_1015327, _1015329, _1015331, _1015333, _1015335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015327), _1015329)), 13580 ^ _779308 : [(13581 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015329), _1015331)), _1015333) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015327), _1015331)), _1015335), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015329), _1015327)), _1015331)), _1015333) = _1015335)], (13587 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015329), _1015327)), _1015331)), _1015333) = _1015335, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015329), _1015331)), _1015333) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015327), _1015331)), _1015335))]]], (13593 ^ _779308) ^ [_1015688, _1015690, _1015692, _1015694, _1015696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015688), _1015690)), 13596 ^ _779308 : [(13597 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015688), _1015692)), _1015694)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015690), _1015692)), _1015696))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015694), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015690), _1015688)), _1015692)), _1015696))))], (13603 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015694), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1015690), _1015688)), _1015692)), _1015696))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015688), _1015692)), _1015694)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015690), _1015692)), _1015696))))]]], (13609 ^ _779308) ^ [_1016079, _1016081, _1016083, _1016085, _1016087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016079), _1016081)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016079), _1016083)), _1016085)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016081), _1016083)), _1016087)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016081), _1016079)), _1016083)), _1016087)))], (13615 ^ _779308) ^ [_1016280, _1016282, _1016284, _1016286, _1016288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016280), _1016282)), 13618 ^ _779308 : [(13619 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016280), _1016284)), _1016286) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016282), _1016284)), _1016288), -(_1016286 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016282), _1016280)), _1016284)), _1016288))], (13625 ^ _779308) ^ [] : [_1016286 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1016282), _1016280)), _1016284)), _1016288), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016280), _1016284)), _1016286) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016282), _1016284)), _1016288))]]], (13631 ^ _779308) ^ [_1016641, _1016643, _1016645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1016641)), 13634 ^ _779308 : [(13635 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016641), _1016643)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016641), _1016645))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016643), _1016645)))], (13641 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016643), _1016645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016641), _1016643)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1016641), _1016645))))]]], (13647 ^ _779308) ^ [_1016924, _1016926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1016924)), 13650 ^ _779308 : [(13651 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016924), _1016926) = c_Groups_Oone__class_Oone(tc_Int_Oint), 13654 ^ _779308 : [(13655 ^ _779308) ^ [] : [-(_1016924 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (13657 ^ _779308) ^ [] : [-(_1016926 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (13659 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1016924), _1016926) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1016924 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1016926 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (13669 ^ _779308) ^ [_1017225, _1017227, _1017229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017225), _1017227)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1017229)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017229), _1017225)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017229), _1017227))))], (13679 ^ _779308) ^ [_1017421, _1017423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017421)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017423))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017421), _1017423)))], (13685 ^ _779308) ^ [_1017526, _1017528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1017526), _1017528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017526)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017528))))], (13691 ^ _779308) ^ [_1017637] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017637), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1017637)], (13693 ^ _779308) ^ [_1017666] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1017666) = _1017666)], (13695 ^ _779308) ^ [_1017707, _1017709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017707)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017709))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1017707), _1017709)))], (13701 ^ _779308) ^ [_1017812, _1017814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1017812), _1017814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017812)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017814))))], (13707 ^ _779308) ^ [_1017923, _1017925, _1017927] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017923), _1017925)), _1017927) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017925), _1017927)))], (13709 ^ _779308) ^ [_1017974, _1017976] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017974)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1017976)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1017974), _1017976)))], (13711 ^ _779308) ^ [_1018020, _1018022] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018020), _1018022) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018022), _1018020))], (13713 ^ _779308) ^ [_1018057, _1018059, _1018061] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018057), _1018059)), _1018061) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018057), _1018061)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018059), _1018061)))], (13715 ^ _779308) ^ [_1018114, _1018116, _1018118] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018114), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1018116), _1018118)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018114), _1018116)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018114), _1018118)))], (13717 ^ _779308) ^ [_1018171, _1018173, _1018175] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018171), _1018173)), _1018175) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018171), _1018175)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018173), _1018175)))], (13719 ^ _779308) ^ [_1018228, _1018230] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1018228)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1018230)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018228), _1018230)))], (13721 ^ _779308) ^ [_1018274, _1018276, _1018278] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018274), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018276), _1018278)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018274), _1018276)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1018274), _1018278)))], (13723 ^ _779308) ^ [_1018331, _1018333, _1018335] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1018331), _1018333)), _1018335) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1018331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1018333), _1018335)))], (13725 ^ _779308) ^ [_1018382, _1018384] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1018382), _1018384) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1018384), _1018382))], (13727 ^ _779308) ^ [_1018419, _1018421] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018419), _1018421) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018421), _1018419))], (13729 ^ _779308) ^ [_1018456, _1018458, _1018460] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018456), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018458), _1018460)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018458), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018456), _1018460)))], (13731 ^ _779308) ^ [_1018507, _1018509, _1018511] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018507), _1018509)), _1018511) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018507), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018509), _1018511)))], (13733 ^ _779308) ^ [_1018558, _1018560, _1018562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018558), _1018560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018562), _1018558)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1018562), _1018560))))], (13739 ^ _779308) ^ [_1018681, _1018683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018681), _1018683)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018683), _1018681)), -(_1018681 = _1018683)], (13749 ^ _779308) ^ [_1018830, _1018832, _1018834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018830), _1018832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018832), _1018834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018830), _1018834)))], (13759 ^ _779308) ^ [_1018989, _1018991] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018989), _1018991))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1018991), _1018989)))], (13765 ^ _779308) ^ [_1019035] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019035), _1019035)))], (13767 ^ _779308) ^ [_1019078, _1019080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019078), _1019080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1019078), _1019080)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13773 ^ _779308) ^ [_1019183, _1019185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1019183), _1019185)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019183), _1019185)))], (13779 ^ _779308) ^ [_1019290, _1019292] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019290), _1019292))), -(_1019290 = _1019292), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019292), _1019290)))], (13789 ^ _779308) ^ [_1019358, _1019360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019358), _1019360)), 13792 ^ _779308 : [(13793 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019358), _1019360)))], (13795 ^ _779308) ^ [] : [_1019358 = _1019360]]], (13797 ^ _779308) ^ [_1019485, _1019487] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019485), _1019487))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019485), _1019487)), -(_1019485 = _1019487)], (13807 ^ _779308) ^ [_1019639, _1019641, _1019643, _1019645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019639), _1019641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1019643), _1019645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019639), _1019643)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019641), _1019645))))], (13817 ^ _779308) ^ [_1019830, _1019832, _1019834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1019830), _1019832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019830), _1019834)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019832), _1019834))))], (13823 ^ _779308) ^ [_1019953] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1019953), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1019953)], (13825 ^ _779308) ^ [_1019982] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1019982) = _1019982)], (13827 ^ _779308) ^ [_1020017] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1020017)), _1020017) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (13829 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (13841 ^ _779308) ^ [_1020200, _1020202] : [13842 ^ _779308 : [(13843 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020200), _1020202))], (13845 ^ _779308) ^ [] : [_1020200 = _1020202]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020200), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020202), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (13831 ^ _779308) ^ [_1020082, _1020084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020082), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020084), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020082), _1020084))), -(_1020082 = _1020084)], (13849 ^ _779308) ^ [_1020361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1020361)), _1020361)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020361), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13855 ^ _779308) ^ [_1020470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020470), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1020470)), _1020470)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13861 ^ _779308) ^ [_1020585, _1020587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020585), _1020587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020585), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1020587)))], (13867 ^ _779308) ^ [_1020694] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1020694)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1020694))))], (13873 ^ _779308) ^ [_1020798, _1020800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020798), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1020800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020798), _1020800)))], (13879 ^ _779308) ^ [_1020903, _1020905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1020903), _1020905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1020903), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1020905)))], (13885 ^ _779308) ^ [_1021029, _1021031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1021031), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021029), _1021031)))], (13891 ^ _779308) ^ [_1021134, _1021136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021134), _1021136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021134), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1021136), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (13897 ^ _779308) ^ [_1021260, _1021262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021262), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021260), _1021262)))], (13903 ^ _779308) ^ [_1021365, _1021367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1021365), _1021367)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1021365), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1021367), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (13909 ^ _779308) ^ [_1021488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1021488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021488)))], (13915 ^ _779308) ^ [_1021567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1021567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1021567)))], (13931 ^ _779308) ^ [_1021782, _1021784, _1021786] : [13932 ^ _779308 : [(13933 ^ _779308) ^ [] : [_1021782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13935 ^ _779308) ^ [] : [_1021784 = _1021786]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021782), _1021784) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021782), _1021786))], (13921 ^ _779308) ^ [_1021670, _1021672, _1021674] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021670), _1021672) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021670), _1021674), -(_1021670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1021672 = _1021674)], (13939 ^ _779308) ^ [_1021925, _1021927, _1021929, _1021931] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021925), _1021927)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021929), _1021927)), _1021931)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1021925), _1021929)), _1021927)), _1021931))], (13941 ^ _779308) ^ [_1021996, _1021998, _1022000] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1021996)), 13944 ^ _779308 : [(13945 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021996), _1021998) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021996), _1022000), -(_1021998 = _1022000)], (13951 ^ _779308) ^ [] : [_1021998 = _1022000, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021996), _1021998) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1021996), _1022000))]]], (13957 ^ _779308) ^ [_1022249, _1022251, _1022253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1022249)), 13960 ^ _779308 : [(13961 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022249), _1022251)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022249), _1022253))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1022251), _1022253)))], (13967 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1022251), _1022253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022249), _1022251)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1022249), _1022253))))]]], (13973 ^ _779308) ^ [_1022532, _1022534, _1022536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022532)), _1022532 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1022534), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022532), _1022536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022536), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (13987 ^ _779308) ^ [_1022761, _1022763, _1022765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022761)), _1022761 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1022763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022761), _1022765)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022763), _1022761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1022765)))], (14001 ^ _779308) ^ [_1022990, _1022992, _1022994, _1022996, _1022998, _1023000] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022990), _1022992)), _1022994) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022996), _1022998)), _1023000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1022996), _1022998)), _1023000)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1022994), _1022990)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1022996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022996), _1022990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1022998), _1022992)))], (14027 ^ _779308) ^ [_1023495, _1023497, _1023499, _1023501, _1023503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023495), _1023497)), _1023499)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023495), _1023501)), _1023503))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023503), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023495), _1023503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023495), _1023499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023501), _1023497)))], (14045 ^ _779308) ^ [_1023850, _1023852, _1023854, _1023856, _1023858, _1023860] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023850), _1023852)), _1023854) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023856), _1023858)), _1023860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1023856), _1023858)), _1023860))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023860), _1023856)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1023856)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023856), _1023850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1023852), _1023858)))], (14071 ^ _779308) ^ [_1024349, _1024351, _1024353, _1024355, _1024357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024349), _1024351)), _1024353)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024349), _1024355)), _1024357))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024353)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024353), _1024349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024357), _1024349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1024351), _1024355)))], (14089 ^ _779308) ^ [_1024698, _1024700, _1024702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024698), _1024700)), _1024702)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024702)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1024700), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14103 ^ _779308) ^ [_1024937, _1024939, _1024941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1024937), _1024939)), _1024941))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1024941), _1024937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1024939)))], (14117 ^ _779308) ^ [_1025170] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1025170) = _1025170)], (14119 ^ _779308) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (14121 ^ _779308) ^ [_1025220, _1025222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1025220), _1025222))))], (14131 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (14133 ^ _779308) ^ [_1025391, _1025393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1025393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1025391), _1025393))))], (14143 ^ _779308) ^ [_1025544, _1025546, _1025548, _1025550] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1025544, _1025546)), c_Nitpick_Opair__box_OPairBox(_1025544, _1025546, _1025548, _1025550)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14145 ^ _779308) ^ [_1025586, _1025588, _1025590, _1025592, _1025594, _1025596] : [-(c_Nitpick_Opair__box_Opair__box__case(_1025586, _1025588, _1025590, _1025592, c_Nitpick_Opair__box_OPairBox(_1025586, _1025588, _1025594, _1025596)) = hAPP(hAPP(_1025592, _1025594), _1025596))], (14147 ^ _779308) ^ [_1025636, _1025638, _1025640, _1025642, _1025644, _1025646] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1025636, _1025638, _1025640, _1025642, c_Nitpick_Opair__box_OPairBox(_1025636, _1025638, _1025644, _1025646)) = hAPP(hAPP(_1025642, _1025644), _1025646))], (14149 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14151 ^ _779308) ^ [_1025704, _1025706] : [class_Int_Onumber__ring(_1025704), 14154 ^ _779308 : [(14155 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1025706))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1025704), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1025706)) = hAPP(c_Int_Onumber__class_Onumber__of(_1025704), _1025706))], (14161 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1025706)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1025704), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1025706)) = c_Groups_Ozero__class_Ozero(_1025704))]]], (14167 ^ _779308) ^ [_1025944, _1025946, _1025948] : [class_Nat_Osemiring__char__0(_1025944), 14170 ^ _779308 : [(14171 ^ _779308) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1025944), _1025946) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1025944), _1025948), -(_1025946 = _1025948)], (14177 ^ _779308) ^ [] : [_1025946 = _1025948, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1025944), _1025946) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1025944), _1025948))]]], (14183 ^ _779308) ^ [_1026197] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1026197)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1026197))))], (14189 ^ _779308) ^ [_1026282] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1026282))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1026282)))], (14195 ^ _779308) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (14197 ^ _779308) ^ [_1026403] : [14199 ^ _779308 : [(14200 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14198 ^ [_1026403])))], (14202 ^ _779308) ^ [] : [hBOOL(hAPP(_1026403, 14198 ^ [_1026403]))]], 14203 ^ _779308 : [(14204 ^ _779308) ^ [_1026530] : [-(hBOOL(hAPP(_1026403, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1026530))))]]], (14206 ^ _779308) ^ [_1026560] : [hBOOL(hAPP(_1026560, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 14207 ^ [_1026560]))), 14210 ^ _779308 : [(14211 ^ _779308) ^ [_1026660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026660)), -(hBOOL(hAPP(_1026560, _1026660)))]]], (14228 ^ _779308) ^ [_1026933] : [14229 ^ _779308 : [(14230 ^ _779308) ^ [_1026990] : [hBOOL(hAPP(_1026933, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1026990)))]], 14232 ^ _779308 : [(14233 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 14231 ^ [_1026933])))], (14235 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1026933, 14231 ^ [_1026933])))]]], (14217 ^ _779308) ^ [_1026763] : [-(hBOOL(hAPP(_1026763, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 14224 ^ [_1026763])))), 14218 ^ _779308 : [(14219 ^ _779308) ^ [_1026815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1026815)), hBOOL(hAPP(_1026763, _1026815))]]], (14237 ^ _779308) ^ [_1027082] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027082))))], (14239 ^ _779308) ^ [_1027125, _1027127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027125)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027125), _1027127)))], (14245 ^ _779308) ^ [_1027230, _1027232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027230), _1027232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027230)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027232))))], (14251 ^ _779308) ^ [_1027356, _1027358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027356)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027358))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027356), _1027358)))], (14257 ^ _779308) ^ [_1027461, _1027463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027461), _1027463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027461)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027463))))], (14263 ^ _779308) ^ [_1027572, _1027574] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027572)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027574)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027572), _1027574)))], (14265 ^ _779308) ^ [_1027618, _1027620] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027618)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027620)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1027618), _1027620)))], (14267 ^ _779308) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (14269 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14271 ^ _779308) ^ [_1027712] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027712) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1027712 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14277 ^ _779308) ^ [_1027789] : [_1027789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027789) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14283 ^ _779308) ^ [_1027872] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027872))))], (14285 ^ _779308) ^ [_1027909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027909)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14287 ^ _779308) ^ [_1027955, _1027957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027955)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1027957))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027955), _1027957)))], (14293 ^ _779308) ^ [_1028060, _1028062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028060), _1028062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028060)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028062))))], (14299 ^ _779308) ^ [_1028186, _1028188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028186)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028188))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028186), _1028188)))], (14305 ^ _779308) ^ [_1028291, _1028293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028291), _1028293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028291)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028293))))], (14311 ^ _779308) ^ [_1028402, _1028404] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028402)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028404)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028402), _1028404)))], (14313 ^ _779308) ^ [_1028448, _1028450, _1028452] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028448)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028450)), _1028452)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028448), _1028450))), _1028452))], (14315 ^ _779308) ^ [_1028523, _1028525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028523), _1028525)), -(_1028525 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1028523), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 14318 ^ [_1028523, _1028525])))], (14322 ^ _779308) ^ [_1028636, _1028638] : [14323 ^ _779308 : [(14324 ^ _779308) ^ [_1028689] : [_1028638 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1028636), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1028689))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1028636), _1028638)))], (14328 ^ _779308) ^ [_1028756, _1028758] : [class_Rings_Olinordered__semidom(_1028756), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028756), c_Groups_Ozero__class_Ozero(_1028756)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1028756), _1028758))))], (14334 ^ _779308) ^ [_1028859, _1028861] : [class_Rings_Olinordered__semidom(_1028859), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028859), c_Groups_Ozero__class_Ozero(_1028859)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1028859), _1028861))))], (14340 ^ _779308) ^ [_1028962, _1028964] : [class_Rings_Olinordered__semidom(_1028962), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028962), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1028962), _1028964)), c_Groups_Ozero__class_Ozero(_1028962)))], (14346 ^ _779308) ^ [_1029066, _1029068] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029066)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029068)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029066), _1029068)))], (14348 ^ _779308) ^ [_1029112, _1029114] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029112), _1029114)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029112)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1029114)))], (14350 ^ _779308) ^ [_1029158] : [class_Rings_Osemiring__1(_1029158), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029158), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1029158))], (14356 ^ _779308) ^ [_1029245, _1029247, _1029249] : [class_Rings_Olinordered__semidom(_1029245), 14359 ^ _779308 : [(14360 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029245), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029245), _1029247)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029245), _1029249))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029247), _1029249)))], (14366 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029247), _1029249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029245), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029245), _1029247)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029245), _1029249))))]]], (14372 ^ _779308) ^ [_1029522, _1029524, _1029526] : [class_Rings_Olinordered__semidom(_1029522), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029524), _1029526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029522), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029522), _1029524)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029522), _1029526))))], (14382 ^ _779308) ^ [_1029697, _1029699, _1029701] : [class_Rings_Olinordered__semidom(_1029697), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029697), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029697), _1029699)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029697), _1029701))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029699), _1029701)))], (14392 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (14394 ^ _779308) ^ [_1029890, _1029892, _1029894] : [class_Rings_Olinordered__semidom(_1029890), 14397 ^ _779308 : [(14398 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029890), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029890), _1029892)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029890), _1029894))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029892), _1029894)))], (14404 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029892), _1029894)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029890), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029890), _1029892)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1029890), _1029894))))]]], (14410 ^ _779308) ^ [_1030167, _1030169, _1030171] : [class_Rings_Osemiring__1(_1030167), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030167), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030169), _1030171)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1030167), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030167), _1030169)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030167), _1030171)))], (14416 ^ _779308) ^ [_1030302, _1030304, _1030306] : [class_Rings_Osemiring__1(_1030302), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030304), _1030306)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030302), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030302), _1030304)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030302), _1030306)))], (14422 ^ _779308) ^ [_1030437] : [class_Rings_Osemiring__1(_1030437), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030437), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1030437))], (14428 ^ _779308) ^ [_1030524, _1030526] : [class_Rings_Oring__1(_1030524), -(hBOOL(hAPP(hAPP(c_member(_1030524), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1030524), _1030526)), c_Int_Oring__1__class_OInts(_1030524))))], (14434 ^ _779308) ^ [_1030639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1030639)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1030639 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14440 ^ _779308) ^ [_1030726] : [_1030726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1030726)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14446 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (14448 ^ _779308) ^ [_1030852, _1030854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1030852), _1030854)), -(_1030854 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1030852), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 14451 ^ [_1030852, _1030854]))))], (14455 ^ _779308) ^ [_1030971, _1030973] : [14456 ^ _779308 : [(14457 ^ _779308) ^ [_1031027] : [_1030973 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1030971), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1031027)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1030971), _1030973)))], (14461 ^ _779308) ^ [_1031097] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1031097)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031097)))], (14463 ^ _779308) ^ [_1031132, _1031134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031132), _1031134)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031134)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031132)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031134), _1031132)))], (14469 ^ _779308) ^ [_1031261, _1031263] : [class_Rings_Osemiring__1(_1031261), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031261), hAPP(c_Nat_OSuc, _1031263)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1031261), c_Groups_Oone__class_Oone(_1031261)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031261), _1031263)))], (14475 ^ _779308) ^ [_1031382, _1031384, _1031386] : [class_Rings_Oring__1(_1031382), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031384), _1031386)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031382), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1031386), _1031384)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1031382), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031382), _1031386)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031382), _1031384)))], (14485 ^ _779308) ^ [_1031593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031593))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1031593)))], (14491 ^ _779308) ^ [_1031678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1031678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031678))))], (14497 ^ _779308) ^ [_1031769, _1031771, _1031773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1031769), _1031771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1031773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031773)), _1031769)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1031773)), _1031771))))], (14507 ^ _779308) ^ [_1031962, _1031964] : [class_Rings_Olinordered__semidom(_1031962), 14510 ^ _779308 : [(14511 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031962), c_Groups_Ozero__class_Ozero(_1031962)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031962), _1031964))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1031964)))], (14517 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1031964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031962), c_Groups_Ozero__class_Ozero(_1031962)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1031962), _1031964))))]]], (14539 ^ _779308) ^ [_1032522, _1032524, _1032526] : [-(hBOOL(hAPP(_1032522, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1032524), _1032526))))), 14542 ^ _779308 : [(14543 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032526), _1032524)))], (14545 ^ _779308) ^ [] : [hBOOL(hAPP(_1032522, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1032524)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1032526))))]], 14546 ^ _779308 : [(14547 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1032524), _1032526)))], (14549 ^ _779308) ^ [] : [hBOOL(hAPP(_1032522, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (14523 ^ _779308) ^ [_1032233, _1032235, _1032237] : [hBOOL(hAPP(_1032233, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1032235), _1032237)))), 14526 ^ _779308 : [(14527 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032237), _1032235)), -(hBOOL(hAPP(_1032233, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1032235)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1032237)))))], (14533 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1032235), _1032237)), -(hBOOL(hAPP(_1032233, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (14553 ^ _779308) ^ [_1032797, _1032799] : [class_Rings_Osemiring__1(_1032797), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1032797), _1032799) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1032797, hAPP(hAPP(c_COMBC(_1032797, _1032797, _1032797), c_Groups_Oplus__class_Oplus(_1032797)), c_Groups_Oone__class_Oone(_1032797)), _1032799, c_Groups_Ozero__class_Ozero(_1032797)))], (14559 ^ _779308) ^ [_1032933, _1032935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1032933), _1032935)), -(c_Nat__Transfer_Otsub(_1032935, _1032933) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1032935), _1032933))], (14565 ^ _779308) ^ [_1033032, _1033034] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1033032), _1033034))), -(c_Nat__Transfer_Otsub(_1033034, _1033032) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14571 ^ _779308) ^ [_1033078, _1033080] : [class_Int_Onumber__ring(_1033078), 14574 ^ _779308 : [(14575 ^ _779308) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1033080))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1033078), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033080)) = c_Groups_Ozero__class_Ozero(_1033078))], (14581 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1033080)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1033078), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033080)) = hAPP(c_Int_Onumber__class_Onumber__of(_1033078), _1033080))]]], (14587 ^ _779308) ^ [_1033318, _1033320, _1033322] : [class_Groups_Oab__semigroup__mult(_1033318), -(_1033320 = c_Orderings_Obot__class_Obot(tc_fun(_1033318, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1033318), _1033320)), -(hBOOL(hAPP(hAPP(c_member(_1033318), _1033322), _1033320))), -(hAPP(c_Finite__Set_Ofold1(_1033318, c_Groups_Otimes__class_Otimes(_1033318)), hAPP(hAPP(c_Set_Oinsert(_1033318), _1033322), _1033320)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033318), _1033322), hAPP(c_Finite__Set_Ofold1(_1033318, c_Groups_Otimes__class_Otimes(_1033318)), _1033320)))], (14605 ^ _779308) ^ [_1033629, _1033631, _1033633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1033629), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033629)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033631)), _1033633)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14611 ^ _779308) ^ [_1033748, _1033750, _1033752] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1033748), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033748)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033750)), _1033752)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1033748), _1033750))), _1033752))], (14617 ^ _779308) ^ [_1033835, _1033837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1033835), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033835)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033837)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14623 ^ _779308) ^ [_1033940, _1033942] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1033940), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033940)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1033942)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1033940), _1033942)))], (14629 ^ _779308) ^ [_1034004, _1034006, _1034008, _1034010] : [class_Groups_Ocomm__monoid__mult(_1034004), hBOOL(hAPP(c_Finite__Set_Ofinite(_1034006), _1034008)), 14639 ^ _779308 : [(14640 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1034006), 14638 ^ [_1034004, _1034006, _1034008, _1034010]), _1034008)))], (14642 ^ _779308) ^ [] : [hAPP(_1034010, 14638 ^ [_1034004, _1034006, _1034008, _1034010]) = c_Groups_Oone__class_Oone(_1034004)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1034004, _1034006, c_Groups_Otimes__class_Otimes(_1034004)), _1034010), c_Groups_Oone__class_Oone(_1034004)), _1034008) = c_Groups_Oone__class_Oone(_1034004))], (14646 ^ _779308) ^ [_1034360, _1034362] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1034360), _1034362)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1034360)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1034362))))], (14652 ^ _779308) ^ [_1034465, _1034467] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1034465)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1034467))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1034465), _1034467)))], (14658 ^ _779308) ^ [_1034591, _1034593] : [_1034591 = _1034593, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1034591) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1034593))], (14664 ^ _779308) ^ [_1034676, _1034678] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1034676) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1034678), -(_1034676 = _1034678)], (14670 ^ _779308) ^ [_1034782, _1034784] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1034782) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1034784), -(_1034782 = _1034784)], (14676 ^ _779308) ^ [_1034867, _1034869] : [_1034867 = _1034869, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1034867) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1034869))], (14682 ^ _779308) ^ [_1034967] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1034967)))], (14684 ^ _779308) ^ [_1034995] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1034995) = hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1034995)))], (14686 ^ _779308) ^ [_1035042, _1035044] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035042) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035044), -(_1035042 = _1035044)], (14692 ^ _779308) ^ [_1035127, _1035129] : [_1035127 = _1035129, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035127) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1035129))], (14698 ^ _779308) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (14700 ^ _779308) ^ [_1035251, _1035253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1035251), _1035253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035251)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035253))))], (14706 ^ _779308) ^ [_1035356, _1035358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035356)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035358))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1035356), _1035358)))], (14712 ^ _779308) ^ [_1035482, _1035484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1035482), _1035484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035482)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035484))))], (14718 ^ _779308) ^ [_1035587, _1035589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035587)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1035589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1035587), _1035589)))], (14724 ^ _779308) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (14726 ^ _779308) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14728 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (14730 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (14732 ^ _779308) ^ [_1035782] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1035782), c_Int_OPls) = _1035782)], (14734 ^ _779308) ^ [_1035811] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1035811) = _1035811)], (14736 ^ _779308) ^ [_1035837] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1035837) = c_Int_OPls)], (14738 ^ _779308) ^ [_1035863] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1035863), c_Int_OPls) = _1035863)], (14740 ^ _779308) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14742 ^ _779308) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (14744 ^ _779308) ^ [_1035940] : [class_Int_Onumber__ring(_1035940), -(c_Groups_Ozero__class_Ozero(_1035940) = hAPP(c_Int_Onumber__class_Onumber__of(_1035940), c_Int_OPls))], (14750 ^ _779308) ^ [_1036027] : [class_Int_Onumber__ring(_1036027), -(hAPP(c_Int_Onumber__class_Onumber__of(_1036027), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1036027))], (14756 ^ _779308) ^ [_1036114, _1036116] : [class_Int_Onumber__ring(_1036114), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036114), hAPP(c_Int_Onumber__class_Onumber__of(_1036114), c_Int_OPls)), _1036116) = _1036116)], (14762 ^ _779308) ^ [_1036215, _1036217] : [class_Int_Onumber__ring(_1036215), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036215), _1036217), hAPP(c_Int_Onumber__class_Onumber__of(_1036215), c_Int_OPls)) = _1036217)], (14768 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))))], (14770 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (14772 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14774 ^ _779308) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (14776 ^ _779308) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (14778 ^ _779308) ^ [_1036412, _1036414, _1036416] : [-(hAPP(c_Finite__Set_Ofold1(_1036412, _1036414), hAPP(hAPP(c_Set_Oinsert(_1036412), _1036416), c_Orderings_Obot__class_Obot(tc_fun(_1036412, tc_HOL_Obool)))) = _1036416)], (14780 ^ _779308) ^ [_1036458, _1036460, _1036462, _1036464] : [_1036458 = c_Finite__Set_Ofold1(_1036460, _1036462), -(hAPP(_1036458, hAPP(hAPP(c_Set_Oinsert(_1036460), _1036464), c_Orderings_Obot__class_Obot(tc_fun(_1036460, tc_HOL_Obool)))) = _1036464)], (14786 ^ _779308) ^ [_1036583] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1036583))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1036583)))], (14792 ^ _779308) ^ [_1036617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1036617)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1036617))], (14798 ^ _779308) ^ [_1036715] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1036715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1036715), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14804 ^ _779308) ^ [_1036800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1036800), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1036800)))], (14810 ^ _779308) ^ [_1036891, _1036893] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1036891), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1036893)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1036891), _1036893)))], (14812 ^ _779308) ^ [_1036934, _1036936, _1036938, _1036940] : [c_Finite__Set_Ofolding__one(_1036934, _1036936, _1036938), hBOOL(hAPP(c_Finite__Set_Ofinite(_1036934), _1036940)), -(hAPP(_1036938, _1036940) = hAPP(c_Finite__Set_Ofold1(_1036934, _1036936), _1036940))], (14822 ^ _779308) ^ [_1037099, _1037101, _1037103] : [class_Rings_Osemiring__1(_1037099), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1037099, _1037101, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1037103) = _1037103)], (14828 ^ _779308) ^ [_1037186, _1037188, _1037190, _1037192] : [class_Rings_Osemiring__1(_1037186), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1037186, _1037188, hAPP(c_Nat_OSuc, _1037190), _1037192) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1037186, _1037188, _1037190, hAPP(_1037188, _1037192)))], (14834 ^ _779308) ^ [_1037309] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1037309) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1037309), c_Int_OPls)))], (14840 ^ _779308) ^ [_1037396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1037396), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1037396) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14846 ^ _779308) ^ [_1037501] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1037501), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1037501), c_Int_OPls)))], (14852 ^ _779308) ^ [_1037588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1037588), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1037588))], (14858 ^ _779308) ^ [_1037696, _1037698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1037696)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1037698))), 14861 ^ _779308 : [(14868 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1037696), _1037698)))], (14862 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1037696), _1037698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1037698)))]]], (14870 ^ _779308) ^ [_1037899, _1037901] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1037899)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1037901)))), 14873 ^ _779308 : [(14874 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1037899), _1037901)))], (14876 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1037901))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1037899), _1037901))], (14892 ^ _779308) ^ [_1038254, _1038256] : [14893 ^ _779308 : [(14894 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038254), _1038256))], (14896 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038254), c_Int_OPls))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038254)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038256))))], (14882 ^ _779308) ^ [_1038124, _1038126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038124)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038126))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038124), _1038126))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038124), c_Int_OPls)))], (14900 ^ _779308) ^ [_1038415, _1038417, _1038419] : [-(hAPP(c_Finite__Set_Ofold1(_1038415, _1038417), _1038419) = c_HOL_OThe(_1038415, c_Finite__Set_Ofold1Set(_1038415, _1038417, _1038419)))], (14902 ^ _779308) ^ [_1038455] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1038455))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038455) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14908 ^ _779308) ^ [_1038552] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1038552))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038552)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (14914 ^ _779308) ^ [_1038643] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1038643)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1038643)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1038643))], (14920 ^ _779308) ^ [_1038693, _1038695] : [class_Int_Onumber__ring(_1038693), class_Rings_Olinordered__idom(_1038693), 14927 ^ _779308 : [(14928 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038693), hAPP(c_Int_Onumber__class_Onumber__of(_1038693), _1038695)), c_Groups_Ozero__class_Ozero(_1038693))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038695), c_Int_OPls)))], (14934 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1038695), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038693), hAPP(c_Int_Onumber__class_Onumber__of(_1038693), _1038695)), c_Groups_Ozero__class_Ozero(_1038693))))]]], (14940 ^ _779308) ^ [_1039007, _1039009] : [class_Int_Onumber__ring(_1039007), class_Rings_Olinordered__idom(_1039007), 14947 ^ _779308 : [(14948 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039007), c_Groups_Ozero__class_Ozero(_1039007)), hAPP(c_Int_Onumber__class_Onumber__of(_1039007), _1039009))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1039009)))], (14954 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1039009)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039007), c_Groups_Ozero__class_Ozero(_1039007)), hAPP(c_Int_Onumber__class_Onumber__of(_1039007), _1039009))))]]], (14960 ^ _779308) ^ [_1039312, _1039314] : [class_Int_Onumber__ring(_1039312), class_Rings_Olinordered__idom(_1039312), 14967 ^ _779308 : [(14968 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039312), hAPP(c_Int_Onumber__class_Onumber__of(_1039312), _1039314)), c_Groups_Ozero__class_Ozero(_1039312))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1039314), c_Int_OPls)))], (14974 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1039314), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039312), hAPP(c_Int_Onumber__class_Onumber__of(_1039312), _1039314)), c_Groups_Ozero__class_Ozero(_1039312))))]]], (14980 ^ _779308) ^ [_1039626, _1039628] : [class_Int_Onumber__ring(_1039626), class_Rings_Olinordered__idom(_1039626), 14987 ^ _779308 : [(14988 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039626), c_Groups_Ozero__class_Ozero(_1039626)), hAPP(c_Int_Onumber__class_Onumber__of(_1039626), _1039628))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1039628)))], (14994 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1039628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1039626), c_Groups_Ozero__class_Ozero(_1039626)), hAPP(c_Int_Onumber__class_Onumber__of(_1039626), _1039628))))]]], (15000 ^ _779308) ^ [_1039943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1039943))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1039943)))], (15006 ^ _779308) ^ [_1040028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1040028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040028))))], (15012 ^ _779308) ^ [_1040128, _1040130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040128), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040128)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040130)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040130))], (15018 ^ _779308) ^ [_1040240, _1040242] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040240), c_Int_OPls))), 15021 ^ _779308 : [(15022 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040242), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040240)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040242)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040240))], (15028 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1040242), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040240)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040242)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1040240), _1040242)))]]], (15034 ^ _779308) ^ [_1040513, _1040515, _1040517] : [class_Lattices_Oab__semigroup__idem__mult(_1040513), -(_1040515 = c_Orderings_Obot__class_Obot(tc_fun(_1040513, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1040513), _1040515)), -(hAPP(c_Finite__Set_Ofold1(_1040513, c_Groups_Otimes__class_Otimes(_1040513)), hAPP(hAPP(c_Set_Oinsert(_1040513), _1040517), _1040515)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040513), _1040517), hAPP(c_Finite__Set_Ofold1(_1040513, c_Groups_Otimes__class_Otimes(_1040513)), _1040515)))], (15074 ^ _779308) ^ [_1041183, _1041185] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041183) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041185)), 15077 ^ _779308 : [(15078 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041183))))], (15080 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041185)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 15081 ^ _779308 : [(15082 ^ _779308) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041183)))], (15084 ^ _779308) ^ [] : [15085 ^ _779308 : [(15086 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041185))))], (15088 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041183) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 15089 ^ _779308 : [(15090 ^ _779308) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041185)))], (15092 ^ _779308) ^ [] : [_1041183 = _1041185]]]]], (15048 ^ _779308) ^ [_1040798, _1040800] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040798) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1040800), 15051 ^ _779308 : [(15052 ^ _779308) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040798))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040800)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15058 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040798)))), 15061 ^ _779308 : [(15062 ^ _779308) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040800))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040798) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15068 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1040800)))), -(_1040798 = _1040800)]]]]], (15096 ^ _779308) ^ [_1041596, _1041598, _1041600] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041596))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041596)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041598)), _1041600)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041598)), _1041600))], (15102 ^ _779308) ^ [_1041734, _1041736, _1041738] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041734)))), 15105 ^ _779308 : [(15106 ^ _779308) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041736))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041734)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041736)), _1041738)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041734)), _1041738))], (15112 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1041736)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041734)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1041736)), _1041738)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1041734), _1041736))), _1041738))]]], (15118 ^ _779308) ^ [_1042059, _1042061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1042059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1042061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1042059, _1042061))))], (15128 ^ _779308) ^ [_1042206, _1042208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1042206), _1042208)), -(c_Nat__Transfer_Otsub(_1042208, _1042206) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1042208), _1042206))], (15134 ^ _779308) ^ [_1042320, _1042322] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042320))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042320)), _1042322)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1042322))], (15140 ^ _779308) ^ [_1042431, _1042433] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042431)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042431)), _1042433)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1042431))), _1042433))], (15146 ^ _779308) ^ [_1042503] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042503))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042503)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15152 ^ _779308) ^ [_1042594] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1042594)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042594)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1042594)))], (15158 ^ _779308) ^ [_1042652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1042652), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042652)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15164 ^ _779308) ^ [_1042743] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1042743), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042743)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1042743)))], (15170 ^ _779308) ^ [_1042801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1042801), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042801)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15176 ^ _779308) ^ [_1042898] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1042898), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042898)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1042898)))], (15182 ^ _779308) ^ [_1042959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1042959), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1042959)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15188 ^ _779308) ^ [_1043056] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1043056), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043056)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1043056)))], (15194 ^ _779308) ^ [_1043111, _1043113] : [class_Groups_Oab__semigroup__mult(_1043111), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043111), _1043113)), -(_1043113 = c_Orderings_Obot__class_Obot(tc_fun(_1043111, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1043111), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043111), 15207 ^ [_1043111, _1043113]), 15208 ^ [_1043111, _1043113])), hAPP(hAPP(c_Set_Oinsert(_1043111), 15207 ^ [_1043111, _1043113]), hAPP(hAPP(c_Set_Oinsert(_1043111), 15208 ^ [_1043111, _1043113]), c_Orderings_Obot__class_Obot(tc_fun(_1043111, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1043111), hAPP(c_Finite__Set_Ofold1(_1043111, c_Groups_Otimes__class_Otimes(_1043111)), _1043113)), _1043113)))], (15214 ^ _779308) ^ [_1043565, _1043567] : [class_Int_Onumber__ring(_1043565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1043567)), -(hBOOL(hAPP(hAPP(c_member(_1043565), hAPP(c_Int_Onumber__class_Onumber__of(_1043565), _1043567)), c_Nat_Osemiring__1__class_ONats(_1043565))))], (15224 ^ _779308) ^ [_1043724, _1043726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1043724)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1043726)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1043724)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043726), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1043724))))], (15230 ^ _779308) ^ [_1043851] : [-(c_Int_Osucc(c_Int_Opred(_1043851)) = _1043851)], (15232 ^ _779308) ^ [_1043893, _1043895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1043893), _1043895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1043893)), _1043895)))], (15238 ^ _779308) ^ [_1043990, _1043992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1043990)), _1043992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1043990), _1043992)))], (15244 ^ _779308) ^ [_1044093] : [-(c_Int_Opred(_1044093) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1044093), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15246 ^ _779308) ^ [_1044124] : [-(c_Int_Osucc(_1044124) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1044124), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15248 ^ _779308) ^ [_1044155] : [class_Rings_Osemiring__1(_1044155), -(hBOOL(hAPP(hAPP(c_member(_1044155), c_Groups_Ozero__class_Ozero(_1044155)), c_Nat_Osemiring__1__class_ONats(_1044155))))], (15254 ^ _779308) ^ [_1044250, _1044252, _1044254] : [class_Rings_Osemiring__1(_1044250), hBOOL(hAPP(hAPP(c_member(_1044250), _1044252), c_Nat_Osemiring__1__class_ONats(_1044250))), hBOOL(hAPP(hAPP(c_member(_1044250), _1044254), c_Nat_Osemiring__1__class_ONats(_1044250))), -(hBOOL(hAPP(hAPP(c_member(_1044250), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044250), _1044252), _1044254)), c_Nat_Osemiring__1__class_ONats(_1044250))))], (15268 ^ _779308) ^ [_1044505, _1044507, _1044509] : [class_Rings_Osemiring__1(_1044505), hBOOL(hAPP(hAPP(c_member(_1044505), _1044507), c_Nat_Osemiring__1__class_ONats(_1044505))), hBOOL(hAPP(hAPP(c_member(_1044505), _1044509), c_Nat_Osemiring__1__class_ONats(_1044505))), -(hBOOL(hAPP(hAPP(c_member(_1044505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044505), _1044507), _1044509)), c_Nat_Osemiring__1__class_ONats(_1044505))))], (15282 ^ _779308) ^ [_1044760] : [class_Rings_Osemiring__1(_1044760), -(hBOOL(hAPP(hAPP(c_member(_1044760), c_Groups_Oone__class_Oone(_1044760)), c_Nat_Osemiring__1__class_ONats(_1044760))))], (15288 ^ _779308) ^ [_1044855, _1044857] : [class_Rings_Osemiring__1(_1044855), -(hBOOL(hAPP(hAPP(c_member(_1044855), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1044855), _1044857)), c_Nat_Osemiring__1__class_ONats(_1044855))))], (15294 ^ _779308) ^ [_1044958, _1044960] : [class_Int_Onumber__ring(_1044958), -(hAPP(c_Int_Onumber__class_Onumber__of(_1044958), c_Int_Osucc(_1044960)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1044958), c_Groups_Oone__class_Oone(_1044958)), hAPP(c_Int_Onumber__class_Onumber__of(_1044958), _1044960)))], (15300 ^ _779308) ^ [_1045089] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1045089)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1045089) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15306 ^ _779308) ^ [_1045180] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1045180) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1045180)))))], (15312 ^ _779308) ^ [_1045277, _1045279, _1045281, _1045283, _1045285] : [-(c_Nat_Onat_Onat__case(_1045277, _1045279, _1045281, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1045283)), _1045285)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1045277), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1045283))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1045277, _1045277), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1045277, tc_fun(_1045277, _1045277)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1045277, tc_fun(_1045277, _1045277)), tc_Int_Oint), c_If(_1045277)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1045277, _1045279, _1045281, _1045285))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1045277, tc_Int_Oint), _1045281), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Int_Onat)), _1045285)))))], (15314 ^ _779308) ^ [_1045410, _1045412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1045410)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1045412))), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1045412))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045410)), c_Int_Onat))))))], (15320 ^ _779308) ^ [_1045555, _1045557] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1045557))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045555)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1045555)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1045557))))], (15326 ^ _779308) ^ [_1045721, _1045723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1045721)), hAPP(c_Nat_OSuc, _1045723))), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1045721))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Int_Onat)), _1045723)))))], (15332 ^ _779308) ^ [_1045848, _1045850] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1045848))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Int_Onat)), _1045850)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1045848)), hAPP(c_Nat_OSuc, _1045850))))], (15338 ^ _779308) ^ [_1045996, _1045998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1045996)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1045998))), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1045998))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045996)), c_Int_Onat))))))], (15344 ^ _779308) ^ [_1046141, _1046143] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1046143))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1046141)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1046141)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1046143))))], (15350 ^ _779308) ^ [_1046307, _1046309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1046307)), hAPP(c_Nat_OSuc, _1046309))), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1046307))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Int_Onat)), _1046309)))))], (15356 ^ _779308) ^ [_1046434, _1046436] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1046434))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Int_Onat)), _1046436)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1046434)), hAPP(c_Nat_OSuc, _1046436))))], (15362 ^ _779308) ^ [_1046567, _1046569, _1046571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1046567)), 15368 ^ _779308 : [(15369 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1046569, 15367 ^ [_1046567, _1046569, _1046571])))], (15371 ^ _779308) ^ [] : [hBOOL(hAPP(_1046569, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 15367 ^ [_1046567, _1046569, _1046571]), _1046567)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1046571)), 15376 ^ _779308 : [(15377 ^ _779308) ^ [_1046856] : [hBOOL(hAPP(_1046569, _1046856)), -(hBOOL(hAPP(_1046569, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1046856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1046571), _1046567)))))]]], (15383 ^ _779308) ^ [_1046985] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1046985))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1046985)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15389 ^ _779308) ^ [_1047074] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1047074)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1047074)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1047074)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_COMBI(tc_Nat_Onat)))))], (15395 ^ _779308) ^ [_1047129, _1047131, _1047133] : [class_Lattices_Oab__semigroup__idem__mult(_1047129), hAPP(_1047131, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047129), 15400 ^ [_1047129, _1047131, _1047133]), 15401 ^ [_1047129, _1047131, _1047133])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047129), hAPP(_1047131, 15400 ^ [_1047129, _1047131, _1047133])), hAPP(_1047131, 15401 ^ [_1047129, _1047131, _1047133])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047129), _1047133)), -(_1047133 = c_Orderings_Obot__class_Obot(tc_fun(_1047129, tc_HOL_Obool))), -(hAPP(_1047131, hAPP(c_Finite__Set_Ofold1(_1047129, c_Groups_Otimes__class_Otimes(_1047129)), _1047133)) = hAPP(c_Finite__Set_Ofold1(_1047129, c_Groups_Otimes__class_Otimes(_1047129)), hAPP(c_Set_Oimage(_1047129, _1047129, _1047131), _1047133)))], (15415 ^ _779308) ^ [_1047567, _1047569] : [c_Int_OBit1(_1047567) = c_Int_OBit1(_1047569), -(_1047567 = _1047569)], (15421 ^ _779308) ^ [_1047648, _1047650] : [_1047648 = _1047650, -(c_Int_OBit1(_1047648) = c_Int_OBit1(_1047650))], (15427 ^ _779308) ^ [_1047750, _1047752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1047750)), c_Int_OBit1(_1047752))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1047750), _1047752)))], (15433 ^ _779308) ^ [_1047851, _1047853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1047851), _1047853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1047851)), c_Int_OBit1(_1047853))))], (15439 ^ _779308) ^ [_1047973, _1047975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1047973)), c_Int_OBit1(_1047975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1047973), _1047975)))], (15445 ^ _779308) ^ [_1048074, _1048076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1048074), _1048076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1048074)), c_Int_OBit1(_1048076))))], (15451 ^ _779308) ^ [_1048196, _1048198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1048196)), c_Int_OBit1(_1048198))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1048196), _1048198)))], (15457 ^ _779308) ^ [_1048297, _1048299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1048297), _1048299)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1048297)), c_Int_OBit1(_1048299))))], (15463 ^ _779308) ^ [_1048419, _1048421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1048419)), c_Int_OBit1(_1048421))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1048419), _1048421)))], (15469 ^ _779308) ^ [_1048520, _1048522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1048520), _1048522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1048520)), c_Int_OBit1(_1048522))))], (15475 ^ _779308) ^ [_1048627] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1048627)) = _1048627)], (15477 ^ _779308) ^ [_1048665] : [c_Int_OBit1(_1048665) = c_Int_OPls], (15479 ^ _779308) ^ [_1048699] : [c_Int_OPls = c_Int_OBit1(_1048699)], (15481 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (15483 ^ _779308) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15485 ^ _779308) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (15487 ^ _779308) ^ [_1048778, _1048780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1048780)), 15494 ^ _779308 : [(15495 ^ _779308) ^ [] : [hAPP(c_Int_Onat, _1048778) = hAPP(c_Int_Onat, _1048780), -(_1048778 = _1048780)], (15501 ^ _779308) ^ [] : [_1048778 = _1048780, -(hAPP(c_Int_Onat, _1048778) = hAPP(c_Int_Onat, _1048780))]]], (15507 ^ _779308) ^ [_1049075] : [15508 ^ _779308 : [(15509 ^ _779308) ^ [_1049132] : [hBOOL(hAPP(_1049075, _1049132))]], 15511 ^ _779308 : [(15512 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15510 ^ [_1049075])))], (15514 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1049075, hAPP(c_Int_Onat, 15510 ^ [_1049075]))))]]], (15516 ^ _779308) ^ [_1049218] : [-(hBOOL(hAPP(_1049218, 15523 ^ [_1049218]))), 15517 ^ _779308 : [(15518 ^ _779308) ^ [_1049270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1049270)), hBOOL(hAPP(_1049218, hAPP(c_Int_Onat, _1049270)))]]], (15538 ^ _779308) ^ [_1049594] : [15540 ^ _779308 : [(15541 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15539 ^ [_1049594])))], (15543 ^ _779308) ^ [] : [hBOOL(hAPP(_1049594, hAPP(c_Int_Onat, 15539 ^ [_1049594])))]], 15544 ^ _779308 : [(15545 ^ _779308) ^ [_1049727] : [-(hBOOL(hAPP(_1049594, _1049727)))]]], (15527 ^ _779308) ^ [_1049409] : [hBOOL(hAPP(_1049409, 15528 ^ [_1049409])), 15531 ^ _779308 : [(15532 ^ _779308) ^ [_1049503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1049503)), -(hBOOL(hAPP(_1049409, hAPP(c_Int_Onat, _1049503))))]]], (15547 ^ _779308) ^ [_1049760, _1049762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1049760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1049762)), 15554 ^ _779308 : [(15555 ^ _779308) ^ [] : [hAPP(c_Int_Onat, _1049760) = hAPP(c_Int_Onat, _1049762), -(_1049760 = _1049762)], (15561 ^ _779308) ^ [] : [_1049760 = _1049762, -(hAPP(c_Int_Onat, _1049760) = hAPP(c_Int_Onat, _1049762))]]], (15567 ^ _779308) ^ [_1050057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1050057)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050057), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15573 ^ _779308) ^ [_1050152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050152), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1050152)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15579 ^ _779308) ^ [_1050253] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1050253) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1050253)))], (15581 ^ _779308) ^ [_1050285] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1050285)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1050285))], (15583 ^ _779308) ^ [_1050329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1050329))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1050329)))], (15589 ^ _779308) ^ [_1050412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1050412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1050412))))], (15595 ^ _779308) ^ [_1050513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1050513)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050513), c_Int_OPls)))], (15601 ^ _779308) ^ [_1050608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1050608), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1050608)), c_Int_OPls)))], (15607 ^ _779308) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (15609 ^ _779308) ^ [_1050727] : [-(c_Int_OBit1(_1050727) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1050727)), _1050727))], (15611 ^ _779308) ^ [_1050761] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1050761)), -(hAPP(c_Int_Onat, _1050761) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15617 ^ _779308) ^ [_1050842] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1050842))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1050842)) = _1050842)], (15623 ^ _779308) ^ [_1050896] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1050896)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1050896))))], (15629 ^ _779308) ^ [_1050991] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1050991))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1050991)))))], (15635 ^ _779308) ^ [_1051092] : [-(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1051092)) = _1051092)], (15637 ^ _779308) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (15639 ^ _779308) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (15641 ^ _779308) ^ [_1051169] : [hAPP(c_Int_Onat, _1051169) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051169), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15647 ^ _779308) ^ [_1051256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051256), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1051256) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15653 ^ _779308) ^ [_1051349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1051349), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1051349) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15659 ^ _779308) ^ [_1051455, _1051457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1051455)), hAPP(c_Int_Onat, _1051457))), 15662 ^ _779308 : [(15663 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1051457)))], (15665 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051455), _1051457)))]]], (15667 ^ _779308) ^ [_1051590, _1051592] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1051590)), hAPP(c_Int_Onat, _1051592)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1051592)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051590), _1051592))], (15677 ^ _779308) ^ [_1051757, _1051759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1051757)), 15680 ^ _779308 : [(15681 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1051759)), hAPP(c_Int_Onat, _1051757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051759), _1051757)))], (15687 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1051759), _1051757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1051759)), hAPP(c_Int_Onat, _1051757))))]]], (15693 ^ _779308) ^ [_1052016, _1052018] : [class_Int_Onumber__ring(_1052016), -(hAPP(c_Int_Onumber__class_Onumber__of(_1052016), c_Int_OBit1(_1052018)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052016), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1052016), c_Groups_Oone__class_Oone(_1052016)), hAPP(c_Int_Onumber__class_Onumber__of(_1052016), _1052018))), hAPP(c_Int_Onumber__class_Onumber__of(_1052016), _1052018)))], (15699 ^ _779308) ^ [_1052161, _1052163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052163)), 15706 ^ _779308 : [(15707 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1052161)), hAPP(c_Int_Onat, _1052163))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052161), _1052163)))], (15713 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1052161), _1052163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1052161)), hAPP(c_Int_Onat, _1052163))))]]], (15719 ^ _779308) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15721 ^ _779308) ^ [_1052494, _1052496] : [class_Int_Onumber__ring(_1052494), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052494), hAPP(c_Int_Onumber__class_Onumber__of(_1052494), c_Int_OBit1(c_Int_OPls))), _1052496) = _1052496)], (15727 ^ _779308) ^ [_1052595, _1052597] : [class_Int_Onumber__ring(_1052595), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052595), _1052597), hAPP(c_Int_Onumber__class_Onumber__of(_1052595), c_Int_OBit1(c_Int_OPls))) = _1052597)], (15733 ^ _779308) ^ [_1052702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052702)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1052702)) = _1052702)], (15739 ^ _779308) ^ [_1052787] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052787))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1052787)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15745 ^ _779308) ^ [_1052846, _1052848] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1052846) = _1052848, 15748 ^ _779308 : [(15749 ^ _779308) ^ [] : [-(_1052846 = hAPP(c_Int_Onat, _1052848))], (15751 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052848)))]]], (15753 ^ _779308) ^ [_1052961, _1052963] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1052961) = _1052963), _1052961 = hAPP(c_Int_Onat, _1052963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1052963))], (15763 ^ _779308) ^ [_1053108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1053108)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1053108)) = _1053108)], (15769 ^ _779308) ^ [_1053214, _1053216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1053214), hAPP(c_Int_Onat, _1053216))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1053214)), _1053216)))], (15775 ^ _779308) ^ [_1053319, _1053321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1053319)), _1053321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1053319), hAPP(c_Int_Onat, _1053321))))], (15781 ^ _779308) ^ [_1053430] : [class_Int_Onumber__ring(_1053430), -(hAPP(c_Int_Onumber__class_Onumber__of(_1053430), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1053430))], (15787 ^ _779308) ^ [_1053517] : [class_Int_Onumber__ring(_1053517), -(c_Groups_Oone__class_Oone(_1053517) = hAPP(c_Int_Onumber__class_Onumber__of(_1053517), c_Int_OBit1(c_Int_OPls)))], (15793 ^ _779308) ^ [_1053616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1053616))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1053616)))], (15799 ^ _779308) ^ [_1053699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1053699)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1053699))))], (15805 ^ _779308) ^ [_1053800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1053800)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1053800), c_Int_OPls)))], (15811 ^ _779308) ^ [_1053895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1053895), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1053895)), c_Int_OPls)))], (15817 ^ _779308) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (15819 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15821 ^ _779308) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (15823 ^ _779308) ^ [_1054062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1054062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054062)))], (15829 ^ _779308) ^ [_1054147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1054147))))], (15835 ^ _779308) ^ [_1054238, _1054240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054238)), 15838 ^ _779308 : [(15839 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1054238)), hAPP(c_Int_Onat, _1054240))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1054238), _1054240)))], (15845 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1054238), _1054240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1054238)), hAPP(c_Int_Onat, _1054240))))]]], (15851 ^ _779308) ^ [_1054497, _1054499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054497)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054499)), 15858 ^ _779308 : [(15859 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1054497)), hAPP(c_Int_Onat, _1054499))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1054497), _1054499)))], (15865 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1054497), _1054499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1054497)), hAPP(c_Int_Onat, _1054499))))]]], (15887 ^ _779308) ^ [_1055019, _1055021] : [-(hAPP(c_Int_Onat, _1055019) = _1055021), 15890 ^ _779308 : [(15891 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055019)))], (15893 ^ _779308) ^ [] : [_1055019 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1055021)]], 15894 ^ _779308 : [(15895 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055019))], (15897 ^ _779308) ^ [] : [_1055021 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (15871 ^ _779308) ^ [_1054827, _1054829] : [hAPP(c_Int_Onat, _1054827) = _1054829, 15874 ^ _779308 : [(15875 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054827)), -(_1054827 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1054829))], (15881 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1054827))), -(_1054829 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (15917 ^ _779308) ^ [_1055450, _1055452] : [-(_1055450 = hAPP(c_Int_Onat, _1055452)), 15920 ^ _779308 : [(15921 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055452)))], (15923 ^ _779308) ^ [] : [_1055452 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1055450)]], 15924 ^ _779308 : [(15925 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055452))], (15927 ^ _779308) ^ [] : [_1055450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (15901 ^ _779308) ^ [_1055258, _1055260] : [_1055258 = hAPP(c_Int_Onat, _1055260), 15904 ^ _779308 : [(15905 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055260)), -(_1055260 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1055258))], (15911 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055260))), -(_1055258 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (15931 ^ _779308) ^ [_1055674, _1055676] : [15932 ^ _779308 : [(15933 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055674))], (15935 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1055676))]], 15936 ^ _779308 : [(15937 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1055674)), hAPP(c_Int_Onat, _1055676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1055674), _1055676)))], (15943 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1055674), _1055676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1055674)), hAPP(c_Int_Onat, _1055676))))]]], (15965 ^ _779308) ^ [_1056253, _1056255] : [-(hBOOL(hAPP(_1056253, hAPP(c_Int_Onat, _1056255)))), 15969 ^ _779308 : [(15970 ^ _779308) ^ [] : [-(_1056255 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 15968 ^ [_1056253, _1056255]))], (15972 ^ _779308) ^ [] : [hBOOL(hAPP(_1056253, 15968 ^ [_1056253, _1056255]))]], 15973 ^ _779308 : [(15974 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1056255), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15976 ^ _779308) ^ [] : [hBOOL(hAPP(_1056253, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (15949 ^ _779308) ^ [_1055990, _1055992] : [hBOOL(hAPP(_1055990, hAPP(c_Int_Onat, _1055992))), 15952 ^ _779308 : [(15953 ^ _779308) ^ [_1056090] : [_1055992 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1056090), -(hBOOL(hAPP(_1055990, _1056090)))], (15959 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1055992), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1055990, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (15980 ^ _779308) ^ [_1056516, _1056518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1056516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1056518)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1056516), _1056518)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1056516)), hAPP(c_Int_Onat, _1056518)))], (15990 ^ _779308) ^ [_1056695, _1056697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1056695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1056697)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1056695)), hAPP(c_Int_Onat, _1056697)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1056695), _1056697)))], (16000 ^ _779308) ^ [_1056889, _1056891] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1056889) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1056891), 16003 ^ _779308 : [(16004 ^ _779308) ^ [] : [-(_1056889 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1056891)))], (16006 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1056891))))]]], (16008 ^ _779308) ^ [_1057022, _1057024] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1057022) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1057024)), _1057022 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1057024)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1057024)))], (16018 ^ _779308) ^ [_1057187, _1057189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057187)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1057187), _1057189)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1057187)), hAPP(c_Int_Onat, _1057189)))], (16024 ^ _779308) ^ [_1057310, _1057312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057312)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1057310)), hAPP(c_Int_Onat, _1057312)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1057310), _1057312)))], (16034 ^ _779308) ^ [_1057489, _1057491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1057489), _1057491)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1057491), _1057489)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1057491)), hAPP(c_Int_Onat, _1057489)))], (16044 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (16046 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (16048 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))))], (16050 ^ _779308) ^ [_1057728] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1057728))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1057728))], (16052 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (16054 ^ _779308) ^ [_1057781, _1057783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1057783)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1057781)), hAPP(c_Int_Onat, _1057783)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1057781, _1057783)))], (16064 ^ _779308) ^ [_1057963, _1057965] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1057963)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1057965)), hAPP(c_Int_Onat, _1057963)) = hAPP(c_Int_Onat, _1057965))], (16070 ^ _779308) ^ [_1058068, _1058070] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1058068))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1058070)), hAPP(c_Int_Onat, _1058068)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1058070), _1058068)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), c_Int_Onat)))], (16076 ^ _779308) ^ [_1058144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(c_Int_Onat, _1058144))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1058144)))], (16082 ^ _779308) ^ [_1058229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1058229)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(c_Int_Onat, _1058229))))], (16088 ^ _779308) ^ [_1058320, _1058322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1058320)), 16091 ^ _779308 : [(16092 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1058320)), _1058322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1058320), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1058322))))], (16098 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1058320), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1058322))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1058320)), _1058322)))]]], (16104 ^ _779308) ^ [_1058579, _1058581] : [class_Int_Onumber__ring(_1058579), class_Rings_Olinordered__idom(_1058579), 16111 ^ _779308 : [(16112 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058579), c_Groups_Oone__class_Oone(_1058579)), hAPP(c_Int_Onumber__class_Onumber__of(_1058579), _1058581))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1058581)))], (16118 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1058581)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058579), c_Groups_Oone__class_Oone(_1058579)), hAPP(c_Int_Onumber__class_Onumber__of(_1058579), _1058581))))]]], (16124 ^ _779308) ^ [_1058884, _1058886] : [class_Int_Onumber__ring(_1058884), class_Rings_Olinordered__idom(_1058884), 16131 ^ _779308 : [(16132 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058884), hAPP(c_Int_Onumber__class_Onumber__of(_1058884), _1058886)), c_Groups_Oone__class_Oone(_1058884))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1058886), c_Int_OBit1(c_Int_OPls))))], (16138 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1058886), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058884), hAPP(c_Int_Onumber__class_Onumber__of(_1058884), _1058886)), c_Groups_Oone__class_Oone(_1058884))))]]], (16144 ^ _779308) ^ [_1059198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1059198)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1059198)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1059198)))], (16150 ^ _779308) ^ [_1059301, _1059303] : [class_Int_Onumber__ring(_1059301), class_Rings_Olinordered__idom(_1059301), 16157 ^ _779308 : [(16158 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059301), hAPP(c_Int_Onumber__class_Onumber__of(_1059301), _1059303)), c_Groups_Oone__class_Oone(_1059301))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1059303), c_Int_OBit1(c_Int_OPls))))], (16164 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1059303), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059301), hAPP(c_Int_Onumber__class_Onumber__of(_1059301), _1059303)), c_Groups_Oone__class_Oone(_1059301))))]]], (16170 ^ _779308) ^ [_1059615, _1059617] : [class_Int_Onumber__ring(_1059615), class_Rings_Olinordered__idom(_1059615), 16177 ^ _779308 : [(16178 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059615), c_Groups_Oone__class_Oone(_1059615)), hAPP(c_Int_Onumber__class_Onumber__of(_1059615), _1059617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1059617)))], (16184 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1059617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059615), c_Groups_Oone__class_Oone(_1059615)), hAPP(c_Int_Onumber__class_Onumber__of(_1059615), _1059617))))]]], (16190 ^ _779308) ^ [_1059920, _1059922] : [class_Int_Onumber__ring(_1059920), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059920), hAPP(c_Int_Onumber__class_Onumber__of(_1059920), _1059922)), c_Groups_Oone__class_Oone(_1059920)) = hAPP(c_Int_Onumber__class_Onumber__of(_1059920), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1059922), c_Int_OBit1(c_Int_OPls))))], (16196 ^ _779308) ^ [_1060047, _1060049] : [class_Int_Onumber__ring(_1060047), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060047), c_Groups_Oone__class_Oone(_1060047)), hAPP(c_Int_Onumber__class_Onumber__of(_1060047), _1060049)) = hAPP(c_Int_Onumber__class_Onumber__of(_1060047), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1060049)))], (16202 ^ _779308) ^ [_1060168, _1060170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1060168)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1060170)), _1060168) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060170), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060168), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (16208 ^ _779308) ^ [_1060306, _1060308] : [hAPP(c_Nat_OSuc, _1060306) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1060308), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1060308))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_fequal), c_Int_Onat)), _1060306))))))], (16214 ^ _779308) ^ [_1060429, _1060431] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1060431))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_fequal), c_Int_Onat)), _1060429))))), -(hAPP(c_Nat_OSuc, _1060429) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1060431))], (16220 ^ _779308) ^ [_1060573, _1060575] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1060573) = hAPP(c_Nat_OSuc, _1060575), -(hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1060573))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_fequal), c_Int_Onat)), _1060575))))))], (16226 ^ _779308) ^ [_1060696, _1060698] : [hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_HOL_Obool), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1060696))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), c_fNot), c_Nat__Numeral_Oneg))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Int_Oint), c_fequal), c_Int_Onat)), _1060698))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1060696) = hAPP(c_Nat_OSuc, _1060698))], (16232 ^ _779308) ^ [_1060825, _1060827, _1060829, _1060831] : [-(c_Nat_Onat_Onat__case(_1060825, _1060827, _1060829, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1060831)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1060825), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1060831))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1060825, _1060825), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1060825, tc_fun(_1060825, _1060825)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1060825, tc_fun(_1060825, _1060825)), tc_Int_Oint), c_If(_1060825)), c_Nat__Numeral_Oneg)), _1060827)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1060825, tc_Int_Oint), _1060829), c_Int_Onat))))], (16234 ^ _779308) ^ [_1060927, _1060929] : [-(c_Int_Onat__aux(_1060927, _1060929) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1060927)), _1060929))], (16236 ^ _779308) ^ [_1060964, _1060966, _1060968, _1060970, _1060972] : [-(hAPP(c_Nat_Onat_Onat__rec(_1060964, _1060966, _1060968), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1060970)), _1060972)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1060964), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1060970))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1060964, _1060964), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1060964, tc_fun(_1060964, _1060964)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1060964, tc_fun(_1060964, _1060964)), tc_Int_Oint), c_If(_1060964)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1060964, _1060966, _1060968), _1060972))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1060964, _1060964), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1060964, _1060964), tc_Int_Oint), _1060968), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Int_Onat)), _1060972))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1060964, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1060964, _1060966, _1060968)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Int_Onat)), _1060972))))))], (16238 ^ _779308) ^ [_1061116, _1061118, _1061120, _1061122] : [-(hAPP(c_Nat_Onat_Onat__rec(_1061116, _1061118, _1061120), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061122)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1061116), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1061122))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1061116, _1061116), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1061116, tc_fun(_1061116, _1061116)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1061116, tc_fun(_1061116, _1061116)), tc_Int_Oint), c_If(_1061116)), c_Nat__Numeral_Oneg)), _1061118)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1061116, _1061116), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1061116, _1061116), tc_Int_Oint), _1061120), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1061116, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1061116, _1061118, _1061120)), c_Int_Onat)))))], (16240 ^ _779308) ^ [] : [-(c_Nat__Transfer_Otransfer__morphism(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16242 ^ _779308) ^ [_1061274, _1061276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1061274), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061276)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061274)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061276))], (16248 ^ _779308) ^ [_1061385, _1061387] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1061385), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061387)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061385)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1061387), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1061385)))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), c_Int_Onat)))], (16254 ^ _779308) ^ [_1061458, _1061460] : [class_Rings_Osemiring__1(_1061458), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1061460)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1061458), hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1061460))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061458), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1061458), hAPP(c_Int_Onat, _1061460))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1061458), hAPP(c_Int_Onat, _1061460))))], (16264 ^ _779308) ^ [_1061659, _1061661, _1061663] : [class_Int_Onumber__ring(_1061659), 16267 ^ _779308 : [(16268 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1061661))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1061659), hAPP(c_Int_Onumber__class_Onumber__of(_1061659), _1061663)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1061661))) = hAPP(hAPP(c_HOL_OLet(_1061659, _1061659), hAPP(hAPP(c_Power_Opower__class_Opower(_1061659), hAPP(c_Int_Onumber__class_Onumber__of(_1061659), _1061663)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1061661))), hAPP(hAPP(c_COMBS(_1061659, _1061659, _1061659), hAPP(hAPP(c_COMBB(_1061659, tc_fun(_1061659, _1061659), _1061659), c_Groups_Otimes__class_Otimes(_1061659)), hAPP(c_Groups_Otimes__class_Otimes(_1061659), hAPP(c_Int_Onumber__class_Onumber__of(_1061659), _1061663)))), c_COMBI(_1061659))))], (16274 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1061661)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1061659), hAPP(c_Int_Onumber__class_Onumber__of(_1061659), _1061663)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1061661))) = c_Groups_Oone__class_Oone(_1061659))]]], (16280 ^ _779308) ^ [_1062057, _1062059] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1062057)), hAPP(c_Nat_OSuc, _1062059)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1062057))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), c_Nat_OSuc), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Int_Oint), c_Orderings_Oord__class_Omin(tc_Nat_Onat)), c_Int_Onat)), _1062059)))))], (16282 ^ _779308) ^ [_1062114, _1062116] : [class_Groups_Oordered__ab__group__add(_1062114), -(c_Fun_Oinj__on(_1062114, _1062114, c_Groups_Ouminus__class_Ouminus(_1062114), _1062116))], (16288 ^ _779308) ^ [_1062197, _1062199] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062197))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062199))))], (16290 ^ _779308) ^ [_1062236, _1062238] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1062236)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062238))))], (16292 ^ _779308) ^ [_1062278, _1062280] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062278)), _1062280) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1062278), _1062280)))], (16294 ^ _779308) ^ [_1062321, _1062323] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1062321), _1062323)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062321)), _1062323))], (16296 ^ _779308) ^ [_1062364, _1062366] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1062364)), _1062366) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1062364), _1062366)))], (16298 ^ _779308) ^ [_1062407, _1062409] : [class_Int_Onumber__ring(_1062407), -(hAPP(c_Int_Onumber__class_Onumber__of(_1062407), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1062409)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1062407), hAPP(c_Int_Onumber__class_Onumber__of(_1062407), _1062409)))], (16304 ^ _779308) ^ [_1062518, _1062520] : [class_Int_Onumber__ring(_1062518), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1062518), hAPP(c_Int_Onumber__class_Onumber__of(_1062518), _1062520)) = hAPP(c_Int_Onumber__class_Onumber__of(_1062518), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1062520)))], (16310 ^ _779308) ^ [_1062629, _1062631, _1062633, _1062635] : [class_Groups_Ouminus(_1062629), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1062631, _1062629)), _1062633), _1062635) = hAPP(c_Groups_Ouminus__class_Ouminus(_1062629), hAPP(_1062633, _1062635)))], (16316 ^ _779308) ^ [_1062746, _1062748] : [class_Groups_Ogroup__add(_1062746), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1062746), hAPP(c_Groups_Ouminus__class_Ouminus(_1062746), _1062748)) = _1062748)], (16322 ^ _779308) ^ [_1062841, _1062843] : [class_Lattices_Oboolean__algebra(_1062841), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1062841), hAPP(c_Groups_Ouminus__class_Ouminus(_1062841), _1062843)) = _1062843)], (16328 ^ _779308) ^ [_1062936, _1062938] : [class_Orderings_Olinorder(_1062936), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1062936), _1062938), _1062938) = _1062938)], (16334 ^ _779308) ^ [_1063027, _1063029, _1063031, _1063033] : [class_Groups_Ouminus(_1063027), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1063029, _1063027)), _1063031), _1063033) = hAPP(c_Groups_Ouminus__class_Ouminus(_1063027), hAPP(_1063031, _1063033)))], (16340 ^ _779308) ^ [_1063144, _1063146, _1063148] : [class_Orderings_Olinorder(_1063144), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063144), _1063146), _1063148) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063144), _1063148), _1063146))], (16346 ^ _779308) ^ [_1063253, _1063255, _1063257] : [class_Orderings_Olinorder(_1063253), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063253), _1063255), _1063257) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063253), _1063257), _1063255))], (16352 ^ _779308) ^ [_1063362, _1063364, _1063366] : [class_Groups_Ogroup__add(_1063362), 16355 ^ _779308 : [(16356 ^ _779308) ^ [] : [_1063364 = hAPP(c_Groups_Ouminus__class_Ouminus(_1063362), _1063366), -(_1063366 = hAPP(c_Groups_Ouminus__class_Ouminus(_1063362), _1063364))], (16362 ^ _779308) ^ [] : [_1063366 = hAPP(c_Groups_Ouminus__class_Ouminus(_1063362), _1063364), -(_1063364 = hAPP(c_Groups_Ouminus__class_Ouminus(_1063362), _1063366))]]], (16368 ^ _779308) ^ [_1063603, _1063605, _1063607] : [class_Orderings_Olinorder(_1063603), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063603), _1063605), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063603), _1063605), _1063607)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063603), _1063605), _1063607))], (16374 ^ _779308) ^ [_1063728, _1063730, _1063732] : [class_Orderings_Olinorder(_1063728), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063728), _1063730), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063728), _1063730), _1063732)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063728), _1063730), _1063732))], (16380 ^ _779308) ^ [_1063853, _1063855, _1063857, _1063859] : [class_Orderings_Olinorder(_1063853), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063853), _1063855), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063853), _1063857), _1063859)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063853), _1063857), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063853), _1063855), _1063859)))], (16386 ^ _779308) ^ [_1063996, _1063998, _1064000, _1064002] : [class_Orderings_Olinorder(_1063996), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063996), _1063998), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063996), _1064000), _1064002)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063996), _1064000), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1063996), _1063998), _1064002)))], (16392 ^ _779308) ^ [_1064139, _1064141, _1064143] : [class_Groups_Ogroup__add(_1064139), 16395 ^ _779308 : [(16396 ^ _779308) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1064139), _1064141) = _1064143, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1064139), _1064143) = _1064141)], (16402 ^ _779308) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1064139), _1064143) = _1064141, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1064139), _1064141) = _1064143)]]], (16408 ^ _779308) ^ [_1064380, _1064382, _1064384] : [class_Groups_Ogroup__add(_1064380), 16411 ^ _779308 : [(16412 ^ _779308) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1064380), _1064382) = hAPP(c_Groups_Ouminus__class_Ouminus(_1064380), _1064384), -(_1064382 = _1064384)], (16418 ^ _779308) ^ [] : [_1064382 = _1064384, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1064380), _1064382) = hAPP(c_Groups_Ouminus__class_Ouminus(_1064380), _1064384))]]], (16424 ^ _779308) ^ [_1064621, _1064623, _1064625] : [class_Lattices_Oboolean__algebra(_1064621), 16427 ^ _779308 : [(16428 ^ _779308) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1064621), _1064623) = hAPP(c_Groups_Ouminus__class_Ouminus(_1064621), _1064625), -(_1064623 = _1064625)], (16434 ^ _779308) ^ [] : [_1064623 = _1064625, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1064621), _1064623) = hAPP(c_Groups_Ouminus__class_Ouminus(_1064621), _1064625))]]], (16440 ^ _779308) ^ [_1064862, _1064864, _1064866, _1064868] : [class_Orderings_Olinorder(_1064862), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064862), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064862), _1064864), _1064866)), _1064868) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064862), _1064864), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064862), _1064866), _1064868)))], (16446 ^ _779308) ^ [_1065005, _1065007, _1065009, _1065011] : [class_Orderings_Olinorder(_1065005), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065005), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065005), _1065007), _1065009)), _1065011) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065005), _1065007), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1065005), _1065009), _1065011)))], (16452 ^ _779308) ^ [_1065148] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1065148)) = _1065148)], (16454 ^ _779308) ^ [_1065177] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1065177)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1065177)))], (16456 ^ _779308) ^ [_1065225, _1065227] : [c_Int_OBit0(_1065225) = c_Int_OBit0(_1065227), -(_1065225 = _1065227)], (16462 ^ _779308) ^ [_1065306, _1065308] : [_1065306 = _1065308, -(c_Int_OBit0(_1065306) = c_Int_OBit0(_1065308))], (16468 ^ _779308) ^ [_1065393, _1065395] : [class_Rings_Oring__1(_1065393), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1065393), hAPP(c_Groups_Ouminus__class_Ouminus(_1065393), _1065395)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_1065393), _1065395), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (16474 ^ _779308) ^ [_1065510, _1065512, _1065514] : [class_Int_Onumber__ring(_1065510), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065510), hAPP(c_Groups_Ouminus__class_Ouminus(_1065510), hAPP(c_Int_Onumber__class_Onumber__of(_1065510), _1065512))), _1065514) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065510), hAPP(c_Int_Onumber__class_Onumber__of(_1065510), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1065512))), _1065514))], (16480 ^ _779308) ^ [_1065655, _1065657, _1065659] : [class_Groups_Oordered__ab__group__add(_1065655), 16483 ^ _779308 : [(16484 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065655), _1065657), hAPP(c_Groups_Ouminus__class_Ouminus(_1065655), _1065659))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065655), _1065659), hAPP(c_Groups_Ouminus__class_Ouminus(_1065655), _1065657))))], (16490 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065655), _1065659), hAPP(c_Groups_Ouminus__class_Ouminus(_1065655), _1065657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065655), _1065657), hAPP(c_Groups_Ouminus__class_Ouminus(_1065655), _1065659))))]]], (16496 ^ _779308) ^ [_1065938, _1065940, _1065942] : [class_Groups_Oordered__ab__group__add(_1065938), 16499 ^ _779308 : [(16500 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065938), hAPP(c_Groups_Ouminus__class_Ouminus(_1065938), _1065940)), _1065942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065938), hAPP(c_Groups_Ouminus__class_Ouminus(_1065938), _1065942)), _1065940)))], (16506 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065938), hAPP(c_Groups_Ouminus__class_Ouminus(_1065938), _1065942)), _1065940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1065938), hAPP(c_Groups_Ouminus__class_Ouminus(_1065938), _1065940)), _1065942)))]]], (16512 ^ _779308) ^ [_1066221, _1066223, _1066225] : [class_Groups_Oordered__ab__group__add(_1066221), 16515 ^ _779308 : [(16516 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066221), hAPP(c_Groups_Ouminus__class_Ouminus(_1066221), _1066223)), hAPP(c_Groups_Ouminus__class_Ouminus(_1066221), _1066225))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066221), _1066225), _1066223)))], (16522 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066221), _1066225), _1066223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066221), hAPP(c_Groups_Ouminus__class_Ouminus(_1066221), _1066223)), hAPP(c_Groups_Ouminus__class_Ouminus(_1066221), _1066225))))]]], (16528 ^ _779308) ^ [_1066504, _1066506, _1066508] : [class_Lattices_Oboolean__algebra(_1066504), 16531 ^ _779308 : [(16532 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066504), hAPP(c_Groups_Ouminus__class_Ouminus(_1066504), _1066506)), hAPP(c_Groups_Ouminus__class_Ouminus(_1066504), _1066508))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066504), _1066508), _1066506)))], (16538 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066504), _1066508), _1066506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066504), hAPP(c_Groups_Ouminus__class_Ouminus(_1066504), _1066506)), hAPP(c_Groups_Ouminus__class_Ouminus(_1066504), _1066508))))]]], (16544 ^ _779308) ^ [_1066787, _1066789, _1066791] : [class_Groups_Oordered__ab__group__add(_1066787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066787), _1066789), _1066791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066787), hAPP(c_Groups_Ouminus__class_Ouminus(_1066787), _1066791)), hAPP(c_Groups_Ouminus__class_Ouminus(_1066787), _1066789))))], (16554 ^ _779308) ^ [_1066966, _1066968, _1066970] : [class_Lattices_Oboolean__algebra(_1066966), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066966), _1066968), _1066970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066966), hAPP(c_Groups_Ouminus__class_Ouminus(_1066966), _1066970)), hAPP(c_Groups_Ouminus__class_Ouminus(_1066966), _1066968))))], (16564 ^ _779308) ^ [_1067145, _1067147, _1067149, _1067151] : [class_Orderings_Olinorder(_1067145), 16567 ^ _779308 : [(16578 ^ _779308) ^ [] : [16579 ^ _779308 : [(16580 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067145), _1067147), _1067151))], (16582 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067145), _1067149), _1067151))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067145), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1067145), _1067147), _1067149)), _1067151)))], (16568 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067145), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1067145), _1067147), _1067149)), _1067151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067145), _1067147), _1067151))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067145), _1067149), _1067151)))]]], (16586 ^ _779308) ^ [_1067494, _1067496, _1067498] : [class_Orderings_Olinorder(_1067494), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067494), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1067494), _1067496), _1067498)), _1067496)))], (16592 ^ _779308) ^ [_1067601, _1067603, _1067605] : [class_Orderings_Olinorder(_1067601), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067601), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1067601), _1067603), _1067605)), _1067605)))], (16598 ^ _779308) ^ [_1067708, _1067710, _1067712] : [class_Orderings_Olinorder(_1067708), 16601 ^ _779308 : [(16602 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067708), _1067710), _1067712)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1067708), _1067710), _1067712) = _1067710)], (16608 ^ _779308) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1067708), _1067710), _1067712) = _1067710, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067708), _1067710), _1067712)))]]], (16614 ^ _779308) ^ [_1067964, _1067966, _1067968, _1067970] : [class_Orderings_Olinorder(_1067964), 16617 ^ _779308 : [(16618 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067964), _1067966), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1067964), _1067968), _1067970))), 16621 ^ _779308 : [(16622 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067964), _1067966), _1067968)))], (16624 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067964), _1067966), _1067970)))]]], (16626 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067964), _1067966), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1067964), _1067968), _1067970)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067964), _1067966), _1067968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067964), _1067966), _1067970))]]], (16636 ^ _779308) ^ [_1068344, _1068346, _1068348, _1068350] : [class_Orderings_Olinorder(_1068344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068344), _1068346), _1068348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068344), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1068344), _1068346), _1068350)), _1068348)))], (16646 ^ _779308) ^ [_1068523, _1068525, _1068527, _1068529] : [class_Orderings_Olinorder(_1068523), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068523), _1068525), _1068527)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068523), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1068523), _1068529), _1068525)), _1068527)))], (16656 ^ _779308) ^ [_1068702, _1068704, _1068706] : [class_Orderings_Olinorder(_1068702), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068702), _1068704), _1068706)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1068702), _1068704), _1068706) = _1068704)], (16666 ^ _779308) ^ [_1068863, _1068865, _1068867] : [class_Orderings_Olinorder(_1068863), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068863), _1068865), _1068867)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1068863), _1068867), _1068865) = _1068865)], (16676 ^ _779308) ^ [_1069024, _1069026, _1069028, _1069030] : [class_Orderings_Olinorder(_1069024), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069024), _1069026), _1069028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069024), _1069026), _1069030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069024), _1069026), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069024), _1069028), _1069030))))], (16690 ^ _779308) ^ [_1069273, _1069275, _1069277, _1069279] : [class_Orderings_Olinorder(_1069273), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069273), _1069275), _1069277)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069273), _1069275), _1069279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069273), _1069275), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069273), _1069277), _1069279))))], (16704 ^ _779308) ^ [_1069522, _1069524, _1069526, _1069528, _1069530] : [class_Orderings_Olinorder(_1069522), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069522), _1069524), _1069526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069522), _1069528), _1069530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069522), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069522), _1069524), _1069528)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069522), _1069526), _1069530))))], (16718 ^ _779308) ^ [_1069793, _1069795, _1069797, _1069799] : [class_Orderings_Olinorder(_1069793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069793), _1069795), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1069793), _1069797), _1069799))), 16725 ^ _779308 : [(16726 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069793), _1069795), _1069797)))], (16728 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069793), _1069795), _1069799)))]]], (16730 ^ _779308) ^ [_1070016] : [class_Groups_Ogroup__add(_1070016), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1070016), c_Groups_Ozero__class_Ozero(_1070016)) = c_Groups_Ozero__class_Ozero(_1070016))], (16736 ^ _779308) ^ [_1070107, _1070109] : [class_Groups_Ogroup__add(_1070107), 16739 ^ _779308 : [(16740 ^ _779308) ^ [] : [c_Groups_Ozero__class_Ozero(_1070107) = hAPP(c_Groups_Ouminus__class_Ouminus(_1070107), _1070109), -(c_Groups_Ozero__class_Ozero(_1070107) = _1070109)], (16746 ^ _779308) ^ [] : [c_Groups_Ozero__class_Ozero(_1070107) = _1070109, -(c_Groups_Ozero__class_Ozero(_1070107) = hAPP(c_Groups_Ouminus__class_Ouminus(_1070107), _1070109))]]], (16752 ^ _779308) ^ [_1070339, _1070341] : [class_Groups_Olinordered__ab__group__add(_1070339), 16755 ^ _779308 : [(16756 ^ _779308) ^ [] : [_1070341 = hAPP(c_Groups_Ouminus__class_Ouminus(_1070339), _1070341), -(_1070341 = c_Groups_Ozero__class_Ozero(_1070339))], (16762 ^ _779308) ^ [] : [_1070341 = c_Groups_Ozero__class_Ozero(_1070339), -(_1070341 = hAPP(c_Groups_Ouminus__class_Ouminus(_1070339), _1070341))]]], (16768 ^ _779308) ^ [_1070565, _1070567] : [class_Groups_Ogroup__add(_1070565), 16771 ^ _779308 : [(16772 ^ _779308) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1070565), _1070567) = c_Groups_Ozero__class_Ozero(_1070565), -(_1070567 = c_Groups_Ozero__class_Ozero(_1070565))], (16778 ^ _779308) ^ [] : [_1070567 = c_Groups_Ozero__class_Ozero(_1070565), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1070565), _1070567) = c_Groups_Ozero__class_Ozero(_1070565))]]], (16784 ^ _779308) ^ [_1070797, _1070799] : [class_Groups_Olinordered__ab__group__add(_1070797), 16787 ^ _779308 : [(16788 ^ _779308) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1070797), _1070799) = _1070799, -(_1070799 = c_Groups_Ozero__class_Ozero(_1070797))], (16794 ^ _779308) ^ [] : [_1070799 = c_Groups_Ozero__class_Ozero(_1070797), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1070797), _1070799) = _1070799)]]], (16800 ^ _779308) ^ [_1071023, _1071025, _1071027] : [class_Groups_Oordered__ab__group__add(_1071023), 16803 ^ _779308 : [(16804 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071023), _1071025), hAPP(c_Groups_Ouminus__class_Ouminus(_1071023), _1071027))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071023), _1071027), hAPP(c_Groups_Ouminus__class_Ouminus(_1071023), _1071025))))], (16810 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071023), _1071027), hAPP(c_Groups_Ouminus__class_Ouminus(_1071023), _1071025))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071023), _1071025), hAPP(c_Groups_Ouminus__class_Ouminus(_1071023), _1071027))))]]], (16816 ^ _779308) ^ [_1071306, _1071308, _1071310] : [class_Groups_Oordered__ab__group__add(_1071306), 16819 ^ _779308 : [(16820 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071306), hAPP(c_Groups_Ouminus__class_Ouminus(_1071306), _1071308)), _1071310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071306), hAPP(c_Groups_Ouminus__class_Ouminus(_1071306), _1071310)), _1071308)))], (16826 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071306), hAPP(c_Groups_Ouminus__class_Ouminus(_1071306), _1071310)), _1071308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071306), hAPP(c_Groups_Ouminus__class_Ouminus(_1071306), _1071308)), _1071310)))]]], (16832 ^ _779308) ^ [_1071589, _1071591, _1071593] : [class_Groups_Oordered__ab__group__add(_1071589), 16835 ^ _779308 : [(16836 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071589), hAPP(c_Groups_Ouminus__class_Ouminus(_1071589), _1071591)), hAPP(c_Groups_Ouminus__class_Ouminus(_1071589), _1071593))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071589), _1071593), _1071591)))], (16842 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071589), _1071593), _1071591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071589), hAPP(c_Groups_Ouminus__class_Ouminus(_1071589), _1071591)), hAPP(c_Groups_Ouminus__class_Ouminus(_1071589), _1071593))))]]], (16848 ^ _779308) ^ [_1071872, _1071874, _1071876, _1071878] : [class_Orderings_Olinorder(_1071872), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071872), _1071874), _1071876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071872), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1071872), _1071874), _1071878)), _1071876)))], (16858 ^ _779308) ^ [_1072051, _1072053, _1072055, _1072057] : [class_Orderings_Olinorder(_1072051), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072051), _1072053), _1072055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072051), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1072051), _1072057), _1072053)), _1072055)))], (16868 ^ _779308) ^ [_1072230, _1072232, _1072234, _1072236] : [class_Orderings_Olinorder(_1072230), 16871 ^ _779308 : [(16872 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072230), _1072232), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1072230), _1072234), _1072236))), 16875 ^ _779308 : [(16876 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072230), _1072232), _1072234)))], (16878 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072230), _1072232), _1072236)))]]], (16880 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072230), _1072232), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1072230), _1072234), _1072236)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072230), _1072232), _1072234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072230), _1072232), _1072236))]]], (16890 ^ _779308) ^ [_1072610, _1072612, _1072614, _1072616] : [class_Orderings_Olinorder(_1072610), 16893 ^ _779308 : [(16904 ^ _779308) ^ [] : [16905 ^ _779308 : [(16906 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072610), _1072612), _1072616))], (16908 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072610), _1072614), _1072616))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072610), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1072610), _1072612), _1072614)), _1072616)))], (16894 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072610), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1072610), _1072612), _1072614)), _1072616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072610), _1072612), _1072616))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072610), _1072614), _1072616)))]]], (16912 ^ _779308) ^ [_1072959, _1072961, _1072963] : [class_Groups_Oab__group__add(_1072959), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1072959), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072959), _1072961), _1072963)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1072959), hAPP(c_Groups_Ouminus__class_Ouminus(_1072959), _1072961)), hAPP(c_Groups_Ouminus__class_Ouminus(_1072959), _1072963)))], (16918 ^ _779308) ^ [_1073098, _1073100, _1073102] : [class_Groups_Ogroup__add(_1073098), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1073098), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073098), _1073100), _1073102)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073098), hAPP(c_Groups_Ouminus__class_Ouminus(_1073098), _1073102)), hAPP(c_Groups_Ouminus__class_Ouminus(_1073098), _1073100)))], (16924 ^ _779308) ^ [_1073237, _1073239, _1073241] : [class_Groups_Ogroup__add(_1073237), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073237), _1073239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073237), hAPP(c_Groups_Ouminus__class_Ouminus(_1073237), _1073239)), _1073241)) = _1073241)], (16930 ^ _779308) ^ [_1073356, _1073358, _1073360] : [class_Groups_Ogroup__add(_1073356), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073356), hAPP(c_Groups_Ouminus__class_Ouminus(_1073356), _1073358)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1073356), _1073358), _1073360)) = _1073360)], (16936 ^ _779308) ^ [_1073475, _1073477, _1073479] : [class_Rings_Oring(_1073475), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1073475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073475), _1073477), _1073479)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073475), _1073477), hAPP(c_Groups_Ouminus__class_Ouminus(_1073475), _1073479)))], (16942 ^ _779308) ^ [_1073604, _1073606, _1073608] : [class_Rings_Oring(_1073604), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1073604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073604), _1073606), _1073608)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073604), hAPP(c_Groups_Ouminus__class_Ouminus(_1073604), _1073606)), _1073608))], (16948 ^ _779308) ^ [_1073733, _1073735, _1073737] : [class_Rings_Oring(_1073733), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073733), hAPP(c_Groups_Ouminus__class_Ouminus(_1073733), _1073735)), _1073737) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073733), _1073735), hAPP(c_Groups_Ouminus__class_Ouminus(_1073733), _1073737)))], (16954 ^ _779308) ^ [_1073862, _1073864, _1073866] : [class_Rings_Oring(_1073862), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073862), hAPP(c_Groups_Ouminus__class_Ouminus(_1073862), _1073864)), hAPP(c_Groups_Ouminus__class_Ouminus(_1073862), _1073866)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073862), _1073864), _1073866))], (16960 ^ _779308) ^ [_1073991, _1073993, _1073995] : [class_Rings_Oidom(_1073991), 16963 ^ _779308 : [(16974 ^ _779308) ^ [] : [16975 ^ _779308 : [(16976 ^ _779308) ^ [] : [_1073993 = _1073995], (16978 ^ _779308) ^ [] : [_1073993 = hAPP(c_Groups_Ouminus__class_Ouminus(_1073991), _1073995)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073991), _1073993), _1073993) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073991), _1073995), _1073995))], (16964 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073991), _1073993), _1073993) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073991), _1073995), _1073995), -(_1073993 = _1073995), -(_1073993 = hAPP(c_Groups_Ouminus__class_Ouminus(_1073991), _1073995))]]], (16982 ^ _779308) ^ [_1074310, _1074312, _1074314, _1074316] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1074310), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074310), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1074310), _1074312), _1074314)), _1074316) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1074310), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074310), _1074312), _1074316)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074310), _1074314), _1074316)))], (16988 ^ _779308) ^ [_1074469, _1074471, _1074473, _1074475] : [class_Rings_Ocomm__semiring__1(_1074469), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1074469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074469), _1074471), _1074473)), _1074475) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074469), hAPP(hAPP(c_Power_Opower__class_Opower(_1074469), _1074471), _1074475)), hAPP(hAPP(c_Power_Opower__class_Opower(_1074469), _1074473), _1074475)))], (16994 ^ _779308) ^ [_1074628, _1074630, _1074632] : [class_Groups_Oab__group__add(_1074628), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1074628), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074628), _1074630), _1074632)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074628), _1074632), _1074630))], (17000 ^ _779308) ^ [_1074747, _1074749, _1074751, _1074753] : [class_Groups_Oordered__ab__group__add(_1074747), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074747), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1074747), _1074749), _1074751)), _1074753) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1074747), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074747), _1074749), _1074753)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074747), _1074751), _1074753)))], (17006 ^ _779308) ^ [_1074906] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1074906) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17008 ^ _779308) ^ [_1074932] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1074932), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17010 ^ _779308) ^ [_1074961, _1074963] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1074961)), hAPP(c_Nat_OSuc, _1074963)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1074961), _1074963)))], (17012 ^ _779308) ^ [_1075007, _1075009, _1075011] : [class_Int_Onumber__ring(_1075007), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1075007), _1075009), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1075011))) = hAPP(hAPP(c_HOL_OLet(_1075007, _1075007), hAPP(hAPP(c_Power_Opower__class_Opower(_1075007), _1075009), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1075011))), hAPP(hAPP(c_COMBS(_1075007, _1075007, _1075007), c_Groups_Otimes__class_Otimes(_1075007)), c_COMBI(_1075007))))], (17018 ^ _779308) ^ [_1075193, _1075195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1075193)), c_Int_OBit0(_1075195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1075193), _1075195)))], (17024 ^ _779308) ^ [_1075294, _1075296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1075294), _1075296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1075294)), c_Int_OBit0(_1075296))))], (17030 ^ _779308) ^ [_1075416, _1075418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1075416)), c_Int_OBit0(_1075418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1075416), _1075418)))], (17036 ^ _779308) ^ [_1075517, _1075519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1075517), _1075519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1075517)), c_Int_OBit0(_1075519))))], (17042 ^ _779308) ^ [_1075639, _1075641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1075639)), c_Int_OBit0(_1075641))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075639), _1075641)))], (17048 ^ _779308) ^ [_1075740, _1075742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075740), _1075742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1075740)), c_Int_OBit0(_1075742))))], (17054 ^ _779308) ^ [_1075862, _1075864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1075862)), c_Int_OBit0(_1075864))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075862), _1075864)))], (17060 ^ _779308) ^ [_1075963, _1075965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1075963), _1075965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1075963)), c_Int_OBit0(_1075965))))], (17066 ^ _779308) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17068 ^ _779308) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (17070 ^ _779308) ^ [_1076118] : [c_Int_OPls = c_Int_OBit0(_1076118), -(c_Int_OPls = _1076118)], (17076 ^ _779308) ^ [_1076193] : [c_Int_OPls = _1076193, -(c_Int_OPls = c_Int_OBit0(_1076193))], (17082 ^ _779308) ^ [_1076286] : [c_Int_OBit0(_1076286) = c_Int_OPls, -(_1076286 = c_Int_OPls)], (17088 ^ _779308) ^ [_1076361] : [_1076361 = c_Int_OPls, -(c_Int_OBit0(_1076361) = c_Int_OPls)], (17094 ^ _779308) ^ [_1076454, _1076456] : [c_Int_OBit0(_1076454) = c_Int_OBit1(_1076456)], (17096 ^ _779308) ^ [_1076495, _1076497] : [c_Int_OBit1(_1076495) = c_Int_OBit0(_1076497)], (17098 ^ _779308) ^ [_1076524] : [-(c_Int_OBit0(_1076524) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1076524), _1076524))], (17100 ^ _779308) ^ [_1076555, _1076557] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1076555)), c_Int_OBit0(_1076557)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1076555), _1076557)))], (17102 ^ _779308) ^ [_1076598, _1076600, _1076602, _1076604] : [class_Rings_Ocomm__semiring__1(_1076598), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1076598), hAPP(hAPP(c_Power_Opower__class_Opower(_1076598), _1076600), _1076602)), _1076604) = hAPP(hAPP(c_Power_Opower__class_Opower(_1076598), _1076600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1076602), _1076604)))], (17108 ^ _779308) ^ [_1076737, _1076739, _1076741] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1076737), _1076739)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1076741), _1076739)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1076737), _1076741)), _1076739))], (17110 ^ _779308) ^ [_1076794, _1076796, _1076798] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1076794), _1076796)), _1076798) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1076794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1076796), _1076798)))], (17112 ^ _779308) ^ [_1076845, _1076847] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1076845), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1076847))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1076845), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1076847))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Groups_Otimes__class_Otimes(tc_Int_Oint)), c_COMBI(tc_Int_Oint))))], (17114 ^ _779308) ^ [_1076896, _1076898] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1076896)), _1076898) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1076896), _1076898)))], (17116 ^ _779308) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (17118 ^ _779308) ^ [_1076955, _1076957] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1076955), _1076957)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1076955)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1076957)))], (17120 ^ _779308) ^ [_1077001] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1077001)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1077001)))], (17122 ^ _779308) ^ [_1077036, _1077038] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1077036)), c_Int_OBit0(_1077038)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1077036), _1077038)))], (17124 ^ _779308) ^ [_1077079, _1077081] : [class_Rings_Ocomm__semiring__1(_1077079), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1077079), _1077081), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1077081)], (17130 ^ _779308) ^ [_1077170, _1077172] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1077170)), _1077172) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1077170), _1077172)))], (17132 ^ _779308) ^ [_1077213, _1077215] : [class_Rings_Oring__1__no__zero__divisors(_1077213), 17135 ^ _779308 : [(17146 ^ _779308) ^ [] : [17147 ^ _779308 : [(17148 ^ _779308) ^ [] : [_1077215 = c_Groups_Oone__class_Oone(_1077213)], (17150 ^ _779308) ^ [] : [_1077215 = hAPP(c_Groups_Ouminus__class_Ouminus(_1077213), c_Groups_Oone__class_Oone(_1077213))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1077213), _1077215), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1077213))], (17136 ^ _779308) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1077213), _1077215), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1077213), -(_1077215 = c_Groups_Oone__class_Oone(_1077213)), -(_1077215 = hAPP(c_Groups_Ouminus__class_Ouminus(_1077213), c_Groups_Oone__class_Oone(_1077213)))]]], (17154 ^ _779308) ^ [_1077520, _1077522, _1077524] : [class_Rings_Oring__1(_1077520), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1077520), hAPP(c_Groups_Ouminus__class_Ouminus(_1077520), _1077522)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1077524)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1077520), _1077522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1077524)))], (17160 ^ _779308) ^ [_1077651] : [class_Orderings_Olinorder(_1077651), -(c_Finite__Set_Ofun__left__comm__idem(_1077651, _1077651, c_Orderings_Oord__class_Omin(_1077651)))], (17166 ^ _779308) ^ [_1077730, _1077732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1077730)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1077730)), _1077732) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1077730), _1077732)))], (17172 ^ _779308) ^ [_1077847, _1077849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1077847)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1077847), _1077849)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1077847)), _1077849))], (17178 ^ _779308) ^ [_1077964, _1077966] : [class_Rings_Oring__1(_1077964), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1077964), hAPP(c_Groups_Ouminus__class_Ouminus(_1077964), c_Groups_Oone__class_Oone(_1077964))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1077966)) = c_Groups_Oone__class_Oone(_1077964))], (17184 ^ _779308) ^ [_1078079, _1078081, _1078083] : [class_Int_Onumber__ring(_1078079), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078079), hAPP(c_Int_Onumber__class_Onumber__of(_1078079), _1078081)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1078083))) = hAPP(hAPP(c_HOL_OLet(_1078079, _1078079), hAPP(hAPP(c_Power_Opower__class_Opower(_1078079), hAPP(c_Int_Onumber__class_Onumber__of(_1078079), _1078081)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1078083))), hAPP(hAPP(c_COMBS(_1078079, _1078079, _1078079), c_Groups_Otimes__class_Otimes(_1078079)), c_COMBI(_1078079))))], (17190 ^ _779308) ^ [_1078270, _1078272] : [class_Rings_Oring__1(_1078270), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078270), hAPP(c_Groups_Ouminus__class_Ouminus(_1078270), c_Groups_Oone__class_Oone(_1078270))), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1078272))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1078270), c_Groups_Oone__class_Oone(_1078270)))], (17196 ^ _779308) ^ [_1078401, _1078403] : [class_Rings_Oring__1__no__zero__divisors(_1078401), 17199 ^ _779308 : [(17200 ^ _779308) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1078401), _1078403), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1078401), -(_1078403 = c_Groups_Ozero__class_Ozero(_1078401))], (17206 ^ _779308) ^ [] : [_1078403 = c_Groups_Ozero__class_Ozero(_1078401), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078401), _1078403), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1078401))]]], (17212 ^ _779308) ^ [_1078642] : [class_Rings_Osemiring__1(_1078642), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078642), c_Groups_Ozero__class_Ozero(_1078642)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1078642))], (17218 ^ _779308) ^ [_1078739, _1078741] : [class_Rings_Ocomm__semiring__1(_1078739), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078739), _1078741), _1078741) = hAPP(hAPP(c_Power_Opower__class_Opower(_1078739), _1078741), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (17224 ^ _779308) ^ [_1078846, _1078848] : [class_Groups_Omonoid__mult(_1078846), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078846), _1078848), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078846), _1078848), _1078848))], (17230 ^ _779308) ^ [_1078953] : [class_Rings_Osemiring__1(_1078953), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1078953), c_Groups_Oone__class_Oone(_1078953)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1078953))], (17236 ^ _779308) ^ [_1079050, _1079052, _1079054] : [class_Groups_Omonoid__mult(_1079050), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1079050), _1079052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1079054)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1079050), hAPP(hAPP(c_Power_Opower__class_Opower(_1079050), _1079052), _1079054)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (17242 ^ _779308) ^ [_1079181, _1079183] : [class_Groups_Oordered__ab__group__add(_1079181), 17245 ^ _779308 : [(17246 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079181), c_Groups_Ozero__class_Ozero(_1079181)), hAPP(c_Groups_Ouminus__class_Ouminus(_1079181), _1079183))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079181), _1079183), c_Groups_Ozero__class_Ozero(_1079181))))], (17252 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079181), _1079183), c_Groups_Ozero__class_Ozero(_1079181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079181), c_Groups_Ozero__class_Ozero(_1079181)), hAPP(c_Groups_Ouminus__class_Ouminus(_1079181), _1079183))))]]], (17258 ^ _779308) ^ [_1079455, _1079457] : [class_Groups_Olinordered__ab__group__add(_1079455), 17261 ^ _779308 : [(17262 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079455), _1079457), hAPP(c_Groups_Ouminus__class_Ouminus(_1079455), _1079457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079455), _1079457), c_Groups_Ozero__class_Ozero(_1079455))))], (17268 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079455), _1079457), c_Groups_Ozero__class_Ozero(_1079455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079455), _1079457), hAPP(c_Groups_Ouminus__class_Ouminus(_1079455), _1079457))))]]], (17274 ^ _779308) ^ [_1079723, _1079725] : [class_Groups_Oordered__ab__group__add(_1079723), 17277 ^ _779308 : [(17278 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079723), hAPP(c_Groups_Ouminus__class_Ouminus(_1079723), _1079725)), c_Groups_Ozero__class_Ozero(_1079723))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079723), c_Groups_Ozero__class_Ozero(_1079723)), _1079725)))], (17284 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079723), c_Groups_Ozero__class_Ozero(_1079723)), _1079725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079723), hAPP(c_Groups_Ouminus__class_Ouminus(_1079723), _1079725)), c_Groups_Ozero__class_Ozero(_1079723))))]]], (17290 ^ _779308) ^ [_1079997, _1079999] : [class_Groups_Olinordered__ab__group__add(_1079997), 17293 ^ _779308 : [(17294 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079997), hAPP(c_Groups_Ouminus__class_Ouminus(_1079997), _1079999)), _1079999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079997), c_Groups_Ozero__class_Ozero(_1079997)), _1079999)))], (17300 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079997), c_Groups_Ozero__class_Ozero(_1079997)), _1079999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079997), hAPP(c_Groups_Ouminus__class_Ouminus(_1079997), _1079999)), _1079999)))]]], (17306 ^ _779308) ^ [_1080265, _1080267] : [class_Rings_Olinordered__idom(_1080265), 17309 ^ _779308 : [(17310 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080265), _1080267), hAPP(c_Groups_Ouminus__class_Ouminus(_1080265), _1080267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080265), _1080267), c_Groups_Ozero__class_Ozero(_1080265))))], (17316 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080265), _1080267), c_Groups_Ozero__class_Ozero(_1080265))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080265), _1080267), hAPP(c_Groups_Ouminus__class_Ouminus(_1080265), _1080267))))]]], (17322 ^ _779308) ^ [_1080533, _1080535] : [class_Groups_Olinordered__ab__group__add(_1080533), 17325 ^ _779308 : [(17326 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080533), hAPP(c_Groups_Ouminus__class_Ouminus(_1080533), _1080535)), _1080535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080533), c_Groups_Ozero__class_Ozero(_1080533)), _1080535)))], (17332 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080533), c_Groups_Ozero__class_Ozero(_1080533)), _1080535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080533), hAPP(c_Groups_Ouminus__class_Ouminus(_1080533), _1080535)), _1080535)))]]], (17338 ^ _779308) ^ [_1080801, _1080803] : [class_Groups_Oordered__ab__group__add(_1080801), 17341 ^ _779308 : [(17342 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080801), hAPP(c_Groups_Ouminus__class_Ouminus(_1080801), _1080803)), c_Groups_Ozero__class_Ozero(_1080801))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080801), c_Groups_Ozero__class_Ozero(_1080801)), _1080803)))], (17348 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080801), c_Groups_Ozero__class_Ozero(_1080801)), _1080803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080801), hAPP(c_Groups_Ouminus__class_Ouminus(_1080801), _1080803)), c_Groups_Ozero__class_Ozero(_1080801))))]]], (17354 ^ _779308) ^ [_1081075, _1081077] : [class_Groups_Oordered__ab__group__add(_1081075), 17357 ^ _779308 : [(17358 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081075), c_Groups_Ozero__class_Ozero(_1081075)), hAPP(c_Groups_Ouminus__class_Ouminus(_1081075), _1081077))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081075), _1081077), c_Groups_Ozero__class_Ozero(_1081075))))], (17364 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081075), _1081077), c_Groups_Ozero__class_Ozero(_1081075))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081075), c_Groups_Ozero__class_Ozero(_1081075)), hAPP(c_Groups_Ouminus__class_Ouminus(_1081075), _1081077))))]]], (17370 ^ _779308) ^ [_1081349, _1081351] : [class_Groups_Ogroup__add(_1081349), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081349), _1081351), hAPP(c_Groups_Ouminus__class_Ouminus(_1081349), _1081351)) = c_Groups_Ozero__class_Ozero(_1081349))], (17376 ^ _779308) ^ [_1081454, _1081456, _1081458] : [class_Groups_Ogroup__add(_1081454), 17379 ^ _779308 : [(17380 ^ _779308) ^ [] : [_1081456 = hAPP(c_Groups_Ouminus__class_Ouminus(_1081454), _1081458), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081454), _1081456), _1081458) = c_Groups_Ozero__class_Ozero(_1081454))], (17386 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081454), _1081456), _1081458) = c_Groups_Ozero__class_Ozero(_1081454), -(_1081456 = hAPP(c_Groups_Ouminus__class_Ouminus(_1081454), _1081458))]]], (17392 ^ _779308) ^ [_1081710, _1081712] : [class_Groups_Ogroup__add(_1081710), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081710), hAPP(c_Groups_Ouminus__class_Ouminus(_1081710), _1081712)), _1081712) = c_Groups_Ozero__class_Ozero(_1081710))], (17398 ^ _779308) ^ [_1081815, _1081817] : [class_Groups_Oab__group__add(_1081815), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081815), hAPP(c_Groups_Ouminus__class_Ouminus(_1081815), _1081817)), _1081817) = c_Groups_Ozero__class_Ozero(_1081815))], (17404 ^ _779308) ^ [_1081920, _1081922, _1081924] : [class_Groups_Ogroup__add(_1081920), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1081920), _1081922), _1081924) = c_Groups_Ozero__class_Ozero(_1081920), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1081920), _1081922) = _1081924)], (17414 ^ _779308) ^ [_1082081, _1082083] : [class_Groups_Ogroup__add(_1082081), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082081), c_Groups_Ozero__class_Ozero(_1082081)), _1082083) = hAPP(c_Groups_Ouminus__class_Ouminus(_1082081), _1082083))], (17420 ^ _779308) ^ [_1082186, _1082188, _1082190] : [class_Int_Onumber(_1082186), class_Orderings_Oord(_1082186), 17427 ^ _779308 : [(17428 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082186), hAPP(c_Int_Onumber__class_Onumber__of(_1082186), _1082188)), hAPP(c_Int_Onumber__class_Onumber__of(_1082186), _1082190))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1082186), hAPP(c_Int_Onumber__class_Onumber__of(_1082186), _1082188)), hAPP(c_Int_Onumber__class_Onumber__of(_1082186), _1082190)) = hAPP(c_Int_Onumber__class_Onumber__of(_1082186), _1082188))], (17434 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082186), hAPP(c_Int_Onumber__class_Onumber__of(_1082186), _1082188)), hAPP(c_Int_Onumber__class_Onumber__of(_1082186), _1082190)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1082186), hAPP(c_Int_Onumber__class_Onumber__of(_1082186), _1082188)), hAPP(c_Int_Onumber__class_Onumber__of(_1082186), _1082190)) = hAPP(c_Int_Onumber__class_Onumber__of(_1082186), _1082190))]]], (17440 ^ _779308) ^ [_1082578, _1082580, _1082582] : [class_Rings_Ocomm__ring__1(_1082578), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082578), _1082580), _1082582) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082578), _1082580), hAPP(c_Groups_Ouminus__class_Ouminus(_1082578), _1082582)))], (17446 ^ _779308) ^ [_1082697, _1082699, _1082701] : [class_Groups_Ogroup__add(_1082697), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082697), _1082699), hAPP(c_Groups_Ouminus__class_Ouminus(_1082697), _1082701)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082697), _1082699), _1082701))], (17452 ^ _779308) ^ [_1082816, _1082818, _1082820] : [class_Groups_Oab__group__add(_1082816), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082816), _1082818), _1082820) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082816), _1082818), hAPP(c_Groups_Ouminus__class_Ouminus(_1082816), _1082820)))], (17458 ^ _779308) ^ [_1082935, _1082937, _1082939] : [class_Groups_Ogroup__add(_1082935), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082935), _1082937), _1082939) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082935), _1082937), hAPP(c_Groups_Ouminus__class_Ouminus(_1082935), _1082939)))], (17464 ^ _779308) ^ [_1083054, _1083056] : [class_Rings_Oring__1__no__zero__divisors(_1083054), 17467 ^ _779308 : [(17478 ^ _779308) ^ [] : [17479 ^ _779308 : [(17480 ^ _779308) ^ [] : [_1083056 = c_Groups_Oone__class_Oone(_1083054)], (17482 ^ _779308) ^ [] : [_1083056 = hAPP(c_Groups_Ouminus__class_Ouminus(_1083054), c_Groups_Oone__class_Oone(_1083054))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083054), _1083056), _1083056) = c_Groups_Oone__class_Oone(_1083054))], (17468 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083054), _1083056), _1083056) = c_Groups_Oone__class_Oone(_1083054), -(_1083056 = c_Groups_Oone__class_Oone(_1083054)), -(_1083056 = hAPP(c_Groups_Ouminus__class_Ouminus(_1083054), c_Groups_Oone__class_Oone(_1083054)))]]], (17486 ^ _779308) ^ [_1083361, _1083363] : [class_Rings_Ocomm__ring__1(_1083361), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1083361), _1083363) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083361), hAPP(c_Groups_Ouminus__class_Ouminus(_1083361), c_Groups_Oone__class_Oone(_1083361))), _1083363))], (17492 ^ _779308) ^ [_1083476, _1083478, _1083480] : [class_Rings_Ocomm__semiring__1(_1083476), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1083476), _1083478), hAPP(c_Nat_OSuc, _1083480)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083476), _1083478), hAPP(hAPP(c_Power_Opower__class_Opower(_1083476), _1083478), _1083480)))], (17498 ^ _779308) ^ [_1083607, _1083609, _1083611] : [class_Rings_Ocomm__semiring__1(_1083607), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083607), _1083609), hAPP(hAPP(c_Power_Opower__class_Opower(_1083607), _1083609), _1083611)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1083607), _1083609), hAPP(c_Nat_OSuc, _1083611)))], (17504 ^ _779308) ^ [_1083738, _1083740, _1083742] : [class_Rings_Ocomm__semiring__1(_1083738), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083738), hAPP(hAPP(c_Power_Opower__class_Opower(_1083738), _1083740), _1083742)), _1083740) = hAPP(hAPP(c_Power_Opower__class_Opower(_1083738), _1083740), hAPP(c_Nat_OSuc, _1083742)))], (17510 ^ _779308) ^ [_1083869, _1083871] : [class_Rings_Ocomm__semiring__1(_1083869), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1083869), _1083871), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1083869))], (17516 ^ _779308) ^ [_1083964, _1083966, _1083968, _1083970] : [class_Rings_Ocomm__semiring__1(_1083964), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083964), hAPP(hAPP(c_Power_Opower__class_Opower(_1083964), _1083966), _1083968)), hAPP(hAPP(c_Power_Opower__class_Opower(_1083964), _1083966), _1083970)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1083964), _1083966), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1083968), _1083970)))], (17522 ^ _779308) ^ [_1084131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1084131)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084131), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17528 ^ _779308) ^ [_1084226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084226), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1084226)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17534 ^ _779308) ^ [_1084327, _1084329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1084327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1084327), _1084329))))], (17540 ^ _779308) ^ [_1084424, _1084426, _1084428] : [-(hAPP(c_Nat_Onat_Onat__rec(_1084424, _1084426, _1084428), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1084426)], (17542 ^ _779308) ^ [_1084458, _1084460, _1084462, _1084464] : [-(hAPP(c_Nat_Onat_Onat__rec(_1084458, _1084460, _1084462), hAPP(c_Nat_OSuc, _1084464)) = hAPP(hAPP(_1084462, _1084464), hAPP(c_Nat_Onat_Onat__rec(_1084458, _1084460, _1084462), _1084464)))], (17544 ^ _779308) ^ [_1084522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1084522))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1084522)))], (17550 ^ _779308) ^ [_1084605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1084605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1084605))))], (17556 ^ _779308) ^ [_1084706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1084706)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084706), c_Int_OPls)))], (17562 ^ _779308) ^ [_1084801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084801), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1084801)), c_Int_OPls)))], (17568 ^ _779308) ^ [_1084917, _1084919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1084917)), c_Int_OBit1(_1084919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084917), _1084919)))], (17574 ^ _779308) ^ [_1085018, _1085020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085018), _1085020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085018)), c_Int_OBit1(_1085020))))], (17580 ^ _779308) ^ [_1085140, _1085142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085140)), c_Int_OBit1(_1085142))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085140), _1085142)))], (17586 ^ _779308) ^ [_1085241, _1085243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085241), _1085243)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1085241)), c_Int_OBit1(_1085243))))], (17592 ^ _779308) ^ [_1085360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1085360)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085360), c_Int_OPls)))], (17598 ^ _779308) ^ [_1085455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085455), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1085455)), c_Int_OPls)))], (17604 ^ _779308) ^ [_1085568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1085568))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1085568)))], (17610 ^ _779308) ^ [_1085651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1085651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1085651))))], (17616 ^ _779308) ^ [_1085755, _1085757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1085755)), c_Int_OBit0(_1085757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085755), _1085757)))], (17622 ^ _779308) ^ [_1085856, _1085858] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085856), _1085858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1085856)), c_Int_OBit0(_1085858))))], (17628 ^ _779308) ^ [_1085978, _1085980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1085978)), c_Int_OBit0(_1085980))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085978), _1085980)))], (17634 ^ _779308) ^ [_1086079, _1086081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086079), _1086081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1086079)), c_Int_OBit0(_1086081))))], (17640 ^ _779308) ^ [_1086186, _1086188] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1086186)), c_Int_OBit0(_1086188)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086186), _1086188)))], (17642 ^ _779308) ^ [_1086229, _1086231] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1086229)), c_Int_OBit1(_1086231)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086229), _1086231)))], (17644 ^ _779308) ^ [_1086272, _1086274, _1086276] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1086272), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086274), _1086276)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1086272), _1086274)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1086272), _1086276)))], (17646 ^ _779308) ^ [_1086329] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1086329)), _1086329) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17648 ^ _779308) ^ [_1086376, _1086378] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1086376)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1086378), 17651 ^ _779308 : [(17652 ^ _779308) ^ [] : [-(_1086376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17654 ^ _779308) ^ [] : [-(_1086378 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (17656 ^ _779308) ^ [_1086493, _1086495] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1086493)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1086495)), _1086493 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1086495 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17666 ^ _779308) ^ [_1086642] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1086642)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1086642)))], (17668 ^ _779308) ^ [_1086675, _1086677] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1086675)), c_Int_OBit1(_1086677)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1086675), _1086677)))], (17670 ^ _779308) ^ [_1086718, _1086720] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1086718)), c_Int_OBit0(_1086720)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1086718), _1086720)))], (17672 ^ _779308) ^ [_1086773, _1086775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1086773)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1086775))))], (17674 ^ _779308) ^ [_1086812, _1086814] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1086812), _1086814) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086812), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1086814)))], (17676 ^ _779308) ^ [_1086852, _1086854] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086852), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1086854)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1086852), _1086854))], (17678 ^ _779308) ^ [_1086892, _1086894] : [class_Rings_Oring__1(_1086892), hBOOL(hAPP(hAPP(c_member(_1086892), _1086894), c_Int_Oring__1__class_OInts(_1086892))), -(hBOOL(hAPP(hAPP(c_member(_1086892), hAPP(c_Groups_Ouminus__class_Ouminus(_1086892), _1086894)), c_Int_Oring__1__class_OInts(_1086892))))], (17688 ^ _779308) ^ [_1087065, _1087067, _1087069] : [class_Rings_Oring__1(_1087065), hBOOL(hAPP(hAPP(c_member(_1087065), _1087067), c_Int_Oring__1__class_OInts(_1087065))), -(hBOOL(hAPP(hAPP(c_member(_1087065), hAPP(hAPP(c_Power_Opower__class_Opower(_1087065), _1087067), _1087069)), c_Int_Oring__1__class_OInts(_1087065))))], (17698 ^ _779308) ^ [_1087260] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1087260)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087260))))], (17704 ^ _779308) ^ [_1087355] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1087355))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1087355)))))], (17710 ^ _779308) ^ [_1087456] : [-(c_Int_Opred(c_Int_OBit0(_1087456)) = c_Int_OBit1(c_Int_Opred(_1087456)))], (17712 ^ _779308) ^ [_1087487] : [-(c_Int_Opred(c_Int_OBit1(_1087487)) = c_Int_OBit0(_1087487))], (17714 ^ _779308) ^ [_1087516] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1087516)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1087516))))], (17716 ^ _779308) ^ [_1087551, _1087553] : [class_Rings_Olinordered__idom(_1087551), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087551), c_Groups_Ozero__class_Ozero(_1087551)), hAPP(hAPP(c_Power_Opower__class_Opower(_1087551), _1087553), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (17722 ^ _779308) ^ [_1087660, _1087662, _1087664] : [class_Rings_Olinordered__semidom(_1087660), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087660), hAPP(hAPP(c_Power_Opower__class_Opower(_1087660), _1087662), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1087660), _1087664), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087660), c_Groups_Ozero__class_Ozero(_1087660)), _1087664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087660), _1087662), _1087664)))], (17736 ^ _779308) ^ [_1087923, _1087925, _1087927] : [class_Rings_Olinordered__semidom(_1087923), hAPP(hAPP(c_Power_Opower__class_Opower(_1087923), _1087925), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_1087923), _1087927), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087923), c_Groups_Ozero__class_Ozero(_1087923)), _1087925)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1087923), c_Groups_Ozero__class_Ozero(_1087923)), _1087927)), -(_1087925 = _1087927)], (17754 ^ _779308) ^ [_1088230, _1088232] : [class_Rings_Olinordered__idom(_1088230), 17757 ^ _779308 : [(17758 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088230), c_Groups_Ozero__class_Ozero(_1088230)), hAPP(hAPP(c_Power_Opower__class_Opower(_1088230), _1088232), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1088232 = c_Groups_Ozero__class_Ozero(_1088230)], (17764 ^ _779308) ^ [] : [-(_1088232 = c_Groups_Ozero__class_Ozero(_1088230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088230), c_Groups_Ozero__class_Ozero(_1088230)), hAPP(hAPP(c_Power_Opower__class_Opower(_1088230), _1088232), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (17770 ^ _779308) ^ [_1088454, _1088456] : [class_Rings_Olinordered__idom(_1088454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1088454), hAPP(hAPP(c_Power_Opower__class_Opower(_1088454), _1088456), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1088454)))], (17776 ^ _779308) ^ [_1088564, _1088566, _1088568] : [class_Rings_Olinordered__idom(_1088564), 17779 ^ _779308 : [(17780 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088564), hAPP(hAPP(c_Power_Opower__class_Opower(_1088564), _1088566), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1088564), _1088568), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1088564), 17783 ^ _779308 : [(17784 ^ _779308) ^ [] : [-(_1088566 = c_Groups_Ozero__class_Ozero(_1088564))], (17786 ^ _779308) ^ [] : [-(_1088568 = c_Groups_Ozero__class_Ozero(_1088564))]]], (17788 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088564), hAPP(hAPP(c_Power_Opower__class_Opower(_1088564), _1088566), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1088564), _1088568), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1088564)), _1088566 = c_Groups_Ozero__class_Ozero(_1088564), _1088568 = c_Groups_Ozero__class_Ozero(_1088564)]]], (17798 ^ _779308) ^ [_1088939, _1088941] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1088939), hAPP(c_Int_Onumber__class_Onumber__of(_1088939), _1088941)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1088939), hAPP(c_Int_Onumber__class_Onumber__of(_1088939), _1088941)), hAPP(c_Int_Onumber__class_Onumber__of(_1088939), _1088941))), class_Groups_Omonoid__mult(_1088939), class_Int_Onumber(_1088939)], (17808 ^ _779308) ^ [_1089126] : [-(c_Int_Osucc(c_Int_OBit1(_1089126)) = c_Int_OBit0(c_Int_Osucc(_1089126)))], (17810 ^ _779308) ^ [_1089157] : [-(c_Int_Osucc(c_Int_OBit0(_1089157)) = c_Int_OBit1(_1089157))], (17812 ^ _779308) ^ [_1089186, _1089188, _1089190] : [class_Rings_Ocomm__semiring__1(_1089186), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1089186), _1089188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1089190)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089186), hAPP(hAPP(c_Power_Opower__class_Opower(_1089186), _1089188), _1089190)), hAPP(hAPP(c_Power_Opower__class_Opower(_1089186), _1089188), _1089190)))], (17818 ^ _779308) ^ [_1089333] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1089333)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089333)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_COMBI(tc_Nat_Onat))))], (17820 ^ _779308) ^ [_1089379, _1089381] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089379))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089379)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089381)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089381)))], (17826 ^ _779308) ^ [_1089496, _1089498] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089496)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089496)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089498)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089496)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089498))))], (17832 ^ _779308) ^ [_1089575, _1089577] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089575))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089575)), _1089577) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1089577))], (17838 ^ _779308) ^ [_1089680, _1089682] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089680)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1089680)), _1089682) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1089680)), _1089682)))], (17844 ^ _779308) ^ [_1089744, _1089746, _1089748] : [class_Rings_Olinordered__semidom(_1089744), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089744), hAPP(hAPP(c_Power_Opower__class_Opower(_1089744), _1089746), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1089744), _1089748), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1089744), c_Groups_Ozero__class_Ozero(_1089744)), _1089748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1089744), _1089746), _1089748)))], (17858 ^ _779308) ^ [_1090007, _1090009, _1090011] : [class_Rings_Olinordered__idom(_1090007), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090007), c_Groups_Ozero__class_Ozero(_1090007)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090007), hAPP(hAPP(c_Power_Opower__class_Opower(_1090007), _1090009), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1090007), _1090011), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (17864 ^ _779308) ^ [_1090150, _1090152, _1090154] : [class_Rings_Olinordered__idom(_1090150), 17867 ^ _779308 : [(17868 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090150), hAPP(hAPP(c_Power_Opower__class_Opower(_1090150), _1090152), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1090150), _1090154), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1090150))), 17871 ^ _779308 : [(17872 ^ _779308) ^ [] : [-(_1090152 = c_Groups_Ozero__class_Ozero(_1090150))], (17874 ^ _779308) ^ [] : [-(_1090154 = c_Groups_Ozero__class_Ozero(_1090150))]]], (17876 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1090150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090150), hAPP(hAPP(c_Power_Opower__class_Opower(_1090150), _1090152), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1090150), _1090154), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1090150)))), _1090152 = c_Groups_Ozero__class_Ozero(_1090150), _1090154 = c_Groups_Ozero__class_Ozero(_1090150)]]], (17886 ^ _779308) ^ [_1090546, _1090548, _1090550] : [class_Rings_Olinordered__idom(_1090546), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090546), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090546), hAPP(hAPP(c_Power_Opower__class_Opower(_1090546), _1090548), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1090546), _1090550), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1090546)))], (17892 ^ _779308) ^ [_1090690, _1090692, _1090694] : [class_Rings_Olinordered__idom(_1090690), 17895 ^ _779308 : [(17906 ^ _779308) ^ [] : [17907 ^ _779308 : [(17908 ^ _779308) ^ [] : [-(_1090692 = c_Groups_Ozero__class_Ozero(_1090690))], (17910 ^ _779308) ^ [] : [-(_1090694 = c_Groups_Ozero__class_Ozero(_1090690))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090690), c_Groups_Ozero__class_Ozero(_1090690)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090690), hAPP(hAPP(c_Power_Opower__class_Opower(_1090690), _1090692), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1090690), _1090694), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (17896 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1090690), c_Groups_Ozero__class_Ozero(_1090690)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090690), hAPP(hAPP(c_Power_Opower__class_Opower(_1090690), _1090692), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1090690), _1090694), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1090692 = c_Groups_Ozero__class_Ozero(_1090690), _1090694 = c_Groups_Ozero__class_Ozero(_1090690)]]], (17914 ^ _779308) ^ [_1091065, _1091067, _1091069] : [class_Int_Onumber__ring(_1091065), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1091065), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091065), _1091067), _1091069)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091065), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091065), hAPP(hAPP(c_Power_Opower__class_Opower(_1091065), _1091067), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1091065), _1091069), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091065), hAPP(c_Int_Onumber__class_Onumber__of(_1091065), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1091067)), _1091069)))], (17920 ^ _779308) ^ [_1091280, _1091282, _1091284] : [class_Rings_Olinordered__idom(_1091280), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1091280), c_Groups_Ozero__class_Ozero(_1091280)), hAPP(hAPP(c_Power_Opower__class_Opower(_1091280), _1091282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1091284)))))], (17926 ^ _779308) ^ [_1091397, _1091399, _1091401] : [class_Groups_Omonoid__mult(_1091397), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1091397), _1091399), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1091401))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091397), _1091399), hAPP(hAPP(c_Power_Opower__class_Opower(_1091397), hAPP(hAPP(c_Power_Opower__class_Opower(_1091397), _1091399), _1091401)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (17932 ^ _779308) ^ [_1091550, _1091552, _1091554] : [class_Rings_Ocomm__semiring__1(_1091550), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1091550), _1091552), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1091554))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091550), _1091552), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091550), hAPP(hAPP(c_Power_Opower__class_Opower(_1091550), _1091552), _1091554)), hAPP(hAPP(c_Power_Opower__class_Opower(_1091550), _1091552), _1091554))))], (17938 ^ _779308) ^ [_1091719, _1091721] : [class_Int_Onumber__ring(_1091719), -(hAPP(c_Int_Onumber__class_Onumber__of(_1091719), c_Int_OBit0(_1091721)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091719), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091719), c_Groups_Ozero__class_Ozero(_1091719)), hAPP(c_Int_Onumber__class_Onumber__of(_1091719), _1091721))), hAPP(c_Int_Onumber__class_Onumber__of(_1091719), _1091721)))], (17944 ^ _779308) ^ [_1091879, _1091881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1091879)), c_Int_OBit0(_1091881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091879), _1091881)))], (17950 ^ _779308) ^ [_1091980, _1091982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1091980), _1091982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1091980)), c_Int_OBit0(_1091982))))], (17956 ^ _779308) ^ [_1092102, _1092104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1092102)), c_Int_OBit0(_1092104))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092102), _1092104)))], (17962 ^ _779308) ^ [_1092203, _1092205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1092203), _1092205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1092203)), c_Int_OBit0(_1092205))))], (17968 ^ _779308) ^ [_1092325, _1092327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1092325)), c_Int_OBit1(_1092327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1092325), _1092327)))], (17974 ^ _779308) ^ [_1092426, _1092428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1092426), _1092428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1092426)), c_Int_OBit1(_1092428))))], (17980 ^ _779308) ^ [_1092548, _1092550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1092548)), c_Int_OBit1(_1092550))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1092548), _1092550)))], (17986 ^ _779308) ^ [_1092649, _1092651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1092649), _1092651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1092649)), c_Int_OBit1(_1092651))))], (17992 ^ _779308) ^ [_1092756, _1092758, _1092760] : [class_Int_Onumber__ring(_1092756), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1092756), hAPP(c_Int_Onumber__class_Onumber__of(_1092756), _1092758)), hAPP(c_Int_Onumber__class_Onumber__of(_1092756), _1092760)) = hAPP(c_Int_Onumber__class_Onumber__of(_1092756), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1092758), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1092760))))], (17998 ^ _779308) ^ [_1092897, _1092899] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1092897)), _1092899) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1092897), _1092899))), _1092899))], (18000 ^ _779308) ^ [_1092959, _1092961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1092959)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1092961)))), 18003 ^ _779308 : [(18004 ^ _779308) ^ [] : [-(_1092959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18006 ^ _779308) ^ [] : [-(_1092961 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18008 ^ _779308) ^ [_1093086, _1093088] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1093086)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1093088))))), _1093086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1093088 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18018 ^ _779308) ^ [_1093245] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1093245))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18020 ^ _779308) ^ [_1093279] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1093279))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18022 ^ _779308) ^ [_1093311, _1093313] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093311)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1093313)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093311), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1093313))))], (18024 ^ _779308) ^ [_1093360] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1093360))))))], (18026 ^ _779308) ^ [_1093394, _1093396] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1093394)), c_Int_OBit1(_1093396)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1093394)), _1093396)))], (18028 ^ _779308) ^ [_1093439, _1093441, _1093443] : [class_Int_Onumber__ring(_1093439), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1093439), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1093439), _1093441), _1093443)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1093439), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093439), hAPP(hAPP(c_Power_Opower__class_Opower(_1093439), _1093441), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), hAPP(hAPP(c_Power_Opower__class_Opower(_1093439), _1093443), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1093439), hAPP(c_Int_Onumber__class_Onumber__of(_1093439), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1093441)), _1093443)))], (18034 ^ _779308) ^ [_1093654, _1093656, _1093658] : [class_Rings_Olinordered__idom(_1093654), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093654), c_Groups_Ozero__class_Ozero(_1093654)), hAPP(hAPP(c_Power_Opower__class_Opower(_1093654), _1093656), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1093658))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093654), c_Groups_Ozero__class_Ozero(_1093654)), _1093656)))], (18044 ^ _779308) ^ [_1093849, _1093851, _1093853] : [class_Rings_Olinordered__idom(_1093849), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093849), _1093851), c_Groups_Ozero__class_Ozero(_1093849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1093849), hAPP(hAPP(c_Power_Opower__class_Opower(_1093849), _1093851), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1093853)))), c_Groups_Ozero__class_Ozero(_1093849))))], (18054 ^ _779308) ^ [_1094044, _1094046] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1094044)), c_Int_OBit1(_1094046)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094044), c_Int_Osucc(_1094046))))], (18056 ^ _779308) ^ [_1094089, _1094091] : [class_Int_Onumber__ring(_1094089), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094089), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094089), c_Groups_Oone__class_Oone(_1094089)), c_Groups_Oone__class_Oone(_1094089))), hAPP(c_Int_Onumber__class_Onumber__of(_1094089), _1094091)) = hAPP(c_Int_Onumber__class_Onumber__of(_1094089), c_Int_OBit0(_1094091)))], (18062 ^ _779308) ^ [_1094228, _1094230] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1094228)), _1094230) = c_Nat_Onat_Onat__case(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1094228)), _1094230))], (18064 ^ _779308) ^ [_1094273, _1094275] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1094273), hAPP(c_Nat_OSuc, _1094275)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Orderings_Oord__class_Omin(tc_Nat_Onat)), _1094275)), _1094273))], (18066 ^ _779308) ^ [_1094318, _1094320] : [class_Groups_Omonoid__mult(_1094318), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1094318), _1094320), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1094318), _1094320), _1094320)), _1094320))], (18072 ^ _779308) ^ [_1094441, _1094443, _1094445, _1094447] : [class_Int_Onumber__ring(_1094441), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094441), hAPP(c_Int_Onumber__class_Onumber__of(_1094441), _1094443)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1094441), _1094445), hAPP(c_Int_Onumber__class_Onumber__of(_1094441), _1094447))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094441), hAPP(c_Int_Onumber__class_Onumber__of(_1094441), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1094443), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1094447)))), _1094445))], (18078 ^ _779308) ^ [_1094616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1094616))), 18081 ^ _779308 : [(18082 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1094616)))))], (18084 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1094616)))))]]], (18086 ^ _779308) ^ [_1094755, _1094757] : [class_Int_Onumber__ring(_1094755), -(hAPP(c_Int_Onumber__class_Onumber__of(_1094755), c_Int_Opred(_1094757)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094755), hAPP(c_Groups_Ouminus__class_Ouminus(_1094755), c_Groups_Oone__class_Oone(_1094755))), hAPP(c_Int_Onumber__class_Onumber__of(_1094755), _1094757)))], (18092 ^ _779308) ^ [_1094893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1094893)))))], (18094 ^ _779308) ^ [_1094927] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1094927)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18096 ^ _779308) ^ [_1094973, _1094975] : [_1094973 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1094975), _1094973) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (18102 ^ _779308) ^ [_1095056, _1095058] : [-(_1095056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1095058), _1095056) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1095058), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1095058), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1095056), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (18108 ^ _779308) ^ [_1095118, _1095120] : [class_Int_Onumber__ring(_1095118), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095118), _1095120), hAPP(c_Int_Onumber__class_Onumber__of(_1095118), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095118), _1095120), _1095120))], (18114 ^ _779308) ^ [_1095235, _1095237] : [class_Int_Onumber__ring(_1095235), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1095235), hAPP(c_Int_Onumber__class_Onumber__of(_1095235), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1095237) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095235), _1095237), _1095237))], (18120 ^ _779308) ^ [_1095352] : [class_Int_Onumber__ring(_1095352), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095352), c_Groups_Oone__class_Oone(_1095352)), c_Groups_Oone__class_Oone(_1095352)) = hAPP(c_Int_Onumber__class_Onumber__of(_1095352), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (18126 ^ _779308) ^ [] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (18128 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18130 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (18132 ^ _779308) ^ [_1095513] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1095513), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1095513)))], (18134 ^ _779308) ^ [_1095548] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1095548) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1095548)))], (18136 ^ _779308) ^ [_1095580] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1095580), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1095580), _1095580))], (18138 ^ _779308) ^ [_1095615] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1095615) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1095615), _1095615))], (18140 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (18142 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (18144 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (18146 ^ _779308) ^ [_1095701, _1095703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095701), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1095701), _1095703)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1095701))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1095703))))], (18152 ^ _779308) ^ [_1095842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1095842), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1095842 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1095842 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18162 ^ _779308) ^ [] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18164 ^ _779308) ^ [_1095958, _1095960] : [class_Int_Onumber__ring(_1095958), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1095958), c_Groups_Oone__class_Oone(_1095958)), hAPP(c_Int_Onumber__class_Onumber__of(_1095958), _1095960)) = hAPP(c_Int_Onumber__class_Onumber__of(_1095958), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1095960))))], (18170 ^ _779308) ^ [_1096085, _1096087] : [class_Int_Onumber__ring(_1096085), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1096085), hAPP(c_Int_Onumber__class_Onumber__of(_1096085), _1096087)), c_Groups_Oone__class_Oone(_1096085)) = hAPP(c_Int_Onumber__class_Onumber__of(_1096085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1096087), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (18176 ^ _779308) ^ [_1096212, _1096214, _1096216] : [class_Int_Onumber__ring(_1096212), 18179 ^ _779308 : [(18180 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1096214))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096212), _1096216), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1096214))) = hAPP(hAPP(c_HOL_OLet(_1096212, _1096212), hAPP(hAPP(c_Power_Opower__class_Opower(_1096212), _1096216), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096214))), hAPP(hAPP(c_COMBS(_1096212, _1096212, _1096212), hAPP(hAPP(c_COMBB(_1096212, tc_fun(_1096212, _1096212), _1096212), c_Groups_Otimes__class_Otimes(_1096212)), hAPP(c_Groups_Otimes__class_Otimes(_1096212), _1096216))), c_COMBI(_1096212))))], (18186 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1096214)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1096212), _1096216), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1096214))) = c_Groups_Oone__class_Oone(_1096212))]]], (18192 ^ _779308) ^ [_1096579, _1096581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1096579))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1096581), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1096579))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1096581), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096579))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Otimes__class_Otimes(tc_Int_Oint)), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1096581))), c_COMBI(tc_Int_Oint))))], (18198 ^ _779308) ^ [_1096736, _1096738] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1096736)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1096738), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1096736))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (18204 ^ _779308) ^ [_1096790, _1096792] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1096790)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1096792)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1096792))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), c_Nat_OSuc), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1096790)), c_Int_Onat)))))], (18206 ^ _779308) ^ [_1096853, _1096855, _1096857] : [class_Orderings_Olinorder(_1096853), -(_1096855 = c_Orderings_Obot__class_Obot(tc_fun(_1096853, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1096853, tc_HOL_Obool)), _1096855), _1096857)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096853), _1096857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096853), hAPP(c_Finite__Set_Ofold1(_1096853, c_Orderings_Oord__class_Omin(_1096853)), _1096857)), hAPP(c_Finite__Set_Ofold1(_1096853, c_Orderings_Oord__class_Omin(_1096853)), _1096855))))], (18224 ^ _779308) ^ [_1097179, _1097181, _1097183, _1097185] : [class_Rings_Olinordered__semidom(_1097179), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097179), _1097181), _1097183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097179), c_Groups_Ozero__class_Ozero(_1097179)), _1097181)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1097185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097179), hAPP(hAPP(c_Power_Opower__class_Opower(_1097179), _1097181), _1097185)), hAPP(hAPP(c_Power_Opower__class_Opower(_1097179), _1097183), _1097185))))], (18242 ^ _779308) ^ [_1097508, _1097510, _1097512] : [class_Orderings_Olinorder(_1097508), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097508), _1097510)), -(_1097510 = c_Orderings_Obot__class_Obot(tc_fun(_1097508, tc_HOL_Obool))), 18253 ^ _779308 : [(18264 ^ _779308) ^ [] : [18266 ^ _779308 : [(18267 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1097508), 18265 ^ [_1097508, _1097510, _1097512]), _1097510)))], (18269 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097508), _1097512), 18265 ^ [_1097508, _1097510, _1097512]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097508), _1097512), hAPP(c_Finite__Set_Ofold1(_1097508, c_Orderings_Oord__class_Omin(_1097508)), _1097510))))], (18254 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097508), _1097512), hAPP(c_Finite__Set_Ofold1(_1097508, c_Orderings_Oord__class_Omin(_1097508)), _1097510))), 18257 ^ _779308 : [(18258 ^ _779308) ^ [_1097801] : [hBOOL(hAPP(hAPP(c_member(_1097508), _1097801), _1097510)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1097508), _1097512), _1097801)))]]]]], (18273 ^ _779308) ^ [_1098086, _1098088, _1098090] : [class_Orderings_Olinorder(_1098086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098086), _1098088)), -(_1098088 = c_Orderings_Obot__class_Obot(tc_fun(_1098086, tc_HOL_Obool))), 18284 ^ _779308 : [(18285 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098086), hAPP(c_Finite__Set_Ofold1(_1098086, c_Orderings_Oord__class_Omin(_1098086)), _1098088)), _1098090)), 18289 ^ _779308 : [(18290 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098086), 18288 ^ [_1098086, _1098088, _1098090]), _1098088)))], (18292 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098086), 18288 ^ [_1098086, _1098088, _1098090]), _1098090)))]]], (18294 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098086), hAPP(c_Finite__Set_Ofold1(_1098086, c_Orderings_Oord__class_Omin(_1098086)), _1098088)), _1098090))), 18295 ^ _779308 : [(18296 ^ _779308) ^ [_1098475] : [hBOOL(hAPP(hAPP(c_member(_1098086), _1098475), _1098088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098086), _1098475), _1098090))]]]]], (18304 ^ _779308) ^ [_1098636, _1098638, _1098640] : [class_Orderings_Olinorder(_1098636), hBOOL(hAPP(c_Finite__Set_Ofinite(_1098636), _1098638)), -(_1098638 = c_Orderings_Obot__class_Obot(tc_fun(_1098636, tc_HOL_Obool))), 18315 ^ _779308 : [(18326 ^ _779308) ^ [] : [18328 ^ _779308 : [(18329 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098636), 18327 ^ [_1098636, _1098638, _1098640]), _1098638)))], (18331 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098636), _1098640), 18327 ^ [_1098636, _1098638, _1098640]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098636), _1098640), hAPP(c_Finite__Set_Ofold1(_1098636, c_Orderings_Oord__class_Omin(_1098636)), _1098638))))], (18316 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098636), _1098640), hAPP(c_Finite__Set_Ofold1(_1098636, c_Orderings_Oord__class_Omin(_1098636)), _1098638))), 18319 ^ _779308 : [(18320 ^ _779308) ^ [_1098929] : [hBOOL(hAPP(hAPP(c_member(_1098636), _1098929), _1098638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098636), _1098640), _1098929)))]]]]], (18335 ^ _779308) ^ [_1099214, _1099216, _1099218] : [class_Orderings_Olinorder(_1099214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099214), _1099216)), -(_1099216 = c_Orderings_Obot__class_Obot(tc_fun(_1099214, tc_HOL_Obool))), 18346 ^ _779308 : [(18347 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099214), hAPP(c_Finite__Set_Ofold1(_1099214, c_Orderings_Oord__class_Omin(_1099214)), _1099216)), _1099218)), 18351 ^ _779308 : [(18352 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099214), 18350 ^ [_1099214, _1099216, _1099218]), _1099216)))], (18354 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099214), 18350 ^ [_1099214, _1099216, _1099218]), _1099218)))]]], (18356 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099214), hAPP(c_Finite__Set_Ofold1(_1099214, c_Orderings_Oord__class_Omin(_1099214)), _1099216)), _1099218))), 18357 ^ _779308 : [(18358 ^ _779308) ^ [_1099603] : [hBOOL(hAPP(hAPP(c_member(_1099214), _1099603), _1099216)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099214), _1099603), _1099218))]]]]], (18366 ^ _779308) ^ [_1099764, _1099766, _1099768] : [class_Orderings_Olinorder(_1099764), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099764), _1099766)), hBOOL(hAPP(hAPP(c_member(_1099764), _1099768), _1099766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099764), hAPP(c_Finite__Set_Ofold1(_1099764, c_Orderings_Oord__class_Omin(_1099764)), _1099766)), _1099768)))], (18380 ^ _779308) ^ [_1099997, _1099999, _1100001] : [-(hBOOL(hAPP(hAPP(c_member(_1099997), _1099999), _1100001))), -(hBOOL(hAPP(hAPP(c_member(_1099997), _1099999), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1099997, tc_HOL_Obool)), _1100001))))], (18386 ^ _779308) ^ [_1100057, _1100059, _1100061] : [hBOOL(hAPP(hAPP(c_member(_1100057), _1100059), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100057, tc_HOL_Obool)), _1100061))), hBOOL(hAPP(hAPP(c_member(_1100057), _1100059), _1100061))], (18392 ^ _779308) ^ [_1100181, _1100183, _1100185] : [hBOOL(hAPP(hAPP(c_member(_1100181), _1100183), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100181, tc_HOL_Obool)), _1100185))), hBOOL(hAPP(hAPP(c_member(_1100181), _1100183), _1100185))], (18398 ^ _779308) ^ [_1100323, _1100325, _1100327] : [hBOOL(hAPP(hAPP(c_member(_1100323), _1100325), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100323, tc_HOL_Obool)), _1100327))), hBOOL(hAPP(hAPP(c_member(_1100323), _1100325), _1100327))], (18404 ^ _779308) ^ [_1100441, _1100443, _1100445] : [-(hBOOL(hAPP(hAPP(c_member(_1100441), _1100443), _1100445))), -(hBOOL(hAPP(hAPP(c_member(_1100441), _1100443), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100441, tc_HOL_Obool)), _1100445))))], (18410 ^ _779308) ^ [_1100503, _1100505, _1100507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1100503, tc_HOL_Obool)), _1100505), _1100507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1100503, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100503, tc_HOL_Obool)), _1100507)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100503, tc_HOL_Obool)), _1100505))))], (18416 ^ _779308) ^ [_1100672, _1100674, _1100676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1100672, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100672, tc_HOL_Obool)), _1100674)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100672, tc_HOL_Obool)), _1100676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1100672, tc_HOL_Obool)), _1100676), _1100674)))], (18422 ^ _779308) ^ [_1100819, _1100821, _1100823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1100819, tc_HOL_Obool)), _1100823), _1100821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1100819, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100819, tc_HOL_Obool)), _1100821)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100819, tc_HOL_Obool)), _1100823))))], (18428 ^ _779308) ^ [_1100987, _1100989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1100987, tc_HOL_Obool)), _1100989), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1100987, tc_HOL_Obool)), _1100989))), -(_1100989 = c_Orderings_Obot__class_Obot(tc_fun(_1100987, tc_HOL_Obool)))], (18434 ^ _779308) ^ [_1101106, _1101108] : [_1101108 = c_Orderings_Obot__class_Obot(tc_fun(_1101106, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101106, tc_HOL_Obool)), _1101108), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1101106, tc_HOL_Obool)), _1101108))))], (18440 ^ _779308) ^ [_1101231, _1101233] : [class_Orderings_Olinorder(_1101231), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1101231), _1101233), _1101233) = _1101233)], (18446 ^ _779308) ^ [_1101322, _1101324, _1101326] : [class_Rings_Oring__1__no__zero__divisors(_1101322), -(_1101324 = c_Groups_Ozero__class_Ozero(_1101322)), hAPP(hAPP(c_Power_Opower__class_Opower(_1101322), _1101324), _1101326) = c_Groups_Ozero__class_Ozero(_1101322)], (18456 ^ _779308) ^ [_1101481] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1101481) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18468 ^ _779308) ^ [_1101620, _1101622] : [18469 ^ _779308 : [(18470 ^ _779308) ^ [] : [_1101622 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18472 ^ _779308) ^ [] : [_1101620 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1101620), _1101622) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18458 ^ _779308) ^ [_1101522, _1101524] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1101522), _1101524) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1101524 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1101522 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18476 ^ _779308) ^ [_1101749, _1101751, _1101753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1101749), _1101751)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1101749), _1101753))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101751), _1101753)))], (18496 ^ _779308) ^ [_1102051, _1102053] : [18497 ^ _779308 : [(18498 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1102051))], (18500 ^ _779308) ^ [] : [_1102053 = 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)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1102051), _1102053))))], (18486 ^ _779308) ^ [_1101945, _1101947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1101945), _1101947))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1101945))), -(_1101947 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18504 ^ _779308) ^ [_1102188, _1102190, _1102192] : [class_Groups_Omonoid__mult(_1102188), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102188), hAPP(hAPP(c_Power_Opower__class_Opower(_1102188), _1102190), _1102192)), _1102190) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102188), _1102190), hAPP(hAPP(c_Power_Opower__class_Opower(_1102188), _1102190), _1102192)))], (18510 ^ _779308) ^ [_1102329, _1102331, _1102333, _1102335] : [class_Groups_Ocomm__monoid__mult(_1102329), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1102329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102329), _1102331), _1102333)), _1102335) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102329), hAPP(hAPP(c_Power_Opower__class_Opower(_1102329), _1102331), _1102335)), hAPP(hAPP(c_Power_Opower__class_Opower(_1102329), _1102333), _1102335)))], (18516 ^ _779308) ^ [_1102488, _1102490] : [class_Groups_Omonoid__mult(_1102488), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1102488), c_Groups_Oone__class_Oone(_1102488)), _1102490) = c_Groups_Oone__class_Oone(_1102488))], (18522 ^ _779308) ^ [_1102587, _1102589, _1102591] : [class_Rings_Osemiring__1(_1102587), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1102587), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1102589), _1102591)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1102587), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1102587), _1102589)), _1102591))], (18528 ^ _779308) ^ [_1102712, _1102714, _1102716, _1102718] : [class_Groups_Omonoid__mult(_1102712), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1102712), _1102714), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1102716), _1102718)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1102712), hAPP(hAPP(c_Power_Opower__class_Opower(_1102712), _1102714), _1102716)), _1102718))], (18534 ^ _779308) ^ [_1102851, _1102853] : [class_Groups_Omonoid__mult(_1102851), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1102851), _1102853), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1102853)], (18540 ^ _779308) ^ [_1102942, _1102944, _1102946, _1102948] : [class_Rings_Olinordered__semidom(_1102942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102942), _1102944), _1102946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102942), c_Groups_Ozero__class_Ozero(_1102942)), _1102944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102942), hAPP(hAPP(c_Power_Opower__class_Opower(_1102942), _1102944), _1102948)), hAPP(hAPP(c_Power_Opower__class_Opower(_1102942), _1102946), _1102948))))], (18554 ^ _779308) ^ [_1103211, _1103213, _1103215] : [class_Rings_Olinordered__semidom(_1103211), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103211), c_Groups_Ozero__class_Ozero(_1103211)), _1103213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103211), c_Groups_Ozero__class_Ozero(_1103211)), hAPP(hAPP(c_Power_Opower__class_Opower(_1103211), _1103213), _1103215))))], (18564 ^ _779308) ^ [_1103394, _1103396, _1103398] : [class_Rings_Olinordered__semidom(_1103394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103394), c_Groups_Ozero__class_Ozero(_1103394)), _1103396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103394), c_Groups_Ozero__class_Ozero(_1103394)), hAPP(hAPP(c_Power_Opower__class_Opower(_1103394), _1103396), _1103398))))], (18574 ^ _779308) ^ [_1103577, _1103579, _1103581] : [class_Power_Opower(_1103577), class_Rings_Omult__zero(_1103577), class_Rings_Ono__zero__divisors(_1103577), class_Rings_Ozero__neq__one(_1103577), 18589 ^ _779308 : [(18590 ^ _779308) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1103577), _1103579), _1103581) = c_Groups_Ozero__class_Ozero(_1103577), 18593 ^ _779308 : [(18594 ^ _779308) ^ [] : [-(_1103579 = c_Groups_Ozero__class_Ozero(_1103577))], (18596 ^ _779308) ^ [] : [_1103581 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (18598 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1103577), _1103579), _1103581) = c_Groups_Ozero__class_Ozero(_1103577)), _1103579 = c_Groups_Ozero__class_Ozero(_1103577), -(_1103581 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18608 ^ _779308) ^ [_1104069, _1104071, _1104073] : [class_Rings_Olinordered__semidom(_1104069), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104069), c_Groups_Oone__class_Oone(_1104069)), _1104071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104069), c_Groups_Oone__class_Oone(_1104069)), hAPP(hAPP(c_Power_Opower__class_Opower(_1104069), _1104071), _1104073))))], (18618 ^ _779308) ^ [_1104252, _1104254] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1104252), c_Groups_Ozero__class_Ozero(_1104252)), hAPP(c_Nat_OSuc, _1104254)) = c_Groups_Ozero__class_Ozero(_1104252)), class_Power_Opower(_1104252), class_Rings_Osemiring__0(_1104252)], (18628 ^ _779308) ^ [_1104407, _1104409, _1104411, _1104413] : [class_Rings_Olinordered__semidom(_1104407), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1104407), c_Groups_Oone__class_Oone(_1104407)), _1104409)), 18635 ^ _779308 : [(18636 ^ _779308) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1104407), _1104409), _1104411) = hAPP(hAPP(c_Power_Opower__class_Opower(_1104407), _1104409), _1104413), -(_1104411 = _1104413)], (18642 ^ _779308) ^ [] : [_1104411 = _1104413, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1104407), _1104409), _1104411) = hAPP(hAPP(c_Power_Opower__class_Opower(_1104407), _1104409), _1104413))]]], (18648 ^ _779308) ^ [_1104746, _1104748, _1104750] : [class_Power_Opower(_1104746), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1104746), _1104748), hAPP(c_Nat_OSuc, _1104750)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104746), _1104748), hAPP(hAPP(c_Power_Opower__class_Opower(_1104746), _1104748), _1104750)))], (18654 ^ _779308) ^ [_1104877, _1104879, _1104881] : [class_Groups_Omonoid__mult(_1104877), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1104877), _1104879), hAPP(c_Nat_OSuc, _1104881)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104877), hAPP(hAPP(c_Power_Opower__class_Opower(_1104877), _1104879), _1104881)), _1104879))], (18660 ^ _779308) ^ [_1105008, _1105010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1105008)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1105008), _1105010))))], (18666 ^ _779308) ^ [_1105105, _1105107] : [class_Power_Opower(_1105105), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1105105), _1105107), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1105105))], (18672 ^ _779308) ^ [_1105200, _1105202, _1105204, _1105206] : [class_Groups_Omonoid__mult(_1105200), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1105200), _1105202), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1105204), _1105206)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1105200), hAPP(hAPP(c_Power_Opower__class_Opower(_1105200), _1105202), _1105204)), hAPP(hAPP(c_Power_Opower__class_Opower(_1105200), _1105202), _1105206)))], (18678 ^ _779308) ^ [_1105355, _1105357, _1105359, _1105361] : [class_Rings_Olinordered__semidom(_1105355), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105355), hAPP(hAPP(c_Power_Opower__class_Opower(_1105355), _1105357), _1105359)), hAPP(hAPP(c_Power_Opower__class_Opower(_1105355), _1105361), _1105359))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105355), c_Groups_Ozero__class_Ozero(_1105355)), _1105361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105355), _1105357), _1105361)))], (18692 ^ _779308) ^ [_1105624, _1105626, _1105628, _1105630] : [class_Rings_Olinordered__semidom(_1105624), hAPP(hAPP(c_Power_Opower__class_Opower(_1105624), _1105626), hAPP(c_Nat_OSuc, _1105628)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1105624), _1105630), hAPP(c_Nat_OSuc, _1105628)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105624), c_Groups_Ozero__class_Ozero(_1105624)), _1105626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105624), c_Groups_Ozero__class_Ozero(_1105624)), _1105630)), -(_1105626 = _1105630)], (18710 ^ _779308) ^ [_1105951, _1105953, _1105955, _1105957] : [class_Rings_Olinordered__semidom(_1105951), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105951), hAPP(hAPP(c_Power_Opower__class_Opower(_1105951), _1105953), hAPP(c_Nat_OSuc, _1105955))), hAPP(hAPP(c_Power_Opower__class_Opower(_1105951), _1105957), hAPP(c_Nat_OSuc, _1105955)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105951), c_Groups_Ozero__class_Ozero(_1105951)), _1105957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105951), _1105953), _1105957)))], (18724 ^ _779308) ^ [_1106232, _1106234, _1106236] : [class_Rings_Olinordered__semidom(_1106232), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106232), c_Groups_Oone__class_Oone(_1106232)), _1106234)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106232), c_Groups_Oone__class_Oone(_1106232)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106232), _1106234), hAPP(hAPP(c_Power_Opower__class_Opower(_1106232), _1106234), _1106236)))))], (18734 ^ _779308) ^ [_1106431, _1106433, _1106435] : [class_Rings_Olinordered__semidom(_1106431), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106431), c_Groups_Oone__class_Oone(_1106431)), _1106433)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106431), hAPP(hAPP(c_Power_Opower__class_Opower(_1106431), _1106433), _1106435)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106431), _1106433), hAPP(hAPP(c_Power_Opower__class_Opower(_1106431), _1106433), _1106435)))))], (18744 ^ _779308) ^ [_1106642, _1106644] : [class_Power_Opower(_1106642), class_Rings_Osemiring__0(_1106642), 18751 ^ _779308 : [(18752 ^ _779308) ^ [] : [_1106644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1106642), c_Groups_Ozero__class_Ozero(_1106642)), _1106644) = c_Groups_Oone__class_Oone(_1106642))], (18758 ^ _779308) ^ [] : [-(_1106644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1106642), c_Groups_Ozero__class_Ozero(_1106642)), _1106644) = c_Groups_Ozero__class_Ozero(_1106642))]]], (18764 ^ _779308) ^ [_1106916, _1106918, _1106920] : [class_Rings_Olinordered__semidom(_1106916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106916), c_Groups_Oone__class_Oone(_1106916)), _1106918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1106916), c_Groups_Oone__class_Oone(_1106916)), hAPP(hAPP(c_Power_Opower__class_Opower(_1106916), _1106918), hAPP(c_Nat_OSuc, _1106920)))))], (18774 ^ _779308) ^ [_1107105, _1107107, _1107109, _1107111] : [class_Rings_Olinordered__semidom(_1107105), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107105), c_Groups_Oone__class_Oone(_1107105)), _1107107)), 18781 ^ _779308 : [(18782 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107105), hAPP(hAPP(c_Power_Opower__class_Opower(_1107105), _1107107), _1107109)), hAPP(hAPP(c_Power_Opower__class_Opower(_1107105), _1107107), _1107111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1107109), _1107111)))], (18788 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1107109), _1107111)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107105), hAPP(hAPP(c_Power_Opower__class_Opower(_1107105), _1107107), _1107109)), hAPP(hAPP(c_Power_Opower__class_Opower(_1107105), _1107107), _1107111))))]]], (18794 ^ _779308) ^ [_1107480, _1107482, _1107484, _1107486] : [class_Rings_Olinordered__semidom(_1107480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107480), c_Groups_Oone__class_Oone(_1107480)), _1107482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107480), hAPP(hAPP(c_Power_Opower__class_Opower(_1107480), _1107482), _1107484)), hAPP(hAPP(c_Power_Opower__class_Opower(_1107480), _1107482), _1107486))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1107484), _1107486)))], (18808 ^ _779308) ^ [_1107745, _1107747, _1107749, _1107751] : [class_Rings_Olinordered__semidom(_1107745), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1107747), _1107749)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107745), c_Groups_Oone__class_Oone(_1107745)), _1107751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1107745), hAPP(hAPP(c_Power_Opower__class_Opower(_1107745), _1107751), _1107747)), hAPP(hAPP(c_Power_Opower__class_Opower(_1107745), _1107751), _1107749))))], (18822 ^ _779308) ^ [_1108010, _1108012, _1108014, _1108016] : [class_Rings_Olinordered__semidom(_1108010), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1108012), _1108014)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108010), c_Groups_Oone__class_Oone(_1108010)), _1108016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108010), hAPP(hAPP(c_Power_Opower__class_Opower(_1108010), _1108016), _1108012)), hAPP(hAPP(c_Power_Opower__class_Opower(_1108010), _1108016), _1108014))))], (18836 ^ _779308) ^ [_1108275, _1108277, _1108279] : [class_Rings_Oring__1(_1108275), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1108275), hAPP(c_Groups_Ouminus__class_Ouminus(_1108275), _1108277)), _1108279) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108275), hAPP(hAPP(c_Power_Opower__class_Opower(_1108275), hAPP(c_Groups_Ouminus__class_Ouminus(_1108275), c_Groups_Oone__class_Oone(_1108275))), _1108279)), hAPP(hAPP(c_Power_Opower__class_Opower(_1108275), _1108277), _1108279)))], (18842 ^ _779308) ^ [_1108440, _1108442, _1108444] : [class_Rings_Olinordered__semidom(_1108440), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108440), c_Groups_Ozero__class_Ozero(_1108440)), _1108442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108440), _1108442), c_Groups_Oone__class_Oone(_1108440))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108440), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108440), _1108442), hAPP(hAPP(c_Power_Opower__class_Opower(_1108440), _1108442), _1108444))), hAPP(hAPP(c_Power_Opower__class_Opower(_1108440), _1108442), _1108444))))], (18856 ^ _779308) ^ [_1108723, _1108725, _1108727, _1108729] : [class_Rings_Olinordered__semidom(_1108723), hAPP(hAPP(c_Power_Opower__class_Opower(_1108723), _1108725), _1108727) = hAPP(hAPP(c_Power_Opower__class_Opower(_1108723), _1108729), _1108727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108723), c_Groups_Ozero__class_Ozero(_1108723)), _1108725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1108723), c_Groups_Ozero__class_Ozero(_1108723)), _1108729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108727)), -(_1108725 = _1108729)], (18878 ^ _779308) ^ [_1109098, _1109100, _1109102] : [class_Rings_Olinordered__semidom(_1109098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109098), c_Groups_Ozero__class_Ozero(_1109098)), _1109100)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109098), _1109100), c_Groups_Oone__class_Oone(_1109098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109098), hAPP(hAPP(c_Power_Opower__class_Opower(_1109098), _1109100), hAPP(c_Nat_OSuc, _1109102))), c_Groups_Oone__class_Oone(_1109098))))], (18892 ^ _779308) ^ [_1109359, _1109361, _1109363, _1109365] : [class_Rings_Olinordered__semidom(_1109359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109361), _1109363)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109359), c_Groups_Ozero__class_Ozero(_1109359)), _1109365)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109359), _1109365), c_Groups_Oone__class_Oone(_1109359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1109359), hAPP(hAPP(c_Power_Opower__class_Opower(_1109359), _1109365), _1109363)), hAPP(hAPP(c_Power_Opower__class_Opower(_1109359), _1109365), _1109361))))], (18910 ^ _779308) ^ [_1109698, _1109700, _1109702, _1109704] : [class_Rings_Olinordered__semidom(_1109698), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109700), _1109702)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109698), c_Groups_Ozero__class_Ozero(_1109698)), _1109704)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109698), _1109704), c_Groups_Oone__class_Oone(_1109698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109698), hAPP(hAPP(c_Power_Opower__class_Opower(_1109698), _1109704), _1109702)), hAPP(hAPP(c_Power_Opower__class_Opower(_1109698), _1109704), _1109700))))], (18928 ^ _779308) ^ [_1110037, _1110039, _1110041, _1110043] : [class_Rings_Olinordered__semidom(_1110037), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110037), c_Groups_Oone__class_Oone(_1110037)), _1110039)), 18935 ^ _779308 : [(18936 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110037), hAPP(hAPP(c_Power_Opower__class_Opower(_1110037), _1110039), _1110041)), hAPP(hAPP(c_Power_Opower__class_Opower(_1110037), _1110039), _1110043))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110041), _1110043)))], (18942 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110041), _1110043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110037), hAPP(hAPP(c_Power_Opower__class_Opower(_1110037), _1110039), _1110041)), hAPP(hAPP(c_Power_Opower__class_Opower(_1110037), _1110039), _1110043))))]]], (18948 ^ _779308) ^ [_1110412, _1110414, _1110416, _1110418] : [class_Rings_Olinordered__semidom(_1110412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110412), c_Groups_Oone__class_Oone(_1110412)), _1110414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110412), hAPP(hAPP(c_Power_Opower__class_Opower(_1110412), _1110414), _1110416)), hAPP(hAPP(c_Power_Opower__class_Opower(_1110412), _1110414), _1110418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110416), _1110418)))], (18962 ^ _779308) ^ [_1110677, _1110679, _1110681] : [class_Rings_Olinordered__semidom(_1110677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110677), c_Groups_Oone__class_Oone(_1110677)), _1110679)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1110681)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1110677), c_Groups_Oone__class_Oone(_1110677)), hAPP(hAPP(c_Power_Opower__class_Opower(_1110677), _1110679), _1110681))))], (18976 ^ _779308) ^ [_1110918, _1110920, _1110922, _1110924] : [c_Big__Operators_Osemilattice__big(_1110918, _1110920, _1110922), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110918), _1110924)), -(hAPP(_1110922, _1110924) = hAPP(c_Finite__Set_Ofold1(_1110918, _1110920), _1110924))], (18986 ^ _779308) ^ [_1111083, _1111085] : [class_Int_Onumber__ring(_1111083), 18989 ^ _779308 : [(18990 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1111083), _1111085) = c_Groups_Oone__class_Oone(_1111083), -(c_Int_Oiszero(_1111083, hAPP(c_Int_Onumber__class_Onumber__of(_1111083), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1111085), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (18996 ^ _779308) ^ [] : [c_Int_Oiszero(_1111083, hAPP(c_Int_Onumber__class_Onumber__of(_1111083), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1111085), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1111083), _1111085) = c_Groups_Oone__class_Oone(_1111083))]]], (19002 ^ _779308) ^ [_1111342, _1111344] : [class_Int_Onumber__ring(_1111342), 19005 ^ _779308 : [(19006 ^ _779308) ^ [] : [c_Groups_Oone__class_Oone(_1111342) = hAPP(c_Int_Onumber__class_Onumber__of(_1111342), _1111344), -(c_Int_Oiszero(_1111342, hAPP(c_Int_Onumber__class_Onumber__of(_1111342), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1111344)))))], (19012 ^ _779308) ^ [] : [c_Int_Oiszero(_1111342, hAPP(c_Int_Onumber__class_Onumber__of(_1111342), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1111344)))), -(c_Groups_Oone__class_Oone(_1111342) = hAPP(c_Int_Onumber__class_Onumber__of(_1111342), _1111344))]]], (19018 ^ _779308) ^ [_1111601, _1111603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1111601), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1111603)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1111601)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1111603), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1111601))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19024 ^ _779308) ^ [_1111761, _1111763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111761))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1111763)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1111761))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111763), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111761)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19030 ^ _779308) ^ [_1111908, _1111910] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111908)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1111910)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1111908))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111910)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1111908)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19036 ^ _779308) ^ [_1111990] : [class_Orderings_Olinorder(_1111990), -(c_Orderings_Oord_Omax(_1111990, hAPP(c_COMBC(_1111990, _1111990, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1111990))) = c_Orderings_Oord__class_Omin(_1111990))], (19042 ^ _779308) ^ [_1112091, _1112093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1112091)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1112093)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1112091)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1112093, _1112091))))], (19048 ^ _779308) ^ [_1112218, _1112220] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1112218, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1112218, tc_HOL_Obool)), _1112220)) = _1112220)], (19050 ^ _779308) ^ [_1112277, _1112279, _1112281] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1112277, tc_HOL_Obool)), _1112279) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1112277, tc_HOL_Obool)), _1112281), -(_1112279 = _1112281)], (19056 ^ _779308) ^ [_1112384, _1112386, _1112388] : [_1112386 = _1112388, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1112384, tc_HOL_Obool)), _1112386) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1112384, tc_HOL_Obool)), _1112388))], (19062 ^ _779308) ^ [_1112497, _1112499, _1112501] : [class_Divides_Osemiring__div(_1112497), -(c_Divides_Odiv__class_Omod(_1112497, c_Divides_Odiv__class_Omod(_1112497, _1112499, _1112501), _1112501) = c_Divides_Odiv__class_Omod(_1112497, _1112499, _1112501))], (19068 ^ _779308) ^ [_1112598, _1112600] : [class_Divides_Osemiring__div(_1112598), -(c_Divides_Odiv__class_Omod(_1112598, _1112600, _1112600) = c_Groups_Ozero__class_Ozero(_1112598))], (19074 ^ _779308) ^ [_1112685, _1112687] : [class_Divides_Osemiring__div(_1112685), -(c_Divides_Odiv__class_Omod(_1112685, _1112687, c_Groups_Ozero__class_Ozero(_1112685)) = _1112687)], (19080 ^ _779308) ^ [_1112772, _1112774] : [class_Divides_Osemiring__div(_1112772), -(c_Divides_Odiv__class_Omod(_1112772, c_Groups_Ozero__class_Ozero(_1112772), _1112774) = c_Groups_Ozero__class_Ozero(_1112772))], (19086 ^ _779308) ^ [_1112863, _1112865, _1112867, _1112869, _1112871, _1112873] : [class_Divides_Osemiring__div(_1112863), c_Divides_Odiv__class_Omod(_1112863, _1112865, _1112867) = c_Divides_Odiv__class_Omod(_1112863, _1112869, _1112867), c_Divides_Odiv__class_Omod(_1112863, _1112871, _1112867) = c_Divides_Odiv__class_Omod(_1112863, _1112873, _1112867), -(c_Divides_Odiv__class_Omod(_1112863, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1112863), _1112865), _1112871), _1112867) = c_Divides_Odiv__class_Omod(_1112863, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1112863), _1112869), _1112873), _1112867))], (19100 ^ _779308) ^ [_1113146, _1113148, _1113150, _1113152] : [class_Divides_Osemiring__div(_1113146), -(c_Divides_Odiv__class_Omod(_1113146, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113146), c_Divides_Odiv__class_Omod(_1113146, _1113148, _1113150)), _1113152), _1113150) = c_Divides_Odiv__class_Omod(_1113146, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113146), _1113148), _1113152), _1113150))], (19106 ^ _779308) ^ [_1113281, _1113283, _1113285, _1113287] : [class_Divides_Osemiring__div(_1113281), -(c_Divides_Odiv__class_Omod(_1113281, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113281), _1113283), c_Divides_Odiv__class_Omod(_1113281, _1113285, _1113287)), _1113287) = c_Divides_Odiv__class_Omod(_1113281, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113281), _1113283), _1113285), _1113287))], (19112 ^ _779308) ^ [_1113416, _1113418, _1113420, _1113422] : [class_Divides_Osemiring__div(_1113416), -(c_Divides_Odiv__class_Omod(_1113416, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113416), _1113418), _1113420), _1113422) = c_Divides_Odiv__class_Omod(_1113416, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113416), c_Divides_Odiv__class_Omod(_1113416, _1113418, _1113422)), c_Divides_Odiv__class_Omod(_1113416, _1113420, _1113422)), _1113422))], (19118 ^ _779308) ^ [_1113559, _1113561, _1113563, _1113565] : [class_Divides_Osemiring__div(_1113559), -(c_Divides_Odiv__class_Omod(_1113559, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113559), _1113561), _1113563), _1113565) = c_Divides_Odiv__class_Omod(_1113559, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113559), c_Divides_Odiv__class_Omod(_1113559, _1113561, _1113565)), _1113563), _1113565))], (19124 ^ _779308) ^ [_1113694, _1113696, _1113698, _1113700] : [class_Divides_Osemiring__div(_1113694), -(c_Divides_Odiv__class_Omod(_1113694, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113694), _1113696), _1113698), _1113700) = c_Divides_Odiv__class_Omod(_1113694, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113694), _1113696), c_Divides_Odiv__class_Omod(_1113694, _1113698, _1113700)), _1113700))], (19130 ^ _779308) ^ [_1113829, _1113831, _1113833] : [class_Divides_Osemiring__div(_1113829), -(c_Divides_Odiv__class_Omod(_1113829, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113829), _1113831), _1113833), _1113831) = c_Divides_Odiv__class_Omod(_1113829, _1113833, _1113831))], (19136 ^ _779308) ^ [_1113938, _1113940, _1113942] : [class_Divides_Osemiring__div(_1113938), -(c_Divides_Odiv__class_Omod(_1113938, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113938), _1113940), _1113942), _1113942) = c_Divides_Odiv__class_Omod(_1113938, _1113940, _1113942))], (19142 ^ _779308) ^ [_1114047, _1114049, _1114051, _1114053, _1114055, _1114057] : [class_Divides_Osemiring__div(_1114047), c_Divides_Odiv__class_Omod(_1114047, _1114049, _1114051) = c_Divides_Odiv__class_Omod(_1114047, _1114053, _1114051), c_Divides_Odiv__class_Omod(_1114047, _1114055, _1114051) = c_Divides_Odiv__class_Omod(_1114047, _1114057, _1114051), -(c_Divides_Odiv__class_Omod(_1114047, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114047), _1114049), _1114055), _1114051) = c_Divides_Odiv__class_Omod(_1114047, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114047), _1114053), _1114057), _1114051))], (19156 ^ _779308) ^ [_1114330, _1114332, _1114334, _1114336] : [class_Divides_Osemiring__div(_1114330), -(c_Divides_Odiv__class_Omod(_1114330, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114330), c_Divides_Odiv__class_Omod(_1114330, _1114332, _1114334)), _1114336), _1114334) = c_Divides_Odiv__class_Omod(_1114330, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114330), _1114332), _1114336), _1114334))], (19162 ^ _779308) ^ [_1114465, _1114467, _1114469, _1114471] : [class_Divides_Osemiring__div(_1114465), -(c_Divides_Odiv__class_Omod(_1114465, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114465), _1114467), _1114469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114465), _1114471), _1114469)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114465), c_Divides_Odiv__class_Omod(_1114465, _1114467, _1114471)), _1114469))], (19168 ^ _779308) ^ [_1114608, _1114610, _1114612, _1114614] : [class_Divides_Osemiring__div(_1114608), -(c_Divides_Odiv__class_Omod(_1114608, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114608), _1114610), _1114612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114608), _1114610), _1114614)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114608), _1114610), c_Divides_Odiv__class_Omod(_1114608, _1114612, _1114614)))], (19174 ^ _779308) ^ [_1114751, _1114753, _1114755, _1114757] : [class_Divides_Osemiring__div(_1114751), -(c_Divides_Odiv__class_Omod(_1114751, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114751), _1114753), _1114755), _1114757) = c_Divides_Odiv__class_Omod(_1114751, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114751), c_Divides_Odiv__class_Omod(_1114751, _1114753, _1114757)), c_Divides_Odiv__class_Omod(_1114751, _1114755, _1114757)), _1114757))], (19180 ^ _779308) ^ [_1114894, _1114896, _1114898, _1114900] : [class_Divides_Osemiring__div(_1114894), -(c_Divides_Odiv__class_Omod(_1114894, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114894), _1114896), _1114898), _1114900) = c_Divides_Odiv__class_Omod(_1114894, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1114894), c_Divides_Odiv__class_Omod(_1114894, _1114896, _1114900)), _1114898), _1114900))], (19186 ^ _779308) ^ [_1115029, _1115031, _1115033, _1115035] : [class_Divides_Osemiring__div(_1115029), -(c_Divides_Odiv__class_Omod(_1115029, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115029), _1115031), _1115033), _1115035) = c_Divides_Odiv__class_Omod(_1115029, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1115029), _1115031), c_Divides_Odiv__class_Omod(_1115029, _1115033, _1115035)), _1115035))], (19192 ^ _779308) ^ [_1115164, _1115166, _1115168, _1115170] : [class_Divides_Oring__div(_1115164), -(c_Divides_Odiv__class_Omod(_1115164, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1115164), _1115166), _1115168), _1115170) = c_Divides_Odiv__class_Omod(_1115164, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1115164), _1115166), c_Divides_Odiv__class_Omod(_1115164, _1115168, _1115170)), _1115170))], (19198 ^ _779308) ^ [_1115299, _1115301, _1115303, _1115305] : [class_Divides_Oring__div(_1115299), -(c_Divides_Odiv__class_Omod(_1115299, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1115299), _1115301), _1115303), _1115305) = c_Divides_Odiv__class_Omod(_1115299, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1115299), c_Divides_Odiv__class_Omod(_1115299, _1115301, _1115305)), _1115303), _1115305))], (19204 ^ _779308) ^ [_1115434, _1115436, _1115438, _1115440] : [class_Divides_Oring__div(_1115434), -(c_Divides_Odiv__class_Omod(_1115434, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1115434), _1115436), _1115438), _1115440) = c_Divides_Odiv__class_Omod(_1115434, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1115434), c_Divides_Odiv__class_Omod(_1115434, _1115436, _1115440)), c_Divides_Odiv__class_Omod(_1115434, _1115438, _1115440)), _1115440))], (19210 ^ _779308) ^ [_1115577, _1115579, _1115581, _1115583, _1115585, _1115587] : [class_Divides_Oring__div(_1115577), c_Divides_Odiv__class_Omod(_1115577, _1115579, _1115581) = c_Divides_Odiv__class_Omod(_1115577, _1115583, _1115581), c_Divides_Odiv__class_Omod(_1115577, _1115585, _1115581) = c_Divides_Odiv__class_Omod(_1115577, _1115587, _1115581), -(c_Divides_Odiv__class_Omod(_1115577, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1115577), _1115579), _1115585), _1115581) = c_Divides_Odiv__class_Omod(_1115577, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1115577), _1115583), _1115587), _1115581))], (19224 ^ _779308) ^ [_1115860, _1115862, _1115864] : [class_Divides_Oring__div(_1115860), -(c_Divides_Odiv__class_Omod(_1115860, hAPP(c_Groups_Ouminus__class_Ouminus(_1115860), _1115862), _1115864) = c_Divides_Odiv__class_Omod(_1115860, hAPP(c_Groups_Ouminus__class_Ouminus(_1115860), c_Divides_Odiv__class_Omod(_1115860, _1115862, _1115864)), _1115864))], (19230 ^ _779308) ^ [_1115981, _1115983, _1115985, _1115987] : [class_Divides_Oring__div(_1115981), c_Divides_Odiv__class_Omod(_1115981, _1115983, _1115985) = c_Divides_Odiv__class_Omod(_1115981, _1115987, _1115985), -(c_Divides_Odiv__class_Omod(_1115981, hAPP(c_Groups_Ouminus__class_Ouminus(_1115981), _1115983), _1115985) = c_Divides_Odiv__class_Omod(_1115981, hAPP(c_Groups_Ouminus__class_Ouminus(_1115981), _1115987), _1115985))], (19240 ^ _779308) ^ [_1116168] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116168, _1116168) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19242 ^ _779308) ^ [_1116195] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1116195) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19244 ^ _779308) ^ [_1116222, _1116224, _1116226] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116222), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116224, _1116226)), _1116226) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116222), _1116224), _1116226))], (19246 ^ _779308) ^ [_1116273, _1116275, _1116277] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116273), _1116275), _1116277) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1116273), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116275, _1116277)), _1116277))], (19248 ^ _779308) ^ [_1116324, _1116326, _1116328] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1116324), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116326, _1116328)), _1116328) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1116324), _1116326), _1116328))], (19250 ^ _779308) ^ [_1116375, _1116377, _1116379] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116375, _1116377)), _1116379), _1116377) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1116375), _1116379), _1116377))], (19252 ^ _779308) ^ [_1116426, _1116428] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116426, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1116428)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1116426), _1116428)))], (19254 ^ _779308) ^ [_1116468, _1116470] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1116468), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1116470)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116468, _1116470)))], (19256 ^ _779308) ^ [_1116510, _1116512] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116510, _1116512)), _1116512) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1116510), _1116512))], (19258 ^ _779308) ^ [_1116553, _1116555, _1116557] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1116553, _1116555)), _1116557), _1116555) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1116553), _1116557), _1116555))], (19260 ^ _779308) ^ [_1116604, _1116606, _1116608] : [class_Divides_Osemiring__div(_1116604), -(c_Divides_Odiv__class_Omod(_1116604, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116604), _1116606), _1116608), _1116606) = c_Groups_Ozero__class_Ozero(_1116604))], (19266 ^ _779308) ^ [_1116709, _1116711, _1116713] : [class_Divides_Osemiring__div(_1116709), -(c_Divides_Odiv__class_Omod(_1116709, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116709), _1116711), _1116713), _1116713) = c_Groups_Ozero__class_Ozero(_1116709))], (19272 ^ _779308) ^ [_1116814, _1116816, _1116818, _1116820] : [class_Divides_Osemiring__div(_1116814), -(c_Divides_Odiv__class_Omod(_1116814, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116814), _1116816), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116814), _1116818), _1116820)), _1116820) = c_Divides_Odiv__class_Omod(_1116814, _1116816, _1116820))], (19278 ^ _779308) ^ [_1116941, _1116943, _1116945, _1116947] : [class_Divides_Osemiring__div(_1116941), -(c_Divides_Odiv__class_Omod(_1116941, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116941), _1116943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116941), _1116945), _1116947)), _1116945) = c_Divides_Odiv__class_Omod(_1116941, _1116943, _1116945))], (19284 ^ _779308) ^ [_1117068, _1117070] : [class_Divides_Osemiring__div(_1117068), -(c_Divides_Odiv__class_Omod(_1117068, _1117070, c_Groups_Oone__class_Oone(_1117068)) = c_Groups_Ozero__class_Ozero(_1117068))], (19290 ^ _779308) ^ [_1117159, _1117161] : [class_Rings_Osemiring__1(_1117159), 19293 ^ _779308 : [(19294 ^ _779308) ^ [] : [c_Int_Oiszero(_1117159, _1117161), -(_1117161 = c_Groups_Ozero__class_Ozero(_1117159))], (19300 ^ _779308) ^ [] : [_1117161 = c_Groups_Ozero__class_Ozero(_1117159), -(c_Int_Oiszero(_1117159, _1117161))]]], (19306 ^ _779308) ^ [_1117370] : [class_Rings_Osemiring__1(_1117370), -(c_Int_Oiszero(_1117370, c_Groups_Ozero__class_Ozero(_1117370)))], (19312 ^ _779308) ^ [_1117447] : [class_Rings_Osemiring__1(_1117447), c_Int_Oiszero(_1117447, c_Groups_Oone__class_Oone(_1117447))], (19318 ^ _779308) ^ [_1117525, _1117527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117527)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1117525, _1117527))))], (19328 ^ _779308) ^ [_1117674, _1117676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1117674, _1117676)), _1117674)))], (19334 ^ _779308) ^ [_1117773, _1117775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1117773), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1117773), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1117775, _1117773))))], (19340 ^ _779308) ^ [_1117878, _1117880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1117880, _1117878)), _1117878)))], (19346 ^ _779308) ^ [_1117992, _1117994] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1117992, _1117994) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1117992 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1117994), 19349 ^ [_1117992, _1117994]))], (19353 ^ _779308) ^ [_1118097, _1118099] : [19354 ^ _779308 : [(19355 ^ _779308) ^ [_1118146] : [_1118097 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1118099), _1118146)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118097, _1118099) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19359 ^ _779308) ^ [_1118208, _1118210] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118208, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1118210)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118208, _1118210) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (19365 ^ _779308) ^ [_1118298, _1118300] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1118298), _1118300) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118298, _1118300) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (19371 ^ _779308) ^ [_1118389, _1118391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118389), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118391), _1118389)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118389, _1118391) = _1118389)], (19381 ^ _779308) ^ [_1118546, _1118548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118546), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19384 ^ _779308 : [(19385 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118548, _1118546)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19387 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118546), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118548, _1118546))))]]], (19389 ^ _779308) ^ [_1118695, _1118697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118695), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118697, _1118695)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19395 ^ _779308) ^ [_1118800, _1118802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118800), _1118802)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118800, _1118802) = _1118800)], (19405 ^ _779308) ^ [_1118951, _1118953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1118951)), 19408 ^ _779308 : [(19409 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118953, _1118951))))], (19411 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1118953, _1118951)), _1118951)))]]], (19413 ^ _779308) ^ [_1119088, _1119090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1119088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119090, _1119088))))], (19419 ^ _779308) ^ [_1119190, _1119192] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119190, _1119192) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119190, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1119192)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19425 ^ _779308) ^ [_1119283, _1119285] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119283, _1119285) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119283, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1119285)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119283, _1119285)), _1119285))], (19431 ^ _779308) ^ [_1119351, _1119353] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119351, _1119353) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1119351), _1119353) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19437 ^ _779308) ^ [_1119444, _1119446] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119444, _1119446) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1119444), _1119446) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1119446), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1119444, _1119446)))], (19443 ^ _779308) ^ [_1119503] : [class_Int_Onumber__ring(_1119503), -(c_Int_Oiszero(_1119503, hAPP(c_Int_Onumber__class_Onumber__of(_1119503), c_Int_OPls)))], (19449 ^ _779308) ^ [_1119586, _1119588] : [c_Int_Oiszero(_1119586, hAPP(c_Int_Onumber__class_Onumber__of(_1119586), c_Int_OBit1(_1119588))), class_Int_Onumber__ring(_1119586), class_Int_Oring__char__0(_1119586)], (19459 ^ _779308) ^ [_1119726, _1119728] : [class_Int_Onumber__ring(_1119726), class_Int_Oring__char__0(_1119726), 19466 ^ _779308 : [(19467 ^ _779308) ^ [] : [c_Int_Oiszero(_1119726, hAPP(c_Int_Onumber__class_Onumber__of(_1119726), c_Int_OBit0(_1119728))), -(c_Int_Oiszero(_1119726, hAPP(c_Int_Onumber__class_Onumber__of(_1119726), _1119728)))], (19473 ^ _779308) ^ [] : [c_Int_Oiszero(_1119726, hAPP(c_Int_Onumber__class_Onumber__of(_1119726), _1119728)), -(c_Int_Oiszero(_1119726, hAPP(c_Int_Onumber__class_Onumber__of(_1119726), c_Int_OBit0(_1119728))))]]], (19479 ^ _779308) ^ [_1120019, _1120021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120019)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1120019), _1120021)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120019, _1120021) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1120019), _1120021))], (19489 ^ _779308) ^ [_1120194, _1120196, _1120198, _1120200] : [_1120194 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1120196), _1120198)), _1120200), -(_1120196 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120194, _1120196) = _1120200), 19496 ^ _779308 : [(19497 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120196)))], (19499 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120200), _1120196))]], 19504 ^ _779308 : [(19505 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120196))], (19507 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120196), _1120200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120200), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (19519 ^ _779308) ^ [_1120659, _1120661, _1120663, _1120665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120661), _1120663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120663), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1120661), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120665, _1120659))), _1120663)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19533 ^ _779308) ^ [_1120918, _1120920, _1120922, _1120924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1120918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120920), _1120922)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1120922), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1120920), _1120918)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1120920), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1120924, _1120918))), _1120922))))], (19547 ^ _779308) ^ [_1121189, _1121191, _1121193, _1121195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121191), _1121193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121193), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1121195, _1121189))), _1121191)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121193), _1121189))))], (19561 ^ _779308) ^ [_1121454, _1121456, _1121458, _1121460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121454)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121456), _1121458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121458), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1121460, _1121454))), _1121456))))], (19621 ^ _779308) ^ [_1122596, _1122598, _1122600] : [-(hBOOL(hAPP(_1122596, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1122598, _1122600)))), 19624 ^ _779308 : [(19625 ^ _779308) ^ [] : [-(_1122600 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19627 ^ _779308) ^ [] : [hBOOL(hAPP(_1122596, _1122598))]], 19630 ^ _779308 : [(19631 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122600)))], (19635 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 19633 ^ [_1122596, _1122598, _1122600])))], (19637 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 19633 ^ [_1122596, _1122598, _1122600]), _1122600)))], (19639 ^ _779308) ^ [] : [-(_1122598 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122600), 19632 ^ [_1122596, _1122598, _1122600])), 19633 ^ [_1122596, _1122598, _1122600]))], (19641 ^ _779308) ^ [] : [hBOOL(hAPP(_1122596, 19633 ^ [_1122596, _1122598, _1122600]))]], 19642 ^ _779308 : [(19643 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122600), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19647 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122600), 19645 ^ [_1122596, _1122598, _1122600])))], (19649 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 19645 ^ [_1122596, _1122598, _1122600]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19651 ^ _779308) ^ [] : [-(_1122598 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1122600), 19644 ^ [_1122596, _1122598, _1122600])), 19645 ^ [_1122596, _1122598, _1122600]))], (19653 ^ _779308) ^ [] : [hBOOL(hAPP(_1122596, 19645 ^ [_1122596, _1122598, _1122600]))]]], (19575 ^ _779308) ^ [_1121719, _1121721, _1121723] : [hBOOL(hAPP(_1121719, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1121721, _1121723))), 19578 ^ _779308 : [(19579 ^ _779308) ^ [] : [_1121723 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1121719, _1121721)))], (19585 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121723)), 19588 ^ _779308 : [(19589 ^ _779308) ^ [_1122049, _1122051] : [-(hBOOL(hAPP(_1121719, _1122049))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1122049), _1121723)), _1121721 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121723), _1122051)), _1122049)]]], (19603 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121723), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19606 ^ _779308 : [(19607 ^ _779308) ^ [_1122341, _1122343] : [-(hBOOL(hAPP(_1121719, _1122341))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1121723), _1122341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1122341), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1121721 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121723), _1122343)), _1122341)]]]]], (19657 ^ _779308) ^ [_1123308, _1123310] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1123308)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1123310))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1123308), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1123310))))], (19659 ^ _779308) ^ [_1123360] : [class_Int_Onumber__ring(_1123360), c_Int_Oiszero(_1123360, hAPP(c_Int_Onumber__class_Onumber__of(_1123360), c_Int_OBit1(c_Int_OPls)))], (19665 ^ _779308) ^ [_1123444, _1123446, _1123448] : [class_Int_Onumber__ring(_1123444), 19668 ^ _779308 : [(19669 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1123444), _1123446) = hAPP(c_Int_Onumber__class_Onumber__of(_1123444), _1123448), -(c_Int_Oiszero(_1123444, hAPP(c_Int_Onumber__class_Onumber__of(_1123444), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123446), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1123448)))))], (19675 ^ _779308) ^ [] : [c_Int_Oiszero(_1123444, hAPP(c_Int_Onumber__class_Onumber__of(_1123444), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123446), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1123448)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1123444), _1123446) = hAPP(c_Int_Onumber__class_Onumber__of(_1123444), _1123448))]]], (19681 ^ _779308) ^ [_1123727, _1123729] : [class_Int_Onumber__ring(_1123727), 19684 ^ _779308 : [(19685 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1123727), _1123729) = c_Groups_Ozero__class_Ozero(_1123727), -(c_Int_Oiszero(_1123727, hAPP(c_Int_Onumber__class_Onumber__of(_1123727), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123729), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (19691 ^ _779308) ^ [] : [c_Int_Oiszero(_1123727, hAPP(c_Int_Onumber__class_Onumber__of(_1123727), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123729), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1123727), _1123729) = c_Groups_Ozero__class_Ozero(_1123727))]]], (19697 ^ _779308) ^ [_1123986, _1123988] : [class_Int_Onumber__ring(_1123986), 19700 ^ _779308 : [(19701 ^ _779308) ^ [] : [c_Groups_Ozero__class_Ozero(_1123986) = hAPP(c_Int_Onumber__class_Onumber__of(_1123986), _1123988), -(c_Int_Oiszero(_1123986, hAPP(c_Int_Onumber__class_Onumber__of(_1123986), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1123988)))))], (19707 ^ _779308) ^ [] : [c_Int_Oiszero(_1123986, hAPP(c_Int_Onumber__class_Onumber__of(_1123986), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1123988)))), -(c_Groups_Ozero__class_Ozero(_1123986) = hAPP(c_Int_Onumber__class_Onumber__of(_1123986), _1123988))]]], (19713 ^ _779308) ^ [_1124254, _1124256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1124254)), -(c_SMT_Oz3mod(_1124256, _1124254) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1124256, _1124254))], (19719 ^ _779308) ^ [_1124343, _1124345] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1124343))), -(c_SMT_Oz3mod(_1124345, _1124343) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1124345, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1124343)))], (19725 ^ _779308) ^ [_1124393, _1124395, _1124397, _1124399, _1124401, _1124403, _1124405] : [c_Big__Operators_Ocomm__monoid__big(_1124393, _1124395, _1124397, _1124399, _1124401), 19728 ^ _779308 : [(19729 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1124395), _1124403)), -(hAPP(hAPP(_1124401, _1124405), _1124403) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1124393, _1124395, _1124397), _1124405), _1124399), _1124403))], (19735 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1124395), _1124403))), -(hAPP(hAPP(_1124401, _1124405), _1124403) = _1124399)]]], (19741 ^ _779308) ^ [_1124661, _1124663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124661), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1124663))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1124661)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1124663), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1124661))], (19747 ^ _779308) ^ [_1124802, _1124804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1124802)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1124804))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1124802)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1124804), _1124802))], (19753 ^ _779308) ^ [_1124925] : [class_Orderings_Oord(_1124925), -(c_Orderings_Oord__class_Omin(_1124925) = c_Orderings_Oord_Omin(_1124925, c_Orderings_Oord__class_Oless__eq(_1124925)))], (19759 ^ _779308) ^ [_1125012] : [class_Power_Opower(_1125012), -(c_Power_Opower__class_Opower(_1125012) = c_Power_Opower_Opower(_1125012, c_Groups_Oone__class_Oone(_1125012), c_Groups_Otimes__class_Otimes(_1125012)))], (19765 ^ _779308) ^ [_1125105] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125105) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19767 ^ _779308) ^ [_1125131, _1125133] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1125131), _1125133) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1125131, _1125133)), _1125133))], (19769 ^ _779308) ^ [_1125174, _1125176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125174), _1125176)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1125174, _1125176) = _1125174)], (19775 ^ _779308) ^ [_1125269, _1125271] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1125269, _1125271)), _1125269)))], (19777 ^ _779308) ^ [_1125303, _1125305, _1125307] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1125303), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1125305, _1125307)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1125303), _1125305), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1125303), _1125307)))], (19779 ^ _779308) ^ [_1125356, _1125358, _1125360] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1125356, _1125358)), _1125360) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1125356), _1125360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1125358), _1125360)))], (19781 ^ _779308) ^ [_1125409, _1125411] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1125409)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1125411)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1125409), _1125411))], (19783 ^ _779308) ^ [_1125452, _1125454] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1125452), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1125454)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1125452)), _1125454))], (19785 ^ _779308) ^ [_1125495, _1125497] : [class_Divides_Osemiring__div(_1125495), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1125495), _1125497), c_Groups_Ozero__class_Ozero(_1125495)) = c_Groups_Ozero__class_Ozero(_1125495))], (19791 ^ _779308) ^ [_1125594, _1125596] : [class_Divides_Osemiring__div(_1125594), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1125594), c_Groups_Ozero__class_Ozero(_1125594)), _1125596) = c_Groups_Ozero__class_Ozero(_1125594))], (19797 ^ _779308) ^ [_1125693, _1125695] : [class_Divides_Osemiring__div(_1125693), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1125693), _1125695), c_Groups_Oone__class_Oone(_1125693)) = _1125695)], (19803 ^ _779308) ^ [_1125788] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1125788, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19805 ^ _779308) ^ [_1125824, _1125826] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1125824, _1125826)) = _1125826, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1125824), _1125826) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19811 ^ _779308) ^ [_1125923, _1125925] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1125923, _1125925)) = _1125925), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1125923), _1125925) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1125923, _1125925)))], (19817 ^ _779308) ^ [_1125982, _1125984] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125982)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1125984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1125982), _1125984))))], (19827 ^ _779308) ^ [_1126135, _1126137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1126135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1126137, _1126135)), _1126135)))], (19833 ^ _779308) ^ [_1126234, _1126236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126234)), 19836 ^ _779308 : [(19837 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1126236), _1126234)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126236), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19843 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126236), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1126236), _1126234)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (19849 ^ _779308) ^ [_1126493, _1126495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126493), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 19852 ^ _779308 : [(19853 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1126495), _1126493)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126495)))], (19859 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1126495), _1126493)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (19865 ^ _779308) ^ [_1126749, _1126751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1126749), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1126751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1126749), _1126751)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19875 ^ _779308) ^ [_1126910] : [-(_1126910 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1126910), _1126910) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (19881 ^ _779308) ^ [_1126965, _1126967] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1126965, _1126967) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1126965 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1126967), 19884 ^ [_1126965, _1126967]))], (19888 ^ _779308) ^ [_1127070, _1127072] : [19889 ^ _779308 : [(19890 ^ _779308) ^ [_1127119] : [_1127070 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127072), _1127119)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127070, _1127072) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19894 ^ _779308) ^ [_1127191, _1127193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127191), _1127193)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127191, _1127193) = _1127191)], (19900 ^ _779308) ^ [_1127280, _1127282] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127280), _1127282))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127280, _1127282) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1127280), _1127282), _1127282))], (19906 ^ _779308) ^ [_1127333, _1127335] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127333), _1127335))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127333, _1127335) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1127333), _1127335), _1127335))], (19912 ^ _779308) ^ [_1127388, _1127390] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1127388))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1127390))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1127388)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1127390)))], (19914 ^ _779308) ^ [_1127441, _1127443] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1127441, _1127443)), _1127443) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19916 ^ _779308) ^ [_1127474] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127474), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19918 ^ _779308) ^ [_1127500] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1127500, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1127500)], (19920 ^ _779308) ^ [_1127529, _1127531, _1127533] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1127529), _1127531)), _1127533), _1127531) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127533, _1127531))], (19922 ^ _779308) ^ [_1127576, _1127578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1127576), _1127578)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127578, _1127576) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1127578), _1127576), _1127576))], (19928 ^ _779308) ^ [_1127691, _1127693, _1127695] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1127691), _1127693)), _1127695) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127691), _1127695)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1127693), _1127695))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1127691, _1127695)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1127693, _1127695))), _1127695)))], (19930 ^ _779308) ^ [_1127774, _1127776] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1127774), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1127776)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127774, _1127776)))], (19932 ^ _779308) ^ [_1127816, _1127818] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1127816, _1127818)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1127816), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1127818)))], (19934 ^ _779308) ^ [_1127858, _1127860, _1127862, _1127864] : [class_Divides_Osemiring__div(_1127858), 19937 ^ _779308 : [(19938 ^ _779308) ^ [] : [_1127860 = c_Groups_Ozero__class_Ozero(_1127858), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1127858), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127858), _1127860), _1127862)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127858), _1127860), _1127864)) = c_Groups_Ozero__class_Ozero(_1127858))], (19944 ^ _779308) ^ [] : [-(_1127860 = c_Groups_Ozero__class_Ozero(_1127858)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1127858), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127858), _1127860), _1127862)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127858), _1127860), _1127864)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1127858), _1127862), _1127864))]]], (19950 ^ _779308) ^ [_1128164, _1128166, _1128168] : [class_Divides_Osemiring__div(_1128164), -(_1128166 = c_Groups_Ozero__class_Ozero(_1128164)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128164), _1128168), _1128166)), _1128166) = _1128168)], (19960 ^ _779308) ^ [_1128292, _1128294, _1128296] : [class_Divides_Osemiring__div(_1128292), -(_1128294 = c_Groups_Ozero__class_Ozero(_1128292)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128292), _1128294), _1128296)), _1128294) = _1128296)], (19970 ^ _779308) ^ [_1128420, _1128422, _1128424, _1128426] : [class_Divides_Osemiring__div(_1128420), -(_1128422 = c_Groups_Ozero__class_Ozero(_1128420)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128420), _1128424), _1128422)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128420), _1128426), _1128422)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128420), _1128424), _1128426))], (19980 ^ _779308) ^ [_1128582, _1128584, _1128586, _1128588] : [class_Divides_Osemiring__div(_1128582), -(_1128584 = c_Groups_Ozero__class_Ozero(_1128582)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128582), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128582), _1128584), _1128586)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1128582), _1128584), _1128588)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128582), _1128586), _1128588))], (19990 ^ _779308) ^ [_1128744, _1128746] : [class_Divides_Osemiring__div(_1128744), -(_1128746 = c_Groups_Ozero__class_Ozero(_1128744)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128744), _1128746), _1128746) = c_Groups_Oone__class_Oone(_1128744))], (20000 ^ _779308) ^ [_1128858, _1128860, _1128862] : [class_Divides_Osemiring__div(_1128858), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1128858), c_Divides_Odiv__class_Omod(_1128858, _1128860, _1128862)), _1128862) = c_Groups_Ozero__class_Ozero(_1128858))], (20006 ^ _779308) ^ [_1128978, _1128980] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1128978), _1128980) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1128980 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20015 ^ _779308 : [(20016 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1128978)))], (20018 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128978), _1128980)))]], 20019 ^ _779308 : [(20020 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1128978), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20022 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1128980), _1128978)))]]], (20024 ^ _779308) ^ [_1129209, _1129211] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129209), _1129211) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20025 ^ _779308 : [(20026 ^ _779308) ^ [] : [_1129211 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (20028 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129209)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129209), _1129211))], (20034 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129209), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1129211), _1129209))]]], (20042 ^ _779308) ^ [_1129504, _1129506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129504)), 20045 ^ _779308 : [(20046 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129506), _1129504))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129506)))], (20052 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129506), _1129504))))]]], (20058 ^ _779308) ^ [_1129745, _1129747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129745)), 20061 ^ _779308 : [(20062 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129747), _1129745))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129745), _1129747)))], (20068 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129745), _1129747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129747), _1129745))))]]], (20074 ^ _779308) ^ [_1129995, _1129997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129995)), 20077 ^ _779308 : [(20078 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129995), _1129997))), 20081 ^ _779308 : [(20082 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129997), _1129995)))], (20084 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129997)))]]], (20086 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1129995), _1129997)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1129997), _1129995)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129997))]]], (20096 ^ _779308) ^ [_1130323, _1130325, _1130327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130323)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130325), _1130327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130323), _1130327)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130323), _1130325))))], (20110 ^ _779308) ^ [_1130562, _1130564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130564), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130562), _1130564)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20120 ^ _779308) ^ [_1130727, _1130729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130727)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130727), _1130729)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130727), _1130729) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20130 ^ _779308) ^ [_1130882, _1130884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130882), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 20133 ^ _779308 : [(20134 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130884), _1130882))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130884), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20140 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1130884), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1130884), _1130882))))]]], (20146 ^ _779308) ^ [_1131138, _1131140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131138), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131138), _1131140)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20156 ^ _779308) ^ [_1131303, _1131305, _1131307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1131303), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131305)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131305), _1131307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131303), _1131305)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131303), _1131307))))], (20170 ^ _779308) ^ [_1131548, _1131550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131548), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1131550), _1131548)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131548), _1131550) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20180 ^ _779308) ^ [_1131709, _1131711, _1131713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131709), _1131711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131709), _1131713)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131711), _1131713))))], (20190 ^ _779308) ^ [_1131890, _1131892, _1131894] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1131890), _1131892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1131894), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131892), _1131894)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1131890), _1131894))))], (20200 ^ _779308) ^ [_1132077, _1132079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1132077)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1132079, _1132077)), _1132077)))], (20206 ^ _779308) ^ [_1132176, _1132178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1132178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132176), _1132178)), _1132176)))], (20216 ^ _779308) ^ [_1132335, _1132337, _1132339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1132335)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132339), _1132335)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132337), _1132339)), _1132335))], (20222 ^ _779308) ^ [_1132466, _1132468, _1132470] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1132466), _1132468)), _1132470)), _1132468) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1132470), _1132468))], (20224 ^ _779308) ^ [_1132519, _1132521, _1132523] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132519), _1132521)), _1132521)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1132519, _1132521))), _1132523) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1132519), _1132523))], (20226 ^ _779308) ^ [_1132580, _1132582, _1132584] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132580), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132582), _1132580))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1132582, _1132580))), _1132584) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1132582), _1132584))], (20228 ^ _779308) ^ [_1132641, _1132643, _1132645] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132641), _1132643)), _1132645) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132641), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132643), _1132645))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132641), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1132643, _1132645))), _1132645)))], (20230 ^ _779308) ^ [_1132714, _1132716] : [-(_1132714 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132716), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132714), _1132716))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1132714, _1132716)))], (20232 ^ _779308) ^ [_1132761, _1132763] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1132761), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132763), _1132761)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1132763), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1132763, _1132761)))], (20234 ^ _779308) ^ [_1132808, _1132810] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1132808, _1132810) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1132808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1132808), _1132810)), _1132810)))], (20236 ^ _779308) ^ [_1132855, _1132857, _1132859, _1132861] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1132855, _1132857, _1132859), _1132861), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1132857)], (20238 ^ _779308) ^ [_1132894, _1132896, _1132898, _1132900, _1132902] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1132894, _1132896, _1132898), _1132900), hAPP(c_Nat_OSuc, _1132902)) = hAPP(hAPP(_1132898, _1132900), hAPP(hAPP(c_Power_Opower_Opower(_1132894, _1132896, _1132898), _1132900), _1132902)))], (20240 ^ _779308) ^ [_1132954, _1132956, _1132958, _1132960] : [class_Divides_Osemiring__div(_1132954), -(_1132956 = c_Groups_Ozero__class_Ozero(_1132954)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132954), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132954), _1132958), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132954), _1132956), _1132960))), _1132956) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132954), _1132960), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1132954), _1132958), _1132956)))], (20250 ^ _779308) ^ [_1133132, _1133134, _1133136, _1133138] : [class_Divides_Osemiring__div(_1133132), -(_1133134 = c_Groups_Ozero__class_Ozero(_1133132)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133132), _1133136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133132), _1133138), _1133134))), _1133134) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133132), _1133138), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133132), _1133136), _1133134)))], (20260 ^ _779308) ^ [_1133310, _1133312, _1133314] : [class_Divides_Osemiring__div(_1133310), -(_1133312 = c_Groups_Ozero__class_Ozero(_1133310)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133310), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133310), _1133312), _1133314)), _1133312) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133310), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133310), _1133314), _1133312)), c_Groups_Oone__class_Oone(_1133310)))], (20270 ^ _779308) ^ [_1133474, _1133476, _1133478] : [class_Divides_Osemiring__div(_1133474), -(_1133476 = c_Groups_Ozero__class_Ozero(_1133474)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133474), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133474), _1133478), _1133476)), _1133476) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133474), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133474), _1133478), _1133476)), c_Groups_Oone__class_Oone(_1133474)))], (20280 ^ _779308) ^ [_1133638, _1133640, _1133642] : [class_Divides_Osemiring__div(_1133638), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133638), c_Divides_Odiv__class_Omod(_1133638, _1133640, _1133642)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133638), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133638), _1133640), _1133642)), _1133642)) = _1133640)], (20286 ^ _779308) ^ [_1133771, _1133773, _1133775] : [class_Divides_Osemiring__div(_1133771), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133771), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133771), _1133773), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133771), _1133775), _1133773))), c_Divides_Odiv__class_Omod(_1133771, _1133775, _1133773)) = _1133775)], (20292 ^ _779308) ^ [_1133904, _1133906, _1133908] : [class_Divides_Osemiring__div(_1133904), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133904), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1133904), _1133906), _1133908)), _1133908)), c_Divides_Odiv__class_Omod(_1133904, _1133906, _1133908)) = _1133906)], (20298 ^ _779308) ^ [_1134037, _1134039, _1134041, _1134043] : [class_Divides_Osemiring__div(_1134037), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134037), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134037), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134037), _1134039), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1134037), _1134041), _1134039))), c_Divides_Odiv__class_Omod(_1134037, _1134041, _1134039))), _1134043) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134037), _1134041), _1134043))], (20304 ^ _779308) ^ [_1134204, _1134206, _1134208, _1134210] : [class_Divides_Osemiring__div(_1134204), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134204), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134204), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134204), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1134204), _1134206), _1134208)), _1134208)), c_Divides_Odiv__class_Omod(_1134204, _1134206, _1134208))), _1134210) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1134204), _1134206), _1134210))], (20334 ^ _779308) ^ [_1134822, _1134824, _1134826] : [-(hBOOL(hAPP(_1134822, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1134824, _1134826)))), 20337 ^ _779308 : [(20338 ^ _779308) ^ [] : [-(_1134826 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20340 ^ _779308) ^ [] : [hBOOL(hAPP(_1134822, _1134824))]], 20341 ^ _779308 : [(20342 ^ _779308) ^ [] : [_1134826 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20346 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20344 ^ [_1134822, _1134824, _1134826]), _1134826)))], (20348 ^ _779308) ^ [] : [-(_1134824 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1134826), 20343 ^ [_1134822, _1134824, _1134826])), 20344 ^ [_1134822, _1134824, _1134826]))], (20350 ^ _779308) ^ [] : [hBOOL(hAPP(_1134822, 20344 ^ [_1134822, _1134824, _1134826]))]]], (20310 ^ _779308) ^ [_1134389, _1134391, _1134393] : [hBOOL(hAPP(_1134389, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1134391, _1134393))), 20313 ^ _779308 : [(20314 ^ _779308) ^ [] : [_1134393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1134389, _1134391)))], (20320 ^ _779308) ^ [] : [-(_1134393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20323 ^ _779308 : [(20324 ^ _779308) ^ [_1134637, _1134639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1134637), _1134393)), _1134391 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1134393), _1134639)), _1134637), -(hBOOL(hAPP(_1134389, _1134637)))]]]]], (20354 ^ _779308) ^ [_1135231, _1135233, _1135235, _1135237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1135231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1135233), _1135235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1135235), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1135237, _1135231))), _1135233)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1135235), _1135231))))], (20364 ^ _779308) ^ [_1135436, _1135438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1135436)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1135436), _1135438)), _1135436) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20370 ^ _779308) ^ [_1135543, _1135545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135543)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135545)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1135543, _1135545)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1135543), hAPP(c_Int_Onat, _1135545)))], (20380 ^ _779308) ^ [_1135714, _1135716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1135716)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1135714), hAPP(c_Int_Onat, _1135716)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1135714, _1135716)))], (20390 ^ _779308) ^ [_1135885, _1135887, _1135889, _1135891, _1135893, _1135895, _1135897] : [c_Big__Operators_Ocomm__monoid__big(_1135885, _1135887, _1135889, _1135891, _1135893), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1135887), _1135895))), -(hAPP(hAPP(_1135893, _1135897), _1135895) = _1135891)], (20446 ^ _779308) ^ [_1136991, _1136993, _1136995] : [-(hBOOL(hAPP(_1136991, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1136993), _1136995)))), 20449 ^ _779308 : [(20450 ^ _779308) ^ [] : [-(_1136995 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20452 ^ _779308) ^ [] : [hBOOL(hAPP(_1136991, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 20455 ^ _779308 : [(20456 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136995)))], (20460 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20458 ^ [_1136991, _1136993, _1136995])))], (20462 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 20458 ^ [_1136991, _1136993, _1136995]), _1136995)))], (20464 ^ _779308) ^ [] : [-(_1136993 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1136995), 20457 ^ [_1136991, _1136993, _1136995])), 20458 ^ [_1136991, _1136993, _1136995]))], (20466 ^ _779308) ^ [] : [hBOOL(hAPP(_1136991, 20457 ^ [_1136991, _1136993, _1136995]))]], 20467 ^ _779308 : [(20468 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1136995), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20472 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1136995), 20470 ^ [_1136991, _1136993, _1136995])))], (20474 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 20470 ^ [_1136991, _1136993, _1136995]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20476 ^ _779308) ^ [] : [-(_1136993 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1136995), 20469 ^ [_1136991, _1136993, _1136995])), 20470 ^ [_1136991, _1136993, _1136995]))], (20478 ^ _779308) ^ [] : [hBOOL(hAPP(_1136991, 20469 ^ [_1136991, _1136993, _1136995]))]]], (20400 ^ _779308) ^ [_1136031, _1136033, _1136035] : [hBOOL(hAPP(_1136031, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1136033), _1136035))), 20403 ^ _779308 : [(20404 ^ _779308) ^ [] : [_1136035 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1136031, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20410 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136035)), 20413 ^ _779308 : [(20414 ^ _779308) ^ [_1136365] : [-(hBOOL(hAPP(_1136031, _1136365))), 20415 ^ _779308 : [(20416 ^ _779308) ^ [_1136436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1136436)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1136436), _1136035)), _1136033 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1136035), _1136365)), _1136436)]]]]], (20428 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1136035), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 20431 ^ _779308 : [(20432 ^ _779308) ^ [_1136695] : [-(hBOOL(hAPP(_1136031, _1136695))), 20433 ^ _779308 : [(20434 ^ _779308) ^ [_1136769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1136035), _1136769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1136769), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1136033 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1136035), _1136695)), _1136769)]]]]]]], (20482 ^ _779308) ^ [_1137705, _1137707, _1137709, _1137711] : [_1137705 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1137707), _1137709)), _1137711), -(_1137707 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1137705), _1137707) = _1137709), 20489 ^ _779308 : [(20490 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137707)))], (20492 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137711), _1137707))]], 20497 ^ _779308 : [(20498 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1137707))], (20500 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137707), _1137711)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1137711), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (20512 ^ _779308) ^ [_1138174, _1138176] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1138174, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1138176)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1138174, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1138176)))], (20514 ^ _779308) ^ [_1138219, _1138221] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1138219))), _1138221) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1138219), _1138221))], (20516 ^ _779308) ^ [_1138264, _1138266] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1138264))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138266)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1138264), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138266)))], (20518 ^ _779308) ^ [_1138315, _1138317, _1138319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1138315)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1138317, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1138319), _1138315)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1138319), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1138317), _1138319), _1138315))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1138317, _1138319)))], (20524 ^ _779308) ^ [_1138470] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1138470)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1138470, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (20526 ^ _779308) ^ [_1138506, _1138508] : [-(_1138506 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20529 ^ _779308 : [(20530 ^ _779308) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1138508, _1138506) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1138508), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1138506)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1138508), _1138506)))], (20536 ^ _779308) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1138508, _1138506) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1138508), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1138506)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1138508), _1138506))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (20542 ^ _779308) ^ [_1138779, _1138781] : [-(_1138779 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20545 ^ _779308 : [(20546 ^ _779308) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1138781, _1138779) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1138781)), _1138779) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1138781), _1138779)))], (20552 ^ _779308) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1138781, _1138779) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1138781)), _1138779) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1138781), _1138779))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (20558 ^ _779308) ^ [_1139053, _1139055, _1139057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139053)), 20561 ^ _779308 : [(20580 ^ _779308) ^ [] : [20583 ^ _779308 : [(20584 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20582 ^ [_1139053, _1139055, _1139057])))], (20586 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 20582 ^ [_1139053, _1139055, _1139057]), _1139053)))], (20588 ^ _779308) ^ [] : [-(_1139057 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139053), 20581 ^ [_1139053, _1139055, _1139057])), 20582 ^ [_1139053, _1139055, _1139057]))], (20590 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1139055, 20581 ^ [_1139053, _1139055, _1139057]), 20582 ^ [_1139053, _1139055, _1139057]))]], -(hBOOL(hAPP(hAPP(_1139055, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139057), _1139053)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139057, _1139053))))], (20562 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1139055, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139057), _1139053)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139057, _1139053))), 20565 ^ _779308 : [(20566 ^ _779308) ^ [_1139254, _1139256] : [-(hBOOL(hAPP(hAPP(_1139055, _1139256), _1139254))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1139254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139254), _1139053)), _1139057 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139053), _1139256)), _1139254)]]]]], (20594 ^ _779308) ^ [_1139768, _1139770, _1139772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139768), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 20597 ^ _779308 : [(20616 ^ _779308) ^ [] : [20619 ^ _779308 : [(20620 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139768), 20618 ^ [_1139768, _1139770, _1139772])))], (20622 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 20618 ^ [_1139768, _1139770, _1139772]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20624 ^ _779308) ^ [] : [-(_1139772 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139768), 20617 ^ [_1139768, _1139770, _1139772])), 20618 ^ [_1139768, _1139770, _1139772]))], (20626 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1139770, 20617 ^ [_1139768, _1139770, _1139772]), 20618 ^ [_1139768, _1139770, _1139772]))]], -(hBOOL(hAPP(hAPP(_1139770, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139772), _1139768)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139772, _1139768))))], (20598 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1139770, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1139772), _1139768)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1139772, _1139768))), 20601 ^ _779308 : [(20602 ^ _779308) ^ [_1139978, _1139980] : [-(hBOOL(hAPP(hAPP(_1139770, _1139980), _1139978))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139768), _1139978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1139978), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1139772 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1139768), _1139980)), _1139978)]]]]], (20630 ^ _779308) ^ [_1140510, _1140512] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1140510))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1140510), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1140512)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20636 ^ _779308) ^ [_1140612, _1140614] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1140612)))), 20639 ^ _779308 : [(20640 ^ _779308) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1140614))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1140612), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1140614)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1140612))], (20646 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1140614)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1140612), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1140614)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1140612), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1140614))))]]], (20652 ^ _779308) ^ [_1140894, _1140896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1140894))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1140896))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1140894))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1140896)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1140894)))], (20658 ^ _779308) ^ [_1141031, _1141033] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141031)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1141033))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1141031))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141033)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141031)))], (20664 ^ _779308) ^ [_1141108, _1141110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1141108)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1141110)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1141110), _1141108)), _1141110) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1141110), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1141108), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (20674 ^ _779308) ^ [_1141305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141305, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141305, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20680 ^ _779308) ^ [_1141396] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141396, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1141396, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20686 ^ _779308) ^ [_1141499] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141499))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141499)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20692 ^ _779308) ^ [_1141592] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141592)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141592)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1141592))))], (20698 ^ _779308) ^ [_1141659, _1141661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1141659)), -(c_SMT_Oz3div(_1141661, _1141659) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1141661), _1141659))], (20704 ^ _779308) ^ [_1141752, _1141754] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1141752))), -(c_SMT_Oz3div(_1141754, _1141752) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1141754), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1141752))))], (20710 ^ _779308) ^ [_1141807, _1141809] : [class_Int_Onumber__ring(_1141807), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1141807), hAPP(c_Int_Onumber__class_Onumber__of(_1141807), c_Int_OMin)), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1141809))) = hAPP(c_Int_Onumber__class_Onumber__of(_1141807), c_Int_OMin))], (20716 ^ _779308) ^ [_1141930, _1141932] : [class_Int_Onumber__ring(_1141930), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1141930), hAPP(c_Int_Onumber__class_Onumber__of(_1141930), c_Int_OMin)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1141932)) = c_Groups_Oone__class_Oone(_1141930))], (20722 ^ _779308) ^ [_1142041, _1142043] : [c_Nat__Transfer_Onat__set(_1142041), c_Nat__Transfer_Onat__set(_1142043), 20729 ^ _779308 : [(20730 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1142041), _1142043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1142041)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1142043))))], (20736 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1142041)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1142043))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1142041), _1142043)))]]], (20742 ^ _779308) ^ [_1142344, _1142346] : [c_Nat__Transfer_Onat__set(_1142344), c_Nat__Transfer_Onat__set(_1142346), 20749 ^ _779308 : [(20750 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1142344), _1142346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1142344)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1142346))))], (20756 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1142344)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1142346))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1142344), _1142346)))]]], (20762 ^ _779308) ^ [_1142647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1142647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1142647), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (20768 ^ _779308) ^ [_1142754, _1142756, _1142758] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1142754), _1142756)), _1142758) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142754), _1142758)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142756), _1142758))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1142754, _1142758)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1142756, _1142758))), _1142758)))], (20770 ^ _779308) ^ [_1142837, _1142839] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142837), _1142839)), _1142837)))], (20772 ^ _779308) ^ [_1142873, _1142875, _1142877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1142873), _1142875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142873), _1142877)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142875), _1142877))))], (20778 ^ _779308) ^ [_1142996, _1142998, _1143000] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1142998), _1143000)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1142996), _1142998)), _1143000))], (20780 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (20782 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (20784 ^ _779308) ^ [] : [c_Int_OMin = c_Int_OPls], (20786 ^ _779308) ^ [] : [c_Int_OPls = c_Int_OMin], (20788 ^ _779308) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (20790 ^ _779308) ^ [_1143167] : [c_Int_OMin = c_Int_OBit1(_1143167), -(c_Int_OMin = _1143167)], (20796 ^ _779308) ^ [_1143242] : [c_Int_OMin = _1143242, -(c_Int_OMin = c_Int_OBit1(_1143242))], (20802 ^ _779308) ^ [_1143335] : [c_Int_OBit1(_1143335) = c_Int_OMin, -(_1143335 = c_Int_OMin)], (20808 ^ _779308) ^ [_1143410] : [_1143410 = c_Int_OMin, -(c_Int_OBit1(_1143410) = c_Int_OMin)], (20814 ^ _779308) ^ [_1143500] : [c_Int_OMin = c_Int_OBit0(_1143500)], (20816 ^ _779308) ^ [_1143534] : [c_Int_OBit0(_1143534) = c_Int_OMin], (20818 ^ _779308) ^ [_1143559] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143559), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1143559)], (20820 ^ _779308) ^ [_1143588, _1143590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1143588), _1143590)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143588), _1143590) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20826 ^ _779308) ^ [_1143699, _1143701, _1143703] : [_1143699 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143699), _1143701)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143699), _1143703)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20832 ^ _779308) ^ [_1143808, _1143810, _1143812] : [-(_1143808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143808), _1143810)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143808), _1143812)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143810), _1143812))], (20838 ^ _779308) ^ [_1143872, _1143874, _1143876] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1143872, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143874), _1143876)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143874), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143872), _1143874), _1143876))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1143872, _1143874)))], (20840 ^ _779308) ^ [_1143935, _1143937, _1143939] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143935), _1143937)), _1143939) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143935), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1143937), _1143939))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1143935), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1143937, _1143939))), _1143939)))], (20842 ^ _779308) ^ [_1144008, _1144010] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144008, _1144010) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144008), _1144010)), _1144010)))], (20844 ^ _779308) ^ [_1144055, _1144057] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1144055), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144057), _1144055)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144057), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144057, _1144055)))], (20846 ^ _779308) ^ [_1144102, _1144104] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144102), _1144104)), _1144104) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1144102), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1144102, _1144104)))], (20848 ^ _779308) ^ [_1144149, _1144151] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144149), _1144151)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144149)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144151)))], (20850 ^ _779308) ^ [_1144195, _1144197] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144195)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1144197)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1144195), _1144197)))], (20852 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20854 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (20856 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (20858 ^ _779308) ^ [_1144313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1144313)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1144313), c_Int_OMin)))], (20864 ^ _779308) ^ [_1144408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1144408), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1144408)), c_Int_OMin)))], (20870 ^ _779308) ^ [_1144521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1144521))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1144521)))], (20876 ^ _779308) ^ [_1144604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1144604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1144604))))], (20882 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (20884 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (20886 ^ _779308) ^ [_1144747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1144747))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1144747)))], (20892 ^ _779308) ^ [_1144830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1144830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1144830))))], (20898 ^ _779308) ^ [_1144931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1144931)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1144931), c_Int_OMin)))], (20904 ^ _779308) ^ [_1145026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1145026), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1145026)), c_Int_OMin)))], (20910 ^ _779308) ^ [_1145139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1145139)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145139), c_Int_OMin)))], (20916 ^ _779308) ^ [_1145234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1145234), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1145234)), c_Int_OMin)))], (20922 ^ _779308) ^ [_1145347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1145347))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1145347)))], (20928 ^ _779308) ^ [_1145430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1145430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1145430))))], (20934 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (20936 ^ _779308) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20938 ^ _779308) ^ [_1145561] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1145561) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1145561))], (20940 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (20942 ^ _779308) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (20944 ^ _779308) ^ [_1145626] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1145626), c_Int_OMin) = c_Int_Opred(_1145626))], (20946 ^ _779308) ^ [_1145657] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1145657) = c_Int_Opred(_1145657))], (20948 ^ _779308) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (20950 ^ _779308) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (20952 ^ _779308) ^ [_1145721] : [class_Int_Onumber__ring(_1145721), c_Int_Oiszero(_1145721, hAPP(c_Int_Onumber__class_Onumber__of(_1145721), c_Int_OMin))], (20958 ^ _779308) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (20960 ^ _779308) ^ [_1145823] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1145823), c_Int_OMin) = c_Int_Osucc(_1145823))], (20972 ^ _779308) ^ [_1146023] : [20974 ^ _779308 : [(20975 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 20973 ^ [_1146023]), _1146023)))], (20977 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 20973 ^ [_1146023]))]], -(c_Nat__Transfer_Onat__set(_1146023))], (20962 ^ _779308) ^ [_1145866] : [c_Nat__Transfer_Onat__set(_1145866), 20965 ^ _779308 : [(20966 ^ _779308) ^ [_1145932] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1145932), _1145866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1145932)))]]], (20981 ^ _779308) ^ [_1146171, _1146173, _1146175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1146171), _1146173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1146175), _1146173)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1146175), _1146171))))], (20991 ^ _779308) ^ [_1146352, _1146354, _1146356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146352)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146352), _1146354)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146352), _1146356)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1146354), _1146356))], (20997 ^ _779308) ^ [_1146483, _1146485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146483)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146485), _1146483)), _1146483) = _1146485)], (21003 ^ _779308) ^ [_1146588, _1146590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146588)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146588), _1146590)), _1146588) = _1146590)], (21009 ^ _779308) ^ [_1146693, _1146695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1146693)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146695)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1146695), _1146693)), _1146695)))], (21019 ^ _779308) ^ [_1146852, _1146854] : [class_Int_Onumber__ring(_1146852), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146852), _1146854), hAPP(c_Int_Onumber__class_Onumber__of(_1146852), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1146852), _1146854))], (21025 ^ _779308) ^ [_1146963, _1146965] : [class_Int_Onumber__ring(_1146963), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146963), hAPP(c_Int_Onumber__class_Onumber__of(_1146963), c_Int_OMin)), _1146965) = hAPP(c_Groups_Ouminus__class_Ouminus(_1146963), _1146965))], (21031 ^ _779308) ^ [_1147074] : [-(c_Nat__Transfer_Onat__set(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1147074)))], (21033 ^ _779308) ^ [_1147099] : [class_Int_Onumber__ring(_1147099), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1147099), c_Groups_Oone__class_Oone(_1147099)) = hAPP(c_Int_Onumber__class_Onumber__of(_1147099), c_Int_OMin))], (21039 ^ _779308) ^ [_1147196] : [class_Int_Onumber__ring(_1147196), -(hAPP(c_Int_Onumber__class_Onumber__of(_1147196), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1147196), c_Groups_Oone__class_Oone(_1147196)))], (21045 ^ _779308) ^ [_1147293, _1147295] : [c_Nat__Transfer_Onat__set(_1147293), c_Nat__Transfer_Onat__set(_1147295), 21052 ^ _779308 : [(21053 ^ _779308) ^ [] : [_1147293 = _1147295, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1147293) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1147295))], (21059 ^ _779308) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1147293) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1147295), -(_1147293 = _1147295)]]], (21065 ^ _779308) ^ [_1147578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1147578)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1147578), c_Int_OMin)))], (21071 ^ _779308) ^ [_1147673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1147673), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1147673)), c_Int_OMin)))], (21077 ^ _779308) ^ [_1147786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1147786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1147786)))], (21083 ^ _779308) ^ [_1147869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1147869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1147869))))], (21089 ^ _779308) ^ [_1147958] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1147958, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21091 ^ _779308) ^ [_1147985] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1147985)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1147985)))], (21093 ^ _779308) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (21095 ^ _779308) ^ [_1148036, _1148038] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1148036), _1148038) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1148036 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1148036 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (21105 ^ _779308) ^ [_1148153, _1148155] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1148153), _1148155) = c_Groups_Oone__class_Oone(tc_Int_Oint), 21110 ^ _779308 : [(21111 ^ _779308) ^ [] : [-(_1148153 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (21113 ^ _779308) ^ [] : [-(_1148155 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 21114 ^ _779308 : [(21115 ^ _779308) ^ [] : [-(_1148153 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (21117 ^ _779308) ^ [] : [-(_1148155 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (21119 ^ _779308) ^ [_1148337, _1148339] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1148337), _1148339) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 21120 ^ _779308 : [(21121 ^ _779308) ^ [] : [_1148337 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1148339 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (21127 ^ _779308) ^ [] : [_1148337 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1148339 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (21135 ^ _779308) ^ [_1148563] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1148563)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1148563)))], (21137 ^ _779308) ^ [_1148596] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1148596)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1148596)))], (21139 ^ _779308) ^ [_1148629] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1148629), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1148629))], (21141 ^ _779308) ^ [_1148661, _1148663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1148661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1148663), _1148661))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1148663), _1148661) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1148663), _1148661)), _1148661)))], (21151 ^ _779308) ^ [_1148809, _1148811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1148809)), 21154 ^ _779308 : [(21155 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1148811), _1148809)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1148811), _1148809) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21161 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1148811), _1148809))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1148811), _1148809) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1148811), _1148809)), _1148809)))]]], (21191 ^ _779308) ^ [_1149518, _1149520, _1149522] : [-(hBOOL(hAPP(_1149518, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1149520), _1149522)))), 21194 ^ _779308 : [(21195 ^ _779308) ^ [] : [-(_1149522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21197 ^ _779308) ^ [] : [hBOOL(hAPP(_1149518, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 21198 ^ _779308 : [(21199 ^ _779308) ^ [] : [_1149522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21203 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 21201 ^ [_1149518, _1149520, _1149522]), _1149522)))], (21205 ^ _779308) ^ [] : [-(_1149520 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1149522), 21200 ^ [_1149518, _1149520, _1149522])), 21201 ^ [_1149518, _1149520, _1149522]))], (21207 ^ _779308) ^ [] : [hBOOL(hAPP(_1149518, 21200 ^ [_1149518, _1149520, _1149522]))]]], (21167 ^ _779308) ^ [_1149081, _1149083, _1149085] : [hBOOL(hAPP(_1149081, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1149083), _1149085))), 21170 ^ _779308 : [(21171 ^ _779308) ^ [] : [_1149085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1149081, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (21177 ^ _779308) ^ [] : [-(_1149085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21180 ^ _779308 : [(21181 ^ _779308) ^ [_1149333, _1149335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1149333), _1149085)), _1149083 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1149085), _1149335)), _1149333), -(hBOOL(hAPP(_1149081, _1149335)))]]]]], (21211 ^ _779308) ^ [_1149940, _1149942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1149940)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1149942)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1149940)), hAPP(c_Int_Onat, _1149942)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1149940), _1149942)))], (21221 ^ _779308) ^ [_1150119, _1150121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150119)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1150119), _1150121)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1150119)), hAPP(c_Int_Onat, _1150121)))], (21227 ^ _779308) ^ [_1150242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150242)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1150242) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (21233 ^ _779308) ^ [_1150327, _1150329] : [c_Nat__Transfer_Onat__set(_1150327), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1150329), _1150327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1150329)))], (21243 ^ _779308) ^ [_1150468, _1150470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1150468), _1150470)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1150470), _1150468) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1150470), _1150468)), _1150468)))], (21253 ^ _779308) ^ [_1150671, _1150673, _1150675] : [hBOOL(hAPP(_1150671, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1150673), _1150675))), 21258 ^ _779308 : [(21259 ^ _779308) ^ [] : [-(_1150675 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21261 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1150671, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 21263 ^ _779308 : [(21264 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150675), 21262 ^ [_1150671, _1150673, _1150675])), _1150673)))], (21266 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150675), hAPP(c_Nat_OSuc, 21262 ^ [_1150671, _1150673, _1150675])))))], (21268 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1150671, 21262 ^ [_1150671, _1150673, _1150675])))]]], (21270 ^ _779308) ^ [_1150975, _1150977, _1150979] : [-(hBOOL(hAPP(_1150975, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1150977), _1150979)))), 21271 ^ _779308 : [(21272 ^ _779308) ^ [] : [_1150979 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1150975, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21278 ^ _779308) ^ [_1151143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150979), _1151143)), _1150977)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150979), hAPP(c_Nat_OSuc, _1151143)))), hBOOL(hAPP(_1150975, _1151143))]]], (21290 ^ _779308) ^ [_1151373, _1151375, _1151377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151373)), 21293 ^ _779308 : [(21304 ^ _779308) ^ [] : [_1151375 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1151377), _1151373), 21307 ^ _779308 : [(21308 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151373), _1151375)), _1151377)))], (21310 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151373), hAPP(c_Nat_OSuc, _1151375)))))]]], (21294 ^ _779308) ^ [] : [-(_1151375 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1151377), _1151373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151373), _1151375)), _1151377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151373), hAPP(c_Nat_OSuc, _1151375))))]]], (21312 ^ _779308) ^ [_1151757, _1151759] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1151757)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151759)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1151757)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1151759)))], (21314 ^ _779308) ^ [_1151812, _1151814] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1151812)))), _1151814) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1151812)), _1151814))], (21316 ^ _779308) ^ [_1151861, _1151863] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1151861), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1151863)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1151861), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1151863)))], (21318 ^ _779308) ^ [_1151910] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1151910))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1151910), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (21320 ^ _779308) ^ [_1151954] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1151954), _1151954)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1151954)], (21322 ^ _779308) ^ [_1151989] : [c_Nat__Transfer_Onat__set(_1151989), -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1151989)) = _1151989)], (21328 ^ _779308) ^ [_1152083, _1152085] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1152083))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152083)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152085)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21334 ^ _779308) ^ [_1152188, _1152190] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1152188)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152188)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152190)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1152188)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1152190))))], (21340 ^ _779308) ^ [_1152258, _1152260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1152258)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1152258), _1152260)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1152258), _1152260) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (21350 ^ _779308) ^ [_1152425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1152425)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1152425) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1152425), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21356 ^ _779308) ^ [_1152524] : [c_Nat__Transfer_Onat__set(_1152524), 21359 ^ _779308 : [(21360 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1152524)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1152524))))], (21366 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1152524))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1152524)))]]], (21372 ^ _779308) ^ [_1152744] : [c_Nat__Transfer_Onat__set(_1152744), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1152744) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1152744)))], (21378 ^ _779308) ^ [_1152835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1152835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1152835), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21384 ^ _779308) ^ [_1152930] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1152930)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1152930))))], (21386 ^ _779308) ^ [_1152974] : [_1152974 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1152974) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21392 ^ _779308) ^ [_1153050] : [-(_1153050 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 21395 ^ _779308 : [(21396 ^ _779308) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1153050, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1153050) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Code__Numeral_Oint__of, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1153050), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21402 ^ _779308) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1153050, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Code__Numeral_Oint__of, _1153050) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Code__Numeral_Oint__of, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1153050), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (21408 ^ _779308) ^ [_1153310, _1153312] : [c_Nat__Transfer_Ois__nat(_1153310), c_Nat__Transfer_Onat__set(_1153312), 21415 ^ _779308 : [(21416 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1153310), _1153312)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1153310)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153312))))], (21422 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1153310)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1153312))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1153310), _1153312)))]]], (21428 ^ _779308) ^ [_1153613, _1153615] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1153613, _1153615)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1153615), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1153613), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21430 ^ _779308) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit1(c_Int_OPls)))], (21432 ^ _779308) ^ [_1153678, _1153680, _1153682] : [class_Orderings_Olinorder(_1153678), hBOOL(hAPP(c_Finite__Set_Ofinite(_1153678), _1153680)), hBOOL(hAPP(hAPP(c_member(_1153678), _1153682), _1153680)), 21443 ^ _779308 : [(21444 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1153678, tc_HOL_Obool)), _1153680), hAPP(hAPP(c_Set_Oinsert(_1153678), _1153682), c_Orderings_Obot__class_Obot(tc_fun(_1153678, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1153678, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1153678, _1153680) = _1153682)], (21450 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1153678, tc_HOL_Obool)), _1153680), hAPP(hAPP(c_Set_Oinsert(_1153678), _1153682), c_Orderings_Obot__class_Obot(tc_fun(_1153678, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1153678, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1153678, _1153680) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1153678), _1153682), c_Big__Operators_Olinorder__class_OMin(_1153678, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1153678, tc_HOL_Obool)), _1153680), hAPP(hAPP(c_Set_Oinsert(_1153678), _1153682), c_Orderings_Obot__class_Obot(tc_fun(_1153678, tc_HOL_Obool)))))))]]], (21456 ^ _779308) ^ [_1154184, _1154186] : [class_Rings_Oring__1(_1154184), 21459 ^ _779308 : [(21460 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154186), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1154184), _1154186) = hAPP(c_Groups_Ouminus__class_Ouminus(_1154184), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1154184), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1154186)))))], (21466 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154186), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1154184), _1154186) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1154184), hAPP(c_Int_Onat, _1154186)))]]], (21472 ^ _779308) ^ [_1154446, _1154448] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1154446, _1154448))))], (21474 ^ _779308) ^ [_1154477, _1154479, _1154481] : [class_Int_Oring__char__0(_1154477), 21477 ^ _779308 : [(21478 ^ _779308) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1154477), _1154479) = hAPP(c_Int_Oring__1__class_Oof__int(_1154477), _1154481), -(_1154479 = _1154481)], (21484 ^ _779308) ^ [] : [_1154479 = _1154481, -(hAPP(c_Int_Oring__1__class_Oof__int(_1154477), _1154479) = hAPP(c_Int_Oring__1__class_Oof__int(_1154477), _1154481))]]], (21490 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (21492 ^ _779308) ^ [_1154736, _1154738] : [class_Int_Onumber__ring(_1154736), -(hAPP(c_Int_Onumber__class_Onumber__of(_1154736), _1154738) = hAPP(c_Int_Oring__1__class_Oof__int(_1154736), _1154738))], (21498 ^ _779308) ^ [_1154831] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1154831) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1154831))], (21500 ^ _779308) ^ [_1154860] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1154860)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1154860))], (21502 ^ _779308) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21504 ^ _779308) ^ [_1154910, _1154912] : [c_Nat__Transfer_Ois__nat(_1154910), c_Nat__Transfer_Ois__nat(_1154912), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1154910), _1154912)))], (21514 ^ _779308) ^ [_1155045] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1155045)))], (21516 ^ _779308) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21518 ^ _779308) ^ [_1155088, _1155090] : [c_Nat__Transfer_Ois__nat(_1155088), c_Nat__Transfer_Ois__nat(_1155090), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1155088), _1155090)))], (21528 ^ _779308) ^ [_1155223, _1155225] : [c_Nat__Transfer_Ois__nat(_1155223), c_Nat__Transfer_Ois__nat(_1155225), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1155223, _1155225)))], (21538 ^ _779308) ^ [_1155354, _1155356] : [c_Nat__Transfer_Ois__nat(_1155354), c_Nat__Transfer_Ois__nat(_1155356), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1155354), _1155356)))], (21548 ^ _779308) ^ [_1155489, _1155491] : [c_Nat__Transfer_Ois__nat(_1155489), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1155489), _1155491)))], (21554 ^ _779308) ^ [_1155574, _1155576] : [c_Nat__Transfer_Ois__nat(_1155574), c_Nat__Transfer_Ois__nat(_1155576), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1155574, _1155576)))], (21564 ^ _779308) ^ [_1155703] : [class_Rings_Oring__1(_1155703), -(hAPP(c_Int_Oring__1__class_Oof__int(_1155703), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1155703))], (21570 ^ _779308) ^ [_1155790, _1155792] : [class_Int_Oring__char__0(_1155790), 21573 ^ _779308 : [(21574 ^ _779308) ^ [] : [c_Groups_Ozero__class_Ozero(_1155790) = hAPP(c_Int_Oring__1__class_Oof__int(_1155790), _1155792), -(_1155792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21580 ^ _779308) ^ [] : [_1155792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1155790) = hAPP(c_Int_Oring__1__class_Oof__int(_1155790), _1155792))]]], (21586 ^ _779308) ^ [_1156016, _1156018] : [class_Int_Oring__char__0(_1156016), 21589 ^ _779308 : [(21590 ^ _779308) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1156016), _1156018) = c_Groups_Ozero__class_Ozero(_1156016), -(_1156018 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21596 ^ _779308) ^ [] : [_1156018 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1156016), _1156018) = c_Groups_Ozero__class_Ozero(_1156016))]]], (21602 ^ _779308) ^ [_1156242, _1156244, _1156246] : [class_Rings_Olinordered__idom(_1156242), 21605 ^ _779308 : [(21606 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156242), hAPP(c_Int_Oring__1__class_Oof__int(_1156242), _1156244)), hAPP(c_Int_Oring__1__class_Oof__int(_1156242), _1156246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1156244), _1156246)))], (21612 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1156244), _1156246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156242), hAPP(c_Int_Oring__1__class_Oof__int(_1156242), _1156244)), hAPP(c_Int_Oring__1__class_Oof__int(_1156242), _1156246))))]]], (21618 ^ _779308) ^ [_1156519, _1156521, _1156523] : [class_Rings_Olinordered__idom(_1156519), 21621 ^ _779308 : [(21622 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156519), hAPP(c_Int_Oring__1__class_Oof__int(_1156519), _1156521)), hAPP(c_Int_Oring__1__class_Oof__int(_1156519), _1156523))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1156521), _1156523)))], (21628 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1156521), _1156523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156519), hAPP(c_Int_Oring__1__class_Oof__int(_1156519), _1156521)), hAPP(c_Int_Oring__1__class_Oof__int(_1156519), _1156523))))]]], (21634 ^ _779308) ^ [_1156796, _1156798, _1156800] : [class_Rings_Oring__1(_1156796), -(hAPP(c_Int_Oring__1__class_Oof__int(_1156796), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1156798), _1156800)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156796), hAPP(c_Int_Oring__1__class_Oof__int(_1156796), _1156798)), hAPP(c_Int_Oring__1__class_Oof__int(_1156796), _1156800)))], (21640 ^ _779308) ^ [_1156931, _1156933] : [class_Int_Onumber__ring(_1156931), -(hAPP(c_Int_Oring__1__class_Oof__int(_1156931), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1156933)) = hAPP(c_Int_Onumber__class_Onumber__of(_1156931), _1156933))], (21646 ^ _779308) ^ [_1157032, _1157034, _1157036] : [class_Rings_Oring__1(_1157032), -(hAPP(c_Int_Oring__1__class_Oof__int(_1157032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1157034), _1157036)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157032), hAPP(c_Int_Oring__1__class_Oof__int(_1157032), _1157034)), hAPP(c_Int_Oring__1__class_Oof__int(_1157032), _1157036)))], (21652 ^ _779308) ^ [_1157167] : [class_Rings_Oring__1(_1157167), -(hAPP(c_Int_Oring__1__class_Oof__int(_1157167), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1157167))], (21658 ^ _779308) ^ [_1157254, _1157256, _1157258] : [class_Rings_Oring__1(_1157254), -(hAPP(c_Int_Oring__1__class_Oof__int(_1157254), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1157256), _1157258)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1157254), hAPP(c_Int_Oring__1__class_Oof__int(_1157254), _1157256)), hAPP(c_Int_Oring__1__class_Oof__int(_1157254), _1157258)))], (21664 ^ _779308) ^ [_1157389, _1157391] : [class_Orderings_Olinorder(_1157389), -(c_Big__Operators_Olinorder__class_OMin(_1157389, hAPP(hAPP(c_Set_Oinsert(_1157389), _1157391), c_Orderings_Obot__class_Obot(tc_fun(_1157389, tc_HOL_Obool)))) = _1157391)], (21670 ^ _779308) ^ [_1157496, _1157498] : [class_Rings_Oring__1(_1157496), -(hAPP(c_Int_Oring__1__class_Oof__int(_1157496), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1157498)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1157496), _1157498))], (21676 ^ _779308) ^ [_1157597, _1157599] : [class_Rings_Oring__1(_1157597), -(hAPP(c_Int_Oring__1__class_Oof__int(_1157597), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1157599)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1157597), hAPP(c_Int_Oring__1__class_Oof__int(_1157597), _1157599)))], (21682 ^ _779308) ^ [_1157708, _1157710] : [class_Rings_Oring__1(_1157708), -(hBOOL(hAPP(hAPP(c_member(_1157708), hAPP(c_Int_Oring__1__class_Oof__int(_1157708), _1157710)), c_Int_Oring__1__class_OInts(_1157708))))], (21688 ^ _779308) ^ [_1157811, _1157813, _1157815] : [class_Rings_Oring__1(_1157811), -(hAPP(c_Int_Oring__1__class_Oof__int(_1157811), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1157813), _1157815)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1157811), hAPP(c_Int_Oring__1__class_Oof__int(_1157811), _1157813)), _1157815))], (21694 ^ _779308) ^ [_1157948] : [c_Nat__Transfer_Ois__nat(_1157948), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1157948)))], (21700 ^ _779308) ^ [_1158021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1158021)), -(c_Nat__Transfer_Ois__nat(_1158021))], (21706 ^ _779308) ^ [_1158100, _1158102, _1158104] : [class_Orderings_Oorder(_1158100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158100), _1158102), _1158104)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1158100, _1158104, _1158102) = c_Orderings_Obot__class_Obot(tc_fun(_1158100, tc_HOL_Obool)))], (21716 ^ _779308) ^ [_1158263, _1158265, _1158267] : [class_Groups_Oordered__ab__group__add(_1158263), -(hAPP(c_Set_Oimage(_1158263, _1158263, c_Groups_Ouminus__class_Ouminus(_1158263)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1158263, _1158265, _1158267)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1158263, hAPP(c_Groups_Ouminus__class_Ouminus(_1158263), _1158267), hAPP(c_Groups_Ouminus__class_Ouminus(_1158263), _1158265)))], (21722 ^ _779308) ^ [_1158394, _1158396, _1158398] : [class_Orderings_Olinorder(_1158394), hBOOL(hAPP(c_Finite__Set_Ofinite(_1158394), _1158396)), hBOOL(hAPP(hAPP(c_member(_1158394), _1158398), _1158396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158394), c_Big__Operators_Olinorder__class_OMin(_1158394, _1158396)), _1158398)))], (21736 ^ _779308) ^ [_1158621, _1158623] : [c_Nat__Transfer_Onat__set(_1158621), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1158623), _1158621)), -(c_Nat__Transfer_Ois__nat(_1158623))], (21746 ^ _779308) ^ [_1158756, _1158758] : [class_Orderings_Olinorder(_1158756), hBOOL(hAPP(c_Finite__Set_Ofinite(_1158756), _1158758)), -(_1158758 = c_Orderings_Obot__class_Obot(tc_fun(_1158756, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1158756), c_Big__Operators_Olinorder__class_OMin(_1158756, _1158758)), _1158758)))], (21760 ^ _779308) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OPls))], (21762 ^ _779308) ^ [_1158954, _1158956, _1158958] : [class_Orderings_Olinorder(_1158954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1158954), _1158956)), hBOOL(hAPP(hAPP(c_member(_1158954), _1158958), _1158956)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158954), _1158958), c_Big__Operators_Olinorder__class_OMin(_1158954, _1158956)) = c_Big__Operators_Olinorder__class_OMin(_1158954, _1158956))], (21776 ^ _779308) ^ [_1159189] : [class_Int_Onumber__ring(_1159189), -(hAPP(c_Int_Oring__1__class_Oof__int(_1159189), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1159189), c_Int_OMin))], (21782 ^ _779308) ^ [_1159282, _1159284] : [class_Orderings_Olinorder(_1159282), hBOOL(hAPP(c_Finite__Set_Ofinite(_1159282), _1159284)), -(c_Big__Operators_Olinorder__class_OMin(_1159282, _1159284) = hAPP(c_Finite__Set_Ofold1(_1159282, c_Orderings_Oord__class_Omin(_1159282)), _1159284))], (21792 ^ _779308) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (21794 ^ _779308) ^ [_1159457, _1159459] : [class_Rings_Olinordered__idom(_1159457), 21797 ^ _779308 : [(21798 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159457), hAPP(c_Int_Oring__1__class_Oof__int(_1159457), _1159459)), c_Groups_Ozero__class_Ozero(_1159457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159459), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21804 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159459), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159457), hAPP(c_Int_Oring__1__class_Oof__int(_1159457), _1159459)), c_Groups_Ozero__class_Ozero(_1159457))))]]], (21810 ^ _779308) ^ [_1159719, _1159721] : [class_Rings_Olinordered__idom(_1159719), 21813 ^ _779308 : [(21814 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159719), c_Groups_Ozero__class_Ozero(_1159719)), hAPP(c_Int_Oring__1__class_Oof__int(_1159719), _1159721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1159721)))], (21820 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1159721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159719), c_Groups_Ozero__class_Ozero(_1159719)), hAPP(c_Int_Oring__1__class_Oof__int(_1159719), _1159721))))]]], (21826 ^ _779308) ^ [_1159972, _1159974] : [class_Rings_Olinordered__idom(_1159972), 21829 ^ _779308 : [(21830 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159972), hAPP(c_Int_Oring__1__class_Oof__int(_1159972), _1159974)), c_Groups_Ozero__class_Ozero(_1159972))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159974), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21836 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159974), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159972), hAPP(c_Int_Oring__1__class_Oof__int(_1159972), _1159974)), c_Groups_Ozero__class_Ozero(_1159972))))]]], (21842 ^ _779308) ^ [_1160234, _1160236] : [class_Rings_Olinordered__idom(_1160234), 21845 ^ _779308 : [(21846 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160234), c_Groups_Ozero__class_Ozero(_1160234)), hAPP(c_Int_Oring__1__class_Oof__int(_1160234), _1160236))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1160236)))], (21852 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1160236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160234), c_Groups_Ozero__class_Ozero(_1160234)), hAPP(c_Int_Oring__1__class_Oof__int(_1160234), _1160236))))]]], (21858 ^ _779308) ^ [_1160487, _1160489, _1160491] : [class_Orderings_Olinorder(_1160487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1160487, tc_HOL_Obool)), _1160489), _1160491)), -(_1160489 = c_Orderings_Obot__class_Obot(tc_fun(_1160487, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1160487), _1160491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160487), c_Big__Operators_Olinorder__class_OMin(_1160487, _1160491)), c_Big__Operators_Olinorder__class_OMin(_1160487, _1160489))))], (21876 ^ _779308) ^ [_1160793, _1160795] : [class_Rings_Oring__1(_1160793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1160795)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1160793), hAPP(c_Int_Onat, _1160795)) = hAPP(c_Int_Oring__1__class_Oof__int(_1160793), _1160795))], (21886 ^ _779308) ^ [_1160950, _1160952, _1160954] : [class_Orderings_Olinorder(_1160950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1160950), _1160952)), -(_1160952 = c_Orderings_Obot__class_Obot(tc_fun(_1160950, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1160950, hAPP(hAPP(c_Set_Oinsert(_1160950), _1160954), _1160952)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160950), _1160954), c_Big__Operators_Olinorder__class_OMin(_1160950, _1160952)))], (21900 ^ _779308) ^ [_1161158, _1161160, _1161162] : [class_Orderings_Olinorder(_1161158), hBOOL(hAPP(c_Finite__Set_Ofinite(_1161158), _1161160)), -(_1161162 = c_Orderings_Obot__class_Obot(tc_fun(_1161158, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1161158, tc_HOL_Obool)), _1161162), _1161160)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1161158), c_Big__Operators_Olinorder__class_OMin(_1161158, _1161162)), c_Big__Operators_Olinorder__class_OMin(_1161158, _1161160)) = c_Big__Operators_Olinorder__class_OMin(_1161158, _1161160))], (21918 ^ _779308) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (21920 ^ _779308) ^ [_1161490, _1161492, _1161494] : [class_Orderings_Olinorder(_1161490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1161490), _1161492)), -(hBOOL(hAPP(hAPP(c_member(_1161490), _1161494), _1161492))), -(_1161492 = c_Orderings_Obot__class_Obot(tc_fun(_1161490, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1161490, hAPP(hAPP(c_Set_Oinsert(_1161490), _1161494), _1161492)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1161490), _1161494), c_Big__Operators_Olinorder__class_OMin(_1161490, _1161492)))], (21938 ^ _779308) ^ [_1161727, _1161729, _1161731] : [class_Orderings_Olinorder(_1161727), hBOOL(hAPP(c_Finite__Set_Ofinite(_1161727), _1161729)), 21945 ^ _779308 : [(21946 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1161727, tc_HOL_Obool)), _1161729), hAPP(hAPP(c_Set_Oinsert(_1161727), _1161731), c_Orderings_Obot__class_Obot(tc_fun(_1161727, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1161727, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1161727, hAPP(hAPP(c_Set_Oinsert(_1161727), _1161731), _1161729)) = _1161731)], (21952 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1161727, tc_HOL_Obool)), _1161729), hAPP(hAPP(c_Set_Oinsert(_1161727), _1161731), c_Orderings_Obot__class_Obot(tc_fun(_1161727, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1161727, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1161727, hAPP(hAPP(c_Set_Oinsert(_1161727), _1161731), _1161729)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1161727), _1161731), c_Big__Operators_Olinorder__class_OMin(_1161727, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1161727, tc_HOL_Obool)), _1161729), hAPP(hAPP(c_Set_Oinsert(_1161727), _1161731), c_Orderings_Obot__class_Obot(tc_fun(_1161727, tc_HOL_Obool)))))))]]], (21958 ^ _779308) ^ [_1162206, _1162208] : [_1162206 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1162206, _1162208) = _1162208)], (21964 ^ _779308) ^ [_1162283, _1162285] : [-(_1162283 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1162283, _1162285) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1162283), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1162285)))], (21970 ^ _779308) ^ [_1162336, _1162338] : [class_Rings_Oring__1(_1162336), 21973 ^ _779308 : [(21974 ^ _779308) ^ [] : [_1162338 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1162336), _1162338) = c_Groups_Ozero__class_Ozero(_1162336))], (21980 ^ _779308) ^ [] : [-(_1162338 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21983 ^ _779308 : [(21984 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162338), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1162336), _1162338) = hAPP(c_Groups_Ouminus__class_Ouminus(_1162336), hAPP(c_Int_Oring__1__class_Oof__int(_1162336), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1162338))))], (21990 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162338), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1162336), _1162338) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1162336), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1162336, _1162336)), tc_fun(tc_Int_Oint, _1162336)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1162336, _1162336), _1162336), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1162336, _1162336)), tc_fun(tc_Int_Oint, _1162336)), tc_Int_Oint), c_COMBB(tc_fun(_1162336, _1162336), _1162336, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1162336, tc_fun(tc_fun(_1162336, _1162336), _1162336), tc_Int_Oint), c_HOL_OLet(_1162336, _1162336)), c_Int_Oring__1__class_Oof__int(_1162336)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1162336, _1162336), tc_fun(_1162336, _1162336)), hAPP(hAPP(c_COMBB(tc_fun(_1162336, tc_fun(_1162336, _1162336)), tc_fun(tc_fun(_1162336, _1162336), tc_fun(_1162336, _1162336)), tc_Int_Oint), c_COMBS(_1162336, _1162336, _1162336)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1162336, _1162336), tc_fun(_1162336, tc_fun(_1162336, _1162336))), hAPP(hAPP(c_COMBB(tc_fun(_1162336, tc_fun(_1162336, _1162336)), tc_fun(tc_fun(_1162336, _1162336), tc_fun(_1162336, tc_fun(_1162336, _1162336))), tc_Int_Oint), c_COMBB(_1162336, tc_fun(_1162336, _1162336), _1162336)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1162336, tc_fun(_1162336, _1162336)), tc_Int_Oint), c_If(_1162336)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), c_fequal), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBS(_1162336, _1162336, _1162336), c_Groups_Oplus__class_Oplus(_1162336)), c_COMBI(_1162336))))), hAPP(hAPP(c_COMBC(_1162336, _1162336, _1162336), hAPP(hAPP(c_COMBB(_1162336, tc_fun(_1162336, _1162336), _1162336), c_Groups_Oplus__class_Oplus(_1162336)), hAPP(hAPP(c_COMBS(_1162336, _1162336, _1162336), c_Groups_Oplus__class_Oplus(_1162336)), c_COMBI(_1162336)))), c_Groups_Oone__class_Oone(_1162336))))), c_Divides_Odivmod__int(_1162338, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (21996 ^ _779308) ^ [_1163249, _1163251] : [class_Orderings_Olinorder(_1163249), hBOOL(hAPP(c_Finite__Set_Ofinite(_1163249), _1163251)), -(_1163251 = c_Orderings_Obot__class_Obot(tc_fun(_1163249, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1163249), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1163249), 22009 ^ [_1163249, _1163251]), 22010 ^ [_1163249, _1163251])), hAPP(hAPP(c_Set_Oinsert(_1163249), 22009 ^ [_1163249, _1163251]), hAPP(hAPP(c_Set_Oinsert(_1163249), 22010 ^ [_1163249, _1163251]), c_Orderings_Obot__class_Obot(tc_fun(_1163249, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1163249), c_Big__Operators_Olinorder__class_OMin(_1163249, _1163251)), _1163251)))], (22016 ^ _779308) ^ [] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22018 ^ _779308) ^ [_1163711, _1163713, _1163715] : [class_Orderings_Olinorder(_1163711), hBOOL(hAPP(c_Finite__Set_Ofinite(_1163711), _1163713)), hBOOL(hAPP(hAPP(c_member(_1163711), _1163715), _1163713)), 22029 ^ _779308 : [(22030 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1163711, tc_HOL_Obool)), _1163713), hAPP(hAPP(c_Set_Oinsert(_1163711), _1163715), c_Orderings_Obot__class_Obot(tc_fun(_1163711, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1163711, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1163711, c_Orderings_Oord__class_Omin(_1163711), _1163713) = _1163715)], (22036 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1163711, tc_HOL_Obool)), _1163713), hAPP(hAPP(c_Set_Oinsert(_1163711), _1163715), c_Orderings_Obot__class_Obot(tc_fun(_1163711, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1163711, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1163711, c_Orderings_Oord__class_Omin(_1163711), _1163713) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1163711), _1163715), c_Big__Operators_Olattice_OInf__fin(_1163711, c_Orderings_Oord__class_Omin(_1163711), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1163711, tc_HOL_Obool)), _1163713), hAPP(hAPP(c_Set_Oinsert(_1163711), _1163715), c_Orderings_Obot__class_Obot(tc_fun(_1163711, tc_HOL_Obool)))))))]]], (22042 ^ _779308) ^ [_1164235, _1164237, _1164239, _1164241, _1164243, _1164245] : [class_Groups_Ocomm__monoid__mult(_1164235), hBOOL(hAPP(c_Finite__Set_Ofinite(_1164237), _1164239)), 22049 ^ _779308 : [(22050 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1164237), _1164241), _1164239)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1164237, _1164235), hAPP(hAPP(c_COMBC(_1164237, _1164235, _1164235), hAPP(hAPP(c_COMBS(_1164237, _1164235, tc_fun(_1164235, _1164235)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1164235, tc_fun(_1164235, _1164235)), _1164237), c_If(_1164235)), hAPP(hAPP(c_COMBC(_1164237, _1164237, tc_HOL_Obool), c_fequal), _1164241))), _1164243)), _1164245)), _1164239) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164235), hAPP(_1164243, _1164241)), hAPP(hAPP(c_Power_Opower__class_Opower(_1164235), _1164245), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1164237), _1164239)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (22056 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1164237), _1164241), _1164239))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1164237, _1164235), hAPP(hAPP(c_COMBC(_1164237, _1164235, _1164235), hAPP(hAPP(c_COMBS(_1164237, _1164235, tc_fun(_1164235, _1164235)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1164235, tc_fun(_1164235, _1164235)), _1164237), c_If(_1164235)), hAPP(hAPP(c_COMBC(_1164237, _1164237, tc_HOL_Obool), c_fequal), _1164241))), _1164243)), _1164245)), _1164239) = hAPP(hAPP(c_Power_Opower__class_Opower(_1164235), _1164245), hAPP(c_Finite__Set_Ocard(_1164237), _1164239)))]]], (22062 ^ _779308) ^ [_1164847, _1164849] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1164847, _1164849))))], (22064 ^ _779308) ^ [_1164878, _1164880, _1164882, _1164884] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1164878), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1164880, tc_Int_Oint), _1164882), _1164884)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1164880, _1164878), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1164878, _1164880), c_Int_Oring__1__class_Oof__int(_1164878)), _1164882)), _1164884)), class_Groups_Ocomm__monoid__mult(_1164878), class_Rings_Oring__1(_1164878)], (22074 ^ _779308) ^ [_1165081, _1165083, _1165085, _1165087] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1165081), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165083, tc_Nat_Onat), _1165085), _1165087)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165083, _1165081), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1165081, _1165083), c_Nat_Osemiring__1__class_Oof__nat(_1165081)), _1165085)), _1165087)), class_Groups_Ocomm__monoid__mult(_1165081), class_Rings_Osemiring__1(_1165081)], (22084 ^ _779308) ^ [_1165284, _1165286, _1165288] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165284, tc_Nat_Onat), _1165286), _1165288)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165284, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1165284), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1165286)), _1165288))], (22086 ^ _779308) ^ [_1165342, _1165344, _1165346] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165342, tc_Nat_Onat), _1165344), _1165346) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165342, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1165342), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1165344)), _1165346)))], (22088 ^ _779308) ^ [_1165400, _1165402, _1165404, _1165406, _1165408] : [class_Groups_Ocomm__monoid__mult(_1165400), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165402, _1165400), hAPP(hAPP(c_COMBS(_1165402, _1165400, _1165400), hAPP(hAPP(c_COMBB(_1165400, tc_fun(_1165400, _1165400), _1165402), c_Groups_Otimes__class_Otimes(_1165400)), _1165404)), _1165406)), _1165408) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165400), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165402, _1165400), _1165404), _1165408)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165402, _1165400), _1165406), _1165408)))], (22094 ^ _779308) ^ [_1165601, _1165603, _1165605] : [class_Groups_Ocomm__monoid__mult(_1165601), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165603, _1165601), hAPP(c_COMBK(_1165601, _1165603), c_Groups_Oone__class_Oone(_1165601))), _1165605) = c_Groups_Oone__class_Oone(_1165601))], (22100 ^ _779308) ^ [_1165716, _1165718, _1165720] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1165716), _1165718), _1165720) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1165716), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1165716, tc_Int_Oint), _1165718), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1165720))), class_Groups_Ocomm__monoid__add(_1165716), class_Groups_Ocomm__monoid__mult(_1165716)], (22110 ^ _779308) ^ [_1165907, _1165909, _1165911, _1165913] : [class_Rings_Ocomm__semiring__1(_1165907), hBOOL(hAPP(c_Finite__Set_Ofinite(_1165909), _1165911)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1165909, _1165907), _1165913), _1165911) = c_Groups_Ozero__class_Ozero(_1165907)), 22119 ^ _779308 : [(22120 ^ _779308) ^ [_1166088] : [hBOOL(hAPP(hAPP(c_member(_1165909), _1166088), _1165911)), hAPP(_1165913, _1166088) = c_Groups_Ozero__class_Ozero(_1165907)]]], (22128 ^ _779308) ^ [_1166237, _1166239, _1166241, _1166243] : [class_Rings_Ocomm__semiring__1(_1166237), class_Rings_Ono__zero__divisors(_1166237), hBOOL(hAPP(c_Finite__Set_Ofinite(_1166239), _1166241)), 22139 ^ _779308 : [(22140 ^ _779308) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166239, _1166237), _1166243), _1166241) = c_Groups_Ozero__class_Ozero(_1166237), 22144 ^ _779308 : [(22145 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1166239), 22143 ^ [_1166237, _1166239, _1166241, _1166243]), _1166241)))], (22147 ^ _779308) ^ [] : [-(hAPP(_1166243, 22143 ^ [_1166237, _1166239, _1166241, _1166243]) = c_Groups_Ozero__class_Ozero(_1166237))]]], (22149 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166239, _1166237), _1166243), _1166241) = c_Groups_Ozero__class_Ozero(_1166237)), 22150 ^ _779308 : [(22151 ^ _779308) ^ [_1166615] : [hBOOL(hAPP(hAPP(c_member(_1166239), _1166615), _1166241)), hAPP(_1166243, _1166615) = c_Groups_Ozero__class_Ozero(_1166237)]]]]], (22159 ^ _779308) ^ [_1166770, _1166772, _1166774] : [class_Groups_Ocomm__monoid__mult(_1166770), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166772, _1166770), _1166774), c_Orderings_Obot__class_Obot(tc_fun(_1166772, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1166770))], (22165 ^ _779308) ^ [_1166879, _1166881, _1166883] : [class_Groups_Ocomm__monoid__mult(_1166879), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166881, _1166879), _1166883), c_Orderings_Obot__class_Obot(tc_fun(_1166881, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1166879))], (22171 ^ _779308) ^ [_1166988, _1166990, _1166992, _1166994] : [class_Groups_Ocomm__monoid__mult(_1166988), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1166990), _1166992))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1166990, _1166988), _1166994), _1166992) = c_Groups_Oone__class_Oone(_1166988))], (22181 ^ _779308) ^ [_1167112, _1167114, _1167116, _1167118] : [class_Groups_Ocomm__monoid__mult(_1167112), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1167114), _1167116))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1167114, _1167112), _1167118), _1167116) = c_Groups_Oone__class_Oone(_1167112))], (22191 ^ _779308) ^ [_1167236, _1167238, _1167240] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1167236), _1167238)), 22194 ^ _779308 : [(22205 ^ _779308) ^ [] : [22207 ^ _779308 : [(22208 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1167236), 22206 ^ [_1167236, _1167238, _1167240]), _1167238)))], (22210 ^ _779308) ^ [] : [hAPP(_1167240, 22206 ^ [_1167236, _1167238, _1167240]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1167236, tc_Nat_Onat), _1167240), _1167238) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (22195 ^ _779308) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1167236, tc_Nat_Onat), _1167240), _1167238) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 22198 ^ _779308 : [(22199 ^ _779308) ^ [_1167398] : [hBOOL(hAPP(hAPP(c_member(_1167236), _1167398), _1167238)), -(hAPP(_1167240, _1167398) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (22214 ^ _779308) ^ [_1167656, _1167658, _1167660] : [class_Groups_Ocomm__monoid__add(_1167656), class_Groups_Ocomm__monoid__mult(_1167656), c_Nat__Transfer_Onat__set(_1167658), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1167656), _1167660), _1167658) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1167656), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1167656, tc_Nat_Onat), _1167660), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1167658)))], (22228 ^ _779308) ^ [_1167901, _1167903, _1167905, _1167907, _1167909] : [class_Groups_Ocomm__monoid__mult(_1167901), hBOOL(hAPP(c_Finite__Set_Ofinite(_1167903), _1167905)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1167903, _1167901), hAPP(hAPP(c_COMBS(_1167903, _1167901, _1167901), hAPP(hAPP(c_COMBB(_1167901, tc_fun(_1167901, _1167901), _1167903), c_Groups_Otimes__class_Otimes(_1167901)), _1167907)), _1167909)), _1167905) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167901), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1167903, _1167901), _1167907), _1167905)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1167903, _1167901), _1167909), _1167905)))], (22238 ^ _779308) ^ [_1168168, _1168170, _1168172] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1168168), _1168170)), 22241 ^ _779308 : [(22252 ^ _779308) ^ [] : [22254 ^ _779308 : [(22255 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1168168), 22253 ^ [_1168168, _1168170, _1168172]), _1168170)))], (22257 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1168172, 22253 ^ [_1168168, _1168170, _1168172])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1168168, tc_Nat_Onat), _1168172), _1168170))))], (22242 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1168168, tc_Nat_Onat), _1168172), _1168170))), 22245 ^ _779308 : [(22246 ^ _779308) ^ [_1168336] : [hBOOL(hAPP(hAPP(c_member(_1168168), _1168336), _1168170)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1168172, _1168336))))]]]]], (22261 ^ _779308) ^ [_1168604, _1168606, _1168608, _1168610, _1168612] : [class_Groups_Ocomm__monoid__mult(_1168604), hBOOL(hAPP(c_Finite__Set_Ofinite(_1168606), _1168608)), 22268 ^ _779308 : [(22269 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1168606), _1168610), _1168608)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1168606, _1168604), hAPP(hAPP(c_COMBC(_1168606, _1168604, _1168604), hAPP(hAPP(c_COMBS(_1168606, _1168604, tc_fun(_1168604, _1168604)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1168604, tc_fun(_1168604, _1168604)), _1168606), c_If(_1168604)), hAPP(c_fequal, _1168610))), _1168612)), c_Groups_Oone__class_Oone(_1168604))), _1168608) = hAPP(_1168612, _1168610))], (22275 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1168606), _1168610), _1168608))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1168606, _1168604), hAPP(hAPP(c_COMBC(_1168606, _1168604, _1168604), hAPP(hAPP(c_COMBS(_1168606, _1168604, tc_fun(_1168604, _1168604)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1168604, tc_fun(_1168604, _1168604)), _1168606), c_If(_1168604)), hAPP(c_fequal, _1168610))), _1168612)), c_Groups_Oone__class_Oone(_1168604))), _1168608) = c_Groups_Oone__class_Oone(_1168604))]]], (22281 ^ _779308) ^ [_1169114, _1169116, _1169118, _1169120, _1169122] : [class_Groups_Ocomm__monoid__mult(_1169114), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169116), _1169118)), 22288 ^ _779308 : [(22289 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1169116), _1169120), _1169118)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1169116, _1169114), hAPP(hAPP(c_COMBC(_1169116, _1169114, _1169114), hAPP(hAPP(c_COMBS(_1169116, _1169114, tc_fun(_1169114, _1169114)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1169114, tc_fun(_1169114, _1169114)), _1169116), c_If(_1169114)), hAPP(hAPP(c_COMBC(_1169116, _1169116, tc_HOL_Obool), c_fequal), _1169120))), _1169122)), c_Groups_Oone__class_Oone(_1169114))), _1169118) = hAPP(_1169122, _1169120))], (22295 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1169116), _1169120), _1169118))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1169116, _1169114), hAPP(hAPP(c_COMBC(_1169116, _1169114, _1169114), hAPP(hAPP(c_COMBS(_1169116, _1169114, tc_fun(_1169114, _1169114)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1169114, tc_fun(_1169114, _1169114)), _1169116), c_If(_1169114)), hAPP(hAPP(c_COMBC(_1169116, _1169116, tc_HOL_Obool), c_fequal), _1169120))), _1169122)), c_Groups_Oone__class_Oone(_1169114))), _1169118) = c_Groups_Oone__class_Oone(_1169114))]]], (22301 ^ _779308) ^ [_1169652, _1169654, _1169656, _1169658] : [class_Groups_Ocomm__monoid__mult(_1169652), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169654), _1169656)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1169654, _1169652), hAPP(c_COMBK(_1169652, _1169654), _1169658)), _1169656) = hAPP(hAPP(c_Power_Opower__class_Opower(_1169652), _1169658), hAPP(c_Finite__Set_Ocard(_1169654), _1169656)))], (22311 ^ _779308) ^ [_1169851, _1169853, _1169855] : [class_Orderings_Olinorder(_1169851), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169851), _1169853)), hBOOL(hAPP(hAPP(c_member(_1169851), _1169855), _1169853)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1169851), _1169855), c_Big__Operators_Olattice_OInf__fin(_1169851, c_Orderings_Oord__class_Omin(_1169851), _1169853)) = c_Big__Operators_Olattice_OInf__fin(_1169851, c_Orderings_Oord__class_Omin(_1169851), _1169853))], (22325 ^ _779308) ^ [_1170098, _1170100] : [class_Orderings_Olinorder(_1170098), -(c_Big__Operators_Olattice_OInf__fin(_1170098, c_Orderings_Oord__class_Omin(_1170098), hAPP(hAPP(c_Set_Oinsert(_1170098), _1170100), c_Orderings_Obot__class_Obot(tc_fun(_1170098, tc_HOL_Obool)))) = _1170100)], (22331 ^ _779308) ^ [_1170211, _1170213, _1170215, _1170217, _1170219] : [class_Groups_Ocomm__monoid__mult(_1170211), hBOOL(hAPP(c_Finite__Set_Ofinite(_1170213), _1170215)), -(hBOOL(hAPP(hAPP(c_member(_1170213), _1170217), _1170215))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1170213, _1170211), _1170219), hAPP(hAPP(c_Set_Oinsert(_1170213), _1170217), _1170215)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170211), hAPP(_1170219, _1170217)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1170213, _1170211), _1170219), _1170215)))], (22345 ^ _779308) ^ [_1170461, _1170463, _1170465, _1170467, _1170469] : [class_Groups_Ocomm__monoid__mult(_1170461), hBOOL(hAPP(c_Finite__Set_Ofinite(_1170463), _1170465)), -(hBOOL(hAPP(hAPP(c_member(_1170463), _1170467), _1170465))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1170463, _1170461), _1170469), hAPP(hAPP(c_Set_Oinsert(_1170463), _1170467), _1170465)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170461), hAPP(_1170469, _1170467)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1170463, _1170461), _1170469), _1170465)))], (22359 ^ _779308) ^ [_1170711, _1170713] : [class_Orderings_Olinorder(_1170711), hBOOL(hAPP(c_Finite__Set_Ofinite(_1170711), _1170713)), -(c_Big__Operators_Olattice_OInf__fin(_1170711, c_Orderings_Oord__class_Omin(_1170711), _1170713) = hAPP(c_Finite__Set_Ofold1(_1170711, c_Orderings_Oord__class_Omin(_1170711)), _1170713))], (22369 ^ _779308) ^ [_1170874, _1170876, _1170878, _1170880] : [class_Groups_Ocomm__monoid__mult(_1170874), hBOOL(hAPP(c_Finite__Set_Ofinite(_1170876), _1170878)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1170876, _1170874), _1170880), _1170878) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1170874, _1170876, c_Groups_Otimes__class_Otimes(_1170874)), _1170880), c_Groups_Oone__class_Oone(_1170874)), _1170878))], (22379 ^ _779308) ^ [_1171069, _1171071, _1171073, _1171075] : [class_Groups_Ocomm__monoid__mult(_1171069), 22382 ^ _779308 : [(22383 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1171071), _1171073)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1171071, _1171069), _1171075), _1171073) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1171069, _1171071, c_Groups_Otimes__class_Otimes(_1171069)), _1171075), c_Groups_Oone__class_Oone(_1171069)), _1171073))], (22389 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1171071), _1171073))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1171071, _1171069), _1171075), _1171073) = c_Groups_Oone__class_Oone(_1171069))]]], (22395 ^ _779308) ^ [_1171341, _1171343, _1171345, _1171347, _1171349] : [class_Groups_Ocomm__monoid__mult(_1171341), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171343), _1171345)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1171343, _1171341), _1171347), hAPP(hAPP(c_Set_Oinsert(_1171343), _1171349), _1171345)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171341), hAPP(_1171347, _1171349)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1171343, _1171341), _1171347), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1171343, tc_HOL_Obool)), _1171345), hAPP(hAPP(c_Set_Oinsert(_1171343), _1171349), c_Orderings_Obot__class_Obot(tc_fun(_1171343, tc_HOL_Obool)))))))], (22405 ^ _779308) ^ [_1171610, _1171612] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1171610, _1171612)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171612), hAPP(c_Nat_OSuc, _1171610)))], (22407 ^ _779308) ^ [_1171651, _1171653, _1171655] : [class_Orderings_Olinorder(_1171651), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171651), _1171653)), -(_1171653 = c_Orderings_Obot__class_Obot(tc_fun(_1171651, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1171651, c_Orderings_Oord__class_Omin(_1171651), hAPP(hAPP(c_Set_Oinsert(_1171651), _1171655), _1171653)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1171651), _1171655), c_Big__Operators_Olattice_OInf__fin(_1171651, c_Orderings_Oord__class_Omin(_1171651), _1171653)))], (22421 ^ _779308) ^ [_1171871, _1171873, _1171875] : [class_Orderings_Olinorder(_1171871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1171871), _1171873)), -(_1171875 = c_Orderings_Obot__class_Obot(tc_fun(_1171871, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1171871, tc_HOL_Obool)), _1171875), _1171873)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1171871), c_Big__Operators_Olattice_OInf__fin(_1171871, c_Orderings_Oord__class_Omin(_1171871), _1171875)), c_Big__Operators_Olattice_OInf__fin(_1171871, c_Orderings_Oord__class_Omin(_1171871), _1171873)) = c_Big__Operators_Olattice_OInf__fin(_1171871, c_Orderings_Oord__class_Omin(_1171871), _1171873))], (22439 ^ _779308) ^ [_1172203, _1172205, _1172207, _1172209, _1172211] : [class_Groups_Ocomm__monoid__mult(_1172203), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172205), _1172207)), hBOOL(hAPP(hAPP(c_member(_1172205), _1172209), _1172207)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1172205, _1172203), _1172211), _1172207) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172203), hAPP(_1172211, _1172209)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1172205, _1172203), _1172211), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172205, tc_HOL_Obool)), _1172207), hAPP(hAPP(c_Set_Oinsert(_1172205), _1172209), c_Orderings_Obot__class_Obot(tc_fun(_1172205, tc_HOL_Obool)))))))], (22453 ^ _779308) ^ [_1172528, _1172530, _1172532] : [class_Orderings_Olinorder(_1172528), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172528), _1172530)), -(hBOOL(hAPP(hAPP(c_member(_1172528), _1172532), _1172530))), -(_1172530 = c_Orderings_Obot__class_Obot(tc_fun(_1172528, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1172528, c_Orderings_Oord__class_Omin(_1172528), hAPP(hAPP(c_Set_Oinsert(_1172528), _1172532), _1172530)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1172528), _1172532), c_Big__Operators_Olattice_OInf__fin(_1172528, c_Orderings_Oord__class_Omin(_1172528), _1172530)))], (22471 ^ _779308) ^ [_1172777, _1172779, _1172781] : [class_Orderings_Olinorder(_1172777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1172777), _1172779)), 22478 ^ _779308 : [(22479 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172777, tc_HOL_Obool)), _1172779), hAPP(hAPP(c_Set_Oinsert(_1172777), _1172781), c_Orderings_Obot__class_Obot(tc_fun(_1172777, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1172777, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1172777, c_Orderings_Oord__class_Omin(_1172777), hAPP(hAPP(c_Set_Oinsert(_1172777), _1172781), _1172779)) = _1172781)], (22485 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172777, tc_HOL_Obool)), _1172779), hAPP(hAPP(c_Set_Oinsert(_1172777), _1172781), c_Orderings_Obot__class_Obot(tc_fun(_1172777, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1172777, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1172777, c_Orderings_Oord__class_Omin(_1172777), hAPP(hAPP(c_Set_Oinsert(_1172777), _1172781), _1172779)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1172777), _1172781), c_Big__Operators_Olattice_OInf__fin(_1172777, c_Orderings_Oord__class_Omin(_1172777), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1172777, tc_HOL_Obool)), _1172779), hAPP(hAPP(c_Set_Oinsert(_1172777), _1172781), c_Orderings_Obot__class_Obot(tc_fun(_1172777, tc_HOL_Obool)))))))]]], (22491 ^ _779308) ^ [_1173265] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1173265)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1173265)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22493 ^ _779308) ^ [_1173300, _1173302] : [class_Orderings_Olinorder(_1173300), hBOOL(hAPP(c_Finite__Set_Ofinite(_1173300), _1173302)), -(_1173302 = c_Orderings_Obot__class_Obot(tc_fun(_1173300, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1173300), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1173300), 22506 ^ [_1173300, _1173302]), 22507 ^ [_1173300, _1173302])), hAPP(hAPP(c_Set_Oinsert(_1173300), 22506 ^ [_1173300, _1173302]), hAPP(hAPP(c_Set_Oinsert(_1173300), 22507 ^ [_1173300, _1173302]), c_Orderings_Obot__class_Obot(tc_fun(_1173300, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1173300), c_Big__Operators_Olattice_OInf__fin(_1173300, c_Orderings_Oord__class_Omin(_1173300), _1173302)), _1173302)))], (22513 ^ _779308) ^ [_1173750, _1173752] : [-(c_Divides_Odivmod__int__rel(_1173750, _1173752) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_Int_Oint), c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Int_Oint), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_Int_Oint), hAPP(c_COMBB(tc_Int_Oint, tc_HOL_Obool, tc_Int_Oint), hAPP(c_fequal, _1173750))), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint)), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1173752)))))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), hAPP(c_fimplies, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173752))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Int_Oint)), _1173752))))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint), hAPP(c_fimplies, hAPP(c_fNot, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173752)))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1173752))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))))], (22515 ^ _779308) ^ [] : [-(c_Nitpick_OFrac = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_Int_Oint), hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_fun(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_Int_Oint), c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_Int_Oint), hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_Int_Oint), c_fequal)), c_Nitpick_Oint__gcd))), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (22517 ^ _779308) ^ [_1173883, _1173885, _1173887, _1173889, _1173891] : [class_Fields_Ofield(_1173883), hBOOL(hAPP(c_Finite__Set_Ofinite(_1173885), _1173887)), -(hAPP(_1173889, _1173891) = c_Groups_Ozero__class_Ozero(_1173883)), 22528 ^ _779308 : [(22529 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1173885), _1173891), _1173887)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1173885, _1173883), _1173889), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1173885, tc_HOL_Obool)), _1173887), hAPP(hAPP(c_Set_Oinsert(_1173885), _1173891), c_Orderings_Obot__class_Obot(tc_fun(_1173885, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1173883), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1173885, _1173883), _1173889), _1173887)), hAPP(_1173889, _1173891)))], (22535 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1173885), _1173891), _1173887))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1173885, _1173883), _1173889), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1173885, tc_HOL_Obool)), _1173887), hAPP(hAPP(c_Set_Oinsert(_1173885), _1173891), c_Orderings_Obot__class_Obot(tc_fun(_1173885, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1173885, _1173883), _1173889), _1173887))]]], (22541 ^ _779308) ^ [_1174424] : [-(c_Divides_Oadjust(_1174424) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_fun(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), hAPP(c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_If(tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_HOL_Obool, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint)), _1174424))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBB(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint)), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint)), _1174424))))), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (22543 ^ _779308) ^ [_1174485, _1174487] : [class_Rings_Odivision__ring__inverse__zero(_1174485), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174485), _1174487), c_Groups_Ozero__class_Ozero(_1174485)) = c_Groups_Ozero__class_Ozero(_1174485))], (22549 ^ _779308) ^ [_1174584, _1174586] : [class_Rings_Odivision__ring(_1174584), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1174584), c_Groups_Ozero__class_Ozero(_1174584)), _1174586) = c_Groups_Ozero__class_Ozero(_1174584))], (22555 ^ _779308) ^ [_1174704, _1174706, _1174708, _1174710] : [hAPP(hAPP(c_COMBC(_1174704, tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_fun(_1174706, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1174706, tc_fun(tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_fun(_1174706, tc_HOL_Obool)), _1174704), c_COMBC(_1174706, tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1174706, tc_prod(_1174704, _1174706)), tc_fun(_1174706, tc_fun(tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_HOL_Obool)), _1174704), hAPP(c_COMBB(tc_prod(_1174704, _1174706), tc_fun(tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_HOL_Obool), _1174706), c_member(tc_prod(_1174704, _1174706)))), c_Product__Type_OPair(_1174704, _1174706)))), _1174708) = hAPP(hAPP(c_COMBC(_1174704, tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_fun(_1174706, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1174706, tc_fun(tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_fun(_1174706, tc_HOL_Obool)), _1174704), c_COMBC(_1174706, tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1174706, tc_prod(_1174704, _1174706)), tc_fun(_1174706, tc_fun(tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_HOL_Obool)), _1174704), hAPP(c_COMBB(tc_prod(_1174704, _1174706), tc_fun(tc_fun(tc_prod(_1174704, _1174706), tc_HOL_Obool), tc_HOL_Obool), _1174706), c_member(tc_prod(_1174704, _1174706)))), c_Product__Type_OPair(_1174704, _1174706)))), _1174710), -(_1174708 = _1174710)], (22561 ^ _779308) ^ [_1175253, _1175255, _1175257, _1175259] : [_1175257 = _1175259, -(hAPP(hAPP(c_COMBC(_1175253, tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_fun(_1175255, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1175255, tc_fun(tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_fun(_1175255, tc_HOL_Obool)), _1175253), c_COMBC(_1175255, tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1175255, tc_prod(_1175253, _1175255)), tc_fun(_1175255, tc_fun(tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_HOL_Obool)), _1175253), hAPP(c_COMBB(tc_prod(_1175253, _1175255), tc_fun(tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_HOL_Obool), _1175255), c_member(tc_prod(_1175253, _1175255)))), c_Product__Type_OPair(_1175253, _1175255)))), _1175257) = hAPP(hAPP(c_COMBC(_1175253, tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_fun(_1175255, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1175255, tc_fun(tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_fun(_1175255, tc_HOL_Obool)), _1175253), c_COMBC(_1175255, tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1175255, tc_prod(_1175253, _1175255)), tc_fun(_1175255, tc_fun(tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_HOL_Obool)), _1175253), hAPP(c_COMBB(tc_prod(_1175253, _1175255), tc_fun(tc_fun(tc_prod(_1175253, _1175255), tc_HOL_Obool), tc_HOL_Obool), _1175255), c_member(tc_prod(_1175253, _1175255)))), c_Product__Type_OPair(_1175253, _1175255)))), _1175259))], (22567 ^ _779308) ^ [_1175829, _1175831, _1175833, _1175835] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1175829, tc_fun(_1175831, tc_HOL_Obool))), _1175833), _1175835)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1175829, _1175831)), hAPP(hAPP(c_Product__Type_OPair(_1175829, _1175831), _1175833), _1175835)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1175829, _1175831), tc_HOL_Obool)))))], (22573 ^ _779308) ^ [_1175986, _1175988, _1175990, _1175992] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1175986, _1175988)), hAPP(hAPP(c_Product__Type_OPair(_1175986, _1175988), _1175990), _1175992)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1175986, _1175988), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1175986, tc_fun(_1175988, tc_HOL_Obool))), _1175990), _1175992)))], (22579 ^ _779308) ^ [_1176170, _1176172, _1176174, _1176176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1176170, tc_fun(_1176172, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1176170, tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_fun(_1176172, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176172, tc_fun(tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_fun(_1176172, tc_HOL_Obool)), _1176170), c_COMBC(_1176172, tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176172, tc_prod(_1176170, _1176172)), tc_fun(_1176172, tc_fun(tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_HOL_Obool)), _1176170), hAPP(c_COMBB(tc_prod(_1176170, _1176172), tc_fun(tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_HOL_Obool), _1176172), c_member(tc_prod(_1176170, _1176172)))), c_Product__Type_OPair(_1176170, _1176172)))), _1176174)), hAPP(hAPP(c_COMBC(_1176170, tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_fun(_1176172, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176172, tc_fun(tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_fun(_1176172, tc_HOL_Obool)), _1176170), c_COMBC(_1176172, tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176172, tc_prod(_1176170, _1176172)), tc_fun(_1176172, tc_fun(tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_HOL_Obool)), _1176170), hAPP(c_COMBB(tc_prod(_1176170, _1176172), tc_fun(tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool), tc_HOL_Obool), _1176172), c_member(tc_prod(_1176170, _1176172)))), c_Product__Type_OPair(_1176170, _1176172)))), _1176176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1176170, _1176172), tc_HOL_Obool)), _1176174), _1176176)))], (22585 ^ _779308) ^ [_1176771, _1176773, _1176775, _1176777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool)), _1176775), _1176777)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1176771, tc_fun(_1176773, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1176771, tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_fun(_1176773, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176773, tc_fun(tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_fun(_1176773, tc_HOL_Obool)), _1176771), c_COMBC(_1176773, tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176773, tc_prod(_1176771, _1176773)), tc_fun(_1176773, tc_fun(tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_HOL_Obool)), _1176771), hAPP(c_COMBB(tc_prod(_1176771, _1176773), tc_fun(tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_HOL_Obool), _1176773), c_member(tc_prod(_1176771, _1176773)))), c_Product__Type_OPair(_1176771, _1176773)))), _1176775)), hAPP(hAPP(c_COMBC(_1176771, tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_fun(_1176773, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176773, tc_fun(tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_fun(_1176773, tc_HOL_Obool)), _1176771), c_COMBC(_1176773, tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1176773, tc_prod(_1176771, _1176773)), tc_fun(_1176773, tc_fun(tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_HOL_Obool)), _1176771), hAPP(c_COMBB(tc_prod(_1176771, _1176773), tc_fun(tc_fun(tc_prod(_1176771, _1176773), tc_HOL_Obool), tc_HOL_Obool), _1176773), c_member(tc_prod(_1176771, _1176773)))), c_Product__Type_OPair(_1176771, _1176773)))), _1176777))))], (22591 ^ _779308) ^ [_1177374] : [-(_1177374 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1177374), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))))], (22597 ^ _779308) ^ [_1177413, _1177415, _1177417] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1177413, _1177413), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1177415), _1177417))), -(_1177413 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1177417 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22607 ^ _779308) ^ [_1177529, _1177531, _1177533, _1177535, _1177537, _1177539] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1177529, _1177531), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1177533), _1177535))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1177529, _1177531), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1177537), _1177539))), -(_1177531 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1177533 = _1177537)], (22621 ^ _779308) ^ [_1177733, _1177735, _1177737, _1177739, _1177741, _1177743] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1177733, _1177735), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1177737), _1177739))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1177733, _1177735), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1177741), _1177743))), -(_1177735 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1177739 = _1177743)], (22635 ^ _779308) ^ [_1177952, _1177954] : [c_Code__Numeral_OSuc__code__numeral(_1177952) = c_Code__Numeral_OSuc__code__numeral(_1177954), -(_1177952 = _1177954)], (22641 ^ _779308) ^ [_1178033, _1178035] : [_1178033 = _1178035, -(c_Code__Numeral_OSuc__code__numeral(_1178033) = c_Code__Numeral_OSuc__code__numeral(_1178035))], (22647 ^ _779308) ^ [_1178120, _1178122, _1178124, _1178126] : [class_Rings_Odivision__ring(_1178120), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178120), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178120), _1178122), _1178124)), _1178126) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178120), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178120), _1178122), _1178126)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178120), _1178124), _1178126)))], (22653 ^ _779308) ^ [_1178279, _1178281, _1178283, _1178285] : [class_Rings_Odivision__ring(_1178279), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178279), _1178281), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178279), _1178283), _1178285)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178279), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178279), _1178281), _1178283)), _1178285))], (22659 ^ _779308) ^ [_1178422, _1178424, _1178426, _1178428] : [class_Rings_Odivision__ring(_1178422), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178422), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1178422), _1178424), _1178426)), _1178428) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1178422), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178422), _1178424), _1178428)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178422), _1178426), _1178428)))], (22665 ^ _779308) ^ [_1178581, _1178583] : [class_Rings_Odivision__ring(_1178581), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178581), _1178583), c_Groups_Oone__class_Oone(_1178581)) = _1178583)], (22671 ^ _779308) ^ [_1178676, _1178678, _1178680] : [class_Rings_Odivision__ring(_1178676), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1178676), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178676), _1178678), _1178680)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178676), hAPP(c_Groups_Ouminus__class_Ouminus(_1178676), _1178678)), _1178680))], (22677 ^ _779308) ^ [_1178805, _1178807, _1178809, _1178811] : [class_Fields_Ofield__inverse__zero(_1178805), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1178805), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178805), _1178807), _1178809)), _1178811) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1178805), hAPP(hAPP(c_Power_Opower__class_Opower(_1178805), _1178807), _1178811)), hAPP(hAPP(c_Power_Opower__class_Opower(_1178805), _1178809), _1178811)))], (22683 ^ _779308) ^ [_1178964, _1178966, _1178968] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1178964, _1178964), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1178966), _1178968))), -(_1178964 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1178966 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22693 ^ _779308) ^ [_1179080, _1179082, _1179084, _1179086] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1179080, _1179082), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1179084), _1179086))), -(_1179082 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179080, _1179082) = _1179086)], (22703 ^ _779308) ^ [_1179206, _1179208, _1179210, _1179212] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1179206, _1179208), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1179210), _1179212))), -(_1179208 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179206), _1179208) = _1179210)], (22713 ^ _779308) ^ [_1179332, _1179334] : [-(_1179332 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1179334, _1179332), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179334), _1179332)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1179334, _1179332)))))], (22719 ^ _779308) ^ [_1179389, _1179391, _1179393, _1179395] : [class_Rings_Odivision__ring(_1179389), -(_1179391 = c_Groups_Ozero__class_Ozero(_1179389)), 22726 ^ _779308 : [(22727 ^ _779308) ^ [] : [_1179393 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179389), _1179395), _1179391), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179389), _1179393), _1179391) = _1179395)], (22733 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179389), _1179393), _1179391) = _1179395, -(_1179393 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179389), _1179395), _1179391))]]], (22739 ^ _779308) ^ [_1179717, _1179719, _1179721, _1179723] : [class_Rings_Odivision__ring(_1179717), -(_1179719 = c_Groups_Ozero__class_Ozero(_1179717)), 22746 ^ _779308 : [(22747 ^ _779308) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179717), _1179721), _1179719) = _1179723, -(_1179721 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179717), _1179723), _1179719))], (22753 ^ _779308) ^ [] : [_1179721 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179717), _1179723), _1179719), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1179717), _1179721), _1179719) = _1179723)]]], (22759 ^ _779308) ^ [_1180045, _1180047, _1180049, _1180051] : [class_Rings_Odivision__ring(_1180045), -(_1180047 = c_Groups_Ozero__class_Ozero(_1180045)), _1180049 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180045), _1180051), _1180047), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180045), _1180049), _1180047) = _1180051)], (22773 ^ _779308) ^ [_1180275, _1180277, _1180279, _1180281] : [class_Rings_Odivision__ring(_1180275), -(_1180277 = c_Groups_Ozero__class_Ozero(_1180275)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180275), _1180279), _1180277) = _1180281, -(_1180279 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180275), _1180281), _1180277))], (22787 ^ _779308) ^ [_1180505, _1180507] : [class_Rings_Odivision__ring__inverse__zero(_1180505), 22790 ^ _779308 : [(22791 ^ _779308) ^ [] : [_1180507 = c_Groups_Ozero__class_Ozero(_1180505), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180505), _1180507), _1180507) = c_Groups_Ozero__class_Ozero(_1180505))], (22797 ^ _779308) ^ [] : [-(_1180507 = c_Groups_Ozero__class_Ozero(_1180505)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180505), _1180507), _1180507) = c_Groups_Oone__class_Oone(_1180505))]]], (22803 ^ _779308) ^ [_1180727, _1180729] : [class_Rings_Odivision__ring(_1180727), -(_1180729 = c_Groups_Ozero__class_Ozero(_1180727)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180727), _1180729), _1180729) = c_Groups_Oone__class_Oone(_1180727))], (22813 ^ _779308) ^ [_1180841, _1180843, _1180845] : [class_Rings_Odivision__ring(_1180841), -(_1180843 = c_Groups_Ozero__class_Ozero(_1180841)), 22820 ^ _779308 : [(22821 ^ _779308) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180841), _1180845), _1180843) = c_Groups_Oone__class_Oone(_1180841), -(_1180845 = _1180843)], (22827 ^ _779308) ^ [] : [_1180845 = _1180843, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1180841), _1180845), _1180843) = c_Groups_Oone__class_Oone(_1180841))]]], (22833 ^ _779308) ^ [_1181143, _1181145, _1181147] : [class_Rings_Odivision__ring(_1181143), -(_1181145 = c_Groups_Ozero__class_Ozero(_1181143)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181143), hAPP(c_Groups_Ouminus__class_Ouminus(_1181143), _1181147)), hAPP(c_Groups_Ouminus__class_Ouminus(_1181143), _1181145)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181143), _1181147), _1181145))], (22843 ^ _779308) ^ [_1181291, _1181293, _1181295] : [class_Rings_Odivision__ring(_1181291), -(_1181293 = c_Groups_Ozero__class_Ozero(_1181291)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1181291), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181291), _1181295), _1181293)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181291), _1181295), hAPP(c_Groups_Ouminus__class_Ouminus(_1181291), _1181293)))], (22853 ^ _779308) ^ [_1181439, _1181441, _1181443, _1181445] : [class_Fields_Ofield(_1181439), -(_1181441 = c_Groups_Ozero__class_Ozero(_1181439)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1181439), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181439), _1181443), _1181441)), _1181445) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181439), hAPP(hAPP(c_Power_Opower__class_Opower(_1181439), _1181443), _1181445)), hAPP(hAPP(c_Power_Opower__class_Opower(_1181439), _1181441), _1181445)))], (22863 ^ _779308) ^ [_1181617, _1181619, _1181621] : [class_Fields_Ofield__inverse__zero(_1181617), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181617), c_Groups_Oone__class_Oone(_1181617)), hAPP(hAPP(c_Power_Opower__class_Opower(_1181617), _1181619), _1181621)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1181617), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1181617), c_Groups_Oone__class_Oone(_1181617)), _1181619)), _1181621))], (22869 ^ _779308) ^ [_1181775] : [c_Code__Numeral_OSuc__code__numeral(_1181775) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (22871 ^ _779308) ^ [_1181809] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1181809)], (22873 ^ _779308) ^ [_1181834, _1181836, _1181838, _1181840, _1181842, _1181844, _1181846] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1181834, _1181836), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1181838), _1181840))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1181842, _1181836), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1181844), _1181846))), -(_1181836 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181834), _1181842), _1181836), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181838), _1181844)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181840), _1181846)), _1181836))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1181840), _1181846), _1181836)))))], (22887 ^ _779308) ^ [_1182144, _1182146, _1182148, _1182150] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1182144, _1182146), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1182148), _1182150))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182144), _1182146), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1182150), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182148)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1182148)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1182150), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1182146), _1182150))))))], (22893 ^ _779308) ^ [_1182371, _1182373, _1182375, _1182377, _1182379] : [class_Fields_Ofield__inverse__zero(_1182371), hBOOL(hAPP(c_Finite__Set_Ofinite(_1182373), _1182375)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1182373, _1182371), hAPP(hAPP(c_COMBS(_1182373, _1182371, _1182371), hAPP(hAPP(c_COMBB(_1182371, tc_fun(_1182371, _1182371), _1182373), c_Rings_Oinverse__class_Odivide(_1182371)), _1182377)), _1182379)), _1182375) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1182371), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1182373, _1182371), _1182377), _1182375)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1182373, _1182371), _1182379), _1182375)))], (22903 ^ _779308) ^ [_1182638, _1182640, _1182642, _1182644] : [_1182638 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182640), _1182642)), _1182644), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1182638, _1182640), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1182642), _1182644)))), 22910 ^ _779308 : [(22911 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182640)))], (22913 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182644), _1182640))]], 22918 ^ _779308 : [(22919 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182640))], (22921 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182640), _1182644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182644), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (22929 ^ _779308) ^ [_1183100, _1183102, _1183104, _1183106] : [class_Fields_Ofield__inverse__zero(_1183100), class_Int_Onumber(_1183100), 22936 ^ _779308 : [(22953 ^ _779308) ^ [] : [-(_1183102 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183100), _1183104), hAPP(c_Int_Onumber__class_Onumber__of(_1183100), _1183106))), 22956 ^ _779308 : [(22957 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1183100), _1183106) = c_Groups_Ozero__class_Ozero(_1183100)], (22959 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183100), _1183102), hAPP(c_Int_Onumber__class_Onumber__of(_1183100), _1183106)) = _1183104]], 22960 ^ _779308 : [(22961 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1183100), _1183106) = c_Groups_Ozero__class_Ozero(_1183100))], (22963 ^ _779308) ^ [] : [_1183102 = c_Groups_Ozero__class_Ozero(_1183100)]]], (22937 ^ _779308) ^ [] : [_1183102 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183100), _1183104), hAPP(c_Int_Onumber__class_Onumber__of(_1183100), _1183106)), 22940 ^ _779308 : [(22941 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1183100), _1183106) = c_Groups_Ozero__class_Ozero(_1183100)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183100), _1183102), hAPP(c_Int_Onumber__class_Onumber__of(_1183100), _1183106)) = _1183104)], (22947 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1183100), _1183106) = c_Groups_Ozero__class_Ozero(_1183100), -(_1183102 = c_Groups_Ozero__class_Ozero(_1183100))]]]]], (22967 ^ _779308) ^ [_1183710, _1183712, _1183714, _1183716] : [class_Fields_Ofield__inverse__zero(_1183710), class_Int_Onumber(_1183710), 22974 ^ _779308 : [(22991 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1183710), _1183712) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183710), _1183714), _1183716)), 22994 ^ _779308 : [(22995 ^ _779308) ^ [] : [_1183716 = c_Groups_Ozero__class_Ozero(_1183710)], (22997 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183710), hAPP(c_Int_Onumber__class_Onumber__of(_1183710), _1183712)), _1183716) = _1183714]], 22998 ^ _779308 : [(22999 ^ _779308) ^ [] : [-(_1183716 = c_Groups_Ozero__class_Ozero(_1183710))], (23001 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1183710), _1183712) = c_Groups_Ozero__class_Ozero(_1183710)]]], (22975 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1183710), _1183712) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1183710), _1183714), _1183716), 22978 ^ _779308 : [(22979 ^ _779308) ^ [] : [-(_1183716 = c_Groups_Ozero__class_Ozero(_1183710)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183710), hAPP(c_Int_Onumber__class_Onumber__of(_1183710), _1183712)), _1183716) = _1183714)], (22985 ^ _779308) ^ [] : [_1183716 = c_Groups_Ozero__class_Ozero(_1183710), -(hAPP(c_Int_Onumber__class_Onumber__of(_1183710), _1183712) = c_Groups_Ozero__class_Ozero(_1183710))]]]]], (23005 ^ _779308) ^ [_1184305, _1184307, _1184309, _1184311] : [class_Fields_Ofield__inverse__zero(_1184305), class_Int_Onumber(_1184305), 23012 ^ _779308 : [(23029 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184305), _1184307), _1184309) = hAPP(c_Int_Onumber__class_Onumber__of(_1184305), _1184311)), 23032 ^ _779308 : [(23033 ^ _779308) ^ [] : [_1184309 = c_Groups_Ozero__class_Ozero(_1184305)], (23035 ^ _779308) ^ [] : [_1184307 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184305), hAPP(c_Int_Onumber__class_Onumber__of(_1184305), _1184311)), _1184309)]], 23036 ^ _779308 : [(23037 ^ _779308) ^ [] : [-(_1184309 = c_Groups_Ozero__class_Ozero(_1184305))], (23039 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1184305), _1184311) = c_Groups_Ozero__class_Ozero(_1184305)]]], (23013 ^ _779308) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184305), _1184307), _1184309) = hAPP(c_Int_Onumber__class_Onumber__of(_1184305), _1184311), 23016 ^ _779308 : [(23017 ^ _779308) ^ [] : [-(_1184309 = c_Groups_Ozero__class_Ozero(_1184305)), -(_1184307 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184305), hAPP(c_Int_Onumber__class_Onumber__of(_1184305), _1184311)), _1184309))], (23023 ^ _779308) ^ [] : [_1184309 = c_Groups_Ozero__class_Ozero(_1184305), -(hAPP(c_Int_Onumber__class_Onumber__of(_1184305), _1184311) = c_Groups_Ozero__class_Ozero(_1184305))]]]]], (23043 ^ _779308) ^ [_1184900, _1184902, _1184904, _1184906] : [class_Fields_Ofield__inverse__zero(_1184900), class_Int_Onumber(_1184900), 23050 ^ _779308 : [(23067 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184900), _1184902), hAPP(c_Int_Onumber__class_Onumber__of(_1184900), _1184904)) = _1184906), 23070 ^ _779308 : [(23071 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1184900), _1184904) = c_Groups_Ozero__class_Ozero(_1184900)], (23073 ^ _779308) ^ [] : [_1184902 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184900), _1184906), hAPP(c_Int_Onumber__class_Onumber__of(_1184900), _1184904))]], 23074 ^ _779308 : [(23075 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1184900), _1184904) = c_Groups_Ozero__class_Ozero(_1184900))], (23077 ^ _779308) ^ [] : [_1184906 = c_Groups_Ozero__class_Ozero(_1184900)]]], (23051 ^ _779308) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1184900), _1184902), hAPP(c_Int_Onumber__class_Onumber__of(_1184900), _1184904)) = _1184906, 23054 ^ _779308 : [(23055 ^ _779308) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1184900), _1184904) = c_Groups_Ozero__class_Ozero(_1184900)), -(_1184902 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184900), _1184906), hAPP(c_Int_Onumber__class_Onumber__of(_1184900), _1184904)))], (23061 ^ _779308) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1184900), _1184904) = c_Groups_Ozero__class_Ozero(_1184900), -(_1184906 = c_Groups_Ozero__class_Ozero(_1184900))]]]]], (23081 ^ _779308) ^ [_1185510, _1185512, _1185514, _1185516, _1185518] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1185510, _1185512), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1185514), _1185516))), -(_1185512 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1185518), _1185510), _1185512), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1185518), _1185514)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1185518), _1185516)), _1185512))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1185518), _1185516), _1185512)))))], (23091 ^ _779308) ^ [_1185732, _1185734] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1185732), _1185734), hAPP(c_Int_Onumber__class_Onumber__of(_1185732), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1185732)), class_Fields_Ofield__inverse__zero(_1185732), class_Int_Onumber__ring(_1185732)], (23101 ^ _779308) ^ [_1185887, _1185889] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1185887), _1185889), hAPP(c_Int_Onumber__class_Onumber__of(_1185887), c_Int_OBit1(c_Int_OPls))) = _1185889), class_Fields_Ofield(_1185887), class_Int_Onumber__ring(_1185887)], (23111 ^ _779308) ^ [_1186038, _1186040] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186038), _1186040), hAPP(c_Int_Onumber__class_Onumber__of(_1186038), c_Int_OBit1(c_Int_OPls))) = _1186040), class_Fields_Ofield(_1186038), class_Int_Onumber__ring(_1186038)], (23121 ^ _779308) ^ [_1186189, _1186191] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186189), _1186191), hAPP(c_Int_Onumber__class_Onumber__of(_1186189), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1186189), _1186191)), class_Fields_Ofield__inverse__zero(_1186189), class_Int_Onumber__ring(_1186189)], (23131 ^ _779308) ^ [_1186346, _1186348] : [-(_1186346 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1186348, _1186346), c_Divides_Odivmod__int(_1186348, _1186346))))], (23137 ^ _779308) ^ [_1186390, _1186392, _1186394, _1186396, _1186398] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1186390, _1186392), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1186394), _1186396))), -(_1186392 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186398)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1186390, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186392), _1186398)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1186394), _1186398)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1186392), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1186394, _1186398))), _1186396)))))], (23151 ^ _779308) ^ [_1186696, _1186698] : [-(c_Divides_Odivmod__int(_1186696, _1186698) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1186696), _1186698)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1186696, _1186698)))], (23153 ^ _779308) ^ [_1186740, _1186742, _1186744, _1186746] : [class_Fields_Olinordered__field__inverse__zero(_1186740), class_Int_Onumber(_1186740), 23160 ^ _779308 : [(23187 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186740), _1186742), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744))), _1186746))), 23190 ^ _779308 : [(23191 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), c_Groups_Ozero__class_Ozero(_1186740)), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744))))], (23193 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), _1186742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186740), _1186746), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744))))]], 23194 ^ _779308 : [(23195 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), c_Groups_Ozero__class_Ozero(_1186740)), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744)))], (23197 ^ _779308) ^ [] : [23198 ^ _779308 : [(23199 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744)), c_Groups_Ozero__class_Ozero(_1186740))))], (23201 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186740), _1186746), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744))), _1186742))]], 23202 ^ _779308 : [(23203 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744)), c_Groups_Ozero__class_Ozero(_1186740)))], (23205 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), c_Groups_Ozero__class_Ozero(_1186740)), _1186746))]]]]], (23161 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1186740), _1186742), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744))), _1186746)), 23164 ^ _779308 : [(23165 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), c_Groups_Ozero__class_Ozero(_1186740)), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), _1186742), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186740), _1186746), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744)))))], (23171 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), c_Groups_Ozero__class_Ozero(_1186740)), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744)))), 23174 ^ _779308 : [(23175 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744)), c_Groups_Ozero__class_Ozero(_1186740))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186740), _1186746), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744))), _1186742)))], (23181 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), hAPP(c_Int_Onumber__class_Onumber__of(_1186740), _1186744)), c_Groups_Ozero__class_Ozero(_1186740)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186740), c_Groups_Ozero__class_Ozero(_1186740)), _1186746)))]]]]]]], (23209 ^ _779308) ^ [_1187854, _1187856, _1187858, _1187860] : [class_Fields_Olinordered__field__inverse__zero(_1187854), class_Int_Onumber(_1187854), 23216 ^ _779308 : [(23243 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187854), _1187856), _1187858)), hAPP(c_Int_Onumber__class_Onumber__of(_1187854), _1187860)))), 23246 ^ _779308 : [(23247 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), c_Groups_Ozero__class_Ozero(_1187854)), _1187858)))], (23249 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), _1187856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187854), hAPP(c_Int_Onumber__class_Onumber__of(_1187854), _1187860)), _1187858)))]], 23250 ^ _779308 : [(23251 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), c_Groups_Ozero__class_Ozero(_1187854)), _1187858))], (23253 ^ _779308) ^ [] : [23254 ^ _779308 : [(23255 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), _1187858), c_Groups_Ozero__class_Ozero(_1187854))))], (23257 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187854), hAPP(c_Int_Onumber__class_Onumber__of(_1187854), _1187860)), _1187858)), _1187856))]], 23258 ^ _779308 : [(23259 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), _1187858), c_Groups_Ozero__class_Ozero(_1187854)))], (23261 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), c_Groups_Ozero__class_Ozero(_1187854)), hAPP(c_Int_Onumber__class_Onumber__of(_1187854), _1187860)))]]]]], (23217 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1187854), _1187856), _1187858)), hAPP(c_Int_Onumber__class_Onumber__of(_1187854), _1187860))), 23220 ^ _779308 : [(23221 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), c_Groups_Ozero__class_Ozero(_1187854)), _1187858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), _1187856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187854), hAPP(c_Int_Onumber__class_Onumber__of(_1187854), _1187860)), _1187858))))], (23227 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), c_Groups_Ozero__class_Ozero(_1187854)), _1187858))), 23230 ^ _779308 : [(23231 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), _1187858), c_Groups_Ozero__class_Ozero(_1187854))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187854), hAPP(c_Int_Onumber__class_Onumber__of(_1187854), _1187860)), _1187858)), _1187856)))], (23237 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), _1187858), c_Groups_Ozero__class_Ozero(_1187854)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187854), c_Groups_Ozero__class_Ozero(_1187854)), hAPP(c_Int_Onumber__class_Onumber__of(_1187854), _1187860))))]]]]]]], (23265 ^ _779308) ^ [_1188923, _1188925, _1188927, _1188929] : [class_Fields_Olinordered__field__inverse__zero(_1188923), class_Int_Onumber(_1188923), 23272 ^ _779308 : [(23299 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), hAPP(c_Int_Onumber__class_Onumber__of(_1188923), _1188925)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1188923), _1188927), _1188929)))), 23302 ^ _779308 : [(23303 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), c_Groups_Ozero__class_Ozero(_1188923)), _1188929)))], (23305 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188923), hAPP(c_Int_Onumber__class_Onumber__of(_1188923), _1188925)), _1188929)), _1188927))]], 23306 ^ _779308 : [(23307 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), c_Groups_Ozero__class_Ozero(_1188923)), _1188929))], (23309 ^ _779308) ^ [] : [23310 ^ _779308 : [(23311 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), _1188929), c_Groups_Ozero__class_Ozero(_1188923))))], (23313 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), _1188927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188923), hAPP(c_Int_Onumber__class_Onumber__of(_1188923), _1188925)), _1188929)))]], 23314 ^ _779308 : [(23315 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), _1188929), c_Groups_Ozero__class_Ozero(_1188923)))], (23317 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), hAPP(c_Int_Onumber__class_Onumber__of(_1188923), _1188925)), c_Groups_Ozero__class_Ozero(_1188923)))]]]]], (23273 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), hAPP(c_Int_Onumber__class_Onumber__of(_1188923), _1188925)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1188923), _1188927), _1188929))), 23276 ^ _779308 : [(23277 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), c_Groups_Ozero__class_Ozero(_1188923)), _1188929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188923), hAPP(c_Int_Onumber__class_Onumber__of(_1188923), _1188925)), _1188929)), _1188927)))], (23283 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), c_Groups_Ozero__class_Ozero(_1188923)), _1188929))), 23286 ^ _779308 : [(23287 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), _1188929), c_Groups_Ozero__class_Ozero(_1188923))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), _1188927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188923), hAPP(c_Int_Onumber__class_Onumber__of(_1188923), _1188925)), _1188929))))], (23293 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), _1188929), c_Groups_Ozero__class_Ozero(_1188923)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188923), hAPP(c_Int_Onumber__class_Onumber__of(_1188923), _1188925)), c_Groups_Ozero__class_Ozero(_1188923))))]]]]]]], (23321 ^ _779308) ^ [_1189992, _1189994, _1189996, _1189998] : [class_Fields_Olinordered__field__inverse__zero(_1189992), class_Int_Onumber(_1189992), 23328 ^ _779308 : [(23355 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), _1189994), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1189992), _1189996), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998))))), 23358 ^ _779308 : [(23359 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), c_Groups_Ozero__class_Ozero(_1189992)), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998))))], (23361 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189992), _1189994), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998))), _1189996))]], 23362 ^ _779308 : [(23363 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), c_Groups_Ozero__class_Ozero(_1189992)), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998)))], (23365 ^ _779308) ^ [] : [23366 ^ _779308 : [(23367 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998)), c_Groups_Ozero__class_Ozero(_1189992))))], (23369 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), _1189996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189992), _1189994), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998))))]], 23370 ^ _779308 : [(23371 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998)), c_Groups_Ozero__class_Ozero(_1189992)))], (23373 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), _1189994), c_Groups_Ozero__class_Ozero(_1189992)))]]]]], (23329 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), _1189994), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1189992), _1189996), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998)))), 23332 ^ _779308 : [(23333 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), c_Groups_Ozero__class_Ozero(_1189992)), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189992), _1189994), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998))), _1189996)))], (23339 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), c_Groups_Ozero__class_Ozero(_1189992)), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998)))), 23342 ^ _779308 : [(23343 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998)), c_Groups_Ozero__class_Ozero(_1189992))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), _1189996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1189992), _1189994), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998)))))], (23349 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), hAPP(c_Int_Onumber__class_Onumber__of(_1189992), _1189998)), c_Groups_Ozero__class_Ozero(_1189992)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189992), _1189994), c_Groups_Ozero__class_Ozero(_1189992))))]]]]]]], (23377 ^ _779308) ^ [_1191106, _1191108, _1191110, _1191112] : [class_Fields_Ofield(_1191106), -(_1191108 = c_Groups_Ozero__class_Ozero(_1191106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1191110), _1191112)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1191106), _1191108), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1191112), _1191110)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1191106), hAPP(hAPP(c_Power_Opower__class_Opower(_1191106), _1191108), _1191112)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191106), _1191108), _1191110)))], (23391 ^ _779308) ^ [_1191390, _1191392] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1191390), hAPP(c_Int_Onumber__class_Onumber__of(_1191390), c_Int_OMin)), _1191392) = hAPP(c_Groups_Ouminus__class_Ouminus(_1191390), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1191390), c_Groups_Oone__class_Oone(_1191390)), _1191392))), class_Fields_Ofield__inverse__zero(_1191390), class_Int_Onumber__ring(_1191390)], (23401 ^ _779308) ^ [_1191571] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1191571)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1191571)], (23403 ^ _779308) ^ [_1191602, _1191604, _1191606, _1191608] : [class_Fields_Olinordered__field__inverse__zero(_1191602), class_Int_Onumber(_1191602), 23410 ^ _779308 : [(23437 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191602), _1191604), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1191602), _1191606), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608))))), 23440 ^ _779308 : [(23441 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191602), c_Groups_Ozero__class_Ozero(_1191602)), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608))))], (23443 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191602), _1191604), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608))), _1191606))]], 23444 ^ _779308 : [(23445 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191602), c_Groups_Ozero__class_Ozero(_1191602)), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608)))], (23447 ^ _779308) ^ [] : [23448 ^ _779308 : [(23449 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191602), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608)), c_Groups_Ozero__class_Ozero(_1191602))))], (23451 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191602), _1191606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191602), _1191604), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608))))]], 23452 ^ _779308 : [(23453 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191602), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608)), c_Groups_Ozero__class_Ozero(_1191602)))], (23455 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191602), _1191604), c_Groups_Ozero__class_Ozero(_1191602)))]]]]], (23411 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191602), _1191604), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1191602), _1191606), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608)))), 23414 ^ _779308 : [(23415 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191602), c_Groups_Ozero__class_Ozero(_1191602)), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191602), _1191604), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608))), _1191606)))], (23421 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191602), c_Groups_Ozero__class_Ozero(_1191602)), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608)))), 23424 ^ _779308 : [(23425 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191602), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608)), c_Groups_Ozero__class_Ozero(_1191602))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191602), _1191606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191602), _1191604), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608)))))], (23431 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191602), hAPP(c_Int_Onumber__class_Onumber__of(_1191602), _1191608)), c_Groups_Ozero__class_Ozero(_1191602)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191602), _1191604), c_Groups_Ozero__class_Ozero(_1191602))))]]]]]]], (23459 ^ _779308) ^ [_1192716, _1192718, _1192720, _1192722] : [class_Fields_Olinordered__field__inverse__zero(_1192716), class_Int_Onumber(_1192716), 23466 ^ _779308 : [(23493 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192716), hAPP(c_Int_Onumber__class_Onumber__of(_1192716), _1192718)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1192716), _1192720), _1192722)))), 23496 ^ _779308 : [(23497 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192716), c_Groups_Ozero__class_Ozero(_1192716)), _1192722)))], (23499 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192716), hAPP(c_Int_Onumber__class_Onumber__of(_1192716), _1192718)), _1192722)), _1192720))]], 23500 ^ _779308 : [(23501 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192716), c_Groups_Ozero__class_Ozero(_1192716)), _1192722))], (23503 ^ _779308) ^ [] : [23504 ^ _779308 : [(23505 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192716), _1192722), c_Groups_Ozero__class_Ozero(_1192716))))], (23507 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192716), _1192720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192716), hAPP(c_Int_Onumber__class_Onumber__of(_1192716), _1192718)), _1192722)))]], 23508 ^ _779308 : [(23509 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192716), _1192722), c_Groups_Ozero__class_Ozero(_1192716)))], (23511 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192716), hAPP(c_Int_Onumber__class_Onumber__of(_1192716), _1192718)), c_Groups_Ozero__class_Ozero(_1192716)))]]]]], (23467 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192716), hAPP(c_Int_Onumber__class_Onumber__of(_1192716), _1192718)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1192716), _1192720), _1192722))), 23470 ^ _779308 : [(23471 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192716), c_Groups_Ozero__class_Ozero(_1192716)), _1192722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192716), hAPP(c_Int_Onumber__class_Onumber__of(_1192716), _1192718)), _1192722)), _1192720)))], (23477 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192716), c_Groups_Ozero__class_Ozero(_1192716)), _1192722))), 23480 ^ _779308 : [(23481 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192716), _1192722), c_Groups_Ozero__class_Ozero(_1192716))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192716), _1192720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192716), hAPP(c_Int_Onumber__class_Onumber__of(_1192716), _1192718)), _1192722))))], (23487 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192716), _1192722), c_Groups_Ozero__class_Ozero(_1192716)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192716), hAPP(c_Int_Onumber__class_Onumber__of(_1192716), _1192718)), c_Groups_Ozero__class_Ozero(_1192716))))]]]]]]], (23515 ^ _779308) ^ [_1193785, _1193787, _1193789, _1193791] : [class_Fields_Olinordered__field__inverse__zero(_1193785), class_Int_Onumber(_1193785), 23522 ^ _779308 : [(23549 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193785), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1193785), _1193787), _1193789)), hAPP(c_Int_Onumber__class_Onumber__of(_1193785), _1193791)))), 23552 ^ _779308 : [(23553 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193785), c_Groups_Ozero__class_Ozero(_1193785)), _1193789)))], (23555 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193785), _1193787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193785), hAPP(c_Int_Onumber__class_Onumber__of(_1193785), _1193791)), _1193789)))]], 23556 ^ _779308 : [(23557 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193785), c_Groups_Ozero__class_Ozero(_1193785)), _1193789))], (23559 ^ _779308) ^ [] : [23560 ^ _779308 : [(23561 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193785), _1193789), c_Groups_Ozero__class_Ozero(_1193785))))], (23563 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193785), hAPP(c_Int_Onumber__class_Onumber__of(_1193785), _1193791)), _1193789)), _1193787))]], 23564 ^ _779308 : [(23565 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193785), _1193789), c_Groups_Ozero__class_Ozero(_1193785)))], (23567 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193785), c_Groups_Ozero__class_Ozero(_1193785)), hAPP(c_Int_Onumber__class_Onumber__of(_1193785), _1193791)))]]]]], (23523 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193785), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1193785), _1193787), _1193789)), hAPP(c_Int_Onumber__class_Onumber__of(_1193785), _1193791))), 23526 ^ _779308 : [(23527 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193785), c_Groups_Ozero__class_Ozero(_1193785)), _1193789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193785), _1193787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193785), hAPP(c_Int_Onumber__class_Onumber__of(_1193785), _1193791)), _1193789))))], (23533 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193785), c_Groups_Ozero__class_Ozero(_1193785)), _1193789))), 23536 ^ _779308 : [(23537 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193785), _1193789), c_Groups_Ozero__class_Ozero(_1193785))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193785), hAPP(c_Int_Onumber__class_Onumber__of(_1193785), _1193791)), _1193789)), _1193787)))], (23543 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193785), _1193789), c_Groups_Ozero__class_Ozero(_1193785)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193785), c_Groups_Ozero__class_Ozero(_1193785)), hAPP(c_Int_Onumber__class_Onumber__of(_1193785), _1193791))))]]]]]]], (23571 ^ _779308) ^ [_1194854, _1194856, _1194858, _1194860] : [class_Fields_Olinordered__field__inverse__zero(_1194854), class_Int_Onumber(_1194854), 23578 ^ _779308 : [(23605 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194854), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1194854), _1194856), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858))), _1194860))), 23608 ^ _779308 : [(23609 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194854), c_Groups_Ozero__class_Ozero(_1194854)), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858))))], (23611 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194854), _1194856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194854), _1194860), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858))))]], 23612 ^ _779308 : [(23613 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194854), c_Groups_Ozero__class_Ozero(_1194854)), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858)))], (23615 ^ _779308) ^ [] : [23616 ^ _779308 : [(23617 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194854), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858)), c_Groups_Ozero__class_Ozero(_1194854))))], (23619 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194854), _1194860), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858))), _1194856))]], 23620 ^ _779308 : [(23621 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194854), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858)), c_Groups_Ozero__class_Ozero(_1194854)))], (23623 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194854), c_Groups_Ozero__class_Ozero(_1194854)), _1194860))]]]]], (23579 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194854), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1194854), _1194856), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858))), _1194860)), 23582 ^ _779308 : [(23583 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194854), c_Groups_Ozero__class_Ozero(_1194854)), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194854), _1194856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194854), _1194860), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858)))))], (23589 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194854), c_Groups_Ozero__class_Ozero(_1194854)), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858)))), 23592 ^ _779308 : [(23593 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194854), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858)), c_Groups_Ozero__class_Ozero(_1194854))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194854), _1194860), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858))), _1194856)))], (23599 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194854), hAPP(c_Int_Onumber__class_Onumber__of(_1194854), _1194858)), c_Groups_Ozero__class_Ozero(_1194854)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194854), c_Groups_Ozero__class_Ozero(_1194854)), _1194860)))]]]]]]], (23627 ^ _779308) ^ [_1195968, _1195970] : [class_Fields_Olinordered__field__inverse__zero(_1195968), class_Int_Onumber__ring(_1195968), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195968), c_Groups_Ozero__class_Ozero(_1195968)), _1195970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195968), c_Groups_Ozero__class_Ozero(_1195968)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1195968), _1195970), hAPP(c_Int_Onumber__class_Onumber__of(_1195968), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (23641 ^ _779308) ^ [_1196209, _1196211] : [class_Fields_Olinordered__field__inverse__zero(_1196209), class_Int_Onumber__ring(_1196209), 23648 ^ _779308 : [(23649 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196209), c_Groups_Ozero__class_Ozero(_1196209)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196209), _1196211), hAPP(c_Int_Onumber__class_Onumber__of(_1196209), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196209), c_Groups_Ozero__class_Ozero(_1196209)), _1196211)))], (23655 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196209), c_Groups_Ozero__class_Ozero(_1196209)), _1196211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196209), c_Groups_Ozero__class_Ozero(_1196209)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1196209), _1196211), hAPP(c_Int_Onumber__class_Onumber__of(_1196209), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (23661 ^ _779308) ^ [_1196559, _1196561, _1196563] : [-(hAPP(c_Divides_Oadjust(_1196559), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1196561), _1196563)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1196563), _1196559)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_If(tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1196561)), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1196561)), _1196563))))], (23663 ^ _779308) ^ [_1196639, _1196641, _1196643, _1196645, _1196647, _1196649, _1196651] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1196639, _1196641)), hAPP(hAPP(c_Product__Type_OPair(_1196639, _1196641), _1196643), _1196645)), _1196647)), -(hBOOL(hAPP(hAPP(c_member(_1196649), hAPP(hAPP(_1196651, _1196643), _1196645)), hAPP(c_Set_Oimage(tc_prod(_1196639, _1196641), _1196649, hAPP(c_Product__Type_Oprod_Oprod__case(_1196639, _1196641, _1196649), _1196651)), _1196647))))], (23669 ^ _779308) ^ [_1196833, _1196835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196833), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1196835, _1196833) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1196835), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1196833)))], (23675 ^ _779308) ^ [_1196939, _1196941] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196939), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 23678 ^ _779308 : [(23679 ^ _779308) ^ [] : [23680 ^ _779308 : [(23681 ^ _779308) ^ [] : [_1196941 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23683 ^ _779308) ^ [] : [_1196939 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1196941, _1196939) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23687 ^ _779308) ^ [] : [-(c_Nitpick_Onorm__frac(_1196941, _1196939) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1196941), _1196939)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1196941))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1196939)))), -(_1196941 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1196939 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (23697 ^ _779308) ^ [_1197237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197237))), 23700 ^ _779308 : [(23701 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197237)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197237)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197237))))], (23707 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197237))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197237)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197237)), c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1197237)))))]]], (23713 ^ _779308) ^ [_1197527, _1197529, _1197531, _1197533, _1197535] : [hBOOL(hAPP(hAPP(_1197527, _1197529), _1197531)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1197533, _1197535, tc_HOL_Obool), _1197527), hAPP(hAPP(c_Product__Type_OPair(_1197533, _1197535), _1197529), _1197531))))], (23719 ^ _779308) ^ [_1197656, _1197658, _1197660, _1197662, _1197664] : [hBOOL(hAPP(hAPP(_1197656, _1197658), _1197660)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1197662, _1197664, tc_HOL_Obool), _1197656), hAPP(hAPP(c_Product__Type_OPair(_1197662, _1197664), _1197658), _1197660))))], (23725 ^ _779308) ^ [_1197785, _1197787, _1197789, _1197791, _1197793, _1197795, _1197797] : [hBOOL(hAPP(hAPP(c_member(_1197785), _1197787), hAPP(hAPP(_1197789, _1197791), _1197793))), -(hBOOL(hAPP(hAPP(c_member(_1197785), _1197787), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1197795, _1197797, tc_fun(_1197785, tc_HOL_Obool)), _1197789), hAPP(hAPP(c_Product__Type_OPair(_1197795, _1197797), _1197791), _1197793)))))], (23731 ^ _779308) ^ [_1197974, _1197976, _1197978, _1197980] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1197974, tc_fun(_1197976, tc_HOL_Obool))), _1197978), _1197980))], (23733 ^ _779308) ^ [_1198016, _1198018, _1198020, _1198022, _1198024, _1198026, _1198028] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1198016, _1198018, tc_fun(_1198020, tc_HOL_Obool)), _1198022), hAPP(hAPP(c_Product__Type_OPair(_1198016, _1198018), _1198024), _1198026)), _1198028)), -(hBOOL(hAPP(hAPP(hAPP(_1198022, _1198024), _1198026), _1198028)))], (23739 ^ _779308) ^ [_1198167, _1198169, _1198171, _1198173, _1198175, _1198177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198167, tc_fun(_1198169, tc_HOL_Obool))), _1198171), _1198173)), hBOOL(hAPP(hAPP(_1198171, _1198175), _1198177)), -(hBOOL(hAPP(hAPP(_1198173, _1198175), _1198177)))], (23749 ^ _779308) ^ [_1198358, _1198360, _1198362, _1198364, _1198366, _1198368] : [hBOOL(hAPP(hAPP(_1198358, _1198360), _1198362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1198364, tc_fun(_1198366, tc_HOL_Obool))), _1198358), _1198368)), -(hBOOL(hAPP(hAPP(_1198368, _1198360), _1198362)))], (23759 ^ _779308) ^ [_1198549, _1198551, _1198553] : [_1198549 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1198551, _1198551), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1198551, _1198551), tc_HOL_Obool)), _1198549), _1198553)))], (23765 ^ _779308) ^ [_1198670, _1198672, _1198674, _1198676, _1198678, _1198680] : [hAPP(hAPP(c_Product__Type_OPair(_1198670, _1198672), _1198674), _1198676) = hAPP(hAPP(c_Product__Type_OPair(_1198670, _1198672), _1198678), _1198680), 23768 ^ _779308 : [(23769 ^ _779308) ^ [] : [-(_1198674 = _1198678)], (23771 ^ _779308) ^ [] : [-(_1198676 = _1198680)]]], (23773 ^ _779308) ^ [_1198848, _1198850, _1198852, _1198854, _1198856, _1198858] : [hAPP(hAPP(c_Product__Type_OPair(_1198848, _1198850), _1198852), _1198854) = hAPP(hAPP(c_Product__Type_OPair(_1198848, _1198850), _1198856), _1198858), 23776 ^ _779308 : [(23777 ^ _779308) ^ [] : [-(_1198852 = _1198856)], (23779 ^ _779308) ^ [] : [-(_1198854 = _1198858)]]], (23781 ^ _779308) ^ [_1198991, _1198993, _1198995, _1198997, _1198999, _1199001] : [-(hAPP(hAPP(c_Product__Type_OPair(_1198991, _1198993), _1198995), _1198997) = hAPP(hAPP(c_Product__Type_OPair(_1198991, _1198993), _1198999), _1199001)), _1198995 = _1198999, _1198997 = _1199001], (23791 ^ _779308) ^ [_1199192, _1199194, _1199196] : [hBOOL(hAPP(_1199192, 23792 ^ [_1199192, _1199194, _1199196])), 23795 ^ _779308 : [(23796 ^ _779308) ^ [_1199303, _1199305] : [-(hBOOL(hAPP(_1199192, hAPP(hAPP(c_Product__Type_OPair(_1199194, _1199196), _1199305), _1199303))))]]], (23798 ^ _779308) ^ [_1199339, _1199341, _1199343] : [hBOOL(hAPP(_1199339, hAPP(hAPP(c_Product__Type_OPair(_1199341, _1199343), 23799 ^ [_1199339, _1199341, _1199343]), 23800 ^ [_1199339, _1199341, _1199343]))), 23803 ^ _779308 : [(23804 ^ _779308) ^ [_1199486] : [-(hBOOL(hAPP(_1199339, _1199486)))]]], (23806 ^ _779308) ^ [_1199517, _1199519, _1199521, _1199523, _1199525, _1199527] : [_1199517 = _1199519, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1199521, _1199523, _1199525), _1199527), _1199517) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1199521, _1199523, _1199525), _1199527), _1199519))], (23812 ^ _779308) ^ [_1199642, _1199644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1199642), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1199644)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1199642, _1199644), c_Divides_OnegDivAlg(_1199642, _1199644))))], (23822 ^ _779308) ^ [_1199801, _1199803, _1199805, _1199807, _1199809, _1199811] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1199801, _1199803, _1199805), _1199807), hAPP(hAPP(c_Product__Type_OPair(_1199801, _1199803), _1199809), _1199811)) = hAPP(hAPP(_1199807, _1199809), _1199811))], (23824 ^ _779308) ^ [_1199859, _1199861, _1199863, _1199865, _1199867, _1199869] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1199859, _1199861, _1199863), _1199865), hAPP(hAPP(c_Product__Type_OPair(_1199859, _1199861), _1199867), _1199869)) = hAPP(hAPP(_1199865, _1199867), _1199869))], (23826 ^ _779308) ^ [_1199917, _1199919, _1199921, _1199923, _1199925] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1199917, _1199919, tc_HOL_Obool), _1199921), hAPP(hAPP(c_Product__Type_OPair(_1199917, _1199919), _1199923), _1199925))), -(hBOOL(hAPP(hAPP(_1199921, _1199923), _1199925)))], (23832 ^ _779308) ^ [_1200046, _1200048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1200046), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200048)), -(c_Divides_OnegDivAlg(_1200046, _1200048) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1200046), _1200048)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1200046, _1200048)))], (23842 ^ _779308) ^ [_1200227] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1200227) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1200227), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (23844 ^ _779308) ^ [_1200262, _1200264, _1200266, _1200268] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1200262, _1200264, _1200266), hAPP(hAPP(c_COMBB(tc_fun(_1200264, tc_prod(_1200262, _1200264)), tc_fun(_1200264, _1200266), _1200262), hAPP(c_COMBB(tc_prod(_1200262, _1200264), _1200266, _1200264), _1200268)), c_Product__Type_OPair(_1200262, _1200264))) = _1200268)], (23846 ^ _779308) ^ [_1200330, _1200332, _1200334, _1200336] : [-(c_HOL_OThe(tc_prod(_1200330, _1200332), hAPP(c_Product__Type_Oprod_Oprod__case(_1200330, _1200332, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1200330, tc_fun(_1200332, tc_HOL_Obool), tc_fun(_1200332, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1200332, tc_HOL_Obool), tc_fun(_1200332, tc_HOL_Obool)), _1200330), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1200332)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1200330), c_fconj), hAPP(c_fequal, _1200334)))), hAPP(c_fequal, _1200336)))) = hAPP(hAPP(c_Product__Type_OPair(_1200330, _1200332), _1200334), _1200336))], (23848 ^ _779308) ^ [_1200436, _1200438, _1200440] : [-(c_HOL_OThe(tc_prod(_1200436, _1200438), _1200440) = c_HOL_OThe(tc_prod(_1200436, _1200438), hAPP(c_Product__Type_Oprod_Oprod__case(_1200436, _1200438, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1200438, tc_prod(_1200436, _1200438)), tc_fun(_1200438, tc_HOL_Obool), _1200436), hAPP(c_COMBB(tc_prod(_1200436, _1200438), tc_HOL_Obool, _1200438), _1200440)), c_Product__Type_OPair(_1200436, _1200438)))))], (23850 ^ _779308) ^ [_1200514, _1200516, _1200518] : [-(c_Fun_Oinj__on(tc_prod(_1200514, _1200516), tc_prod(_1200516, _1200514), hAPP(c_Product__Type_Oprod_Oprod__case(_1200514, _1200516, tc_prod(_1200516, _1200514)), hAPP(c_COMBC(_1200516, _1200514, tc_prod(_1200516, _1200514)), c_Product__Type_OPair(_1200516, _1200514))), _1200518))], (23852 ^ _779308) ^ [_1200572, _1200574, _1200576, _1200578, _1200580, _1200582, _1200584, _1200586] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1200572, _1200574, _1200576), _1200578), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1200580, _1200582, tc_prod(_1200572, _1200574)), _1200584), _1200586)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1200580, _1200582, _1200576), hAPP(hAPP(c_COMBB(tc_fun(_1200582, tc_prod(_1200572, _1200574)), tc_fun(_1200582, _1200576), _1200580), hAPP(c_COMBB(tc_prod(_1200572, _1200574), _1200576, _1200582), hAPP(c_Product__Type_Oprod_Oprod__case(_1200572, _1200574, _1200576), _1200578))), _1200584)), _1200586))], (23854 ^ _779308) ^ [_1200687, _1200689] : [23855 ^ _779308 : [(23856 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1200687), _1200689)))], (23858 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1200689), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1200687, _1200689) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1200687), _1200689)))], (23862 ^ _779308) ^ [_1200846, _1200848] : [-(c_Divides_OnegDivAlg(_1200846, _1200848) = hAPP(c_Divides_Oadjust(_1200848), c_Divides_OnegDivAlg(_1200846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1200848)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1200846), _1200848)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1200848), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23872 ^ _779308) ^ [_1200918, _1200920] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200918)), 23875 ^ _779308 : [(23876 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1200920), _1200918))), -(c_Divides_OnegDivAlg(_1200920, _1200918) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1200920), _1200918)))], (23882 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1200920), _1200918)))), -(c_Divides_OnegDivAlg(_1200920, _1200918) = hAPP(c_Divides_Oadjust(_1200918), c_Divides_OnegDivAlg(_1200920, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1200918))))]]], (23888 ^ _779308) ^ [_1201182, _1201184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201182))), 23891 ^ _779308 : [(23892 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201184)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201182)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201184), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201182)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201184)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201182))))], (23898 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201184)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201182))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201184), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201182)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201182)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201184), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1201182)))))]]], (23904 ^ _779308) ^ [_1201554, _1201556, _1201558, _1201560, _1201562] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1201554, _1201556, _1201558), _1201560), _1201562)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1201554, _1201556)), hAPP(hAPP(c_Product__Type_OPair(_1201554, _1201556), _1201560), _1201562)), _1201558)))], (23910 ^ _779308) ^ [_1201689, _1201691, _1201693, _1201695, _1201697] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1201689, _1201691)), hAPP(hAPP(c_Product__Type_OPair(_1201689, _1201691), _1201695), _1201697)), _1201693)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1201689, _1201691, _1201693), _1201695), _1201697)))], (23916 ^ _779308) ^ [_1201830, _1201832] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1201830, _1201832) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1201830), _1201832)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1201830, _1201832)))], (23918 ^ _779308) ^ [_1201874, _1201876, _1201878, _1201880] : [class_Fields_Olinordered__field__inverse__zero(_1201874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1201874), _1201876), _1201878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1201874), _1201880), c_Groups_Ozero__class_Ozero(_1201874))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201874), c_Groups_Ozero__class_Ozero(_1201874)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201874), _1201876), _1201878))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1201874), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1201874), _1201880), _1201876)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1201874), _1201880), _1201878))))], (23936 ^ _779308) ^ [_1202233, _1202235, _1202237, _1202239] : [class_Fields_Olinordered__field(_1202233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202233), _1202235), _1202237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202233), c_Groups_Ozero__class_Ozero(_1202233)), _1202239)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202233), c_Groups_Ozero__class_Ozero(_1202233)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202233), _1202237), _1202235))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202233), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202233), _1202239), _1202237)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202233), _1202239), _1202235))))], (23954 ^ _779308) ^ [_1202592, _1202594, _1202596, _1202598] : [class_Fields_Olinordered__field(_1202592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1202592), _1202594), c_Groups_Ozero__class_Ozero(_1202592))), 23961 ^ _779308 : [(23962 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202592), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202592), _1202596), _1202594)), _1202598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202592), _1202598), _1202594)), _1202596)))], (23968 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202592), _1202598), _1202594)), _1202596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1202592), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202592), _1202596), _1202594)), _1202598)))]]], (23974 ^ _779308) ^ [_1202973, _1202975, _1202977, _1202979, _1202981] : [class_Fields_Ofield__inverse__zero(_1202973), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202973), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202973), _1202975), _1202977)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202973), _1202979), _1202981)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1202973), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202973), _1202975), _1202979)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202973), _1202977), _1202981)))], (23980 ^ _779308) ^ [_1203150, _1203152, _1203154] : [class_Fields_Ofield__inverse__zero(_1203150), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203150), hAPP(c_Groups_Ouminus__class_Ouminus(_1203150), _1203152)), hAPP(c_Groups_Ouminus__class_Ouminus(_1203150), _1203154)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203150), _1203152), _1203154))], (23986 ^ _779308) ^ [_1203279, _1203281, _1203283] : [class_Fields_Ofield__inverse__zero(_1203279), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1203279), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203279), _1203281), _1203283)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203279), _1203281), hAPP(c_Groups_Ouminus__class_Ouminus(_1203279), _1203283)))], (23992 ^ _779308) ^ [_1203408, _1203410, _1203412, _1203414] : [class_Fields_Olinordered__field__inverse__zero(_1203408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203408), _1203410), _1203412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203408), _1203414), c_Groups_Ozero__class_Ozero(_1203408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203408), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203408), _1203412), _1203414)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203408), _1203410), _1203414))))], (24006 ^ _779308) ^ [_1203677, _1203679, _1203681, _1203683] : [class_Fields_Olinordered__field__inverse__zero(_1203677), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203677), _1203679), _1203681)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203677), c_Groups_Ozero__class_Ozero(_1203677)), _1203683)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203677), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203677), _1203679), _1203683)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203677), _1203681), _1203683))))], (24020 ^ _779308) ^ [_1203946, _1203948, _1203950] : [class_Fields_Olinordered__field__inverse__zero(_1203946), 24023 ^ _779308 : [(24024 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203946), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203946), _1203948), _1203950)), c_Groups_Ozero__class_Ozero(_1203946))), 24029 ^ _779308 : [(24030 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203946), c_Groups_Ozero__class_Ozero(_1203946)), _1203948)))], (24032 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203946), _1203950), c_Groups_Ozero__class_Ozero(_1203946))))]], 24033 ^ _779308 : [(24034 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203946), _1203948), c_Groups_Ozero__class_Ozero(_1203946))))], (24036 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203946), c_Groups_Ozero__class_Ozero(_1203946)), _1203950)))]]], (24038 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203946), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1203946), _1203948), _1203950)), c_Groups_Ozero__class_Ozero(_1203946)))), 24039 ^ _779308 : [(24040 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203946), c_Groups_Ozero__class_Ozero(_1203946)), _1203948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203946), _1203950), c_Groups_Ozero__class_Ozero(_1203946)))], (24046 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203946), _1203948), c_Groups_Ozero__class_Ozero(_1203946))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1203946), c_Groups_Ozero__class_Ozero(_1203946)), _1203950))]]]]], (24054 ^ _779308) ^ [_1204536, _1204538, _1204540] : [class_Fields_Olinordered__field__inverse__zero(_1204536), 24057 ^ _779308 : [(24058 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204536), c_Groups_Ozero__class_Ozero(_1204536)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1204536), _1204538), _1204540))), 24063 ^ _779308 : [(24064 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204536), c_Groups_Ozero__class_Ozero(_1204536)), _1204538)))], (24066 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204536), c_Groups_Ozero__class_Ozero(_1204536)), _1204540)))]], 24067 ^ _779308 : [(24068 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204536), _1204538), c_Groups_Ozero__class_Ozero(_1204536))))], (24070 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204536), _1204540), c_Groups_Ozero__class_Ozero(_1204536))))]]], (24072 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204536), c_Groups_Ozero__class_Ozero(_1204536)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1204536), _1204538), _1204540)))), 24073 ^ _779308 : [(24074 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204536), c_Groups_Ozero__class_Ozero(_1204536)), _1204538)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204536), c_Groups_Ozero__class_Ozero(_1204536)), _1204540))], (24080 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204536), _1204538), c_Groups_Ozero__class_Ozero(_1204536))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204536), _1204540), c_Groups_Ozero__class_Ozero(_1204536)))]]]]], (24088 ^ _779308) ^ [_1205126, _1205128, _1205130, _1205132] : [class_Fields_Olinordered__field(_1205126), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205126), _1205128), _1205130)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205126), _1205132), c_Groups_Ozero__class_Ozero(_1205126))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205126), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205126), _1205130), _1205132)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205126), _1205128), _1205132))))], (24102 ^ _779308) ^ [_1205395, _1205397, _1205399, _1205401] : [class_Fields_Olinordered__field(_1205395), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205395), _1205397), _1205399)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205395), c_Groups_Ozero__class_Ozero(_1205395)), _1205401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205395), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205395), _1205397), _1205401)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205395), _1205399), _1205401))))], (24116 ^ _779308) ^ [_1205664, _1205666, _1205668] : [class_Fields_Olinordered__field(_1205664), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205664), _1205666), c_Groups_Ozero__class_Ozero(_1205664))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205664), _1205668), c_Groups_Ozero__class_Ozero(_1205664))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205664), c_Groups_Ozero__class_Ozero(_1205664)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205664), _1205666), _1205668))))], (24130 ^ _779308) ^ [_1205919, _1205921, _1205923] : [class_Fields_Olinordered__field(_1205919), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205919), _1205921), c_Groups_Ozero__class_Ozero(_1205919))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205919), c_Groups_Ozero__class_Ozero(_1205919)), _1205923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205919), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1205919), _1205921), _1205923)), c_Groups_Ozero__class_Ozero(_1205919))))], (24144 ^ _779308) ^ [_1206174, _1206176, _1206178] : [class_Fields_Olinordered__field(_1206174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206174), c_Groups_Ozero__class_Ozero(_1206174)), _1206176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206174), _1206178), c_Groups_Ozero__class_Ozero(_1206174))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206174), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1206174), _1206176), _1206178)), c_Groups_Ozero__class_Ozero(_1206174))))], (24158 ^ _779308) ^ [_1206429, _1206431, _1206433] : [class_Fields_Olinordered__field(_1206429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206429), c_Groups_Ozero__class_Ozero(_1206429)), _1206431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206429), c_Groups_Ozero__class_Ozero(_1206429)), _1206433)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206429), c_Groups_Ozero__class_Ozero(_1206429)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1206429), _1206431), _1206433))))], (24172 ^ _779308) ^ [_1206684, _1206686, _1206688] : [class_Fields_Olinordered__field__inverse__zero(_1206684), 24175 ^ _779308 : [(24176 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206684), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1206684), _1206686), _1206688)), c_Groups_Ozero__class_Ozero(_1206684))), 24181 ^ _779308 : [(24182 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206684), c_Groups_Ozero__class_Ozero(_1206684)), _1206686)))], (24184 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206684), _1206688), c_Groups_Ozero__class_Ozero(_1206684))))]], 24185 ^ _779308 : [(24186 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206684), _1206686), c_Groups_Ozero__class_Ozero(_1206684))))], (24188 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206684), c_Groups_Ozero__class_Ozero(_1206684)), _1206688)))]]], (24190 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206684), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1206684), _1206686), _1206688)), c_Groups_Ozero__class_Ozero(_1206684)))), 24191 ^ _779308 : [(24192 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206684), c_Groups_Ozero__class_Ozero(_1206684)), _1206686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206684), _1206688), c_Groups_Ozero__class_Ozero(_1206684)))], (24198 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206684), _1206686), c_Groups_Ozero__class_Ozero(_1206684))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206684), c_Groups_Ozero__class_Ozero(_1206684)), _1206688))]]]]], (24206 ^ _779308) ^ [_1207274, _1207276, _1207278] : [class_Fields_Olinordered__field__inverse__zero(_1207274), 24209 ^ _779308 : [(24210 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207274), c_Groups_Ozero__class_Ozero(_1207274)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1207274), _1207276), _1207278))), 24215 ^ _779308 : [(24216 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207274), c_Groups_Ozero__class_Ozero(_1207274)), _1207276)))], (24218 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207274), c_Groups_Ozero__class_Ozero(_1207274)), _1207278)))]], 24219 ^ _779308 : [(24220 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207274), _1207276), c_Groups_Ozero__class_Ozero(_1207274))))], (24222 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207274), _1207278), c_Groups_Ozero__class_Ozero(_1207274))))]]], (24224 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207274), c_Groups_Ozero__class_Ozero(_1207274)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1207274), _1207276), _1207278)))), 24225 ^ _779308 : [(24226 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207274), c_Groups_Ozero__class_Ozero(_1207274)), _1207276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207274), c_Groups_Ozero__class_Ozero(_1207274)), _1207278))], (24232 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207274), _1207276), c_Groups_Ozero__class_Ozero(_1207274))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207274), _1207278), c_Groups_Ozero__class_Ozero(_1207274)))]]]]], (24240 ^ _779308) ^ [_1207864, _1207866, _1207868, _1207870] : [class_Fields_Ofield__inverse__zero(_1207864), 24243 ^ _779308 : [(24260 ^ _779308) ^ [] : [-(_1207866 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1207864), _1207868), _1207870)), 24263 ^ _779308 : [(24264 ^ _779308) ^ [] : [_1207870 = c_Groups_Ozero__class_Ozero(_1207864)], (24266 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207864), _1207866), _1207870) = _1207868]], 24267 ^ _779308 : [(24268 ^ _779308) ^ [] : [-(_1207870 = c_Groups_Ozero__class_Ozero(_1207864))], (24270 ^ _779308) ^ [] : [_1207866 = c_Groups_Ozero__class_Ozero(_1207864)]]], (24244 ^ _779308) ^ [] : [_1207866 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1207864), _1207868), _1207870), 24247 ^ _779308 : [(24248 ^ _779308) ^ [] : [-(_1207870 = c_Groups_Ozero__class_Ozero(_1207864)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207864), _1207866), _1207870) = _1207868)], (24254 ^ _779308) ^ [] : [_1207870 = c_Groups_Ozero__class_Ozero(_1207864), -(_1207866 = c_Groups_Ozero__class_Ozero(_1207864))]]]]], (24274 ^ _779308) ^ [_1208358, _1208360, _1208362, _1208364] : [class_Fields_Ofield__inverse__zero(_1208358), 24277 ^ _779308 : [(24294 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1208358), _1208360), _1208362) = _1208364), 24297 ^ _779308 : [(24298 ^ _779308) ^ [] : [_1208362 = c_Groups_Ozero__class_Ozero(_1208358)], (24300 ^ _779308) ^ [] : [_1208360 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208358), _1208364), _1208362)]], 24301 ^ _779308 : [(24302 ^ _779308) ^ [] : [-(_1208362 = c_Groups_Ozero__class_Ozero(_1208358))], (24304 ^ _779308) ^ [] : [_1208364 = c_Groups_Ozero__class_Ozero(_1208358)]]], (24278 ^ _779308) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1208358), _1208360), _1208362) = _1208364, 24281 ^ _779308 : [(24282 ^ _779308) ^ [] : [-(_1208362 = c_Groups_Ozero__class_Ozero(_1208358)), -(_1208360 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208358), _1208364), _1208362))], (24288 ^ _779308) ^ [] : [_1208362 = c_Groups_Ozero__class_Ozero(_1208358), -(_1208364 = c_Groups_Ozero__class_Ozero(_1208358))]]]]], (24308 ^ _779308) ^ [_1208852, _1208854, _1208856, _1208858] : [class_Fields_Ofield__inverse__zero(_1208852), -(_1208854 = c_Groups_Ozero__class_Ozero(_1208852)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1208852), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208852), _1208856), _1208854)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208852), _1208858), _1208854)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1208852), _1208856), _1208858))], (24318 ^ _779308) ^ [_1209014, _1209016, _1209018, _1209020] : [class_Fields_Ofield__inverse__zero(_1209014), -(_1209016 = c_Groups_Ozero__class_Ozero(_1209014)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209014), _1209016), _1209018)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209014), _1209016), _1209020)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209014), _1209018), _1209020))], (24328 ^ _779308) ^ [_1209176, _1209178, _1209180, _1209182, _1209184] : [class_Fields_Ofield(_1209176), -(_1209178 = c_Groups_Ozero__class_Ozero(_1209176)), -(_1209180 = c_Groups_Ozero__class_Ozero(_1209176)), 24339 ^ _779308 : [(24340 ^ _779308) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209176), _1209182), _1209178) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209176), _1209184), _1209180), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209176), _1209182), _1209180) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209176), _1209184), _1209178))], (24346 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209176), _1209182), _1209180) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209176), _1209184), _1209178), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209176), _1209182), _1209178) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209176), _1209184), _1209180))]]], (24352 ^ _779308) ^ [_1209625, _1209627, _1209629] : [class_Fields_Olinordered__field(_1209625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209625), _1209627), c_Groups_Ozero__class_Ozero(_1209625))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209625), _1209629), c_Groups_Ozero__class_Ozero(_1209625))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209625), c_Groups_Ozero__class_Ozero(_1209625)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209625), _1209627), _1209629))))], (24366 ^ _779308) ^ [_1209880, _1209882, _1209884] : [class_Fields_Olinordered__field(_1209880), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209880), _1209882), c_Groups_Ozero__class_Ozero(_1209880))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1209880), c_Groups_Ozero__class_Ozero(_1209880)), _1209884)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1209880), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1209880), _1209882), _1209884)), c_Groups_Ozero__class_Ozero(_1209880))))], (24380 ^ _779308) ^ [_1210135, _1210137, _1210139, _1210141, _1210143] : [class_Fields_Olinordered__field(_1210135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210135), c_Groups_Ozero__class_Ozero(_1210135)), _1210137)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210135), _1210137), _1210139)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210135), c_Groups_Ozero__class_Ozero(_1210135)), _1210141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210135), _1210141), _1210143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210135), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210135), _1210137), _1210143)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210135), _1210139), _1210141))))], (24402 ^ _779308) ^ [_1210558, _1210560, _1210562, _1210564, _1210566] : [class_Fields_Olinordered__field(_1210558), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210558), c_Groups_Ozero__class_Ozero(_1210558)), _1210560)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210558), _1210560), _1210562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210558), c_Groups_Ozero__class_Ozero(_1210558)), _1210564)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210558), _1210564), _1210566)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210558), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210558), _1210560), _1210566)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210558), _1210562), _1210564))))], (24424 ^ _779308) ^ [_1210981, _1210983, _1210985, _1210987, _1210989] : [class_Fields_Olinordered__field(_1210981), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210981), c_Groups_Ozero__class_Ozero(_1210981)), _1210983)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210981), _1210983), _1210985)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210981), c_Groups_Ozero__class_Ozero(_1210981)), _1210987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210981), _1210987), _1210989)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1210981), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210981), _1210983), _1210989)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1210981), _1210985), _1210987))))], (24446 ^ _779308) ^ [_1211404, _1211406, _1211408] : [class_Fields_Olinordered__field(_1211404), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211404), c_Groups_Ozero__class_Ozero(_1211404)), _1211406)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211404), _1211408), c_Groups_Ozero__class_Ozero(_1211404))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211404), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1211404), _1211406), _1211408)), c_Groups_Ozero__class_Ozero(_1211404))))], (24460 ^ _779308) ^ [_1211659, _1211661, _1211663] : [class_Fields_Olinordered__field(_1211659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211659), c_Groups_Ozero__class_Ozero(_1211659)), _1211661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211659), c_Groups_Ozero__class_Ozero(_1211659)), _1211663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211659), c_Groups_Ozero__class_Ozero(_1211659)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1211659), _1211661), _1211663))))], (24474 ^ _779308) ^ [_1211914, _1211916, _1211918, _1211920] : [class_Fields_Olinordered__field(_1211914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211914), _1211916), _1211918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211914), _1211920), c_Groups_Ozero__class_Ozero(_1211914))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211914), c_Groups_Ozero__class_Ozero(_1211914)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1211914), _1211916), _1211918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211914), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1211914), _1211920), _1211916)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1211914), _1211920), _1211918))))], (24492 ^ _779308) ^ [_1212273, _1212275, _1212277, _1212279] : [class_Fields_Olinordered__field(_1212273), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212273), _1212275), _1212277)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212273), c_Groups_Ozero__class_Ozero(_1212273)), _1212279)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212273), c_Groups_Ozero__class_Ozero(_1212273)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212273), _1212277), _1212275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212273), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1212273), _1212279), _1212277)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1212273), _1212279), _1212275))))], (24510 ^ _779308) ^ [_1212632, _1212634, _1212636, _1212638] : [class_Fields_Olinordered__field(_1212632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212632), _1212634), c_Groups_Ozero__class_Ozero(_1212632))), 24517 ^ _779308 : [(24518 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212632), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1212632), _1212636), _1212634)), _1212638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212632), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212632), _1212638), _1212634)), _1212636)))], (24524 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212632), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212632), _1212638), _1212634)), _1212636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1212632), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1212632), _1212636), _1212634)), _1212638)))]]], (24530 ^ _779308) ^ [_1213013, _1213015, _1213017, _1213019] : [class_Fields_Olinordered__field(_1213013), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213013), _1213015), c_Groups_Ozero__class_Ozero(_1213013))), 24537 ^ _779308 : [(24538 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213013), _1213017), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213013), _1213019), _1213015))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213013), _1213019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213013), _1213017), _1213015))))], (24544 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213013), _1213019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213013), _1213017), _1213015))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213013), _1213017), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213013), _1213019), _1213015))))]]], (24550 ^ _779308) ^ [_1213394, _1213396, _1213398, _1213400] : [class_Fields_Olinordered__field(_1213394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213394), c_Groups_Ozero__class_Ozero(_1213394)), _1213396)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213394), _1213398), _1213396)), _1213400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213394), _1213398), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213394), _1213400), _1213396))))], (24564 ^ _779308) ^ [_1213663, _1213665, _1213667, _1213669] : [class_Fields_Olinordered__field(_1213663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213663), c_Groups_Ozero__class_Ozero(_1213663)), _1213665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213663), _1213667), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213663), _1213669), _1213665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213663), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213663), _1213667), _1213665)), _1213669)))], (24578 ^ _779308) ^ [_1213932, _1213934, _1213936, _1213938] : [class_Fields_Olinordered__field(_1213932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213932), c_Groups_Ozero__class_Ozero(_1213932)), _1213934)), 24585 ^ _779308 : [(24586 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213932), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213932), _1213936), _1213934)), _1213938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213932), _1213936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213932), _1213938), _1213934))))], (24592 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213932), _1213936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213932), _1213938), _1213934))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213932), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1213932), _1213936), _1213934)), _1213938)))]]], (24598 ^ _779308) ^ [_1214313, _1214315, _1214317, _1214319] : [class_Fields_Olinordered__field(_1214313), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214313), c_Groups_Ozero__class_Ozero(_1214313)), _1214315)), 24605 ^ _779308 : [(24606 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214313), _1214317), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214313), _1214319), _1214315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214313), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214313), _1214317), _1214315)), _1214319)))], (24612 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214313), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214313), _1214317), _1214315)), _1214319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214313), _1214317), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214313), _1214319), _1214315))))]]], (24618 ^ _779308) ^ [_1214694, _1214696, _1214698, _1214700] : [class_Fields_Olinordered__field__inverse__zero(_1214694), 24621 ^ _779308 : [(24648 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214694), _1214696), _1214698)), _1214700))), 24651 ^ _779308 : [(24652 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), c_Groups_Ozero__class_Ozero(_1214694)), _1214698)))], (24654 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), _1214696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214694), _1214700), _1214698)))]], 24655 ^ _779308 : [(24656 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), c_Groups_Ozero__class_Ozero(_1214694)), _1214698))], (24658 ^ _779308) ^ [] : [24659 ^ _779308 : [(24660 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), _1214698), c_Groups_Ozero__class_Ozero(_1214694))))], (24662 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214694), _1214700), _1214698)), _1214696))]], 24663 ^ _779308 : [(24664 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), _1214698), c_Groups_Ozero__class_Ozero(_1214694)))], (24666 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), c_Groups_Ozero__class_Ozero(_1214694)), _1214700))]]]]], (24622 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1214694), _1214696), _1214698)), _1214700)), 24625 ^ _779308 : [(24626 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), c_Groups_Ozero__class_Ozero(_1214694)), _1214698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), _1214696), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214694), _1214700), _1214698))))], (24632 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), c_Groups_Ozero__class_Ozero(_1214694)), _1214698))), 24635 ^ _779308 : [(24636 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), _1214698), c_Groups_Ozero__class_Ozero(_1214694))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214694), _1214700), _1214698)), _1214696)))], (24642 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), _1214698), c_Groups_Ozero__class_Ozero(_1214694)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214694), c_Groups_Ozero__class_Ozero(_1214694)), _1214700)))]]]]]]], (24670 ^ _779308) ^ [_1215647, _1215649, _1215651, _1215653] : [class_Fields_Olinordered__field__inverse__zero(_1215647), 24673 ^ _779308 : [(24700 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), _1215649), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1215647), _1215651), _1215653)))), 24703 ^ _779308 : [(24704 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), c_Groups_Ozero__class_Ozero(_1215647)), _1215653)))], (24706 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215647), _1215649), _1215653)), _1215651))]], 24707 ^ _779308 : [(24708 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), c_Groups_Ozero__class_Ozero(_1215647)), _1215653))], (24710 ^ _779308) ^ [] : [24711 ^ _779308 : [(24712 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), _1215653), c_Groups_Ozero__class_Ozero(_1215647))))], (24714 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), _1215651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215647), _1215649), _1215653)))]], 24715 ^ _779308 : [(24716 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), _1215653), c_Groups_Ozero__class_Ozero(_1215647)))], (24718 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), _1215649), c_Groups_Ozero__class_Ozero(_1215647)))]]]]], (24674 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), _1215649), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1215647), _1215651), _1215653))), 24677 ^ _779308 : [(24678 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), c_Groups_Ozero__class_Ozero(_1215647)), _1215653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215647), _1215649), _1215653)), _1215651)))], (24684 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), c_Groups_Ozero__class_Ozero(_1215647)), _1215653))), 24687 ^ _779308 : [(24688 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), _1215653), c_Groups_Ozero__class_Ozero(_1215647))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), _1215651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215647), _1215649), _1215653))))], (24694 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), _1215653), c_Groups_Ozero__class_Ozero(_1215647)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215647), _1215649), c_Groups_Ozero__class_Ozero(_1215647))))]]]]]]], (24722 ^ _779308) ^ [_1216600, _1216602, _1216604, _1216606] : [class_Fields_Ofield__inverse__zero(_1216600), -(_1216602 = c_Groups_Ozero__class_Ozero(_1216600)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216600), _1216604), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216600), _1216606), _1216602)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216600), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216600), _1216606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216600), _1216604), _1216602))), _1216602))], (24732 ^ _779308) ^ [_1216778, _1216780, _1216782, _1216784] : [class_Fields_Ofield(_1216778), -(_1216780 = c_Groups_Ozero__class_Ozero(_1216778)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216778), _1216782), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216778), _1216784), _1216780)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216778), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216778), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216778), _1216780), _1216782)), _1216784)), _1216780))], (24742 ^ _779308) ^ [_1216956, _1216958, _1216960, _1216962] : [class_Fields_Ofield__inverse__zero(_1216956), -(_1216958 = c_Groups_Ozero__class_Ozero(_1216956)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216956), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216956), _1216960), _1216958)), _1216962) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216956), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1216956), _1216960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216956), _1216962), _1216958))), _1216958))], (24752 ^ _779308) ^ [_1217134, _1217136, _1217138, _1217140] : [class_Fields_Ofield(_1217134), -(_1217136 = c_Groups_Ozero__class_Ozero(_1217134)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217134), _1217138), _1217136)), _1217140) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217134), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217134), _1217138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217134), _1217136), _1217140))), _1217136))], (24762 ^ _779308) ^ [_1217312, _1217314, _1217316, _1217318, _1217320] : [class_Fields_Ofield(_1217312), -(_1217314 = c_Groups_Ozero__class_Ozero(_1217312)), -(_1217316 = c_Groups_Ozero__class_Ozero(_1217312)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217312), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217312), _1217318), _1217314)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217312), _1217320), _1217316)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217312), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217312), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217312), _1217318), _1217316)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217312), _1217320), _1217314))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217312), _1217314), _1217316)))], (24776 ^ _779308) ^ [_1217559, _1217561, _1217563, _1217565] : [class_Fields_Ofield(_1217559), -(_1217561 = c_Groups_Ozero__class_Ozero(_1217559)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1217559), _1217563), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217559), _1217565), _1217561)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217559), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1217559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217559), _1217561), _1217563)), _1217565)), _1217561))], (24786 ^ _779308) ^ [_1217737, _1217739, _1217741, _1217743] : [class_Fields_Ofield(_1217737), -(_1217739 = c_Groups_Ozero__class_Ozero(_1217737)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1217737), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217737), _1217741), _1217739)), _1217743) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217737), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1217737), _1217741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217737), _1217739), _1217743))), _1217739))], (24796 ^ _779308) ^ [_1217915, _1217917, _1217919, _1217921, _1217923] : [class_Fields_Ofield(_1217915), -(_1217917 = c_Groups_Ozero__class_Ozero(_1217915)), -(_1217919 = c_Groups_Ozero__class_Ozero(_1217915)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1217915), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217915), _1217921), _1217917)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217915), _1217923), _1217919)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1217915), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1217915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217915), _1217921), _1217919)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217915), _1217923), _1217917))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217915), _1217917), _1217919)))], (24810 ^ _779308) ^ [_1218162, _1218164, _1218166] : [class_Fields_Olinordered__field(_1218162), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218162), _1218164), _1218166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218162), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218162), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218162), _1218164), _1218166)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218162), c_Groups_Oone__class_Oone(_1218162)), c_Groups_Oone__class_Oone(_1218162)))), _1218166)))], (24820 ^ _779308) ^ [_1218377, _1218379, _1218381] : [class_Fields_Olinordered__field(_1218377), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218377), _1218379), _1218381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218377), _1218379), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218377), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218377), _1218379), _1218381)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218377), c_Groups_Oone__class_Oone(_1218377)), c_Groups_Oone__class_Oone(_1218377))))))], (24830 ^ _779308) ^ [_1218592, _1218594, _1218596, _1218598] : [class_Fields_Olinordered__field__inverse__zero(_1218592), 24833 ^ _779308 : [(24860 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218592), _1218594), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218592), _1218596), _1218598)))), 24863 ^ _779308 : [(24864 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218592), c_Groups_Ozero__class_Ozero(_1218592)), _1218598)))], (24866 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218592), _1218594), _1218598)), _1218596))]], 24867 ^ _779308 : [(24868 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218592), c_Groups_Ozero__class_Ozero(_1218592)), _1218598))], (24870 ^ _779308) ^ [] : [24871 ^ _779308 : [(24872 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218592), _1218598), c_Groups_Ozero__class_Ozero(_1218592))))], (24874 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218592), _1218596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218592), _1218594), _1218598)))]], 24875 ^ _779308 : [(24876 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218592), _1218598), c_Groups_Ozero__class_Ozero(_1218592)))], (24878 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218592), _1218594), c_Groups_Ozero__class_Ozero(_1218592)))]]]]], (24834 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218592), _1218594), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1218592), _1218596), _1218598))), 24837 ^ _779308 : [(24838 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218592), c_Groups_Ozero__class_Ozero(_1218592)), _1218598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218592), _1218594), _1218598)), _1218596)))], (24844 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218592), c_Groups_Ozero__class_Ozero(_1218592)), _1218598))), 24847 ^ _779308 : [(24848 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218592), _1218598), c_Groups_Ozero__class_Ozero(_1218592))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218592), _1218596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218592), _1218594), _1218598))))], (24854 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218592), _1218598), c_Groups_Ozero__class_Ozero(_1218592)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218592), _1218594), c_Groups_Ozero__class_Ozero(_1218592))))]]]]]]], (24882 ^ _779308) ^ [_1219545, _1219547, _1219549, _1219551] : [class_Fields_Olinordered__field__inverse__zero(_1219545), 24885 ^ _779308 : [(24912 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219545), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219545), _1219547), _1219549)), _1219551))), 24915 ^ _779308 : [(24916 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219545), c_Groups_Ozero__class_Ozero(_1219545)), _1219549)))], (24918 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219545), _1219547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219545), _1219551), _1219549)))]], 24919 ^ _779308 : [(24920 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219545), c_Groups_Ozero__class_Ozero(_1219545)), _1219549))], (24922 ^ _779308) ^ [] : [24923 ^ _779308 : [(24924 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219545), _1219549), c_Groups_Ozero__class_Ozero(_1219545))))], (24926 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219545), _1219551), _1219549)), _1219547))]], 24927 ^ _779308 : [(24928 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219545), _1219549), c_Groups_Ozero__class_Ozero(_1219545)))], (24930 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219545), c_Groups_Ozero__class_Ozero(_1219545)), _1219551))]]]]], (24886 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219545), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219545), _1219547), _1219549)), _1219551)), 24889 ^ _779308 : [(24890 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219545), c_Groups_Ozero__class_Ozero(_1219545)), _1219549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219545), _1219547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219545), _1219551), _1219549))))], (24896 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219545), c_Groups_Ozero__class_Ozero(_1219545)), _1219549))), 24899 ^ _779308 : [(24900 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219545), _1219549), c_Groups_Ozero__class_Ozero(_1219545))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1219545), _1219551), _1219549)), _1219547)))], (24906 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219545), _1219549), c_Groups_Ozero__class_Ozero(_1219545)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219545), c_Groups_Ozero__class_Ozero(_1219545)), _1219551)))]]]]]]], (24934 ^ _779308) ^ [_1220498, _1220500, _1220502, _1220504] : [class_Fields_Olinordered__field(_1220498), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220498), c_Groups_Ozero__class_Ozero(_1220498)), _1220500)), 24941 ^ _779308 : [(24942 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220498), _1220502), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220498), _1220504), _1220500))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220498), _1220502), _1220500)), _1220504)))], (24948 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220498), _1220502), _1220500)), _1220504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220498), _1220502), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220498), _1220504), _1220500))))]]], (24954 ^ _779308) ^ [_1220879, _1220881, _1220883, _1220885] : [class_Fields_Olinordered__field(_1220879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220879), c_Groups_Ozero__class_Ozero(_1220879)), _1220881)), 24961 ^ _779308 : [(24962 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220879), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220879), _1220883), _1220881)), _1220885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220879), _1220883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220879), _1220885), _1220881))))], (24968 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220879), _1220883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1220879), _1220885), _1220881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220879), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1220879), _1220883), _1220881)), _1220885)))]]], (24974 ^ _779308) ^ [_1221260, _1221262, _1221264, _1221266] : [class_Fields_Olinordered__field(_1221260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221260), c_Groups_Ozero__class_Ozero(_1221260)), _1221262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221260), _1221264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221260), _1221266), _1221262))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221260), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221260), _1221264), _1221262)), _1221266)))], (24988 ^ _779308) ^ [_1221529, _1221531, _1221533, _1221535] : [class_Fields_Olinordered__field(_1221529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221529), c_Groups_Ozero__class_Ozero(_1221529)), _1221531)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221529), _1221533), _1221531)), _1221535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221529), _1221533), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221529), _1221535), _1221531))))], (25002 ^ _779308) ^ [_1221798, _1221800, _1221802, _1221804] : [class_Fields_Olinordered__field(_1221798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221798), _1221800), c_Groups_Ozero__class_Ozero(_1221798))), 25009 ^ _779308 : [(25010 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221798), _1221802), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221798), _1221804), _1221800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221798), _1221804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221798), _1221802), _1221800))))], (25016 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221798), _1221804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221798), _1221802), _1221800))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221798), _1221802), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221798), _1221804), _1221800))))]]], (25022 ^ _779308) ^ [_1222194, _1222196] : [c_Nitpick_Orefl_H(_1222194, _1222196), 25025 ^ _779308 : [(25026 ^ _779308) ^ [_1222272] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1222194, _1222194)), hAPP(hAPP(c_Product__Type_OPair(_1222194, _1222194), _1222272), _1222272)), _1222196)))]]], (25028 ^ _779308) ^ [_1222314, _1222316] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1222314, _1222314)), hAPP(hAPP(c_Product__Type_OPair(_1222314, _1222314), 25029 ^ [_1222314, _1222316]), 25029 ^ [_1222314, _1222316])), _1222316)), -(c_Nitpick_Orefl_H(_1222314, _1222316))], (25035 ^ _779308) ^ [_1222481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222481))), 25038 ^ _779308 : [(25039 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222481))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222481)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25045 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222481)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222481)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222481)), c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1222481)))))]]], (25051 ^ _779308) ^ [_1222750, _1222752] : [25052 ^ _779308 : [(25053 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222750), _1222752))], (25055 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1222752), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1222750, _1222752) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222750))], (25059 ^ _779308) ^ [_1222891, _1222893] : [-(c_Divides_OposDivAlg(_1222891, _1222893) = hAPP(c_Divides_Oadjust(_1222893), c_Divides_OposDivAlg(_1222891, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1222893)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222891), _1222893))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1222893), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25069 ^ _779308) ^ [_1222960, _1222962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222960)), 25072 ^ _779308 : [(25073 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222962), _1222960)), -(c_Divides_OposDivAlg(_1222962, _1222960) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222962))], (25079 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222962), _1222960))), -(c_Divides_OposDivAlg(_1222962, _1222960) = hAPP(c_Divides_Oadjust(_1222960), c_Divides_OposDivAlg(_1222962, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1222960))))]]], (25085 ^ _779308) ^ [_1223200, _1223202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223200))), 25088 ^ _779308 : [(25089 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223202)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223200))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223202), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223200)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223202)))], (25095 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223202)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223200)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223202), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223200)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223200)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223202), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1223200)))))]]], (25101 ^ _779308) ^ [_1223518] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1223518) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (25103 ^ _779308) ^ [_1223544, _1223546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223546)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1223544, _1223546), c_Divides_OposDivAlg(_1223544, _1223546))))], (25113 ^ _779308) ^ [_1223697, _1223699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223697)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223699)), -(c_Divides_OposDivAlg(_1223697, _1223699) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1223697), _1223699)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1223697, _1223699)))], (25149 ^ _779308) ^ [_1224251, _1224253] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224251))), 25152 ^ _779308 : [(25153 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224253)), -(c_Divides_Odivmod__int(_1224251, _1224253) = c_Divides_OnegDivAlg(_1224251, _1224253))], (25159 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224253))), -(c_Divides_Odivmod__int(_1224251, _1224253) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1224251), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1224253))))]]], (25123 ^ _779308) ^ [_1223881, _1223883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223881)), 25126 ^ _779308 : [(25127 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223883)), -(c_Divides_Odivmod__int(_1223881, _1223883) = c_Divides_OposDivAlg(_1223881, _1223883))], (25133 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223883))), 25136 ^ _779308 : [(25137 ^ _779308) ^ [] : [_1223881 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1223881, _1223883) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (25143 ^ _779308) ^ [] : [-(_1223881 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1223881, _1223883) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1223881), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1223883))))]]]]], (25165 ^ _779308) ^ [_1224479, _1224481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1224479)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1224479), _1224481)), -(c_Divides_Odivmod__nat(_1224481, _1224479) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1224481), _1224479)), _1224479))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1224481), _1224479), _1224479)))], (25175 ^ _779308) ^ [_1224690] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1224690)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1224690)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25177 ^ _779308) ^ [_1224727, _1224729] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1224727), _1224729))), 25180 ^ _779308 : [(25181 ^ _779308) ^ [] : [25182 ^ _779308 : [(25183 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224727), _1224729)))], (25185 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224729), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1224727, _1224729) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224727), _1224729)))], (25189 ^ _779308) ^ [] : [-(c_Divides_OnegDivAlg(_1224727, _1224729) = hAPP(c_Divides_Oadjust(_1224729), c_Divides_OnegDivAlg(_1224727, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1224729)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224727), _1224729)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224729), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25199 ^ _779308) ^ [_1225074, _1225076, _1225078] : [25201 ^ _779308 : [(25202 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1225074), 25200 ^ [_1225074, _1225076, _1225078]), _1225076)))], (25204 ^ _779308) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1225078, 25200 ^ [_1225074, _1225076, _1225078]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1225074, tc_Int_Oint), _1225078), _1225076) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1225074, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1225074), c_Int_Onat), _1225078)), _1225076)))], (25208 ^ _779308) ^ [_1225304] : [-(c_Divides_Odivmod__nat(_1225304, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225304))], (25210 ^ _779308) ^ [_1225333, _1225335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1225333), _1225335)), -(c_Divides_Odivmod__nat(_1225333, _1225335) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225333))], (25216 ^ _779308) ^ [_1225432, _1225434] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1225432), _1225434)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1225432), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1225434)))], (25218 ^ _779308) ^ [_1225475, _1225477] : [-(c_Divides_Odivmod__nat(_1225475, _1225477) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1225475), _1225477)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1225475, _1225477)))], (25220 ^ _779308) ^ [_1225519, _1225521, _1225523] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1225519), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1225521)), _1225523)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1225519, _1225521), hAPP(c_Divides_OnegateSnd, _1225523))))], (25226 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25228 ^ _779308) ^ [_1225663, _1225665] : [25229 ^ _779308 : [(25230 ^ _779308) ^ [] : [_1225663 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25232 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1225665), _1225663))]], -(c_Divides_Odivmod__nat(_1225665, _1225663) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225665))], (25236 ^ _779308) ^ [_1225794, _1225796] : [-(c_Divides_Odivmod__nat(_1225796, _1225794) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat, tc_Nat_Onat, tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_prod(tc_Nat_Onat, tc_Nat_Onat)), tc_Nat_Onat), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat)), c_Nat_OSuc)), c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1225796), _1225794), _1225794))), -(_1225794 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1225796), _1225794)))], (25246 ^ _779308) ^ [_1225859, _1225861] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1225859), _1225861))), 25249 ^ _779308 : [(25250 ^ _779308) ^ [] : [25251 ^ _779308 : [(25252 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225859), _1225861))], (25254 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225861), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1225859, _1225861) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225859))], (25258 ^ _779308) ^ [] : [-(c_Divides_OposDivAlg(_1225859, _1225861) = hAPP(c_Divides_Oadjust(_1225861), c_Divides_OposDivAlg(_1225859, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1225861)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225859), _1225861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225861), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25268 ^ _779308) ^ [_1226182, _1226184] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Nitpick_Onorm__frac__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1226182), _1226184))), 25271 ^ _779308 : [(25272 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226184), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1226182, _1226184) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226182), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1226184)))], (25278 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226184), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 25281 ^ _779308 : [(25282 ^ _779308) ^ [] : [25283 ^ _779308 : [(25284 ^ _779308) ^ [] : [_1226182 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (25286 ^ _779308) ^ [] : [_1226184 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1226182, _1226184) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25290 ^ _779308) ^ [] : [-(c_Nitpick_Onorm__frac(_1226182, _1226184) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1226182), _1226184)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1226182))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1226184)))), -(_1226182 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1226184 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (25300 ^ _779308) ^ [_1226674, _1226676, _1226678] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1226674), _1226676))), -(hBOOL(hAPP(hAPP(_1226678, _1226674), _1226676))), 25307 ^ _779308 : [(25308 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 25305 ^ [_1226674, _1226676, _1226678]), 25306 ^ [_1226674, _1226676, _1226678]))))], (25320 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1226678, 25305 ^ [_1226674, _1226676, _1226678]), 25306 ^ [_1226674, _1226676, _1226678]))], (25310 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1226678, 25305 ^ [_1226674, _1226676, _1226678]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), 25306 ^ [_1226674, _1226676, _1226678])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 25305 ^ [_1226674, _1226676, _1226678]), 25306 ^ [_1226674, _1226676, _1226678])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 25306 ^ [_1226674, _1226676, _1226678]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25324 ^ _779308) ^ [_1227169, _1227171, _1227173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1227169, tc_fun(_1227169, tc_HOL_Obool))), _1227171), _1227173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1227169, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1227169, _1227173)), c_Wellfounded_Oaccp(_1227169, _1227171))))], (25330 ^ _779308) ^ [_1227306, _1227308, _1227310, _1227312, _1227314] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1227306, _1227308), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1227310), _1227312))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227308)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227314)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1227306, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227308), _1227314)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1227310), _1227314)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227308), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1227310, _1227314))), _1227312)))))], (25344 ^ _779308) ^ [_1227613, _1227615, _1227617, _1227619] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1227613, _1227615), _1227617)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1227613, _1227615), _1227619)), -(_1227617 = _1227619)], (25354 ^ _779308) ^ [_1227770, _1227772] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1227770, _1227772), c_Divides_Odivmod__nat(_1227770, _1227772))))], (25356 ^ _779308) ^ [_1227803, _1227805, _1227807] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1227803, _1227805), _1227807)), -(c_Divides_Odivmod__nat(_1227803, _1227805) = _1227807)], (25362 ^ _779308) ^ [_1227898, _1227900] : [-(c_Divides_Odivmod__nat(_1227898, _1227900) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1227898, _1227900)))], (25364 ^ _779308) ^ [_1227932, _1227934, _1227936, _1227938] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1227932, _1227934), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1227936), _1227938))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1227932, _1227934) = _1227938)], (25370 ^ _779308) ^ [_1228043, _1228045, _1228047, _1228049] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1228043, _1228045), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1228047), _1228049))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1228043), _1228045) = _1228047)], (25376 ^ _779308) ^ [_1228158, _1228160, _1228162, _1228164] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1228158, _1228160), _1228162)), hBOOL(hAPP(hAPP(_1228160, _1228164), _1228162)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1228158, _1228160), _1228164)))], (25396 ^ _779308) ^ [_1228529, _1228531, _1228533] : [25398 ^ _779308 : [(25399 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1228531, 25397 ^ [_1228529, _1228531, _1228533]), _1228533)))], (25401 ^ _779308) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1228529, _1228531), 25397 ^ [_1228529, _1228531, _1228533]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1228529, _1228531), _1228533)))], (25386 ^ _779308) ^ [_1228343, _1228345, _1228347] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1228343, _1228345), _1228347)), 25389 ^ _779308 : [(25390 ^ _779308) ^ [_1228428] : [hBOOL(hAPP(hAPP(_1228345, _1228428), _1228347)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1228343, _1228345), _1228428)))]]], (25415 ^ _779308) ^ [_1228919, _1228921, _1228923] : [25417 ^ _779308 : [(25418 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1228921, 25416 ^ [_1228919, _1228921, _1228923]), _1228923)))], (25420 ^ _779308) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1228919, _1228921), 25416 ^ [_1228919, _1228921, _1228923]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1228919, _1228921), _1228923)))], (25405 ^ _779308) ^ [_1228733, _1228735, _1228737] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1228733, _1228735), _1228737)), 25408 ^ _779308 : [(25409 ^ _779308) ^ [_1228818] : [hBOOL(hAPP(hAPP(_1228735, _1228818), _1228737)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1228733, _1228735), _1228818)))]]], (25424 ^ _779308) ^ [_1229105, _1229107] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1229105, _1229107), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1229105), _1229107)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1229105, _1229107)))))], (25426 ^ _779308) ^ [_1229151, _1229153, _1229155, _1229157, _1229159, _1229161, _1229163] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1229151, _1229153), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1229155), _1229157))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1229159, _1229153), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1229161), _1229163))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1229153)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1229151), _1229159), _1229153), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1229155), _1229161)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1229157), _1229163)), _1229153))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1229157), _1229163), _1229153)))))], (25440 ^ _779308) ^ [_1229512, _1229514, _1229516, _1229518, _1229520] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1229512, _1229514), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1229516), _1229518))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1229514)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1229520), _1229512), _1229514), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1229520), _1229516)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1229520), _1229518)), _1229514))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1229520), _1229518), _1229514)))))], (25450 ^ _779308) ^ [_1229781, _1229783, _1229785] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1229781), _1229783))), -(hBOOL(hAPP(hAPP(_1229785, _1229781), _1229783))), 25457 ^ _779308 : [(25458 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 25455 ^ [_1229781, _1229783, _1229785]), 25456 ^ [_1229781, _1229783, _1229785]))))], (25470 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1229785, 25455 ^ [_1229781, _1229783, _1229785]), 25456 ^ [_1229781, _1229783, _1229785]))], (25460 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1229785, 25455 ^ [_1229781, _1229783, _1229785]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), 25456 ^ [_1229781, _1229783, _1229785])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 25455 ^ [_1229781, _1229783, _1229785]), 25456 ^ [_1229781, _1229783, _1229785]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 25456 ^ [_1229781, _1229783, _1229785]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (25474 ^ _779308) ^ [_1230267] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1230267)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1230267)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25476 ^ _779308) ^ [_1230303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1230303)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1230303)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1230303))))))], (25482 ^ _779308) ^ [_1230459, _1230461, _1230463, _1230465] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1230459, _1230459)), hAPP(hAPP(c_Product__Type_OPair(_1230459, _1230459), _1230461), _1230463)), hAPP(c_Wellfounded_Omeasure(_1230459), _1230465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1230465, _1230461)), hAPP(_1230465, _1230463))))], (25488 ^ _779308) ^ [_1230606, _1230608, _1230610, _1230612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1230612, _1230608)), hAPP(_1230612, _1230610))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1230606, _1230606)), hAPP(hAPP(c_Product__Type_OPair(_1230606, _1230606), _1230608), _1230610)), hAPP(c_Wellfounded_Omeasure(_1230606), _1230612))))], (25494 ^ _779308) ^ [_1230759, _1230761, _1230763] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Nitpick_Onorm__frac__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1230759), _1230761))), -(hBOOL(hAPP(hAPP(_1230763, _1230759), _1230761))), 25501 ^ _779308 : [(25502 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Nitpick_Onorm__frac__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 25499 ^ [_1230759, _1230761, _1230763]), 25500 ^ [_1230759, _1230761, _1230763]))))], (25510 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1230763, 25499 ^ [_1230759, _1230761, _1230763]), 25500 ^ [_1230759, _1230761, _1230763]))], (25504 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 25500 ^ [_1230759, _1230761, _1230763]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1230763, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 25499 ^ [_1230759, _1230761, _1230763])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 25500 ^ [_1230759, _1230761, _1230763]))))]]], (25514 ^ _779308) ^ [_1231232, _1231234, _1231236, _1231238, _1231240] : [hAPP(c_Product__Type_Osnd(_1231232, _1231234), hAPP(hAPP(c_Product__Type_OPair(_1231232, _1231234), _1231236), _1231238)) = _1231240, -(_1231238 = _1231240)], (25520 ^ _779308) ^ [_1231345, _1231347, _1231349, _1231351] : [-(hAPP(c_Product__Type_Osnd(_1231345, _1231347), hAPP(hAPP(c_Product__Type_OPair(_1231345, _1231347), _1231349), _1231351)) = _1231351)], (25522 ^ _779308) ^ [_1231389, _1231391, _1231393] : [-(hAPP(c_Product__Type_Osnd(_1231389, _1231391), _1231393) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1231389, _1231391, _1231391), hAPP(c_COMBK(tc_fun(_1231391, _1231391), _1231389), c_COMBI(_1231391))), _1231393))], (25524 ^ _779308) ^ [_1231443, _1231445] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1231443, _1231445) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1231443, _1231445)))], (25526 ^ _779308) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25528 ^ _779308) ^ [_1231496, _1231498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231496), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231498)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1231496, _1231498) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1231496, _1231498)))], (25538 ^ _779308) ^ [_1231659, _1231661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231661)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1231659, _1231661) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1231659, _1231661)))], (25548 ^ _779308) ^ [_1231816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1231816))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1231816)) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1231816))))], (25554 ^ _779308) ^ [_1231933, _1231935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231935), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1231933, _1231935) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1231933), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1231935)))))], (25564 ^ _779308) ^ [_1232114, _1232116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232114), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232116), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1232114, _1232116) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1232114), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1232116)))))], (25574 ^ _779308) ^ [_1232301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1232301)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1232301)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1232301))))))], (25580 ^ _779308) ^ [_1232434, _1232436, _1232438, _1232440, _1232442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1232434, _1232436)), hAPP(_1232434, _1232438))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1232440, _1232440)), hAPP(hAPP(c_Product__Type_OPair(_1232440, _1232440), _1232436), _1232438)), _1232442)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1232440, _1232440)), hAPP(hAPP(c_Product__Type_OPair(_1232440, _1232440), _1232436), _1232438)), c_Wellfounded_Omlex__prod(_1232440, _1232434, _1232442))))], (25590 ^ _779308) ^ [_1232681, _1232683, _1232685, _1232687, _1232689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1232681, _1232683)), hAPP(_1232681, _1232685))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1232687, _1232687)), hAPP(hAPP(c_Product__Type_OPair(_1232687, _1232687), _1232683), _1232685)), c_Wellfounded_Omlex__prod(_1232687, _1232681, _1232689))))], (25596 ^ _779308) ^ [_1232832, _1232834] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232832), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232834), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232832), _1232834) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1232832), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1232834)))))], (25606 ^ _779308) ^ [_1233023] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1233023)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1233023)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25608 ^ _779308) ^ [_1233061] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1233061) = _1233061)], (25610 ^ _779308) ^ [_1233087, _1233089, _1233091, _1233093] : [-(hAPP(c_Product__Type_Ofst(_1233087, _1233089), hAPP(hAPP(c_Product__Type_OPair(_1233087, _1233089), _1233091), _1233093)) = _1233091)], (25612 ^ _779308) ^ [_1233131, _1233133, _1233135, _1233137, _1233139] : [hAPP(c_Product__Type_Ofst(_1233131, _1233133), hAPP(hAPP(c_Product__Type_OPair(_1233131, _1233133), _1233135), _1233137)) = _1233139, -(_1233135 = _1233139)], (25618 ^ _779308) ^ [_1233265, _1233267, _1233269, _1233271] : [_1233265 = _1233267, 25621 ^ _779308 : [(25622 ^ _779308) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1233269, _1233271), _1233265) = hAPP(c_Product__Type_Ofst(_1233269, _1233271), _1233267))], (25624 ^ _779308) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1233269, _1233271), _1233265) = hAPP(c_Product__Type_Osnd(_1233269, _1233271), _1233267))]]], (25626 ^ _779308) ^ [_1233416, _1233418, _1233420, _1233422] : [-(_1233416 = _1233418), hAPP(c_Product__Type_Ofst(_1233420, _1233422), _1233416) = hAPP(c_Product__Type_Ofst(_1233420, _1233422), _1233418), hAPP(c_Product__Type_Osnd(_1233420, _1233422), _1233416) = hAPP(c_Product__Type_Osnd(_1233420, _1233422), _1233418)], (25636 ^ _779308) ^ [_1233603, _1233605, _1233607, _1233609] : [hAPP(c_Product__Type_Ofst(_1233603, _1233605), _1233607) = hAPP(c_Product__Type_Ofst(_1233603, _1233605), _1233609), hAPP(c_Product__Type_Osnd(_1233603, _1233605), _1233607) = hAPP(c_Product__Type_Osnd(_1233603, _1233605), _1233609), -(_1233607 = _1233609)], (25646 ^ _779308) ^ [_1233788, _1233790, _1233792] : [-(hAPP(c_Product__Type_Ofst(_1233788, _1233790), _1233792) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1233788, _1233790, _1233788), c_COMBK(_1233788, _1233790)), _1233792))], (25648 ^ _779308) ^ [_1233834, _1233836, _1233838] : [-(hAPP(hAPP(c_Product__Type_OPair(_1233834, _1233836), hAPP(c_Product__Type_Ofst(_1233834, _1233836), _1233838)), hAPP(c_Product__Type_Osnd(_1233834, _1233836), _1233838)) = _1233838)], (25650 ^ _779308) ^ [_1233882, _1233884, _1233886] : [-(_1233882 = hAPP(hAPP(c_Product__Type_OPair(_1233884, _1233886), hAPP(c_Product__Type_Ofst(_1233884, _1233886), _1233882)), hAPP(c_Product__Type_Osnd(_1233884, _1233886), _1233882)))], (25652 ^ _779308) ^ [_1233930, _1233932, _1233934, _1233936, _1233938] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1233930, _1233932, _1233934), _1233936), _1233938) = hAPP(hAPP(_1233936, hAPP(c_Product__Type_Ofst(_1233930, _1233932), _1233938)), hAPP(c_Product__Type_Osnd(_1233930, _1233932), _1233938)))], (25654 ^ _779308) ^ [_1233989, _1233991] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233989), _1233991) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1233989, _1233991)))], (25656 ^ _779308) ^ [_1234026, _1234028] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1234026, _1234028) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1234026, _1234028)))], (25658 ^ _779308) ^ [_1234061, _1234063, _1234065, _1234067, _1234069, _1234071] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1234061, _1234063), _1234063, _1234065), hAPP(hAPP(c_COMBB(_1234067, tc_fun(_1234063, _1234065), tc_prod(_1234061, _1234063)), _1234069), hAPP(hAPP(c_COMBB(_1234061, _1234067, tc_prod(_1234061, _1234063)), _1234071), c_Product__Type_Ofst(_1234061, _1234063)))), c_Product__Type_Osnd(_1234061, _1234063)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1234061, _1234063, _1234065), hAPP(hAPP(c_COMBB(_1234067, tc_fun(_1234063, _1234065), _1234061), _1234069), _1234071)))], (25660 ^ _779308) ^ [_1234162, _1234164, _1234166, _1234168, _1234170] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1234162, _1234164, _1234166), _1234168), _1234170) = hAPP(hAPP(_1234168, hAPP(c_Product__Type_Ofst(_1234162, _1234164), _1234170)), hAPP(c_Product__Type_Osnd(_1234162, _1234164), _1234170)))], (25662 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25664 ^ _779308) ^ [_1234239, _1234241, _1234243, _1234245, _1234247] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1234239, _1234241, _1234243), _1234245), _1234247) = hAPP(hAPP(_1234245, hAPP(c_Product__Type_Ofst(_1234239, _1234241), _1234247)), hAPP(c_Product__Type_Osnd(_1234239, _1234241), _1234247)))], (25666 ^ _779308) ^ [_1234298, _1234300, _1234302] : [-(c_HOL_OThe(tc_prod(_1234298, _1234300), hAPP(c_Product__Type_Oprod_Oprod__case(_1234298, _1234300, tc_HOL_Obool), _1234302)) = c_HOL_OThe(tc_prod(_1234298, _1234300), hAPP(hAPP(c_COMBS(tc_prod(_1234298, _1234300), _1234300, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1234298, tc_fun(_1234300, tc_HOL_Obool), tc_prod(_1234298, _1234300)), _1234302), c_Product__Type_Ofst(_1234298, _1234300))), c_Product__Type_Osnd(_1234298, _1234300))))], (25668 ^ _779308) ^ [_1234379, _1234381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234379), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234381)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234379), _1234381) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1234379, _1234381)))], (25678 ^ _779308) ^ [_1234546, _1234548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234548)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234546), _1234548) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1234546, _1234548)))], (25688 ^ _779308) ^ [_1234707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1234707))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1234707)) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1234707))))], (25694 ^ _779308) ^ [_1234822, _1234824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234824), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234822), _1234824) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234822), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1234824)))))], (25704 ^ _779308) ^ [_1235007, _1235009, _1235011, _1235013, _1235015] : [-(c_Product__Type_Oprod_Oprod__size(_1235007, _1235009, _1235011, _1235013, _1235015) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1235011, hAPP(c_Product__Type_Ofst(_1235007, _1235009), _1235015))), hAPP(_1235013, hAPP(c_Product__Type_Osnd(_1235007, _1235009), _1235015)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25706 ^ _779308) ^ [_1235074, _1235076, _1235078, _1235080, _1235082] : [hBOOL(hAPP(hAPP(_1235074, _1235076), _1235078)), -(hBOOL(hAPP(hAPP(_1235074, hAPP(c_Product__Type_Osnd(_1235080, _1235082), hAPP(hAPP(c_Product__Type_OPair(_1235080, _1235082), _1235078), _1235076))), hAPP(c_Product__Type_Ofst(_1235080, _1235082), hAPP(hAPP(c_Product__Type_OPair(_1235080, _1235082), _1235078), _1235076)))))], (25712 ^ _779308) ^ [_1235237, _1235239, _1235241, _1235243, _1235245, _1235247] : [hBOOL(hAPP(_1235237, _1235239)), hBOOL(hAPP(_1235241, _1235243)), 25719 ^ _779308 : [(25720 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1235237, hAPP(c_Product__Type_Ofst(_1235245, _1235247), hAPP(hAPP(c_Product__Type_OPair(_1235245, _1235247), _1235239), _1235243)))))], (25722 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1235241, hAPP(c_Product__Type_Osnd(_1235245, _1235247), hAPP(hAPP(c_Product__Type_OPair(_1235245, _1235247), _1235239), _1235243)))))]]], (25724 ^ _779308) ^ [_1235484, _1235486, _1235488, _1235490, _1235492, _1235494] : [-(c_Product__Type_Oprod_Oprod__rec(_1235484, _1235486, _1235488, _1235490, hAPP(hAPP(c_Product__Type_OPair(_1235484, _1235486), _1235492), _1235494)) = hAPP(hAPP(_1235490, _1235492), _1235494))], (25726 ^ _779308) ^ [_1235571, _1235573, _1235575, _1235577, _1235579, _1235581, _1235583, _1235585] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1235571, _1235573), tc_prod(_1235571, _1235573))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1235571, _1235573), tc_prod(_1235571, _1235573)), hAPP(hAPP(c_Product__Type_OPair(_1235571, _1235573), _1235575), _1235577)), hAPP(hAPP(c_Product__Type_OPair(_1235571, _1235573), _1235579), _1235581))), c_Wellfounded_Olex__prod(_1235571, _1235573, _1235583, _1235585))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1235571, _1235571)), hAPP(hAPP(c_Product__Type_OPair(_1235571, _1235571), _1235575), _1235579)), _1235583))), 25733 ^ _779308 : [(25734 ^ _779308) ^ [] : [-(_1235575 = _1235579)], (25736 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1235573, _1235573)), hAPP(hAPP(c_Product__Type_OPair(_1235573, _1235573), _1235577), _1235581)), _1235585)))]]], (25738 ^ _779308) ^ [_1235896, _1235898, _1235900, _1235902, _1235904, _1235906, _1235908, _1235910] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1235896, _1235898), tc_prod(_1235896, _1235898))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1235896, _1235898), tc_prod(_1235896, _1235898)), hAPP(hAPP(c_Product__Type_OPair(_1235896, _1235898), _1235900), _1235902)), hAPP(hAPP(c_Product__Type_OPair(_1235896, _1235898), _1235904), _1235906))), c_Wellfounded_Olex__prod(_1235896, _1235898, _1235908, _1235910)))), 25739 ^ _779308 : [(25740 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1235896, _1235896)), hAPP(hAPP(c_Product__Type_OPair(_1235896, _1235896), _1235900), _1235904)), _1235908))], (25742 ^ _779308) ^ [] : [_1235900 = _1235904, hBOOL(hAPP(hAPP(c_member(tc_prod(_1235898, _1235898)), hAPP(hAPP(c_Product__Type_OPair(_1235898, _1235898), _1235902), _1235906)), _1235910))]]], (25750 ^ _779308) ^ [_1236271, _1236273] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1236271), _1236273) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1236271, _1236273)))], (25784 ^ _779308) ^ [_1236862, _1236864, _1236866] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1236862, _1236864), _1236866))), _1236862 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1236866)), _1236864)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1236866)), 25791 ^ _779308 : [(25792 ^ _779308) ^ [] : [-(_1236864 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25794 ^ _779308) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1236866) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 25795 ^ _779308 : [(25796 ^ _779308) ^ [] : [_1236864 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25798 ^ _779308) ^ [] : [25799 ^ _779308 : [(25800 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1236864)))], (25802 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1236866))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1236866)), _1236864))]], 25807 ^ _779308 : [(25808 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1236864))], (25810 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1236864), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1236866))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1236866)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (25752 ^ _779308) ^ [_1236326, _1236328, _1236330] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1236326, _1236328), _1236330)), 25755 ^ _779308 : [(25756 ^ _779308) ^ [] : [-(_1236326 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1236330)), _1236328)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1236330)))], (25758 ^ _779308) ^ [] : [_1236328 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1236330) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25764 ^ _779308) ^ [] : [-(_1236328 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25767 ^ _779308 : [(25768 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1236328)), 25771 ^ _779308 : [(25772 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1236330))))], (25774 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1236330)), _1236328)))]]], (25776 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1236328))), 25779 ^ _779308 : [(25780 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1236328), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1236330))))], (25782 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1236330)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (25818 ^ _779308) ^ [_1237471, _1237473, _1237475, _1237477, _1237479, _1237481, _1237483] : [hBOOL(hAPP(_1237471, _1237473)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1237475, _1237475)), hAPP(hAPP(c_Product__Type_OPair(_1237475, _1237475), _1237477), _1237479)), hAPP(_1237481, _1237473))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1237483, _1237475), tc_prod(_1237483, _1237475))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1237483, _1237475), tc_prod(_1237483, _1237475)), hAPP(hAPP(c_Product__Type_OPair(_1237483, _1237475), _1237473), _1237477)), hAPP(hAPP(c_Product__Type_OPair(_1237483, _1237475), _1237473), _1237479))), c_Recdef_Osame__fst(_1237483, _1237475, _1237471, _1237481))))], (25828 ^ _779308) ^ [_1237794, _1237796, _1237798] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1237794, tc_HOL_Obool), tc_fun(_1237794, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1237794, tc_HOL_Obool), tc_fun(_1237794, tc_HOL_Obool)), _1237796), _1237798)), c_Wellfounded_Ofinite__psubset(_1237794))), 25831 ^ _779308 : [(25832 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1237794, tc_HOL_Obool)), _1237796), _1237798)))], (25834 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1237794), _1237798)))]]], (25836 ^ _779308) ^ [_1237989, _1237991, _1237993] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1237989, tc_HOL_Obool), tc_fun(_1237989, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1237989, tc_HOL_Obool), tc_fun(_1237989, tc_HOL_Obool)), _1237991), _1237993)), c_Wellfounded_Ofinite__psubset(_1237989)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1237989, tc_HOL_Obool)), _1237991), _1237993)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1237989), _1237993))], (25846 ^ _779308) ^ [_1238218, _1238220] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1238218)), hAPP(c_Nat_OSuc, _1238220)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1238218))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_OSuc, _1238220))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), c_Nat_OSuc), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Int_Oint), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Int_Onat)), _1238220)))))], (25848 ^ _779308) ^ [_1238284, _1238286] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1238284)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1238286)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1238286))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_Int_Oint), c_If(tc_Nat_Onat)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_OSuc, _1238284))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), c_Nat_OSuc), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Int_Oint), hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1238284)), c_Int_Onat)))))], (25850 ^ _779308) ^ [_1238356, _1238358, _1238360, _1238362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1238356), _1238358)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1238360), _1238362)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1238356), _1238360)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1238358), _1238362))), c_FunDef_Opair__less)))], (25860 ^ _779308) ^ [_1238559, _1238561] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1238559)), hAPP(c_Nat_OSuc, _1238561)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1238559), _1238561)))], (25862 ^ _779308) ^ [_1238605, _1238607, _1238609, _1238611] : [class_Orderings_Olinorder(_1238605), 25865 ^ _779308 : [(25866 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238605), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1238605), _1238607), _1238609)), _1238611)), 25869 ^ _779308 : [(25870 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238605), _1238607), _1238611)))], (25872 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238605), _1238609), _1238611)))]]], (25874 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238605), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1238605), _1238607), _1238609)), _1238611))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238605), _1238607), _1238611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238605), _1238609), _1238611))]]], (25884 ^ _779308) ^ [_1238985, _1238987, _1238989, _1238991] : [class_Orderings_Olinorder(_1238985), 25887 ^ _779308 : [(25898 ^ _779308) ^ [] : [25899 ^ _779308 : [(25900 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238985), _1238987), _1238989))], (25902 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238985), _1238987), _1238991))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238985), _1238987), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1238985), _1238989), _1238991))))], (25888 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238985), _1238987), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1238985), _1238989), _1238991))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238985), _1238987), _1238989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1238985), _1238987), _1238991)))]]], (25906 ^ _779308) ^ [_1239334, _1239336, _1239338, _1239340] : [class_Orderings_Olinorder(_1239334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239334), _1239336), _1239338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239334), _1239336), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239334), _1239340), _1239338))))], (25916 ^ _779308) ^ [_1239513, _1239515, _1239517, _1239519] : [class_Orderings_Olinorder(_1239513), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239513), _1239515), _1239517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239513), _1239515), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239513), _1239517), _1239519))))], (25926 ^ _779308) ^ [_1239692, _1239694] : [class_Orderings_Olinorder(_1239692), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239692), _1239694), _1239694) = _1239694)], (25932 ^ _779308) ^ [_1239783, _1239785] : [class_Orderings_Olinorder(_1239783), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239783), _1239785), _1239785) = _1239785)], (25938 ^ _779308) ^ [_1239874, _1239876, _1239878] : [class_Orderings_Olinorder(_1239874), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239874), _1239876), _1239878) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239874), _1239878), _1239876))], (25944 ^ _779308) ^ [_1239983, _1239985, _1239987] : [class_Orderings_Olinorder(_1239983), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239983), _1239985), _1239987) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1239983), _1239987), _1239985))], (25950 ^ _779308) ^ [_1240092, _1240094, _1240096] : [class_Orderings_Olinorder(_1240092), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240092), _1240094), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240092), _1240094), _1240096)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240092), _1240094), _1240096))], (25956 ^ _779308) ^ [_1240217, _1240219, _1240221] : [class_Orderings_Olinorder(_1240217), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240217), _1240219), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240217), _1240219), _1240221)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240217), _1240219), _1240221))], (25962 ^ _779308) ^ [_1240342, _1240344, _1240346, _1240348] : [class_Orderings_Olinorder(_1240342), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240342), _1240344), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240342), _1240346), _1240348)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240342), _1240346), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240342), _1240344), _1240348)))], (25968 ^ _779308) ^ [_1240485, _1240487, _1240489, _1240491] : [class_Orderings_Olinorder(_1240485), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240485), _1240487), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240485), _1240489), _1240491)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240485), _1240489), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240485), _1240487), _1240491)))], (25974 ^ _779308) ^ [_1240628, _1240630, _1240632, _1240634] : [class_Orderings_Olinorder(_1240628), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240628), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240628), _1240630), _1240632)), _1240634) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240628), _1240630), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240628), _1240632), _1240634)))], (25980 ^ _779308) ^ [_1240771, _1240773, _1240775, _1240777] : [class_Orderings_Olinorder(_1240771), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240771), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240771), _1240773), _1240775)), _1240777) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240771), _1240773), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240771), _1240775), _1240777)))], (25986 ^ _779308) ^ [_1240914] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1240914), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1240914)], (25988 ^ _779308) ^ [_1240943] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1240943) = _1240943)], (25990 ^ _779308) ^ [_1240969, _1240971, _1240973, _1240975] : [class_Groups_Oordered__ab__group__add(_1240969), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1240969), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240969), _1240971), _1240973)), _1240975) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1240969), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1240969), _1240971), _1240975)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1240969), _1240973), _1240975)))], (25996 ^ _779308) ^ [_1241128, _1241130, _1241132, _1241134] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1241128), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1241128), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241128), _1241130), _1241132)), _1241134) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241128), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1241128), _1241130), _1241134)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1241128), _1241132), _1241134)))], (26002 ^ _779308) ^ [_1241287, _1241289, _1241291, _1241293] : [class_Orderings_Olinorder(_1241287), 26005 ^ _779308 : [(26016 ^ _779308) ^ [] : [26017 ^ _779308 : [(26018 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241287), _1241289), _1241291))], (26020 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241287), _1241289), _1241293))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241287), _1241289), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241287), _1241291), _1241293))))], (26006 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241287), _1241289), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241287), _1241291), _1241293))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241287), _1241289), _1241291))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241287), _1241289), _1241293)))]]], (26024 ^ _779308) ^ [_1241636, _1241638, _1241640] : [class_Orderings_Olinorder(_1241636), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241636), _1241638), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241636), _1241638), _1241640))))], (26030 ^ _779308) ^ [_1241743, _1241745, _1241747] : [class_Orderings_Olinorder(_1241743), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241743), _1241745), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241743), _1241747), _1241745))))], (26036 ^ _779308) ^ [_1241850, _1241852, _1241854] : [class_Orderings_Olinorder(_1241850), 26039 ^ _779308 : [(26040 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241850), _1241852), _1241854)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241850), _1241852), _1241854) = _1241854)], (26046 ^ _779308) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1241850), _1241852), _1241854) = _1241854, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241850), _1241852), _1241854)))]]], (26052 ^ _779308) ^ [_1242106, _1242108, _1242110, _1242112] : [class_Orderings_Olinorder(_1242106), 26055 ^ _779308 : [(26056 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242106), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242106), _1242108), _1242110)), _1242112)), 26059 ^ _779308 : [(26060 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242106), _1242108), _1242112)))], (26062 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242106), _1242110), _1242112)))]]], (26064 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242106), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242106), _1242108), _1242110)), _1242112))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242106), _1242108), _1242112)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242106), _1242110), _1242112))]]], (26074 ^ _779308) ^ [_1242486, _1242488, _1242490, _1242492] : [class_Orderings_Olinorder(_1242486), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242486), _1242488), _1242490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242486), _1242488), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242486), _1242490), _1242492))))], (26084 ^ _779308) ^ [_1242665, _1242667, _1242669, _1242671] : [class_Orderings_Olinorder(_1242665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242665), _1242667), _1242669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242665), _1242667), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242665), _1242671), _1242669))))], (26094 ^ _779308) ^ [_1242844, _1242846, _1242848] : [class_Orderings_Olinorder(_1242844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242844), _1242846), _1242848)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1242844), _1242846), _1242848) = _1242848)], (26104 ^ _779308) ^ [_1243005, _1243007, _1243009] : [class_Orderings_Olinorder(_1243005), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243005), _1243007), _1243009)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243005), _1243009), _1243007) = _1243009)], (26114 ^ _779308) ^ [_1243166, _1243168, _1243170, _1243172] : [class_Orderings_Olinorder(_1243166), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243166), _1243168), _1243170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243166), _1243172), _1243170)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243166), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243166), _1243168), _1243172)), _1243170)))], (26128 ^ _779308) ^ [_1243415, _1243417, _1243419, _1243421] : [class_Orderings_Olinorder(_1243415), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243415), _1243417), _1243419)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243415), _1243421), _1243419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243415), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243415), _1243417), _1243421)), _1243419)))], (26142 ^ _779308) ^ [_1243664, _1243666, _1243668, _1243670, _1243672] : [class_Orderings_Olinorder(_1243664), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243664), _1243666), _1243668)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243664), _1243670), _1243672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243664), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243664), _1243666), _1243670)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243664), _1243668), _1243672))))], (26156 ^ _779308) ^ [_1243935, _1243937, _1243939, _1243941] : [class_Orderings_Olinorder(_1243935), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243935), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1243935), _1243937), _1243939)), _1243941)), 26163 ^ _779308 : [(26164 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243935), _1243937), _1243941)))], (26166 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243935), _1243939), _1243941)))]]], (26168 ^ _779308) ^ [_1244158, _1244160, _1244162, _1244164] : [class_Orderings_Olinorder(_1244158), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244158), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244158), _1244160), _1244162)), _1244164) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244158), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244158), _1244160), _1244164)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244158), _1244162), _1244164)))], (26174 ^ _779308) ^ [_1244317, _1244319, _1244321, _1244323] : [class_Orderings_Olinorder(_1244317), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244317), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244317), _1244319), _1244321)), _1244323) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244317), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244317), _1244319), _1244323)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244317), _1244321), _1244323)))], (26180 ^ _779308) ^ [_1244476, _1244478, _1244480, _1244482] : [class_Orderings_Olinorder(_1244476), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244476), _1244478), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244476), _1244480), _1244482)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244476), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244476), _1244478), _1244480)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244476), _1244478), _1244482)))], (26186 ^ _779308) ^ [_1244635, _1244637, _1244639, _1244641] : [class_Orderings_Olinorder(_1244635), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244635), _1244637), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244635), _1244639), _1244641)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244635), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244635), _1244637), _1244639)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244635), _1244637), _1244641)))], (26192 ^ _779308) ^ [_1244794, _1244796, _1244798] : [class_Orderings_Olinorder(_1244794), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244794), _1244796), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244794), _1244796), _1244798)) = _1244796)], (26198 ^ _779308) ^ [_1244903, _1244905, _1244907] : [class_Orderings_Olinorder(_1244903), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244903), _1244905), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244903), _1244905), _1244907)) = _1244905)], (26204 ^ _779308) ^ [_1245012] : [class_Orderings_Olinorder(_1245012), -(c_Finite__Set_Ofun__left__comm__idem(_1245012, _1245012, c_Orderings_Oord__class_Omax(_1245012)))], (26210 ^ _779308) ^ [_1245091, _1245093, _1245095] : [class_Int_Onumber(_1245091), class_Orderings_Oord(_1245091), 26217 ^ _779308 : [(26218 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245091), hAPP(c_Int_Onumber__class_Onumber__of(_1245091), _1245093)), hAPP(c_Int_Onumber__class_Onumber__of(_1245091), _1245095))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245091), hAPP(c_Int_Onumber__class_Onumber__of(_1245091), _1245093)), hAPP(c_Int_Onumber__class_Onumber__of(_1245091), _1245095)) = hAPP(c_Int_Onumber__class_Onumber__of(_1245091), _1245095))], (26224 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245091), hAPP(c_Int_Onumber__class_Onumber__of(_1245091), _1245093)), hAPP(c_Int_Onumber__class_Onumber__of(_1245091), _1245095)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245091), hAPP(c_Int_Onumber__class_Onumber__of(_1245091), _1245093)), hAPP(c_Int_Onumber__class_Onumber__of(_1245091), _1245095)) = hAPP(c_Int_Onumber__class_Onumber__of(_1245091), _1245093))]]], (26230 ^ _779308) ^ [_1245483, _1245485, _1245487, _1245489] : [class_Orderings_Olinorder(_1245483), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245483), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245483), _1245485), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245483), _1245487), _1245489))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245483), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245483), _1245485), _1245487)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245483), _1245485), _1245489)))))], (26236 ^ _779308) ^ [_1245656, _1245658, _1245660, _1245662] : [class_Orderings_Olinorder(_1245656), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1245656), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245656), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245656), _1245658), _1245660)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245656), _1245658), _1245662))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245656), _1245658), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245656), _1245660), _1245662)))))], (26242 ^ _779308) ^ [_1245829, _1245831, _1245833] : [class_Groups_Olinordered__ab__group__add(_1245829), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1245829), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245829), _1245831), _1245833)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245829), hAPP(c_Groups_Ouminus__class_Ouminus(_1245829), _1245831)), hAPP(c_Groups_Ouminus__class_Ouminus(_1245829), _1245833)))], (26248 ^ _779308) ^ [_1245968, _1245970, _1245972] : [class_Groups_Olinordered__ab__group__add(_1245968), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1245968), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1245968), _1245970), _1245972)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1245968), hAPP(c_Groups_Ouminus__class_Ouminus(_1245968), _1245970)), hAPP(c_Groups_Ouminus__class_Ouminus(_1245968), _1245972)))], (26254 ^ _779308) ^ [_1246107, _1246109] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1246107), _1246109)), _1246109) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1246107), _1246109))], (26256 ^ _779308) ^ [_1246150, _1246152] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1246150), hAPP(c_Nat_OSuc, _1246152)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1246152), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), _1246152)), _1246150))], (26258 ^ _779308) ^ [_1246198, _1246200] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1246198)), _1246200) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1246198), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1246198)), _1246200))], (26260 ^ _779308) ^ [_1246246] : [class_Orderings_Oord(_1246246), -(c_Orderings_Oord__class_Omax(_1246246) = c_Orderings_Oord_Omax(_1246246, c_Orderings_Oord__class_Oless__eq(_1246246)))], (26266 ^ _779308) ^ [_1246333] : [class_Orderings_Olinorder(_1246333), -(c_Orderings_Oord_Omin(_1246333, hAPP(c_COMBC(_1246333, _1246333, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1246333))) = c_Orderings_Oord__class_Omax(_1246333))], (26272 ^ _779308) ^ [_1246434, _1246436, _1246438] : [class_Orderings_Olinorder(_1246434), hBOOL(hAPP(c_Finite__Set_Ofinite(_1246434), _1246436)), hBOOL(hAPP(hAPP(c_member(_1246434), _1246438), _1246436)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1246434), _1246438), c_Big__Operators_Olattice_OInf__fin(_1246434, c_Orderings_Oord__class_Omin(_1246434), _1246436)) = _1246438)], (26286 ^ _779308) ^ [_1246669, _1246671, _1246673, _1246675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246669), _1246671)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1246669), _1246673)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1246671), _1246675))), c_FunDef_Opair__less)))], (26292 ^ _779308) ^ [_1246806, _1246808, _1246810, _1246812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1246806), _1246808)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1246810), _1246812)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1246806), _1246810)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1246808), _1246812))), c_FunDef_Opair__leq)))], (26302 ^ _779308) ^ [_1247009, _1247011, _1247013, _1247015] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1247009), _1247011)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1247013), _1247009)), c_FunDef_Opair__less)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1247015), _1247011)), c_FunDef_Omax__strict)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1247013), _1247015)), _1247011)), c_FunDef_Omax__strict)))], (26316 ^ _779308) ^ [_1247290, _1247292, _1247294, _1247296] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1247290), _1247292)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1247290), _1247294)), c_FunDef_Opair__less)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1247292), _1247296)), c_FunDef_Omin__strict)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1247292), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1247294), _1247296))), c_FunDef_Omin__strict)))], (26330 ^ _779308) ^ [_1247571, _1247573, _1247575, _1247577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1247571), _1247573)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1247571), _1247575)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1247573), _1247577))), c_FunDef_Opair__leq)))], (26336 ^ _779308) ^ [_1247708, _1247710, _1247712] : [class_Orderings_Olinorder(_1247708), hBOOL(hAPP(c_Finite__Set_Ofinite(_1247708), _1247710)), hBOOL(hAPP(hAPP(c_member(_1247708), _1247712), _1247710)), 26347 ^ _779308 : [(26348 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1247708, tc_HOL_Obool)), _1247710), hAPP(hAPP(c_Set_Oinsert(_1247708), _1247712), c_Orderings_Obot__class_Obot(tc_fun(_1247708, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1247708, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1247708, _1247710) = _1247712)], (26354 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1247708, tc_HOL_Obool)), _1247710), hAPP(hAPP(c_Set_Oinsert(_1247708), _1247712), c_Orderings_Obot__class_Obot(tc_fun(_1247708, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1247708, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1247708, _1247710) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1247708), _1247712), c_Big__Operators_Olinorder__class_OMax(_1247708, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1247708, tc_HOL_Obool)), _1247710), hAPP(hAPP(c_Set_Oinsert(_1247708), _1247712), c_Orderings_Obot__class_Obot(tc_fun(_1247708, tc_HOL_Obool)))))))]]], (26360 ^ _779308) ^ [_1248214] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1248214)), -(_1248214 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), _1248214)), c_FunDef_Omax__strict)))], (26370 ^ _779308) ^ [_1248320] : [-(_1248320 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1248320), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (26376 ^ _779308) ^ [_1248365, _1248367] : [class_Orderings_Olinorder(_1248365), -(c_Big__Operators_Olinorder__class_OMax(_1248365, hAPP(hAPP(c_Set_Oinsert(_1248365), _1248367), c_Orderings_Obot__class_Obot(tc_fun(_1248365, tc_HOL_Obool)))) = _1248367)], (26382 ^ _779308) ^ [_1248472, _1248474, _1248476] : [class_Orderings_Olinorder(_1248472), hBOOL(hAPP(c_Finite__Set_Ofinite(_1248472), _1248474)), hBOOL(hAPP(hAPP(c_member(_1248472), _1248476), _1248474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248472), _1248476), c_Big__Operators_Olinorder__class_OMax(_1248472, _1248474))))], (26396 ^ _779308) ^ [_1248699, _1248701] : [class_Orderings_Olinorder(_1248699), hBOOL(hAPP(c_Finite__Set_Ofinite(_1248699), _1248701)), -(_1248701 = c_Orderings_Obot__class_Obot(tc_fun(_1248699, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1248699), c_Big__Operators_Olinorder__class_OMax(_1248699, _1248701)), _1248701)))], (26410 ^ _779308) ^ [_1248879, _1248881, _1248883] : [class_Orderings_Olinorder(_1248879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1248879), _1248881)), hBOOL(hAPP(hAPP(c_member(_1248879), _1248883), _1248881)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1248879), _1248883), c_Big__Operators_Olinorder__class_OMax(_1248879, _1248881)) = c_Big__Operators_Olinorder__class_OMax(_1248879, _1248881))], (26424 ^ _779308) ^ [_1249114, _1249116] : [class_Orderings_Olinorder(_1249114), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249114), _1249116)), -(c_Big__Operators_Olinorder__class_OMax(_1249114, _1249116) = hAPP(c_Finite__Set_Ofold1(_1249114, c_Orderings_Oord__class_Omax(_1249114)), _1249116))], (26434 ^ _779308) ^ [_1249271, _1249273, _1249275] : [class_Orderings_Olinorder(_1249271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1249271, tc_HOL_Obool)), _1249273), _1249275)), -(_1249273 = c_Orderings_Obot__class_Obot(tc_fun(_1249271, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249271), _1249275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1249271), c_Big__Operators_Olinorder__class_OMax(_1249271, _1249273)), c_Big__Operators_Olinorder__class_OMax(_1249271, _1249275))))], (26452 ^ _779308) ^ [_1249577, _1249579, _1249581] : [class_Orderings_Olinorder(_1249577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249577), _1249579)), -(_1249579 = c_Orderings_Obot__class_Obot(tc_fun(_1249577, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1249577, hAPP(hAPP(c_Set_Oinsert(_1249577), _1249581), _1249579)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1249577), _1249581), c_Big__Operators_Olinorder__class_OMax(_1249577, _1249579)))], (26466 ^ _779308) ^ [_1249785, _1249787, _1249789] : [class_Orderings_Olinorder(_1249785), hBOOL(hAPP(c_Finite__Set_Ofinite(_1249785), _1249787)), -(_1249789 = c_Orderings_Obot__class_Obot(tc_fun(_1249785, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1249785, tc_HOL_Obool)), _1249789), _1249787)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1249785), c_Big__Operators_Olinorder__class_OMax(_1249785, _1249789)), c_Big__Operators_Olinorder__class_OMax(_1249785, _1249787)) = c_Big__Operators_Olinorder__class_OMax(_1249785, _1249787))], (26484 ^ _779308) ^ [_1250099, _1250101, _1250103] : [class_Orderings_Olinorder(_1250099), hBOOL(hAPP(c_Finite__Set_Ofinite(_1250099), _1250101)), -(hBOOL(hAPP(hAPP(c_member(_1250099), _1250103), _1250101))), -(_1250101 = c_Orderings_Obot__class_Obot(tc_fun(_1250099, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1250099, hAPP(hAPP(c_Set_Oinsert(_1250099), _1250103), _1250101)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1250099), _1250103), c_Big__Operators_Olinorder__class_OMax(_1250099, _1250101)))], (26502 ^ _779308) ^ [_1250336, _1250338, _1250340] : [class_Orderings_Olinorder(_1250336), hBOOL(hAPP(c_Finite__Set_Ofinite(_1250336), _1250338)), 26509 ^ _779308 : [(26510 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1250336, tc_HOL_Obool)), _1250338), hAPP(hAPP(c_Set_Oinsert(_1250336), _1250340), c_Orderings_Obot__class_Obot(tc_fun(_1250336, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1250336, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1250336, hAPP(hAPP(c_Set_Oinsert(_1250336), _1250340), _1250338)) = _1250340)], (26516 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1250336, tc_HOL_Obool)), _1250338), hAPP(hAPP(c_Set_Oinsert(_1250336), _1250340), c_Orderings_Obot__class_Obot(tc_fun(_1250336, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1250336, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1250336, hAPP(hAPP(c_Set_Oinsert(_1250336), _1250340), _1250338)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1250336), _1250340), c_Big__Operators_Olinorder__class_OMax(_1250336, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1250336, tc_HOL_Obool)), _1250338), hAPP(hAPP(c_Set_Oinsert(_1250336), _1250340), c_Orderings_Obot__class_Obot(tc_fun(_1250336, tc_HOL_Obool)))))))]]], (26522 ^ _779308) ^ [_1250806, _1250808] : [class_Groups_Olinordered__ab__group__add(_1250806), hBOOL(hAPP(c_Finite__Set_Ofinite(_1250806), _1250808)), -(_1250808 = c_Orderings_Obot__class_Obot(tc_fun(_1250806, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1250806), c_Big__Operators_Olinorder__class_OMin(_1250806, _1250808)) = c_Big__Operators_Olinorder__class_OMax(_1250806, hAPP(c_Set_Oimage(_1250806, _1250806, c_Groups_Ouminus__class_Ouminus(_1250806)), _1250808)))], (26536 ^ _779308) ^ [_1251006, _1251008] : [class_Groups_Olinordered__ab__group__add(_1251006), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251006), _1251008)), -(_1251008 = c_Orderings_Obot__class_Obot(tc_fun(_1251006, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1251006), c_Big__Operators_Olinorder__class_OMax(_1251006, _1251008)) = c_Big__Operators_Olinorder__class_OMin(_1251006, hAPP(c_Set_Oimage(_1251006, _1251006, c_Groups_Ouminus__class_Ouminus(_1251006)), _1251008)))], (26550 ^ _779308) ^ [_1251206, _1251208, _1251210, _1251212] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1251206), _1251208)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1251206), _1251210)), c_FunDef_Opair__leq)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1251208), _1251212)), c_FunDef_Omin__weak)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1251208), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1251210), _1251212))), c_FunDef_Omin__weak)))], (26564 ^ _779308) ^ [_1251487, _1251489, _1251491, _1251493] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1251487), _1251489)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1251491), _1251487)), c_FunDef_Opair__leq)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1251493), _1251489)), c_FunDef_Omax__weak)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1251491), _1251493)), _1251489)), c_FunDef_Omax__weak)))], (26578 ^ _779308) ^ [_1251768, _1251770] : [class_Orderings_Olinorder(_1251768), hBOOL(hAPP(c_Finite__Set_Ofinite(_1251768), _1251770)), -(_1251770 = c_Orderings_Obot__class_Obot(tc_fun(_1251768, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1251768), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1251768), 26591 ^ [_1251768, _1251770]), 26592 ^ [_1251768, _1251770])), hAPP(hAPP(c_Set_Oinsert(_1251768), 26591 ^ [_1251768, _1251770]), hAPP(hAPP(c_Set_Oinsert(_1251768), 26592 ^ [_1251768, _1251770]), c_Orderings_Obot__class_Obot(tc_fun(_1251768, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1251768), c_Big__Operators_Olinorder__class_OMax(_1251768, _1251770)), _1251770)))], (26598 ^ _779308) ^ [_1252212] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1252212)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), _1252212)), c_FunDef_Omax__weak)))], (26604 ^ _779308) ^ [_1252307] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1252307), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (26606 ^ _779308) ^ [] : [-(c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool), tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)), c_FunDef_Omax__strict), c_FunDef_Omax__weak)))], (26608 ^ _779308) ^ [] : [-(c_FunDef_Oreduction__pair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool), tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)), c_FunDef_Omin__strict), c_FunDef_Omin__weak)))], (26610 ^ _779308) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (26612 ^ _779308) ^ [_1252410, _1252412] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1252410), _1252412)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1252410), _1252412)))], (26618 ^ _779308) ^ [_1252515, _1252517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1252515), _1252517)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1252515), _1252517)), c_Wellfounded_Oless__than)))], (26624 ^ _779308) ^ [_1252647, _1252649, _1252651, _1252653] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1252647), _1252649)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1252651), _1252653))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1252647), _1252653) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1252651), _1252649))], (26630 ^ _779308) ^ [_1252794, _1252796, _1252798, _1252800] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1252794), _1252800) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1252798), _1252796), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1252794), _1252796)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1252798), _1252800))), c_Int_Ointrel)))], (26636 ^ _779308) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (26638 ^ _779308) ^ [_1252965, _1252967, _1252969] : [-(c_Wellfounded_Omlex__prod(_1252965, _1252967, _1252969) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1252965), _1252965), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1252965, c_Wellfounded_Oless__than, _1252969)), hAPP(hAPP(c_COMBS(_1252965, _1252965, tc_prod(tc_Nat_Onat, _1252965)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1252965, tc_prod(tc_Nat_Onat, _1252965)), _1252965), c_Product__Type_OPair(tc_Nat_Onat, _1252965)), _1252967)), c_COMBI(_1252965))))], (26640 ^ _779308) ^ [] : [-(c_FunDef_Omin__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__leq)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)))))], (26642 ^ _779308) ^ [_1253065, _1253067] : [class_Orderings_Olinorder(_1253065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1253065), _1253067)), -(_1253067 = c_Orderings_Obot__class_Obot(tc_fun(_1253065, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253065), c_Big__Operators_Olattice_OInf__fin(_1253065, c_Orderings_Oord__class_Omin(_1253065), _1253067)), c_Big__Operators_Olattice_OSup__fin(_1253065, c_Orderings_Oord__class_Omax(_1253065), _1253067))))], (26656 ^ _779308) ^ [_1253263, _1253265, _1253267] : [class_Orderings_Olinorder(_1253263), hBOOL(hAPP(c_Finite__Set_Ofinite(_1253263), _1253265)), hBOOL(hAPP(hAPP(c_member(_1253263), _1253267), _1253265)), 26667 ^ _779308 : [(26668 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1253263, tc_HOL_Obool)), _1253265), hAPP(hAPP(c_Set_Oinsert(_1253263), _1253267), c_Orderings_Obot__class_Obot(tc_fun(_1253263, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1253263, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1253263, c_Orderings_Oord__class_Omax(_1253263), _1253265) = _1253267)], (26674 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1253263, tc_HOL_Obool)), _1253265), hAPP(hAPP(c_Set_Oinsert(_1253263), _1253267), c_Orderings_Obot__class_Obot(tc_fun(_1253263, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1253263, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1253263, c_Orderings_Oord__class_Omax(_1253263), _1253265) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1253263), _1253267), c_Big__Operators_Olattice_OSup__fin(_1253263, c_Orderings_Oord__class_Omax(_1253263), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1253263, tc_HOL_Obool)), _1253265), hAPP(hAPP(c_Set_Oinsert(_1253263), _1253267), c_Orderings_Obot__class_Obot(tc_fun(_1253263, tc_HOL_Obool)))))))]]], (26680 ^ _779308) ^ [_1253787, _1253789, _1253791, _1253793] : [c_FunDef_Oreduction__pair(_1253787, _1253789), -(c_FunDef_Oreduction__pair(_1253791, hAPP(hAPP(c_FunDef_Orp__inv__image(_1253787, _1253791), _1253789), _1253793)))], (26686 ^ _779308) ^ [_1253886, _1253888, _1253890, _1253892] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1253886, tc_HOL_Obool)), _1253888), _1253890), _1253892)), -(hBOOL(hAPP(_1253888, _1253892))), -(hBOOL(hAPP(_1253890, _1253892)))], (26696 ^ _779308) ^ [_1254016, _1254018, _1254020, _1254022] : [26697 ^ _779308 : [(26698 ^ _779308) ^ [] : [hBOOL(hAPP(_1254016, _1254018))], (26700 ^ _779308) ^ [] : [hBOOL(hAPP(_1254020, _1254018))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254022, tc_HOL_Obool)), _1254020), _1254016), _1254018)))], (26704 ^ _779308) ^ [_1254171, _1254173, _1254175, _1254177] : [hBOOL(hAPP(hAPP(c_member(_1254171), _1254173), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254171, tc_HOL_Obool)), _1254175), _1254177))), -(hBOOL(hAPP(hAPP(c_member(_1254171), _1254173), _1254175))), -(hBOOL(hAPP(hAPP(c_member(_1254171), _1254173), _1254177)))], (26714 ^ _779308) ^ [_1254331, _1254333, _1254335, _1254337] : [26715 ^ _779308 : [(26716 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1254331), _1254333), _1254335))], (26718 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1254331), _1254333), _1254337))]], -(hBOOL(hAPP(hAPP(c_member(_1254331), _1254333), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254331, tc_HOL_Obool)), _1254337), _1254335))))], (26732 ^ _779308) ^ [_1254691, _1254693, _1254695, _1254697] : [26733 ^ _779308 : [(26734 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1254691), _1254693), _1254695))], (26736 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1254691), _1254693), _1254697))]], -(hBOOL(hAPP(hAPP(c_member(_1254691), _1254693), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254691, tc_HOL_Obool)), _1254695), _1254697))))], (26722 ^ _779308) ^ [_1254537, _1254539, _1254541, _1254543] : [hBOOL(hAPP(hAPP(c_member(_1254537), _1254539), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254537, tc_HOL_Obool)), _1254541), _1254543))), -(hBOOL(hAPP(hAPP(c_member(_1254537), _1254539), _1254541))), -(hBOOL(hAPP(hAPP(c_member(_1254537), _1254539), _1254543)))], (26740 ^ _779308) ^ [_1254876, _1254878, _1254880, _1254882] : [hBOOL(hAPP(hAPP(c_member(_1254876), _1254878), _1254880)), -(hBOOL(hAPP(hAPP(c_member(_1254876), _1254878), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254876, tc_HOL_Obool)), _1254880), _1254882))))], (26746 ^ _779308) ^ [_1255007, _1255009, _1255011, _1255013] : [hBOOL(hAPP(hAPP(c_member(_1255007), _1255009), _1255011)), -(hBOOL(hAPP(hAPP(c_member(_1255007), _1255009), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255007, tc_HOL_Obool)), _1255013), _1255011))))], (26752 ^ _779308) ^ [_1255138] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1255138) = c_Orderings_Oord__class_Omax(_1255138)), class_Lattices_Osemilattice__sup(_1255138), class_Orderings_Olinorder(_1255138)], (26762 ^ _779308) ^ [_1255267, _1255269, _1255271, _1255273] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255267, tc_HOL_Obool)), _1255269), hAPP(hAPP(c_Set_Oinsert(_1255267), _1255271), _1255273)) = hAPP(hAPP(c_Set_Oinsert(_1255267), _1255271), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255267, tc_HOL_Obool)), _1255269), _1255273)))], (26764 ^ _779308) ^ [_1255334, _1255336, _1255338, _1255340] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255334, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1255334), _1255336), _1255338)), _1255340) = hAPP(hAPP(c_Set_Oinsert(_1255334), _1255336), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255334, tc_HOL_Obool)), _1255338), _1255340)))], (26766 ^ _779308) ^ [_1255401, _1255403, _1255405, _1255407, _1255409] : [class_Lattices_Olattice(_1255401), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255403, _1255401)), _1255405), _1255407), _1255409) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255401), hAPP(_1255405, _1255409)), hAPP(_1255407, _1255409)))], (26772 ^ _779308) ^ [_1255538, _1255540, _1255542] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255538, tc_HOL_Obool)), _1255540), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1255538, tc_HOL_Obool)), _1255542), _1255540)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255538, tc_HOL_Obool)), _1255540), _1255542))], (26774 ^ _779308) ^ [_1255598, _1255600, _1255602] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255598, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1255598, tc_HOL_Obool)), _1255600), _1255602)), _1255602) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255598, tc_HOL_Obool)), _1255600), _1255602))], (26776 ^ _779308) ^ [_1255658, _1255660, _1255662, _1255664] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1255658, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255658, tc_HOL_Obool)), _1255660), _1255662)), _1255664) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1255658, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1255658, tc_HOL_Obool)), _1255660), _1255664)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1255658, tc_HOL_Obool)), _1255662), _1255664)))], (26778 ^ _779308) ^ [_1255742, _1255744, _1255746, _1255748] : [class_Lattices_Osemilattice__sup(_1255742), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255742), _1255744), _1255746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255742), _1255744), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255742), _1255748), _1255746))))], (26788 ^ _779308) ^ [_1255921, _1255923, _1255925, _1255927] : [class_Lattices_Osemilattice__sup(_1255921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255921), _1255923), _1255925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255921), _1255923), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1255921), _1255925), _1255927))))], (26798 ^ _779308) ^ [_1256100, _1256102] : [class_Lattices_Olattice(_1256100), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256100), _1256102), _1256102) = _1256102)], (26804 ^ _779308) ^ [_1256191, _1256193] : [class_Lattices_Osemilattice__sup(_1256191), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256191), _1256193), _1256193) = _1256193)], (26810 ^ _779308) ^ [_1256282, _1256284] : [class_Lattices_Osemilattice__sup(_1256282), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256282), _1256284), _1256284) = _1256284)], (26816 ^ _779308) ^ [_1256373, _1256375, _1256377] : [class_Lattices_Osemilattice__sup(_1256373), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256373), _1256375), _1256377) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256373), _1256377), _1256375))], (26822 ^ _779308) ^ [_1256482, _1256484, _1256486] : [class_Lattices_Olattice(_1256482), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256482), _1256484), _1256486) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256482), _1256486), _1256484))], (26828 ^ _779308) ^ [_1256591, _1256593, _1256595] : [class_Lattices_Osemilattice__sup(_1256591), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256591), _1256593), _1256595) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256591), _1256595), _1256593))], (26834 ^ _779308) ^ [_1256700, _1256702, _1256704] : [class_Lattices_Osemilattice__sup(_1256700), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256700), _1256702), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256700), _1256702), _1256704)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256700), _1256702), _1256704))], (26840 ^ _779308) ^ [_1256825, _1256827, _1256829] : [class_Lattices_Olattice(_1256825), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256825), _1256827), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256825), _1256827), _1256829)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256825), _1256827), _1256829))], (26846 ^ _779308) ^ [_1256950, _1256952, _1256954] : [class_Lattices_Osemilattice__sup(_1256950), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256950), _1256952), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256950), _1256952), _1256954)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1256950), _1256952), _1256954))], (26852 ^ _779308) ^ [_1257075, _1257077, _1257079, _1257081] : [class_Lattices_Osemilattice__sup(_1257075), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257075), _1257077), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257075), _1257079), _1257081)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257075), _1257079), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257075), _1257077), _1257081)))], (26858 ^ _779308) ^ [_1257218, _1257220, _1257222, _1257224] : [class_Lattices_Olattice(_1257218), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257218), _1257220), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257218), _1257222), _1257224)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257218), _1257222), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257218), _1257220), _1257224)))], (26864 ^ _779308) ^ [_1257361, _1257363, _1257365, _1257367] : [class_Lattices_Osemilattice__sup(_1257361), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257361), _1257363), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257361), _1257365), _1257367)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257361), _1257365), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257361), _1257363), _1257367)))], (26870 ^ _779308) ^ [_1257504, _1257506, _1257508, _1257510] : [class_Lattices_Osemilattice__sup(_1257504), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257504), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257504), _1257506), _1257508)), _1257510) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257504), _1257506), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257504), _1257508), _1257510)))], (26876 ^ _779308) ^ [_1257647, _1257649, _1257651, _1257653] : [class_Lattices_Olattice(_1257647), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257647), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257647), _1257649), _1257651)), _1257653) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257647), _1257649), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257647), _1257651), _1257653)))], (26882 ^ _779308) ^ [_1257790, _1257792, _1257794, _1257796] : [class_Lattices_Osemilattice__sup(_1257790), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257790), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257790), _1257792), _1257794)), _1257796) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257790), _1257792), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257790), _1257794), _1257796)))], (26888 ^ _779308) ^ [_1257933, _1257935, _1257937, _1257939, _1257941] : [class_Lattices_Olattice(_1257933), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1257935, _1257933)), _1257937), _1257939), _1257941) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1257933), hAPP(_1257937, _1257941)), hAPP(_1257939, _1257941)))], (26894 ^ _779308) ^ [_1258070, _1258072] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258070, tc_HOL_Obool)), _1258072), _1258072) = _1258072)], (26896 ^ _779308) ^ [_1258106, _1258108, _1258110] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258106, tc_HOL_Obool)), _1258108), _1258110) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258106, tc_HOL_Obool)), _1258110), _1258108))], (26898 ^ _779308) ^ [_1258155, _1258157, _1258159] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258155, tc_HOL_Obool)), _1258157), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258155, tc_HOL_Obool)), _1258157), _1258159)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258155, tc_HOL_Obool)), _1258157), _1258159))], (26900 ^ _779308) ^ [_1258215, _1258217, _1258219, _1258221] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258215, tc_HOL_Obool)), _1258217), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258215, tc_HOL_Obool)), _1258219), _1258221)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258215, tc_HOL_Obool)), _1258219), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258215, tc_HOL_Obool)), _1258217), _1258221)))], (26902 ^ _779308) ^ [_1258288, _1258290, _1258292, _1258294] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258288, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258288, tc_HOL_Obool)), _1258290), _1258292)), _1258294) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258288, tc_HOL_Obool)), _1258290), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258288, tc_HOL_Obool)), _1258292), _1258294)))], (26904 ^ _779308) ^ [_1258382, _1258384, _1258386, _1258388] : [26905 ^ _779308 : [(26906 ^ _779308) ^ [_1258492] : [hBOOL(hAPP(hAPP(c_member(_1258382), _1258492), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258382, tc_HOL_Obool)), _1258384), _1258386))), hBOOL(hAPP(_1258388, _1258492))]], 26914 ^ _779308 : [(26915 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1258382), 26913 ^ [_1258382, _1258384, _1258386, _1258388]), _1258384)))], (26917 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1258388, 26913 ^ [_1258382, _1258384, _1258386, _1258388])))]], 26919 ^ _779308 : [(26920 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1258382), 26918 ^ [_1258382, _1258384, _1258386, _1258388]), _1258386)))], (26922 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1258388, 26918 ^ [_1258382, _1258384, _1258386, _1258388])))]]], (26924 ^ _779308) ^ [_1258781, _1258783, _1258785, _1258787] : [26938 ^ _779308 : [(26939 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1258781), 26937 ^ [_1258781, _1258783, _1258785, _1258787]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1258781, tc_HOL_Obool)), _1258783), _1258785))))], (26941 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1258787, 26937 ^ [_1258781, _1258783, _1258785, _1258787])))]], 26925 ^ _779308 : [(26926 ^ _779308) ^ [_1258894] : [hBOOL(hAPP(hAPP(c_member(_1258781), _1258894), _1258783)), hBOOL(hAPP(_1258787, _1258894))], (26932 ^ _779308) ^ [_1258990] : [hBOOL(hAPP(hAPP(c_member(_1258781), _1258990), _1258785)), hBOOL(hAPP(_1258787, _1258990))]]], (26962 ^ _779308) ^ [_1259627, _1259629, _1259631, _1259633] : [26966 ^ _779308 : [(26967 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1259627), 26965 ^ [_1259627, _1259629, _1259631, _1259633]), _1259629)))], (26969 ^ _779308) ^ [] : [hBOOL(hAPP(_1259633, 26965 ^ [_1259627, _1259629, _1259631, _1259633]))]], 26971 ^ _779308 : [(26972 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1259627), 26970 ^ [_1259627, _1259629, _1259631, _1259633]), _1259631)))], (26974 ^ _779308) ^ [] : [hBOOL(hAPP(_1259633, 26970 ^ [_1259627, _1259629, _1259631, _1259633]))]], 26975 ^ _779308 : [(26976 ^ _779308) ^ [_1259960] : [hBOOL(hAPP(hAPP(c_member(_1259627), _1259960), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259627, tc_HOL_Obool)), _1259629), _1259631))), -(hBOOL(hAPP(_1259633, _1259960)))]]], (26943 ^ _779308) ^ [_1259205, _1259207, _1259209, _1259211] : [26945 ^ _779308 : [(26946 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1259205), 26944 ^ [_1259205, _1259207, _1259209, _1259211]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259205, tc_HOL_Obool)), _1259207), _1259209))))], (26948 ^ _779308) ^ [] : [hBOOL(hAPP(_1259211, 26944 ^ [_1259205, _1259207, _1259209, _1259211]))]], 26949 ^ _779308 : [(26950 ^ _779308) ^ [_1259425] : [hBOOL(hAPP(hAPP(c_member(_1259205), _1259425), _1259207)), -(hBOOL(hAPP(_1259211, _1259425)))], (26956 ^ _779308) ^ [_1259522] : [hBOOL(hAPP(hAPP(c_member(_1259205), _1259522), _1259209)), -(hBOOL(hAPP(_1259211, _1259522)))]]], (26982 ^ _779308) ^ [_1260091, _1260093, _1260095, _1260097] : [hBOOL(hAPP(_1260091, _1260093)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260095, tc_HOL_Obool)), _1260091), _1260097), _1260093)))], (26988 ^ _779308) ^ [_1260202, _1260204, _1260206, _1260208] : [hBOOL(hAPP(_1260202, _1260204)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260206, tc_HOL_Obool)), _1260208), _1260202), _1260204)))], (26994 ^ _779308) ^ [_1260313, _1260315, _1260317] : [class_Lattices_Olattice(_1260313), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260313), _1260315), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1260313), _1260315), _1260317))))], (27000 ^ _779308) ^ [_1260420, _1260422, _1260424] : [class_Lattices_Osemilattice__sup(_1260420), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260420), _1260422), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1260420), _1260422), _1260424))))], (27006 ^ _779308) ^ [_1260527, _1260529, _1260531] : [class_Lattices_Olattice(_1260527), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260527), _1260529), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1260527), _1260531), _1260529))))], (27012 ^ _779308) ^ [_1260634, _1260636, _1260638] : [class_Lattices_Osemilattice__sup(_1260634), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260634), _1260636), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1260634), _1260638), _1260636))))], (27018 ^ _779308) ^ [_1260741, _1260743, _1260745] : [class_Lattices_Osemilattice__sup(_1260741), 27021 ^ _779308 : [(27022 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260741), _1260743), _1260745)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1260741), _1260743), _1260745) = _1260745)], (27028 ^ _779308) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1260741), _1260743), _1260745) = _1260745, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260741), _1260743), _1260745)))]]], (27034 ^ _779308) ^ [_1260997, _1260999, _1261001, _1261003] : [class_Lattices_Osemilattice__sup(_1260997), 27037 ^ _779308 : [(27038 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260997), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1260997), _1260999), _1261001)), _1261003)), 27041 ^ _779308 : [(27042 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260997), _1260999), _1261003)))], (27044 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260997), _1261001), _1261003)))]]], (27046 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260997), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1260997), _1260999), _1261001)), _1261003))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260997), _1260999), _1261003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1260997), _1261001), _1261003))]]], (27056 ^ _779308) ^ [_1261377, _1261379, _1261381, _1261383] : [class_Lattices_Osemilattice__sup(_1261377), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261377), _1261379), _1261381)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261377), _1261379), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1261377), _1261381), _1261383))))], (27066 ^ _779308) ^ [_1261556, _1261558, _1261560, _1261562] : [class_Lattices_Osemilattice__sup(_1261556), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261556), _1261558), _1261560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261556), _1261558), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1261556), _1261562), _1261560))))], (27076 ^ _779308) ^ [_1261735, _1261737, _1261739] : [class_Lattices_Osemilattice__sup(_1261735), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261735), _1261737), _1261739)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1261735), _1261737), _1261739) = _1261739)], (27086 ^ _779308) ^ [_1261896, _1261898, _1261900] : [class_Lattices_Osemilattice__sup(_1261896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261896), _1261898), _1261900)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1261896), _1261900), _1261898) = _1261900)], (27096 ^ _779308) ^ [_1262057, _1262059, _1262061, _1262063] : [class_Lattices_Osemilattice__sup(_1262057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262057), _1262059), _1262061)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262057), _1262063), _1262061)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262057), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262057), _1262059), _1262063)), _1262061)))], (27110 ^ _779308) ^ [_1262306, _1262308, _1262310, _1262312] : [class_Lattices_Osemilattice__sup(_1262306), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262306), _1262308), _1262310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262306), _1262312), _1262310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262306), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262306), _1262308), _1262312)), _1262310)))], (27124 ^ _779308) ^ [_1262555, _1262557, _1262559, _1262561, _1262563] : [class_Lattices_Osemilattice__sup(_1262555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262555), _1262557), _1262559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262555), _1262561), _1262563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262555), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262555), _1262557), _1262561)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262555), _1262559), _1262563))))], (27138 ^ _779308) ^ [_1262826, _1262828, _1262830, _1262832] : [class_Lattices_Osemilattice__sup(_1262826), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262826), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262826), _1262828), _1262830)), _1262832)), 27145 ^ _779308 : [(27146 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262826), _1262828), _1262832)))], (27148 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262826), _1262830), _1262832)))]]], (27150 ^ _779308) ^ [_1263049, _1263051, _1263053, _1263055, _1263057] : [-(hAPP(c_Set_Oimage(_1263049, _1263051, _1263053), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263049, tc_HOL_Obool)), _1263055), _1263057)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263051, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1263049, _1263051, _1263053), _1263055)), hAPP(c_Set_Oimage(_1263049, _1263051, _1263053), _1263057)))], (27152 ^ _779308) ^ [_1263123, _1263125, _1263127, _1263129, _1263131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263123, tc_HOL_Obool)), _1263125), _1263127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263123, tc_HOL_Obool)), _1263129), _1263131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263123, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263123, tc_HOL_Obool)), _1263125), _1263129)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263123, tc_HOL_Obool)), _1263127), _1263131))))], (27162 ^ _779308) ^ [_1263368, _1263370, _1263372, _1263374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263368, tc_HOL_Obool)), _1263370), _1263372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263368, tc_HOL_Obool)), _1263374), _1263372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263368, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263368, tc_HOL_Obool)), _1263370), _1263374)), _1263372)))], (27172 ^ _779308) ^ [_1263587, _1263589, _1263591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263587, tc_HOL_Obool)), _1263589), _1263591)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263587, tc_HOL_Obool)), _1263591), _1263589) = _1263591)], (27178 ^ _779308) ^ [_1263708, _1263710, _1263712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263708, tc_HOL_Obool)), _1263710), _1263712)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263708, tc_HOL_Obool)), _1263710), _1263712) = _1263712)], (27184 ^ _779308) ^ [_1263847, _1263849, _1263851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263847, tc_HOL_Obool)), _1263849), _1263851)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263847, tc_HOL_Obool)), _1263849), _1263851) = _1263851)], (27190 ^ _779308) ^ [_1263964, _1263966, _1263968] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263964, tc_HOL_Obool)), _1263966), _1263968) = _1263968, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1263964, tc_HOL_Obool)), _1263966), _1263968)))], (27196 ^ _779308) ^ [_1264087, _1264089, _1264091] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264087, tc_HOL_Obool)), _1264089), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264087, tc_HOL_Obool)), _1264091), _1264089))))], (27198 ^ _779308) ^ [_1264135, _1264137, _1264139] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264135, tc_HOL_Obool)), _1264137), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264135, tc_HOL_Obool)), _1264137), _1264139))))], (27200 ^ _779308) ^ [_1264183, _1264185] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264183, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1264183, tc_HOL_Obool))), _1264185) = _1264185)], (27202 ^ _779308) ^ [_1264224, _1264226] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264224, tc_HOL_Obool)), _1264226), c_Orderings_Obot__class_Obot(tc_fun(_1264224, tc_HOL_Obool))) = _1264226)], (27204 ^ _779308) ^ [_1264283, _1264285, _1264287] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264283, tc_HOL_Obool)), _1264285), _1264287) = c_Orderings_Obot__class_Obot(tc_fun(_1264283, tc_HOL_Obool)), 27207 ^ _779308 : [(27208 ^ _779308) ^ [] : [-(_1264285 = c_Orderings_Obot__class_Obot(tc_fun(_1264283, tc_HOL_Obool)))], (27210 ^ _779308) ^ [] : [-(_1264287 = c_Orderings_Obot__class_Obot(tc_fun(_1264283, tc_HOL_Obool)))]]], (27212 ^ _779308) ^ [_1264436, _1264438, _1264440] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264436, tc_HOL_Obool)), _1264438), _1264440) = c_Orderings_Obot__class_Obot(tc_fun(_1264436, tc_HOL_Obool))), _1264438 = c_Orderings_Obot__class_Obot(tc_fun(_1264436, tc_HOL_Obool)), _1264440 = c_Orderings_Obot__class_Obot(tc_fun(_1264436, tc_HOL_Obool))], (27222 ^ _779308) ^ [_1264641, _1264643, _1264645] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1264641), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264641, tc_HOL_Obool)), _1264643), _1264645))), 27225 ^ _779308 : [(27226 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1264641), _1264643)))], (27228 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1264641), _1264645)))]]], (27230 ^ _779308) ^ [_1264788, _1264790, _1264792] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1264788), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264788, tc_HOL_Obool)), _1264790), _1264792)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264788), _1264790)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264788), _1264792))], (27240 ^ _779308) ^ [_1264969, _1264971, _1264973] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1264969), _1264971)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264969), _1264973)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1264969), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264969, tc_HOL_Obool)), _1264971), _1264973))))], (27250 ^ _779308) ^ [_1265148, _1265150] : [class_Lattices_Obounded__lattice__bot(_1265148), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265148), c_Orderings_Obot__class_Obot(_1265148)), _1265150) = _1265150)], (27256 ^ _779308) ^ [_1265243, _1265245] : [class_Lattices_Obounded__lattice__bot(_1265243), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265243), _1265245), c_Orderings_Obot__class_Obot(_1265243)) = _1265245)], (27262 ^ _779308) ^ [_1265338, _1265340, _1265342] : [class_Lattices_Obounded__lattice__bot(_1265338), 27265 ^ _779308 : [(27266 ^ _779308) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265338), _1265340), _1265342) = c_Orderings_Obot__class_Obot(_1265338), 27269 ^ _779308 : [(27270 ^ _779308) ^ [] : [-(_1265340 = c_Orderings_Obot__class_Obot(_1265338))], (27272 ^ _779308) ^ [] : [-(_1265342 = c_Orderings_Obot__class_Obot(_1265338))]]], (27274 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265338), _1265340), _1265342) = c_Orderings_Obot__class_Obot(_1265338)), _1265340 = c_Orderings_Obot__class_Obot(_1265338), _1265342 = c_Orderings_Obot__class_Obot(_1265338)]]], (27284 ^ _779308) ^ [_1265665] : [class_Lattices_Osemilattice__sup(_1265665), -(c_Finite__Set_Ofun__left__comm__idem(_1265665, _1265665, c_Lattices_Osemilattice__sup__class_Osup(_1265665)))], (27290 ^ _779308) ^ [_1265765, _1265767, _1265769, _1265771] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265765, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1265765, tc_fun(_1265765, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265765)), _1265767)), hAPP(hAPP(c_COMBC(_1265765, tc_fun(_1265765, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265765)), _1265769)), _1265771)), -(hBOOL(hAPP(hAPP(c_member(_1265765), _1265771), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265765, tc_HOL_Obool)), _1265767), _1265769))))], (27296 ^ _779308) ^ [_1265964, _1265966, _1265968, _1265970] : [hBOOL(hAPP(hAPP(c_member(_1265964), _1265970), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265964, tc_HOL_Obool)), _1265966), _1265968))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265964, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1265964, tc_fun(_1265964, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265964)), _1265966)), hAPP(hAPP(c_COMBC(_1265964, tc_fun(_1265964, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265964)), _1265968)), _1265970)))], (27302 ^ _779308) ^ [_1266169, _1266171, _1266173] : [class_Orderings_Olinorder(_1266169), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266169), _1266171)), -(_1266171 = c_Orderings_Obot__class_Obot(tc_fun(_1266169, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266169), _1266173)), -(_1266173 = c_Orderings_Obot__class_Obot(tc_fun(_1266169, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1266169, c_Orderings_Oord__class_Omax(_1266169), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266169, tc_HOL_Obool)), _1266171), _1266173)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1266169), c_Big__Operators_Olattice_OSup__fin(_1266169, c_Orderings_Oord__class_Omax(_1266169), _1266171)), c_Big__Operators_Olattice_OSup__fin(_1266169, c_Orderings_Oord__class_Omax(_1266169), _1266173)))], (27324 ^ _779308) ^ [_1266536, _1266538, _1266540] : [-(hAPP(hAPP(c_Set_Oinsert(_1266536), _1266538), _1266540) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266536, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1266536), _1266538), c_Orderings_Obot__class_Obot(tc_fun(_1266536, tc_HOL_Obool)))), _1266540))], (27326 ^ _779308) ^ [_1266595, _1266597, _1266599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1266595, tc_HOL_Obool)), _1266597), _1266599)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266595, tc_HOL_Obool)), _1266597), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266595, tc_HOL_Obool)), _1266599), _1266597)) = _1266599)], (27332 ^ _779308) ^ [_1266759, _1266761, _1266763, _1266765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1266759, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266759, tc_HOL_Obool)), _1266761), _1266763)), _1266765)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1266759, tc_HOL_Obool)), _1266761), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266759, tc_HOL_Obool)), _1266763), _1266765))))], (27338 ^ _779308) ^ [_1266920, _1266922, _1266924, _1266926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1266920, tc_HOL_Obool)), _1266922), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266920, tc_HOL_Obool)), _1266924), _1266926))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1266920, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1266920, tc_HOL_Obool)), _1266922), _1266924)), _1266926)))], (27344 ^ _779308) ^ [_1267087, _1267089, _1267091, _1267093, _1267095] : [c_Fun_Oinj__on(_1267087, _1267089, _1267091, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267087, tc_HOL_Obool)), _1267093), _1267095)), 27347 ^ _779308 : [(27348 ^ _779308) ^ [] : [hAPP(c_Set_Oimage(_1267087, _1267089, _1267091), _1267093) = hAPP(c_Set_Oimage(_1267087, _1267089, _1267091), _1267095), -(_1267093 = _1267095)], (27354 ^ _779308) ^ [] : [_1267093 = _1267095, -(hAPP(c_Set_Oimage(_1267087, _1267089, _1267091), _1267093) = hAPP(c_Set_Oimage(_1267087, _1267089, _1267091), _1267095))]]], (27360 ^ _779308) ^ [_1267380, _1267382, _1267384] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1267380, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1267380, tc_HOL_Obool)), _1267382), _1267384)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267380, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1267380, tc_HOL_Obool)), _1267382)), _1267384))], (27362 ^ _779308) ^ [_1267445, _1267447] : [-(c_FunDef_Orp__inv__image(_1267445, _1267447) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1267445, _1267445), tc_HOL_Obool), tc_fun(tc_prod(_1267445, _1267445), tc_HOL_Obool), tc_fun(tc_fun(_1267447, _1267445), tc_prod(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1267445, _1267445), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1267445, _1267445), tc_HOL_Obool), tc_fun(tc_fun(_1267447, _1267445), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1267445, _1267445), tc_HOL_Obool), tc_fun(tc_fun(_1267447, _1267445), tc_prod(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1267447, _1267445), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool)), tc_fun(tc_fun(_1267447, _1267445), tc_prod(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1267445, _1267445), tc_HOL_Obool), tc_fun(tc_fun(_1267447, _1267445), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1267445, _1267445), tc_HOL_Obool), tc_fun(tc_fun(_1267447, _1267445), tc_prod(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool))))), tc_fun(tc_prod(_1267445, _1267445), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1267447, _1267445), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool)), tc_fun(tc_fun(_1267447, _1267445), tc_prod(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool))), tc_fun(tc_prod(_1267445, _1267445), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1267447, _1267445), tc_fun(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1267447, _1267445), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool)), tc_fun(tc_fun(_1267447, _1267445), tc_prod(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool)))), tc_fun(tc_prod(_1267445, _1267445), tc_HOL_Obool)), c_COMBS(tc_fun(_1267447, _1267445), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1267447, _1267445), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool)), tc_fun(tc_fun(_1267447, _1267445), tc_fun(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool)))), tc_fun(tc_prod(_1267445, _1267445), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool))), tc_fun(_1267447, _1267445)), c_Product__Type_OPair(tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool), tc_fun(tc_prod(_1267447, _1267447), tc_HOL_Obool)))), c_Relation_Oinv__image(_1267445, _1267447))))), c_Relation_Oinv__image(_1267445, _1267447))))], (27364 ^ _779308) ^ [_1267958, _1267960, _1267962, _1267964, _1267966, _1267968, _1267970, _1267972] : [c_Finite__Set_Ofolding__image__simple__idem(_1267958, _1267960, _1267962, _1267964, _1267966, _1267968), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267960), _1267970)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267960), _1267972)), -(hAPP(_1267968, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267960, tc_HOL_Obool)), _1267970), _1267972)) = hAPP(hAPP(_1267962, hAPP(_1267968, _1267970)), hAPP(_1267968, _1267972)))], (27378 ^ _779308) ^ [_1268251, _1268253, _1268255] : [class_Orderings_Olinorder(_1268251), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268251), _1268253)), hBOOL(hAPP(hAPP(c_member(_1268251), _1268255), _1268253)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1268251), _1268255), c_Big__Operators_Olattice_OSup__fin(_1268251, c_Orderings_Oord__class_Omax(_1268251), _1268253)) = c_Big__Operators_Olattice_OSup__fin(_1268251, c_Orderings_Oord__class_Omax(_1268251), _1268253))], (27392 ^ _779308) ^ [_1268498, _1268500] : [class_Orderings_Olinorder(_1268498), -(c_Big__Operators_Olattice_OSup__fin(_1268498, c_Orderings_Oord__class_Omax(_1268498), hAPP(hAPP(c_Set_Oinsert(_1268498), _1268500), c_Orderings_Obot__class_Obot(tc_fun(_1268498, tc_HOL_Obool)))) = _1268500)], (27398 ^ _779308) ^ [_1268611, _1268613, _1268615, _1268617, _1268619] : [c_Finite__Set_Ofolding__one__idem(_1268611, _1268613, _1268615), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268611), _1268617)), -(_1268617 = c_Orderings_Obot__class_Obot(tc_fun(_1268611, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268611), _1268619)), -(_1268619 = c_Orderings_Obot__class_Obot(tc_fun(_1268611, tc_HOL_Obool))), -(hAPP(_1268615, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1268611, tc_HOL_Obool)), _1268617), _1268619)) = hAPP(hAPP(_1268613, hAPP(_1268615, _1268617)), hAPP(_1268615, _1268619)))], (27420 ^ _779308) ^ [_1268976, _1268978] : [class_Orderings_Olinorder(_1268976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268976), _1268978)), -(c_Big__Operators_Olattice_OSup__fin(_1268976, c_Orderings_Oord__class_Omax(_1268976), _1268978) = hAPP(c_Finite__Set_Ofold1(_1268976, c_Orderings_Oord__class_Omax(_1268976)), _1268978))], (27430 ^ _779308) ^ [_1269139, _1269141, _1269143] : [class_Lattices_Oab__semigroup__idem__mult(_1269139), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269139), _1269141)), -(_1269141 = c_Orderings_Obot__class_Obot(tc_fun(_1269139, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269139), _1269143)), -(_1269143 = c_Orderings_Obot__class_Obot(tc_fun(_1269139, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1269139, c_Groups_Otimes__class_Otimes(_1269139)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1269139, tc_HOL_Obool)), _1269141), _1269143)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1269139), hAPP(c_Finite__Set_Ofold1(_1269139, c_Groups_Otimes__class_Otimes(_1269139)), _1269141)), hAPP(c_Finite__Set_Ofold1(_1269139, c_Groups_Otimes__class_Otimes(_1269139)), _1269143)))], (27452 ^ _779308) ^ [_1269518, _1269520, _1269522] : [class_Orderings_Olinorder(_1269518), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269518), _1269520)), -(_1269520 = c_Orderings_Obot__class_Obot(tc_fun(_1269518, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269518), _1269522)), -(_1269522 = c_Orderings_Obot__class_Obot(tc_fun(_1269518, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1269518, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1269518, tc_HOL_Obool)), _1269520), _1269522)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1269518), c_Big__Operators_Olinorder__class_OMin(_1269518, _1269520)), c_Big__Operators_Olinorder__class_OMin(_1269518, _1269522)))], (27474 ^ _779308) ^ [_1269867, _1269869, _1269871] : [class_Orderings_Olinorder(_1269867), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269867), _1269869)), -(_1269869 = c_Orderings_Obot__class_Obot(tc_fun(_1269867, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269867), _1269871)), -(_1269871 = c_Orderings_Obot__class_Obot(tc_fun(_1269867, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1269867, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1269867, tc_HOL_Obool)), _1269869), _1269871)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269867), c_Big__Operators_Olinorder__class_OMax(_1269867, _1269869)), c_Big__Operators_Olinorder__class_OMax(_1269867, _1269871)))], (27496 ^ _779308) ^ [_1270216, _1270218, _1270220] : [class_Orderings_Olinorder(_1270216), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270216), _1270218)), -(_1270218 = c_Orderings_Obot__class_Obot(tc_fun(_1270216, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270216), _1270220)), -(_1270220 = c_Orderings_Obot__class_Obot(tc_fun(_1270216, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1270216, c_Orderings_Oord__class_Omin(_1270216), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270216, tc_HOL_Obool)), _1270218), _1270220)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1270216), c_Big__Operators_Olattice_OInf__fin(_1270216, c_Orderings_Oord__class_Omin(_1270216), _1270218)), c_Big__Operators_Olattice_OInf__fin(_1270216, c_Orderings_Oord__class_Omin(_1270216), _1270220)))], (27518 ^ _779308) ^ [_1270583, _1270585, _1270587, _1270589] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1270583), _1270585)), -(hAPP(c_Set_Oimage(_1270583, _1270587, _1270589), _1270585) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1270587, tc_HOL_Obool), _1270583, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270587, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1270583, tc_fun(_1270587, tc_HOL_Obool), tc_fun(_1270587, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1270587, tc_fun(tc_fun(_1270587, tc_HOL_Obool), tc_fun(_1270587, tc_HOL_Obool)), _1270583), c_Set_Oinsert(_1270587)), _1270589)), c_Orderings_Obot__class_Obot(tc_fun(_1270587, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1270587, tc_HOL_Obool))), _1270585))], (27524 ^ _779308) ^ [_1270822, _1270824, _1270826] : [class_Orderings_Olinorder(_1270822), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270822), _1270824)), -(_1270824 = c_Orderings_Obot__class_Obot(tc_fun(_1270822, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1270822, c_Orderings_Oord__class_Omax(_1270822), hAPP(hAPP(c_Set_Oinsert(_1270822), _1270826), _1270824)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1270822), _1270826), c_Big__Operators_Olattice_OSup__fin(_1270822, c_Orderings_Oord__class_Omax(_1270822), _1270824)))], (27538 ^ _779308) ^ [_1271042, _1271044, _1271046] : [class_Orderings_Olinorder(_1271042), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271042), _1271044)), -(_1271046 = c_Orderings_Obot__class_Obot(tc_fun(_1271042, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271042, tc_HOL_Obool)), _1271046), _1271044)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271042), c_Big__Operators_Olattice_OSup__fin(_1271042, c_Orderings_Oord__class_Omax(_1271042), _1271046)), c_Big__Operators_Olattice_OSup__fin(_1271042, c_Orderings_Oord__class_Omax(_1271042), _1271044)) = c_Big__Operators_Olattice_OSup__fin(_1271042, c_Orderings_Oord__class_Omax(_1271042), _1271044))], (27556 ^ _779308) ^ [_1271374, _1271376, _1271378] : [class_Orderings_Olinorder(_1271374), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271374), _1271376)), hBOOL(hAPP(hAPP(c_member(_1271374), _1271378), _1271376)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1271374), _1271378), c_Big__Operators_Olattice_OSup__fin(_1271374, c_Orderings_Oord__class_Omax(_1271374), _1271376)) = _1271378)], (27570 ^ _779308) ^ [_1271609, _1271611, _1271613] : [class_Orderings_Olinorder(_1271609), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271609), _1271611)), -(hBOOL(hAPP(hAPP(c_member(_1271609), _1271613), _1271611))), -(_1271611 = c_Orderings_Obot__class_Obot(tc_fun(_1271609, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1271609, c_Orderings_Oord__class_Omax(_1271609), hAPP(hAPP(c_Set_Oinsert(_1271609), _1271613), _1271611)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271609), _1271613), c_Big__Operators_Olattice_OSup__fin(_1271609, c_Orderings_Oord__class_Omax(_1271609), _1271611)))], (27588 ^ _779308) ^ [_1271858, _1271860, _1271862] : [class_Orderings_Olinorder(_1271858), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271858), _1271860)), 27595 ^ _779308 : [(27596 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1271858, tc_HOL_Obool)), _1271860), hAPP(hAPP(c_Set_Oinsert(_1271858), _1271862), c_Orderings_Obot__class_Obot(tc_fun(_1271858, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1271858, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1271858, c_Orderings_Oord__class_Omax(_1271858), hAPP(hAPP(c_Set_Oinsert(_1271858), _1271862), _1271860)) = _1271862)], (27602 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1271858, tc_HOL_Obool)), _1271860), hAPP(hAPP(c_Set_Oinsert(_1271858), _1271862), c_Orderings_Obot__class_Obot(tc_fun(_1271858, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1271858, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1271858, c_Orderings_Oord__class_Omax(_1271858), hAPP(hAPP(c_Set_Oinsert(_1271858), _1271862), _1271860)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1271858), _1271862), c_Big__Operators_Olattice_OSup__fin(_1271858, c_Orderings_Oord__class_Omax(_1271858), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1271858, tc_HOL_Obool)), _1271860), hAPP(hAPP(c_Set_Oinsert(_1271858), _1271862), c_Orderings_Obot__class_Obot(tc_fun(_1271858, tc_HOL_Obool)))))))]]], (27608 ^ _779308) ^ [] : [-(c_FunDef_Omax__weak = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__leq)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_HOL_Obool)))))], (27610 ^ _779308) ^ [_1272391, _1272393, _1272395, _1272397, _1272399, _1272401] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1272391, _1272391)), hAPP(hAPP(c_Product__Type_OPair(_1272391, _1272391), _1272393), _1272395)), hAPP(hAPP(c_Relation_Oinv__image(_1272397, _1272391), _1272399), _1272401))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1272397, _1272397)), hAPP(hAPP(c_Product__Type_OPair(_1272397, _1272397), hAPP(_1272401, _1272393)), hAPP(_1272401, _1272395))), _1272399)))], (27616 ^ _779308) ^ [_1272578, _1272580, _1272582, _1272584, _1272586, _1272588] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1272584, _1272584)), hAPP(hAPP(c_Product__Type_OPair(_1272584, _1272584), hAPP(_1272588, _1272580)), hAPP(_1272588, _1272582))), _1272586)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1272578, _1272578)), hAPP(hAPP(c_Product__Type_OPair(_1272578, _1272578), _1272580), _1272582)), hAPP(hAPP(c_Relation_Oinv__image(_1272584, _1272578), _1272586), _1272588))))], (27622 ^ _779308) ^ [_1272771, _1272773] : [class_Orderings_Olinorder(_1272771), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272771), _1272773)), -(_1272773 = c_Orderings_Obot__class_Obot(tc_fun(_1272771, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1272771), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1272771), 27635 ^ [_1272771, _1272773]), 27636 ^ [_1272771, _1272773])), hAPP(hAPP(c_Set_Oinsert(_1272771), 27635 ^ [_1272771, _1272773]), hAPP(hAPP(c_Set_Oinsert(_1272771), 27636 ^ [_1272771, _1272773]), c_Orderings_Obot__class_Obot(tc_fun(_1272771, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1272771), c_Big__Operators_Olattice_OSup__fin(_1272771, c_Orderings_Oord__class_Omax(_1272771), _1272773)), _1272773)))], (27642 ^ _779308) ^ [_1273221, _1273223, _1273225] : [class_Orderings_Olinorder(_1273221), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273221), _1273223), _1273225)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273221, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1273221, _1273223, _1273225)), hAPP(hAPP(c_Set_Oinsert(_1273221), _1273225), c_Orderings_Obot__class_Obot(tc_fun(_1273221, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1273221, _1273223, _1273225))], (27652 ^ _779308) ^ [_1273430, _1273432, _1273434] : [class_Lattices_Olattice(_1273430), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273430), _1273432)), hBOOL(hAPP(hAPP(c_member(_1273430), _1273434), _1273432)), 27663 ^ _779308 : [(27664 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273430, tc_HOL_Obool)), _1273432), hAPP(hAPP(c_Set_Oinsert(_1273430), _1273434), c_Orderings_Obot__class_Obot(tc_fun(_1273430, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1273430, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1273430, _1273432) = _1273434)], (27670 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273430, tc_HOL_Obool)), _1273432), hAPP(hAPP(c_Set_Oinsert(_1273430), _1273434), c_Orderings_Obot__class_Obot(tc_fun(_1273430, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1273430, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1273430, _1273432) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1273430), _1273434), c_Big__Operators_Olattice__class_OSup__fin(_1273430, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1273430, tc_HOL_Obool)), _1273432), hAPP(hAPP(c_Set_Oinsert(_1273430), _1273434), c_Orderings_Obot__class_Obot(tc_fun(_1273430, tc_HOL_Obool)))))))]]], (27676 ^ _779308) ^ [_1273936, _1273938] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1273936, _1273938))))], (27678 ^ _779308) ^ [_1273967, _1273969] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1273967, _1273969))))], (27680 ^ _779308) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (27682 ^ _779308) ^ [_1274016, _1274018] : [c_Nat__Transfer_Onat__set(_1274016), c_Nat__Transfer_Onat__set(_1274018), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1274016), _1274018)))], (27692 ^ _779308) ^ [_1274151, _1274153] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1274151), _1274153) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1274151)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1274153))))], (27694 ^ _779308) ^ [_1274197, _1274199] : [class_Lattices_Olattice(_1274197), -(c_Big__Operators_Olattice__class_OSup__fin(_1274197, hAPP(hAPP(c_Set_Oinsert(_1274197), _1274199), c_Orderings_Obot__class_Obot(tc_fun(_1274197, tc_HOL_Obool)))) = _1274199)], (27700 ^ _779308) ^ [_1274304, _1274306] : [c_Nat__Transfer_Onat__set(_1274304), c_Nat__Transfer_Onat__set(_1274306), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1274304), _1274306) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1274304)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1274306))))], (27710 ^ _779308) ^ [_1274471, _1274473, _1274475] : [class_Orderings_Oorder(_1274471), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274471), _1274473), _1274475)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1274471, _1274475, _1274473) = c_Orderings_Obot__class_Obot(tc_fun(_1274471, tc_HOL_Obool)))], (27720 ^ _779308) ^ [_1274634, _1274636, _1274638] : [class_Orderings_Oorder(_1274634), 27723 ^ _779308 : [(27724 ^ _779308) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1274634, _1274636, _1274638) = c_Orderings_Obot__class_Obot(tc_fun(_1274634, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274634), _1274636), _1274638))], (27730 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274634), _1274636), _1274638))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1274634, _1274636, _1274638) = c_Orderings_Obot__class_Obot(tc_fun(_1274634, tc_HOL_Obool)))]]], (27736 ^ _779308) ^ [_1274853, _1274855, _1274857] : [class_Orderings_Oorder(_1274853), 27739 ^ _779308 : [(27740 ^ _779308) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1274853, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1274853, _1274855, _1274857), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274853), _1274855), _1274857))], (27746 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274853), _1274855), _1274857))), -(c_Orderings_Obot__class_Obot(tc_fun(_1274853, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1274853, _1274855, _1274857))]]], (27752 ^ _779308) ^ [_1275072, _1275074, _1275076, _1275078] : [class_Orderings_Olinorder(_1275072), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275072), _1275074), _1275076)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275072), _1275076), _1275078)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275072, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1275072, _1275074, _1275076)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1275072, _1275076, _1275078)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1275072, _1275074, _1275078))], (27766 ^ _779308) ^ [_1275337, _1275339] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1275337, _1275339)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1275339), _1275337))], (27768 ^ _779308) ^ [_1275402, _1275404, _1275406, _1275408, _1275410, _1275412] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275402, tc_fun(_1275404, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1275402, tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_fun(_1275404, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1275404, tc_fun(tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_fun(_1275404, tc_HOL_Obool)), _1275402), c_COMBC(_1275404, tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1275404, tc_prod(_1275402, _1275404)), tc_fun(_1275404, tc_fun(tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_HOL_Obool)), _1275402), hAPP(c_COMBB(tc_prod(_1275402, _1275404), tc_fun(tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_HOL_Obool), _1275404), c_member(tc_prod(_1275402, _1275404)))), c_Product__Type_OPair(_1275402, _1275404)))), _1275406)), hAPP(hAPP(c_COMBC(_1275402, tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_fun(_1275404, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1275404, tc_fun(tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_fun(_1275404, tc_HOL_Obool)), _1275402), c_COMBC(_1275404, tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1275404, tc_prod(_1275402, _1275404)), tc_fun(_1275404, tc_fun(tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_HOL_Obool)), _1275402), hAPP(c_COMBB(tc_prod(_1275402, _1275404), tc_fun(tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool), tc_HOL_Obool), _1275404), c_member(tc_prod(_1275402, _1275404)))), c_Product__Type_OPair(_1275402, _1275404)))), _1275408)), _1275410), _1275412)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1275402, _1275404)), hAPP(hAPP(c_Product__Type_OPair(_1275402, _1275404), _1275410), _1275412)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1275402, _1275404), tc_HOL_Obool)), _1275406), _1275408))))], (27774 ^ _779308) ^ [_1276059, _1276061, _1276063, _1276065, _1276067, _1276069] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1276059, _1276061)), hAPP(hAPP(c_Product__Type_OPair(_1276059, _1276061), _1276067), _1276069)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool)), _1276063), _1276065))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276059, tc_fun(_1276061, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1276059, tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_fun(_1276061, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276061, tc_fun(tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_fun(_1276061, tc_HOL_Obool)), _1276059), c_COMBC(_1276061, tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276061, tc_prod(_1276059, _1276061)), tc_fun(_1276061, tc_fun(tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_HOL_Obool)), _1276059), hAPP(c_COMBB(tc_prod(_1276059, _1276061), tc_fun(tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_HOL_Obool), _1276061), c_member(tc_prod(_1276059, _1276061)))), c_Product__Type_OPair(_1276059, _1276061)))), _1276063)), hAPP(hAPP(c_COMBC(_1276059, tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_fun(_1276061, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276061, tc_fun(tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_fun(_1276061, tc_HOL_Obool)), _1276059), c_COMBC(_1276061, tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1276061, tc_prod(_1276059, _1276061)), tc_fun(_1276061, tc_fun(tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_HOL_Obool)), _1276059), hAPP(c_COMBB(tc_prod(_1276059, _1276061), tc_fun(tc_fun(tc_prod(_1276059, _1276061), tc_HOL_Obool), tc_HOL_Obool), _1276061), c_member(tc_prod(_1276059, _1276061)))), c_Product__Type_OPair(_1276059, _1276061)))), _1276065)), _1276067), _1276069)))], (27780 ^ _779308) ^ [_1276722, _1276724, _1276726] : [class_Lattices_Olattice(_1276722), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276722), _1276724)), hBOOL(hAPP(hAPP(c_member(_1276722), _1276726), _1276724)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1276722), _1276726), c_Big__Operators_Olattice__class_OSup__fin(_1276722, _1276724)) = c_Big__Operators_Olattice__class_OSup__fin(_1276722, _1276724))], (27794 ^ _779308) ^ [_1276957, _1276959] : [class_Lattices_Olattice(_1276957), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276957), _1276959)), -(c_Big__Operators_Olattice__class_OSup__fin(_1276957, _1276959) = hAPP(c_Finite__Set_Ofold1(_1276957, c_Lattices_Osemilattice__sup__class_Osup(_1276957)), _1276959))], (27804 ^ _779308) ^ [_1277114, _1277116, _1277118] : [class_Lattices_Olattice(_1277114), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277114), _1277116)), -(_1277116 = c_Orderings_Obot__class_Obot(tc_fun(_1277114, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1277114, hAPP(hAPP(c_Set_Oinsert(_1277114), _1277118), _1277116)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1277114), _1277118), c_Big__Operators_Olattice__class_OSup__fin(_1277114, _1277116)))], (27818 ^ _779308) ^ [_1277322, _1277324, _1277326] : [class_Lattices_Olattice(_1277322), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277322), _1277324)), -(_1277326 = c_Orderings_Obot__class_Obot(tc_fun(_1277322, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277322, tc_HOL_Obool)), _1277326), _1277324)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1277322), c_Big__Operators_Olattice__class_OSup__fin(_1277322, _1277326)), c_Big__Operators_Olattice__class_OSup__fin(_1277322, _1277324)) = c_Big__Operators_Olattice__class_OSup__fin(_1277322, _1277324))], (27836 ^ _779308) ^ [_1277636, _1277638] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1277636, _1277638)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1277638), _1277636)))], (27838 ^ _779308) ^ [_1277677, _1277679, _1277681] : [class_Lattices_Olattice(_1277677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277677), _1277679)), -(_1277679 = c_Orderings_Obot__class_Obot(tc_fun(_1277677, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277677), _1277681)), -(_1277681 = c_Orderings_Obot__class_Obot(tc_fun(_1277677, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1277677, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277677, tc_HOL_Obool)), _1277679), _1277681)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1277677), c_Big__Operators_Olattice__class_OSup__fin(_1277677, _1277679)), c_Big__Operators_Olattice__class_OSup__fin(_1277677, _1277681)))], (27860 ^ _779308) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (27862 ^ _779308) ^ [_1278044, _1278046, _1278048, _1278050] : [class_Orderings_Olinorder(_1278044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278044), _1278046), _1278048)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278044), _1278048), _1278050)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1278044, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1278044, _1278046, _1278048)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1278044, _1278048, _1278050)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1278044, _1278046, _1278050))], (27876 ^ _779308) ^ [_1278309] : [-(c_Wellfounded_Omeasure(_1278309) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1278309), c_Wellfounded_Oless__than))], (27878 ^ _779308) ^ [_1278340, _1278342, _1278344] : [class_Lattices_Olattice(_1278340), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278340), _1278342)), -(hBOOL(hAPP(hAPP(c_member(_1278340), _1278344), _1278342))), -(_1278342 = c_Orderings_Obot__class_Obot(tc_fun(_1278340, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1278340, hAPP(hAPP(c_Set_Oinsert(_1278340), _1278344), _1278342)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278340), _1278344), c_Big__Operators_Olattice__class_OSup__fin(_1278340, _1278342)))], (27896 ^ _779308) ^ [_1278577, _1278579, _1278581] : [class_Lattices_Olattice(_1278577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278577), _1278579)), 27903 ^ _779308 : [(27904 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278577, tc_HOL_Obool)), _1278579), hAPP(hAPP(c_Set_Oinsert(_1278577), _1278581), c_Orderings_Obot__class_Obot(tc_fun(_1278577, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1278577, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1278577, hAPP(hAPP(c_Set_Oinsert(_1278577), _1278581), _1278579)) = _1278581)], (27910 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278577, tc_HOL_Obool)), _1278579), hAPP(hAPP(c_Set_Oinsert(_1278577), _1278581), c_Orderings_Obot__class_Obot(tc_fun(_1278577, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1278577, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1278577, hAPP(hAPP(c_Set_Oinsert(_1278577), _1278581), _1278579)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1278577), _1278581), c_Big__Operators_Olattice__class_OSup__fin(_1278577, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278577, tc_HOL_Obool)), _1278579), hAPP(hAPP(c_Set_Oinsert(_1278577), _1278581), c_Orderings_Obot__class_Obot(tc_fun(_1278577, tc_HOL_Obool)))))))]]], (27916 ^ _779308) ^ [_1279047, _1279049, _1279051, _1279053, _1279055, _1279057] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1279047, tc_HOL_Obool), tc_fun(_1279047, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1279047, tc_HOL_Obool), tc_fun(_1279047, tc_HOL_Obool)), _1279049), _1279051)), c_Wellfounded_Omax__ext(_1279047, _1279053))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1279047, tc_HOL_Obool), tc_fun(_1279047, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1279047, tc_HOL_Obool), tc_fun(_1279047, tc_HOL_Obool)), _1279055), _1279057)), c_Wellfounded_Omax__ext(_1279047, _1279053))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1279047, tc_HOL_Obool), tc_fun(_1279047, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1279047, tc_HOL_Obool), tc_fun(_1279047, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279047, tc_HOL_Obool)), _1279049), _1279055)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279047, tc_HOL_Obool)), _1279051), _1279057))), c_Wellfounded_Omax__ext(_1279047, _1279053))))], (27926 ^ _779308) ^ [_1279461, _1279463, _1279465, _1279467] : [c_Wellfounded_Omax__extp(_1279461, hAPP(hAPP(c_COMBC(_1279461, tc_fun(tc_prod(_1279461, _1279461), tc_HOL_Obool), tc_fun(_1279461, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1279461, tc_fun(tc_fun(tc_prod(_1279461, _1279461), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1279461, _1279461), tc_HOL_Obool), tc_fun(_1279461, tc_HOL_Obool)), _1279461), c_COMBC(_1279461, tc_fun(tc_prod(_1279461, _1279461), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1279461, tc_prod(_1279461, _1279461)), tc_fun(_1279461, tc_fun(tc_fun(tc_prod(_1279461, _1279461), tc_HOL_Obool), tc_HOL_Obool)), _1279461), hAPP(c_COMBB(tc_prod(_1279461, _1279461), tc_fun(tc_fun(tc_prod(_1279461, _1279461), tc_HOL_Obool), tc_HOL_Obool), _1279461), c_member(tc_prod(_1279461, _1279461)))), c_Product__Type_OPair(_1279461, _1279461)))), _1279463), _1279465, _1279467), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1279461, tc_HOL_Obool), tc_fun(_1279461, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1279461, tc_HOL_Obool), tc_fun(_1279461, tc_HOL_Obool)), _1279465), _1279467)), c_Wellfounded_Omax__ext(_1279461, _1279463))))], (27932 ^ _779308) ^ [_1279846, _1279848, _1279850, _1279852] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1279846, tc_HOL_Obool), tc_fun(_1279846, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1279846, tc_HOL_Obool), tc_fun(_1279846, tc_HOL_Obool)), _1279850), _1279852)), c_Wellfounded_Omax__ext(_1279846, _1279848))), -(c_Wellfounded_Omax__extp(_1279846, hAPP(hAPP(c_COMBC(_1279846, tc_fun(tc_prod(_1279846, _1279846), tc_HOL_Obool), tc_fun(_1279846, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1279846, tc_fun(tc_fun(tc_prod(_1279846, _1279846), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1279846, _1279846), tc_HOL_Obool), tc_fun(_1279846, tc_HOL_Obool)), _1279846), c_COMBC(_1279846, tc_fun(tc_prod(_1279846, _1279846), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1279846, tc_prod(_1279846, _1279846)), tc_fun(_1279846, tc_fun(tc_fun(tc_prod(_1279846, _1279846), tc_HOL_Obool), tc_HOL_Obool)), _1279846), hAPP(c_COMBB(tc_prod(_1279846, _1279846), tc_fun(tc_fun(tc_prod(_1279846, _1279846), tc_HOL_Obool), tc_HOL_Obool), _1279846), c_member(tc_prod(_1279846, _1279846)))), c_Product__Type_OPair(_1279846, _1279846)))), _1279848), _1279850, _1279852))], (27938 ^ _779308) ^ [_1280252, _1280254] : [c_Relation_Oirrefl(_1280252, _1280254), 27941 ^ _779308 : [(27942 ^ _779308) ^ [_1280334] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1280252, _1280252)), hAPP(hAPP(c_Product__Type_OPair(_1280252, _1280252), _1280334), _1280334)), _1280254))]]], (27944 ^ _779308) ^ [_1280374, _1280376] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1280374, _1280374)), hAPP(hAPP(c_Product__Type_OPair(_1280374, _1280374), 27945 ^ [_1280374, _1280376]), 27945 ^ [_1280374, _1280376])), _1280376))), -(c_Relation_Oirrefl(_1280374, _1280376))], (27951 ^ _779308) ^ [_1280445, _1280447, _1280449, _1280451] : [-(hAPP(c_Relation_OField(_1280445), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1280445, _1280445)), hAPP(hAPP(c_Product__Type_OPair(_1280445, _1280445), _1280447), _1280449)), _1280451)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280445, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1280445), _1280447), hAPP(hAPP(c_Set_Oinsert(_1280445), _1280449), c_Orderings_Obot__class_Obot(tc_fun(_1280445, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1280445), _1280451)))], (27953 ^ _779308) ^ [_1280536, _1280538] : [class_Lattices_Olattice(_1280536), hBOOL(hAPP(c_Finite__Set_Ofinite(_1280536), _1280538)), -(_1280538 = c_Orderings_Obot__class_Obot(tc_fun(_1280536, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1280536), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280536), 27966 ^ [_1280536, _1280538]), 27967 ^ [_1280536, _1280538])), hAPP(hAPP(c_Set_Oinsert(_1280536), 27966 ^ [_1280536, _1280538]), hAPP(hAPP(c_Set_Oinsert(_1280536), 27967 ^ [_1280536, _1280538]), c_Orderings_Obot__class_Obot(tc_fun(_1280536, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1280536), c_Big__Operators_Olattice__class_OSup__fin(_1280536, _1280538)), _1280538)))], (27973 ^ _779308) ^ [_1280980, _1280982, _1280984] : [class_Orderings_Olinorder(_1280980), hAPP(_1280982, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280980), 27978 ^ [_1280980, _1280982, _1280984]), 27979 ^ [_1280980, _1280982, _1280984])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280980), hAPP(_1280982, 27978 ^ [_1280980, _1280982, _1280984])), hAPP(_1280982, 27979 ^ [_1280980, _1280982, _1280984])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1280980), _1280984)), -(_1280984 = c_Orderings_Obot__class_Obot(tc_fun(_1280980, tc_HOL_Obool))), -(hAPP(_1280982, c_Big__Operators_Olattice_OSup__fin(_1280980, c_Orderings_Oord__class_Omax(_1280980), _1280984)) = c_Big__Operators_Olattice_OSup__fin(_1280980, c_Orderings_Oord__class_Omax(_1280980), hAPP(c_Set_Oimage(_1280980, _1280980, _1280982), _1280984)))], (27993 ^ _779308) ^ [_1281395, _1281397, _1281399, _1281401, _1281403, _1281405] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281395, tc_fun(_1281397, tc_HOL_Obool))), _1281399), _1281401), _1281403), _1281405)), -(hBOOL(hAPP(hAPP(_1281399, _1281403), _1281405))), -(hBOOL(hAPP(hAPP(_1281401, _1281403), _1281405)))], (28003 ^ _779308) ^ [_1281553, _1281555, _1281557, _1281559, _1281561, _1281563] : [28004 ^ _779308 : [(28005 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1281553, _1281555), _1281557))], (28007 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1281559, _1281555), _1281557))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281561, tc_fun(_1281563, tc_HOL_Obool))), _1281559), _1281553), _1281555), _1281557)))], (28011 ^ _779308) ^ [_1281736, _1281738, _1281740, _1281742, _1281744, _1281746] : [hBOOL(hAPP(hAPP(_1281736, _1281738), _1281740)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281742, tc_fun(_1281744, tc_HOL_Obool))), _1281736), _1281746), _1281738), _1281740)))], (28017 ^ _779308) ^ [_1281869, _1281871, _1281873, _1281875, _1281877, _1281879] : [hBOOL(hAPP(hAPP(_1281869, _1281871), _1281873)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281875, tc_fun(_1281877, tc_HOL_Obool))), _1281879), _1281869), _1281871), _1281873)))], (28023 ^ _779308) ^ [_1282002] : [-(hAPP(c_Relation_OField(_1282002), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1282002, _1282002), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1282002, tc_HOL_Obool)))], (28025 ^ _779308) ^ [_1282043, _1282045, _1282047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1282043, _1282043), tc_HOL_Obool)), _1282045), _1282047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282043, tc_HOL_Obool)), hAPP(c_Relation_OField(_1282043), _1282045)), hAPP(c_Relation_OField(_1282043), _1282047))))], (28031 ^ _779308) ^ [_1282188, _1282190, _1282192] : [-(hAPP(c_Relation_OField(_1282188), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1282188, _1282188), tc_HOL_Obool)), _1282190), _1282192)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282188, tc_HOL_Obool)), hAPP(c_Relation_OField(_1282188), _1282190)), hAPP(c_Relation_OField(_1282188), _1282192)))], (28033 ^ _779308) ^ [_1282255, _1282257] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1282255, _1282255)), _1282257)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282255), hAPP(c_Relation_OField(_1282255), _1282257))))], (28039 ^ _779308) ^ [_1282364, _1282366, _1282368] : [class_Orderings_Olinorder(_1282364), hAPP(_1282366, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1282364), 28044 ^ [_1282364, _1282366, _1282368]), 28045 ^ [_1282364, _1282366, _1282368])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1282364), hAPP(_1282366, 28044 ^ [_1282364, _1282366, _1282368])), hAPP(_1282366, 28045 ^ [_1282364, _1282366, _1282368])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282364), _1282368)), -(_1282368 = c_Orderings_Obot__class_Obot(tc_fun(_1282364, tc_HOL_Obool))), -(hAPP(_1282366, c_Big__Operators_Olattice_OInf__fin(_1282364, c_Orderings_Oord__class_Omin(_1282364), _1282368)) = c_Big__Operators_Olattice_OInf__fin(_1282364, c_Orderings_Oord__class_Omin(_1282364), hAPP(c_Set_Oimage(_1282364, _1282364, _1282366), _1282368)))], (28059 ^ _779308) ^ [_1282779, _1282781, _1282783] : [class_Orderings_Olinorder(_1282779), hAPP(_1282781, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282779), 28064 ^ [_1282779, _1282781, _1282783]), 28065 ^ [_1282779, _1282781, _1282783])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282779), hAPP(_1282781, 28064 ^ [_1282779, _1282781, _1282783])), hAPP(_1282781, 28065 ^ [_1282779, _1282781, _1282783])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282779), _1282783)), -(_1282783 = c_Orderings_Obot__class_Obot(tc_fun(_1282779, tc_HOL_Obool))), -(hAPP(_1282781, c_Big__Operators_Olinorder__class_OMax(_1282779, _1282783)) = c_Big__Operators_Olinorder__class_OMax(_1282779, hAPP(c_Set_Oimage(_1282779, _1282779, _1282781), _1282783)))], (28079 ^ _779308) ^ [_1283182, _1283184, _1283186] : [class_Orderings_Olinorder(_1283182), hAPP(_1283184, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283182), 28084 ^ [_1283182, _1283184, _1283186]), 28085 ^ [_1283182, _1283184, _1283186])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283182), hAPP(_1283184, 28084 ^ [_1283182, _1283184, _1283186])), hAPP(_1283184, 28085 ^ [_1283182, _1283184, _1283186])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283182), _1283186)), -(_1283186 = c_Orderings_Obot__class_Obot(tc_fun(_1283182, tc_HOL_Obool))), -(hAPP(_1283184, c_Big__Operators_Olinorder__class_OMin(_1283182, _1283186)) = c_Big__Operators_Olinorder__class_OMin(_1283182, hAPP(c_Set_Oimage(_1283182, _1283182, _1283184), _1283186)))], (28099 ^ _779308) ^ [_1283585, _1283587, _1283589] : [class_Lattices_Olattice(_1283585), hAPP(_1283587, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283585), 28104 ^ [_1283585, _1283587, _1283589]), 28105 ^ [_1283585, _1283587, _1283589])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1283585), hAPP(_1283587, 28104 ^ [_1283585, _1283587, _1283589])), hAPP(_1283587, 28105 ^ [_1283585, _1283587, _1283589])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283585), _1283589)), -(_1283589 = c_Orderings_Obot__class_Obot(tc_fun(_1283585, tc_HOL_Obool))), -(hAPP(_1283587, c_Big__Operators_Olattice__class_OSup__fin(_1283585, _1283589)) = c_Big__Operators_Olattice__class_OSup__fin(_1283585, hAPP(c_Set_Oimage(_1283585, _1283585, _1283587), _1283589)))], (28119 ^ _779308) ^ [_1283988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1283988), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1283988 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 28122 ^ [_1283988]))))], (28126 ^ _779308) ^ [_1284101, _1284103, _1284105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284101)), 28132 ^ _779308 : [(28133 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1284103, 28131 ^ [_1284101, _1284103, _1284105])))], (28135 ^ _779308) ^ [] : [hBOOL(hAPP(_1284103, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28131 ^ [_1284101, _1284103, _1284105]), _1284101)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284105)), 28140 ^ _779308 : [(28141 ^ _779308) ^ [_1284390] : [hBOOL(hAPP(_1284103, _1284390)), -(hBOOL(hAPP(_1284103, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1284390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1284105), _1284101)))))]]], (28147 ^ _779308) ^ [_1284513, _1284515, _1284517, _1284519, _1284521] : [class_Groups_Ocomm__monoid__mult(_1284513), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284515), _1284517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284515, tc_HOL_Obool)), _1284519), _1284517)), 28161 ^ _779308 : [(28162 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1284515), 28160 ^ [_1284513, _1284515, _1284517, _1284519, _1284521]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1284515, tc_HOL_Obool)), _1284517), _1284519))))], (28164 ^ _779308) ^ [] : [hAPP(_1284521, 28160 ^ [_1284513, _1284515, _1284517, _1284519, _1284521]) = c_Groups_Oone__class_Oone(_1284513)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284515, _1284513), _1284521), _1284519) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284515, _1284513), _1284521), _1284517))], (28168 ^ _779308) ^ [_1284964, _1284966, _1284968, _1284970, _1284972] : [class_Groups_Ocomm__monoid__mult(_1284964), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284966), _1284968)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284966, tc_HOL_Obool)), _1284970), _1284968)), 28182 ^ _779308 : [(28183 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1284966), 28181 ^ [_1284964, _1284966, _1284968, _1284970, _1284972]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1284966, tc_HOL_Obool)), _1284968), _1284970))))], (28185 ^ _779308) ^ [] : [hAPP(_1284972, 28181 ^ [_1284964, _1284966, _1284968, _1284970, _1284972]) = c_Groups_Oone__class_Oone(_1284964)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284966, _1284964), _1284972), _1284968) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1284966, _1284964), _1284972), _1284970))], (28189 ^ _779308) ^ [_1285415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1285415)), 28193 ^ _779308 : [(28194 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28192 ^ [_1285415])))], (28196 ^ _779308) ^ [] : [-(_1285415 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 28192 ^ [_1285415]))]]], (28198 ^ _779308) ^ [_1285545, _1285547] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1285545), _1285547)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1285545, tc_HOL_Obool)), hAPP(c_Set_OPow(_1285545), _1285547)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Finite__Set_Ocard(_1285545), _1285547)))], (28204 ^ _779308) ^ [_1285672, _1285674, _1285676, _1285678] : [class_Orderings_Olinorder(_1285672), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285672), _1285674), _1285676)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285672), _1285676), _1285678)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285672, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1285672, _1285674, _1285676)), c_SetInterval_Oord__class_OatLeastAtMost(_1285672, _1285676, _1285678)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1285672, _1285674, _1285678))], (28218 ^ _779308) ^ [_1285952, _1285954] : [hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1285952), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1285954), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1285952), _1285954)), c_Int_Ointrel)))], (28224 ^ _779308) ^ [_1286083, _1286085] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1286083), _1286085)), c_Int_Ointrel)), -(hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1286083), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))) = hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1286085), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (28230 ^ _779308) ^ [_1286220, _1286222] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1286220, _1286222))))], (28232 ^ _779308) ^ [_1286251, _1286253] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1286251, _1286253))))], (28234 ^ _779308) ^ [_1286282, _1286284, _1286286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1286282, tc_HOL_Obool)), _1286284), _1286286)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1286282, tc_HOL_Obool)), _1286284), hAPP(c_Set_OPow(_1286282), _1286286))))], (28240 ^ _779308) ^ [_1286411, _1286413, _1286415, _1286417, _1286419] : [-(hAPP(c_Relation_OImage(_1286411, _1286413, _1286415), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286411, tc_HOL_Obool)), _1286417), _1286419)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286413, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1286411, _1286413, _1286415), _1286417)), hAPP(c_Relation_OImage(_1286411, _1286413, _1286415), _1286419)))], (28242 ^ _779308) ^ [_1286497, _1286499] : [hAPP(c_Set_OPow(_1286497), _1286499) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1286497, tc_HOL_Obool), tc_HOL_Obool))], (28244 ^ _779308) ^ [_1286535, _1286537] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1286535, _1286537)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1286535), hAPP(c_Nat_OSuc, _1286537)))], (28246 ^ _779308) ^ [_1286593, _1286595, _1286597] : [hAPP(c_Set_Oimage(_1286595, tc_fun(_1286595, tc_HOL_Obool), _1286593), _1286597) = hAPP(c_Set_OPow(_1286595), _1286597)], (28248 ^ _779308) ^ [_1286635, _1286637] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1286635, tc_HOL_Obool)), _1286637), hAPP(c_Set_OPow(_1286635), _1286637))))], (28250 ^ _779308) ^ [_1286675, _1286677, _1286679] : [-(hAPP(c_Relation_OImage(_1286675, _1286677, _1286679), c_Orderings_Obot__class_Obot(tc_fun(_1286675, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1286677, tc_HOL_Obool)))], (28252 ^ _779308) ^ [_1286719] : [-(hAPP(c_Set_OPow(_1286719), c_Orderings_Obot__class_Obot(tc_fun(_1286719, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1286719, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1286719, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1286719, tc_HOL_Obool), tc_HOL_Obool))))], (28254 ^ _779308) ^ [_1286776, _1286778] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1286776, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1286776, tc_HOL_Obool))), hAPP(c_Set_OPow(_1286776), _1286778))))], (28256 ^ _779308) ^ [_1286836, _1286838] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1286836, tc_HOL_Obool)), hAPP(c_Set_OPow(_1286836), _1286838))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1286836), _1286838)))], (28262 ^ _779308) ^ [_1286941, _1286943] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1286941), _1286943)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1286941, tc_HOL_Obool)), hAPP(c_Set_OPow(_1286941), _1286943))))], (28268 ^ _779308) ^ [_1287052, _1287054, _1287056] : [-(hAPP(c_Set_OPow(_1287052), hAPP(hAPP(c_Set_Oinsert(_1287052), _1287054), _1287056)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1287052, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1287052), _1287056)), hAPP(c_Set_Oimage(tc_fun(_1287052, tc_HOL_Obool), tc_fun(_1287052, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1287052), _1287054)), hAPP(c_Set_OPow(_1287052), _1287056))))], (28270 ^ _779308) ^ [_1287152, _1287154, _1287156] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1287152, tc_HOL_Obool)), _1287154), hAPP(c_Set_OPow(_1287152), _1287156))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287152, tc_HOL_Obool)), _1287154), _1287156)))], (28276 ^ _779308) ^ [_1287277, _1287279, _1287281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287277, tc_HOL_Obool)), _1287279), _1287281)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1287277, tc_HOL_Obool)), _1287279), hAPP(c_Set_OPow(_1287277), _1287281))))], (28282 ^ _779308) ^ [_1287408, _1287410, _1287412] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1287408, tc_HOL_Obool)), _1287410), hAPP(c_Set_OPow(_1287408), _1287412))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287408, tc_HOL_Obool)), _1287410), _1287412)))], (28288 ^ _779308) ^ [_1287537, _1287539, _1287541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287537, tc_HOL_Obool)), _1287539), _1287541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1287537, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1287537), _1287539)), hAPP(c_Set_OPow(_1287537), _1287541))))], (28294 ^ _779308) ^ [_1287682, _1287684, _1287686, _1287688, _1287690] : [hAPP(c_Set_Oimage(_1287682, _1287684, _1287686), _1287688) = _1287690, -(hAPP(c_Set_Oimage(tc_fun(_1287682, tc_HOL_Obool), tc_fun(_1287684, tc_HOL_Obool), c_Set_Oimage(_1287682, _1287684, _1287686)), hAPP(c_Set_OPow(_1287682), _1287688)) = hAPP(c_Set_OPow(_1287684), _1287690))], (28300 ^ _779308) ^ [_1287833, _1287835, _1287837] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1287833, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1287833, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1287833), _1287835)), hAPP(c_Set_OPow(_1287833), _1287837))), hAPP(c_Set_OPow(_1287833), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287833, tc_HOL_Obool)), _1287835), _1287837)))))], (28302 ^ _779308) ^ [_1287913, _1287915, _1287917] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1287913)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1287915, _1287917)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1287915), _1287913), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1287917), _1287913)))], (28304 ^ _779308) ^ [_1287970, _1287972] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1287970, _1287972) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1287970), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1287972))))], (28306 ^ _779308) ^ [_1288012, _1288014] : [c_Nat__Transfer_Ois__nat(_1288012), c_Nat__Transfer_Ois__nat(_1288014), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1288012, _1288014) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Int_Onat, _1288012), hAPP(c_Int_Onat, _1288014))))], (28316 ^ _779308) ^ [_1288171, _1288173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1288171), hAPP(c_Nat_OSuc, _1288173))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1288171, hAPP(c_Nat_OSuc, _1288173)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1288173)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1288171, _1288173)))], (28322 ^ _779308) ^ [_1288304, _1288306, _1288308, _1288310, _1288312, _1288314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1288304, _1288306), tc_HOL_Obool)), _1288308), _1288310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288304, tc_HOL_Obool)), _1288312), _1288314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1288306, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1288304, _1288306, _1288308), _1288312)), hAPP(c_Relation_OImage(_1288304, _1288306, _1288310), _1288314))))], (28332 ^ _779308) ^ [_1288543, _1288545, _1288547, _1288549, _1288551] : [-(hAPP(c_Relation_OImage(_1288543, _1288545, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1288543, _1288545), tc_HOL_Obool)), _1288547), _1288549)), _1288551) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288545, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1288543, _1288545, _1288547), _1288551)), hAPP(c_Relation_OImage(_1288543, _1288545, _1288549), _1288551)))], (28334 ^ _779308) ^ [_1288620, _1288622] : [c_Nat__Transfer_Ois__nat(_1288620), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1288620, _1288622)))], (28340 ^ _779308) ^ [_1288701, _1288703, _1288705] : [class_Orderings_Oorder(_1288701), 28343 ^ _779308 : [(28344 ^ _779308) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1288701, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1288701, _1288703, _1288705), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288701), _1288703), _1288705))], (28350 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288701), _1288703), _1288705))), -(c_Orderings_Obot__class_Obot(tc_fun(_1288701, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1288701, _1288703, _1288705))]]], (28356 ^ _779308) ^ [_1288920, _1288922, _1288924] : [class_Orderings_Oorder(_1288920), 28359 ^ _779308 : [(28360 ^ _779308) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1288920, _1288922, _1288924) = c_Orderings_Obot__class_Obot(tc_fun(_1288920, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288920), _1288922), _1288924))], (28366 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288920), _1288922), _1288924))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1288920, _1288922, _1288924) = c_Orderings_Obot__class_Obot(tc_fun(_1288920, tc_HOL_Obool)))]]], (28372 ^ _779308) ^ [_1289139, _1289141, _1289143] : [class_Orderings_Oorder(_1289139), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289139), _1289141), _1289143)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1289139, _1289143, _1289141) = c_Orderings_Obot__class_Obot(tc_fun(_1289139, tc_HOL_Obool)))], (28382 ^ _779308) ^ [_1289302, _1289304, _1289306, _1289308, _1289310] : [class_Orderings_Oorder(_1289302), 28385 ^ _779308 : [(28386 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1289302, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1289302, _1289304, _1289306)), c_SetInterval_Oord__class_OatLeastAtMost(_1289302, _1289308, _1289310))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289302), _1289304), _1289306)), 28393 ^ _779308 : [(28394 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289302), _1289308), _1289304)))], (28396 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289302), _1289306), _1289310)))]]], (28398 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1289302, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1289302, _1289304, _1289306)), c_SetInterval_Oord__class_OatLeastAtMost(_1289302, _1289308, _1289310)))), 28399 ^ _779308 : [(28400 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289302), _1289304), _1289306)))], (28402 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289302), _1289308), _1289304)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289302), _1289306), _1289310))]]]]], (28410 ^ _779308) ^ [_1289805, _1289807, _1289809] : [class_Orderings_Oorder(_1289805), _1289807 = _1289809, -(c_SetInterval_Oord__class_OatLeastAtMost(_1289805, _1289807, _1289809) = hAPP(hAPP(c_Set_Oinsert(_1289805), _1289807), c_Orderings_Obot__class_Obot(tc_fun(_1289805, tc_HOL_Obool))))], (28420 ^ _779308) ^ [_1289970, _1289972, _1289974, _1289976] : [class_Orderings_Oorder(_1289970), 28423 ^ _779308 : [(28424 ^ _779308) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1289970, _1289972, _1289974) = hAPP(hAPP(c_Set_Oinsert(_1289970), _1289976), c_Orderings_Obot__class_Obot(tc_fun(_1289970, tc_HOL_Obool))), 28427 ^ _779308 : [(28428 ^ _779308) ^ [] : [-(_1289972 = _1289974)], (28430 ^ _779308) ^ [] : [-(_1289974 = _1289976)]]], (28432 ^ _779308) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1289970, _1289972, _1289974) = hAPP(hAPP(c_Set_Oinsert(_1289970), _1289976), c_Orderings_Obot__class_Obot(tc_fun(_1289970, tc_HOL_Obool)))), _1289972 = _1289974, _1289974 = _1289976]]], (28442 ^ _779308) ^ [_1290314, _1290316] : [class_Orderings_Oorder(_1290314), -(c_SetInterval_Oord__class_OatLeastAtMost(_1290314, _1290316, _1290316) = hAPP(hAPP(c_Set_Oinsert(_1290314), _1290316), c_Orderings_Obot__class_Obot(tc_fun(_1290314, tc_HOL_Obool))))], (28448 ^ _779308) ^ [_1290423, _1290425, _1290427] : [class_Groups_Oordered__ab__group__add(_1290423), -(hAPP(c_Set_Oimage(_1290423, _1290423, c_Groups_Ouminus__class_Ouminus(_1290423)), c_SetInterval_Oord__class_OatLeastAtMost(_1290423, _1290425, _1290427)) = c_SetInterval_Oord__class_OatLeastAtMost(_1290423, hAPP(c_Groups_Ouminus__class_Ouminus(_1290423), _1290427), hAPP(c_Groups_Ouminus__class_Ouminus(_1290423), _1290425)))], (28454 ^ _779308) ^ [_1290554, _1290556, _1290558, _1290560, _1290562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290554, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1290556, _1290554, _1290558), _1290560)), _1290562)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1290554, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1290556, tc_HOL_Obool), tc_fun(_1290554, tc_HOL_Obool), c_Set_Oimage(_1290556, _1290554, _1290558)), hAPP(c_Set_OPow(_1290556), _1290560))), hAPP(c_Set_OPow(_1290554), _1290562))))], (28460 ^ _779308) ^ [_1290751, _1290753] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1290751), _1290753) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1290751, _1290753))], (28462 ^ _779308) ^ [_1290787, _1290789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1290787)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1290787, _1290789)))], (28468 ^ _779308) ^ [_1290898, _1290900, _1290902, _1290904, _1290906] : [hBOOL(hAPP(hAPP(c_member(_1290898), _1290900), hAPP(c_Relation_OImage(_1290902, _1290898, _1290904), _1290906))), 28472 ^ _779308 : [(28473 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290902), 28471 ^ [_1290898, _1290900, _1290902, _1290904, _1290906]), _1290906)))], (28475 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1290902, _1290898)), hAPP(hAPP(c_Product__Type_OPair(_1290902, _1290898), 28471 ^ [_1290898, _1290900, _1290902, _1290904, _1290906]), _1290900)), _1290904)))]]], (28477 ^ _779308) ^ [_1291114, _1291116, _1291118, _1291120, _1291122] : [-(hBOOL(hAPP(hAPP(c_member(_1291114), _1291116), hAPP(c_Relation_OImage(_1291118, _1291114, _1291120), _1291122)))), 28478 ^ _779308 : [(28479 ^ _779308) ^ [_1291200] : [hBOOL(hAPP(hAPP(c_member(_1291118), _1291200), _1291122)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1291118, _1291114)), hAPP(hAPP(c_Product__Type_OPair(_1291118, _1291114), _1291200), _1291116)), _1291120))]]], (28487 ^ _779308) ^ [_1291380, _1291382, _1291384, _1291386, _1291388, _1291390] : [hBOOL(hAPP(hAPP(c_member(_1291380), _1291382), _1291384)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1291380, _1291386)), hAPP(hAPP(c_Product__Type_OPair(_1291380, _1291386), _1291382), _1291388)), _1291390)), -(hBOOL(hAPP(hAPP(c_member(_1291386), _1291388), hAPP(c_Relation_OImage(_1291380, _1291386, _1291390), _1291384))))], (28497 ^ _779308) ^ [_1291605, _1291607] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1291605, _1291607)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1291607)), _1291605))], (28499 ^ _779308) ^ [_1291646, _1291648] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1291646), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1291648) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1291646, _1291648))], (28501 ^ _779308) ^ [_1291685, _1291687, _1291689, _1291691, _1291693] : [class_Orderings_Oorder(_1291685), 28504 ^ _779308 : [(28505 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1291685, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1291685, _1291687, _1291689)), c_SetInterval_Oord__class_OatLeastAtMost(_1291685, _1291691, _1291693))), 28508 ^ _779308 : [(28523 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291685), _1291691), _1291693)))], (28509 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291685), _1291687), _1291689)), 28512 ^ _779308 : [(28513 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291685), _1291691), _1291687)))], (28515 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291685), _1291689), _1291693)))], (28517 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291685), _1291691), _1291687))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291685), _1291689), _1291693)))]]]]], (28525 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1291685, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1291685, _1291687, _1291689)), c_SetInterval_Oord__class_OatLeastAtMost(_1291685, _1291691, _1291693)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291685), _1291691), _1291693)), 28528 ^ _779308 : [(28529 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291685), _1291687), _1291689)))], (28531 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291685), _1291691), _1291687)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291685), _1291689), _1291693)), 28538 ^ _779308 : [(28539 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291685), _1291691), _1291687))], (28541 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291685), _1291689), _1291693))]]]]]]], (28547 ^ _779308) ^ [_1292456, _1292458, _1292460, _1292462] : [class_Orderings_Olinorder(_1292456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292456), _1292458), _1292460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292456), _1292460), _1292462)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292456, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1292456, _1292458, _1292460)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1292456, _1292460, _1292462)) = c_SetInterval_Oord__class_OatLeastAtMost(_1292456, _1292458, _1292462))], (28561 ^ _779308) ^ [_1292730, _1292732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1292730), _1292732)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1292732, _1292730) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (28567 ^ _779308) ^ [_1292819, _1292821] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1292819), _1292821))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1292821, _1292819) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1292821), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1292821), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1292819)))], (28573 ^ _779308) ^ [_1292906, _1292908, _1292910, _1292912, _1292914] : [hBOOL(hAPP(hAPP(c_member(_1292906), _1292908), hAPP(c_Relation_OImage(_1292910, _1292906, _1292912), hAPP(hAPP(c_Set_Oinsert(_1292910), _1292914), c_Orderings_Obot__class_Obot(tc_fun(_1292910, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1292910, _1292906)), hAPP(hAPP(c_Product__Type_OPair(_1292910, _1292906), _1292914), _1292908)), _1292912)))], (28579 ^ _779308) ^ [_1293077, _1293079, _1293081, _1293083, _1293085] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1293081, _1293077)), hAPP(hAPP(c_Product__Type_OPair(_1293081, _1293077), _1293085), _1293079)), _1293083)), -(hBOOL(hAPP(hAPP(c_member(_1293077), _1293079), hAPP(c_Relation_OImage(_1293081, _1293077, _1293083), hAPP(hAPP(c_Set_Oinsert(_1293081), _1293085), c_Orderings_Obot__class_Obot(tc_fun(_1293081, tc_HOL_Obool)))))))], (28585 ^ _779308) ^ [_1293254, _1293256] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1293254, _1293256)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1293256), _1293254)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (28587 ^ _779308) ^ [_1293301, _1293303, _1293305] : [class_Orderings_Olinorder(_1293301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1293301), _1293303), _1293305)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293301, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1293301), _1293303), c_Orderings_Obot__class_Obot(tc_fun(_1293301, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1293301, _1293303, _1293305)) = c_SetInterval_Oord__class_OatLeastAtMost(_1293301, _1293303, _1293305))], (28597 ^ _779308) ^ [_1293510, _1293512, _1293514] : [class_Rings_Oring__1(_1293510), -(hAPP(c_Int_Oring__1__class_Oof__int(_1293510), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1293512), _1293514)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1293510), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1293510), _1293512)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1293510), _1293514)))], (28603 ^ _779308) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (28605 ^ _779308) ^ [_1293687, _1293689, _1293691, _1293693] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1293687), _1293689)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1293691), _1293693)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1293687), _1293691)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1293689), _1293693))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1293687), _1293693)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1293689), _1293691)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (28607 ^ _779308) ^ [_1293833, _1293835, _1293837, _1293839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1293833), _1293835)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1293837), _1293839)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1293833), _1293839)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1293837), _1293835))))], (28613 ^ _779308) ^ [_1294026, _1294028, _1294030, _1294032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294026), _1294032)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294030), _1294028))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294026), _1294028)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294030), _1294032)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (28619 ^ _779308) ^ [_1294225, _1294227] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294225), _1294227)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294227), _1294225)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (28621 ^ _779308) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (28623 ^ _779308) ^ [_1294307] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1294307) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294307), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (28625 ^ _779308) ^ [_1294351, _1294353, _1294355, _1294357] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294351), _1294353)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294355), _1294357)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294351), _1294355)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294353), _1294357))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (28627 ^ _779308) ^ [_1294452, _1294454] : [-(hAPP(c_Int_Onat, hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294452), _1294454)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1294452), _1294454))], (28629 ^ _779308) ^ [_1294525, _1294527, _1294529, _1294531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294525), _1294527)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294529), _1294531)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294525), _1294531)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294529), _1294527))))], (28635 ^ _779308) ^ [_1294718, _1294720, _1294722, _1294724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294718), _1294724)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294722), _1294720))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294718), _1294720)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))), hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1294722), _1294724)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (28641 ^ _779308) ^ [_1294932, _1294934] : [28649 ^ _779308 : [(28650 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 28648 ^ [_1294932, _1294934]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1294932))))], (28652 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1294934, 28648 ^ [_1294932, _1294934])))]], 28642 ^ _779308 : [(28643 ^ _779308) ^ [_1295001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1295001), _1294932)), hBOOL(hAPP(_1294934, _1295001))]]], (28654 ^ _779308) ^ [_1295162, _1295164] : [28662 ^ _779308 : [(28663 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 28661 ^ [_1295162, _1295164]), _1295162)))], (28665 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1295164, 28661 ^ [_1295162, _1295164])))]], 28655 ^ _779308 : [(28656 ^ _779308) ^ [_1295231] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1295231), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1295162))), hBOOL(hAPP(_1295164, _1295231))]]], (28667 ^ _779308) ^ [_1295417, _1295419] : [28669 ^ _779308 : [(28670 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 28668 ^ [_1295417, _1295419]), _1295417)))], (28672 ^ _779308) ^ [] : [hBOOL(hAPP(_1295419, 28668 ^ [_1295417, _1295419]))]], 28673 ^ _779308 : [(28674 ^ _779308) ^ [_1295568] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1295568), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1295417))), -(hBOOL(hAPP(_1295419, _1295568)))]]], (28680 ^ _779308) ^ [_1295671, _1295673] : [28682 ^ _779308 : [(28683 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 28681 ^ [_1295671, _1295673]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1295671))))], (28685 ^ _779308) ^ [] : [hBOOL(hAPP(_1295673, 28681 ^ [_1295671, _1295673]))]], 28686 ^ _779308 : [(28687 ^ _779308) ^ [_1295826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1295826), _1295671)), -(hBOOL(hAPP(_1295673, _1295826)))]]], (28693 ^ _779308) ^ [_1295927, _1295929, _1295931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1295927)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1295929), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1295931)), 28700 ^ _779308 : [(28701 ^ _779308) ^ [_1296135] : [28703 ^ _779308 : [(28704 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28702 ^ [_1295927, _1295929, _1295931, _1296135]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1295927))))], (28707 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28705 ^ [_1295927, _1295929, _1295931, _1296135]), _1295931)))], (28709 ^ _779308) ^ [] : [-(_1296135 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28705 ^ [_1295927, _1295929, _1295931, _1296135]), 28702 ^ [_1295927, _1295929, _1295931, _1296135]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296135), _1295929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1296135), _1295927)), _1295929)))]]], (28717 ^ _779308) ^ [_1296411, _1296413, _1296415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1296411)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1296413), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1296415)), 28724 ^ _779308 : [(28725 ^ _779308) ^ [_1296619] : [28727 ^ _779308 : [(28728 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28726 ^ [_1296411, _1296413, _1296415, _1296619]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1296411))))], (28731 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28729 ^ [_1296411, _1296413, _1296415, _1296619]), _1296415)))], (28733 ^ _779308) ^ [] : [-(_1296619 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28729 ^ [_1296411, _1296413, _1296415, _1296619]), 28726 ^ [_1296411, _1296413, _1296415, _1296619]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296413), _1296619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296413), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1296619), _1296411))))]]], (28741 ^ _779308) ^ [_1296913, _1296915, _1296917] : [hBOOL(hAPP(c_Predicate_OPowp(_1296913, hAPP(hAPP(c_COMBC(_1296913, tc_fun(_1296913, tc_HOL_Obool), tc_HOL_Obool), c_member(_1296913)), _1296915)), _1296917)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1296913, tc_HOL_Obool)), _1296917), hAPP(c_Set_OPow(_1296913), _1296915))))], (28747 ^ _779308) ^ [_1297058, _1297060, _1297062] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1297058, tc_HOL_Obool)), _1297062), hAPP(c_Set_OPow(_1297058), _1297060))), -(hBOOL(hAPP(c_Predicate_OPowp(_1297058, hAPP(hAPP(c_COMBC(_1297058, tc_fun(_1297058, tc_HOL_Obool), tc_HOL_Obool), c_member(_1297058)), _1297060)), _1297062)))], (28753 ^ _779308) ^ [_1297209, _1297211, _1297213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1297209)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1297211), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1297213)), 28763 ^ _779308 : [(28764 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28762 ^ [_1297209, _1297211, _1297213]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1297209))))], (28767 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28765 ^ [_1297209, _1297211, _1297213]), _1297213)))], (28769 ^ _779308) ^ [] : [-(_1297211 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28765 ^ [_1297209, _1297211, _1297213]), 28762 ^ [_1297209, _1297211, _1297213]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1297211), _1297209) = _1297211)], (28773 ^ _779308) ^ [_1297548, _1297550, _1297552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1297548)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1297550), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1297552)), 28783 ^ _779308 : [(28784 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28782 ^ [_1297548, _1297550, _1297552]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1297548))))], (28787 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28785 ^ [_1297548, _1297550, _1297552]), _1297552)))], (28789 ^ _779308) ^ [] : [-(_1297550 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28785 ^ [_1297548, _1297550, _1297552]), 28782 ^ [_1297548, _1297550, _1297552]))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1297550), _1297548) = _1297550)], (28793 ^ _779308) ^ [_1297887, _1297889, _1297891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1297887)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1297889), _1297891)), 28800 ^ _779308 : [(28801 ^ _779308) ^ [_1298083] : [28803 ^ _779308 : [(28804 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28802 ^ [_1297887, _1297889, _1297891, _1298083]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1297887))))], (28807 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28805 ^ [_1297887, _1297889, _1297891, _1298083]), _1297891)))], (28809 ^ _779308) ^ [] : [-(_1298083 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28805 ^ [_1297887, _1297889, _1297891, _1298083]), 28802 ^ [_1297887, _1297889, _1297891, _1298083]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1298083), _1297889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1298083), _1297887)), _1297889)))]]], (28817 ^ _779308) ^ [_1298359, _1298361, _1298363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1298359, tc_HOL_Obool)), _1298361), _1298363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1298359, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1298359, _1298361)), c_Predicate_OPowp(_1298359, _1298363))))], (28823 ^ _779308) ^ [_1298496, _1298498, _1298500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298496)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1298498), _1298500)), 28830 ^ _779308 : [(28831 ^ _779308) ^ [_1298686] : [28833 ^ _779308 : [(28834 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28832 ^ [_1298496, _1298498, _1298500, _1298686]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1298496))))], (28837 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28835 ^ [_1298496, _1298498, _1298500, _1298686]), _1298500)))], (28839 ^ _779308) ^ [] : [-(_1298686 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28835 ^ [_1298496, _1298498, _1298500, _1298686]), 28832 ^ [_1298496, _1298498, _1298500, _1298686]))]], -(_1298686 = _1298498), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1298686), _1298496) = _1298498]]], (28847 ^ _779308) ^ [_1298946, _1298948, _1298950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298946)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1298948), _1298950)), 28854 ^ _779308 : [(28855 ^ _779308) ^ [_1299136] : [28857 ^ _779308 : [(28858 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28856 ^ [_1298946, _1298948, _1298950, _1299136]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1298946))))], (28861 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28859 ^ [_1298946, _1298948, _1298950, _1299136]), _1298950)))], (28863 ^ _779308) ^ [] : [-(_1299136 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28859 ^ [_1298946, _1298948, _1298950, _1299136]), 28856 ^ [_1298946, _1298948, _1298950, _1299136]))]], -(_1299136 = _1298948), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1299136), _1298946) = _1298948]]], (28871 ^ _779308) ^ [_1299396, _1299398, _1299400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299396)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1299398), _1299400)), 28878 ^ _779308 : [(28879 ^ _779308) ^ [_1299592] : [28881 ^ _779308 : [(28882 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28880 ^ [_1299396, _1299398, _1299400, _1299592]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1299396))))], (28885 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28883 ^ [_1299396, _1299398, _1299400, _1299592]), _1299400)))], (28887 ^ _779308) ^ [] : [-(_1299592 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28883 ^ [_1299396, _1299398, _1299400, _1299592]), 28880 ^ [_1299396, _1299398, _1299400, _1299592]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299398), _1299592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299398), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1299592), _1299396))))]]], (28895 ^ _779308) ^ [_1299868, _1299870, _1299872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299868)), 28898 ^ _779308 : [(28899 ^ _779308) ^ [_1300002] : [28901 ^ _779308 : [(28902 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28900 ^ [_1299868, _1299870, _1299872, _1300002]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1299868))))], (28905 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28903 ^ [_1299868, _1299870, _1299872, _1300002]), _1299870)))], (28907 ^ _779308) ^ [] : [-(_1300002 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28903 ^ [_1299868, _1299870, _1299872, _1300002]), 28900 ^ [_1299868, _1299870, _1299872, _1300002]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1300002), _1299872)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1300002), _1299868)), _1299872)))]]], (28915 ^ _779308) ^ [_1300276, _1300278, _1300280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300276)), 28918 ^ _779308 : [(28919 ^ _779308) ^ [_1300410] : [28921 ^ _779308 : [(28922 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28920 ^ [_1300276, _1300278, _1300280, _1300410]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1300276))))], (28925 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28923 ^ [_1300276, _1300278, _1300280, _1300410]), _1300278)))], (28927 ^ _779308) ^ [] : [-(_1300410 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28923 ^ [_1300276, _1300278, _1300280, _1300410]), 28920 ^ [_1300276, _1300278, _1300280, _1300410]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1300280), _1300410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1300280), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1300410), _1300276))))]]], (28937 ^ _779308) ^ [_1300684] : [-(_1300684 = hAPP(c_Int_OAbs__Integ, hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), 28934 ^ [_1300684]), 28935 ^ [_1300684])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (28939 ^ _779308) ^ [_1300735, _1300737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300735)), 28948 ^ _779308 : [(28949 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1300737, 28944 ^ [_1300735, _1300737])))], (28951 ^ _779308) ^ [] : [hBOOL(hAPP(_1300737, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28944 ^ [_1300735, _1300737]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 28945 ^ [_1300735, _1300737]), _1300735))))]], 28952 ^ _779308 : [(28953 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1300737, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28944 ^ [_1300735, _1300737]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 28945 ^ [_1300735, _1300737]), _1300735)))))], (28955 ^ _779308) ^ [] : [hBOOL(hAPP(_1300737, 28944 ^ [_1300735, _1300737]))]], 28956 ^ _779308 : [(28957 ^ _779308) ^ [] : [28958 ^ _779308 : [(28959 ^ _779308) ^ [_1301167] : [hBOOL(hAPP(_1300737, _1301167))]], 28961 ^ _779308 : [(28962 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28960 ^ [_1300735, _1300737]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1300735))))], (28964 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1300737, 28960 ^ [_1300735, _1300737])))]]], (28966 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1300737, 28973 ^ [_1300735, _1300737]))), 28967 ^ _779308 : [(28968 ^ _779308) ^ [_1301282] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1301282), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1300735))), hBOOL(hAPP(_1300737, _1301282))]]]]], (28977 ^ _779308) ^ [_1301429, _1301431, _1301433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301429)), 28980 ^ _779308 : [(28981 ^ _779308) ^ [_1301563] : [28983 ^ _779308 : [(28984 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28982 ^ [_1301429, _1301431, _1301433, _1301563]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1301429))))], (28987 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28985 ^ [_1301429, _1301431, _1301433, _1301563]), _1301431)))], (28989 ^ _779308) ^ [] : [-(_1301563 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28985 ^ [_1301429, _1301431, _1301433, _1301563]), 28982 ^ [_1301429, _1301431, _1301433, _1301563]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301433), _1301563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301433), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1301563), _1301429))))]]], (28997 ^ _779308) ^ [_1301837, _1301839, _1301841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301837)), 29000 ^ _779308 : [(29001 ^ _779308) ^ [_1301971] : [29003 ^ _779308 : [(29004 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29002 ^ [_1301837, _1301839, _1301841, _1301971]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1301837))))], (29007 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29005 ^ [_1301837, _1301839, _1301841, _1301971]), _1301839)))], (29009 ^ _779308) ^ [] : [-(_1301971 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 29005 ^ [_1301837, _1301839, _1301841, _1301971]), 29002 ^ [_1301837, _1301839, _1301841, _1301971]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1301971), _1301841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1301971), _1301837)), _1301841)))]]], (29017 ^ _779308) ^ [_1302257, _1302259, _1302261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1302257), _1302259)), -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), _1302257)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1302261), _1302259)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1302261), _1302257)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1302259), _1302257)))], (29023 ^ _779308) ^ [_1302409, _1302411, _1302413] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1302409), _1302411))), 29026 ^ _779308 : [(29027 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1302413), _1302411)), -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), _1302409)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1302413), _1302411)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (29033 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1302413), _1302411))), -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), _1302409)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1302413), _1302411)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (29039 ^ _779308) ^ [_1302678] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1302678) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1302678))))], (29041 ^ _779308) ^ [_1302714, _1302716, _1302718, _1302720, _1302722] : [hBOOL(hAPP(hAPP(c_member(_1302714), _1302716), hAPP(c_Relation_OImage(_1302718, _1302714, _1302720), _1302722))), 29045 ^ _779308 : [(29046 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1302718, _1302714)), hAPP(hAPP(c_Product__Type_OPair(_1302718, _1302714), 29044 ^ [_1302714, _1302716, _1302718, _1302720, _1302722]), _1302716)), _1302720)))], (29048 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1302718), 29044 ^ [_1302714, _1302716, _1302718, _1302720, _1302722]), _1302722)))]]], (29050 ^ _779308) ^ [_1302938, _1302940] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1302938), _1302940))))], (29052 ^ _779308) ^ [_1302971] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1302971))))], (29054 ^ _779308) ^ [_1302999, _1303001, _1303003, _1303005, _1303007] : [class_Orderings_Olinorder(_1302999), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302999), _1303001), _1303003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302999), _1303005), _1303007)), 29065 ^ _779308 : [(29066 ^ _779308) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1302999, _1303001), _1303003) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1302999, _1303005), _1303007), 29069 ^ _779308 : [(29070 ^ _779308) ^ [] : [-(_1303001 = _1303005)], (29072 ^ _779308) ^ [] : [-(_1303003 = _1303007)]]], (29074 ^ _779308) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1302999, _1303001), _1303003) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1302999, _1303005), _1303007)), _1303001 = _1303005, _1303003 = _1303007]]], (29084 ^ _779308) ^ [_1303480, _1303482, _1303484, _1303486, _1303488] : [class_Orderings_Olinorder(_1303480), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1303480, _1303482), _1303484) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1303480, _1303486), _1303488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303480), _1303482), _1303484)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303480), _1303486), _1303488)), -(_1303482 = _1303486)], (29102 ^ _779308) ^ [_1303787, _1303789, _1303791, _1303793, _1303795] : [class_Orderings_Olinorder(_1303787), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1303787, _1303789), _1303791) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1303787, _1303793), _1303795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303787), _1303789), _1303791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303787), _1303793), _1303795)), -(_1303791 = _1303795)], (29120 ^ _779308) ^ [_1304094, _1304096, _1304098] : [class_Orderings_Olinorder(_1304094), 29123 ^ _779308 : [(29124 ^ _779308) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1304094), _1304096) = hAPP(c_SetInterval_Oord__class_OatMost(_1304094), _1304098), -(_1304096 = _1304098)], (29130 ^ _779308) ^ [] : [_1304096 = _1304098, -(hAPP(c_SetInterval_Oord__class_OatMost(_1304094), _1304096) = hAPP(c_SetInterval_Oord__class_OatMost(_1304094), _1304098))]]], (29136 ^ _779308) ^ [_1304350, _1304352] : [29144 ^ _779308 : [(29145 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29143 ^ [_1304350, _1304352]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1304350))))], (29147 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1304352, 29143 ^ [_1304350, _1304352])))]], 29137 ^ _779308 : [(29138 ^ _779308) ^ [_1304418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1304418), _1304350)), hBOOL(hAPP(_1304352, _1304418))]]], (29149 ^ _779308) ^ [_1304578, _1304580] : [29157 ^ _779308 : [(29158 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29156 ^ [_1304578, _1304580]), _1304578)))], (29160 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1304580, 29156 ^ [_1304578, _1304580])))]], 29150 ^ _779308 : [(29151 ^ _779308) ^ [_1304646] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1304646), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1304578))), hBOOL(hAPP(_1304580, _1304646))]]], (29162 ^ _779308) ^ [_1304830, _1304832] : [29164 ^ _779308 : [(29165 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29163 ^ [_1304830, _1304832]), _1304830)))], (29167 ^ _779308) ^ [] : [hBOOL(hAPP(_1304832, 29163 ^ [_1304830, _1304832]))]], 29168 ^ _779308 : [(29169 ^ _779308) ^ [_1304980] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1304980), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1304830))), -(hBOOL(hAPP(_1304832, _1304980)))]]], (29175 ^ _779308) ^ [_1305081, _1305083] : [29177 ^ _779308 : [(29178 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 29176 ^ [_1305081, _1305083]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1305081))))], (29180 ^ _779308) ^ [] : [hBOOL(hAPP(_1305083, 29176 ^ [_1305081, _1305083]))]], 29181 ^ _779308 : [(29182 ^ _779308) ^ [_1305234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1305234), _1305081)), -(hBOOL(hAPP(_1305083, _1305234)))]]], (29188 ^ _779308) ^ [_1305335, _1305337] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1305335), hAPP(c_Nat_OSuc, _1305337)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1305335, _1305337))], (29190 ^ _779308) ^ [_1305373] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1305373), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (29192 ^ _779308) ^ [_1305402, _1305404] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1305402), _1305404)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1305404), _1305402))], (29194 ^ _779308) ^ [_1305442, _1305444] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1305442), _1305444)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1305442)), hAPP(c_Nat_OSuc, _1305444)))], (29196 ^ _779308) ^ [_1305488, _1305490, _1305492] : [class_Orderings_Oorder(_1305488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305488), _1305490), _1305492)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1305488, _1305492), _1305490) = c_Orderings_Obot__class_Obot(tc_fun(_1305488, tc_HOL_Obool)))], (29206 ^ _779308) ^ [_1305655, _1305657, _1305659] : [class_Orderings_Oorder(_1305655), 29209 ^ _779308 : [(29210 ^ _779308) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1305655, _1305657), _1305659) = c_Orderings_Obot__class_Obot(tc_fun(_1305655, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305655), _1305657), _1305659))], (29216 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305655), _1305657), _1305659))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1305655, _1305657), _1305659) = c_Orderings_Obot__class_Obot(tc_fun(_1305655, tc_HOL_Obool)))]]], (29222 ^ _779308) ^ [_1305880, _1305882, _1305884] : [class_Orderings_Oorder(_1305880), 29225 ^ _779308 : [(29226 ^ _779308) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1305880, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1305880, _1305882), _1305884), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305880), _1305882), _1305884))], (29232 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305880), _1305882), _1305884))), -(c_Orderings_Obot__class_Obot(tc_fun(_1305880, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1305880, _1305882), _1305884))]]], (29238 ^ _779308) ^ [_1306105, _1306107, _1306109, _1306111, _1306113] : [class_Orderings_Olinorder(_1306105), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306105, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306105, _1306107), _1306109)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306105, _1306111), _1306113))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306105), _1306109), _1306107))), 29249 ^ _779308 : [(29250 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306105), _1306111), _1306107)))], (29252 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306105), _1306109), _1306113)))]]], (29254 ^ _779308) ^ [_1306386, _1306388, _1306390, _1306392] : [class_Orderings_Olinorder(_1306386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306386), _1306388), _1306390)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306386), _1306390), _1306392)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306386, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306386, _1306388), _1306390)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306386, _1306390), _1306392)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306386, _1306388), _1306392))], (29268 ^ _779308) ^ [_1306663, _1306665, _1306667, _1306669] : [class_Orderings_Olinorder(_1306663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306663), _1306665), _1306667)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1306663, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306663, _1306665), _1306669)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306663, _1306665), _1306667)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306663, _1306667), _1306669))], (29278 ^ _779308) ^ [_1306870, _1306872] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1306870)), _1306872) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1306870, _1306872))], (29280 ^ _779308) ^ [_1306908] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1306908) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1306908))], (29282 ^ _779308) ^ [_1306938, _1306940, _1306942] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1306938)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1306940), _1306942)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1306940), _1306938)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1306942), _1306938)))], (29284 ^ _779308) ^ [_1306999] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1306999)) = hAPP(c_Nat_OSuc, _1306999))], (29286 ^ _779308) ^ [_1307031] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1307031)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1307031)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1307031)))], (29288 ^ _779308) ^ [_1307072, _1307074, _1307076] : [class_Orderings_Oord(_1307072), 29291 ^ _779308 : [(29292 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1307072), _1307074), hAPP(c_SetInterval_Oord__class_OatMost(_1307072), _1307076))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307072), _1307074), _1307076)))], (29298 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307072), _1307074), _1307076)), -(hBOOL(hAPP(hAPP(c_member(_1307072), _1307074), hAPP(c_SetInterval_Oord__class_OatMost(_1307072), _1307076))))]]], (29304 ^ _779308) ^ [_1307340, _1307342, _1307344] : [class_Orderings_Oorder(_1307340), 29307 ^ _779308 : [(29308 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307340, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1307340), _1307342)), hAPP(c_SetInterval_Oord__class_OatMost(_1307340), _1307344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307340), _1307342), _1307344)))], (29314 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307340), _1307342), _1307344)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307340, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1307340), _1307342)), hAPP(c_SetInterval_Oord__class_OatMost(_1307340), _1307344))))]]], (29320 ^ _779308) ^ [_1307632] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1307632), hAPP(c_Nat_OSuc, _1307632)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1307632), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (29322 ^ _779308) ^ [_1307670, _1307672, _1307674, _1307676] : [class_Orderings_Olinorder(_1307670), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307670), _1307672), _1307674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307670), _1307674), _1307676)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307670, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1307670, _1307672), _1307674)), c_SetInterval_Oord__class_OatLeastAtMost(_1307670, _1307674, _1307676)) = c_SetInterval_Oord__class_OatLeastAtMost(_1307670, _1307672, _1307676))], (29336 ^ _779308) ^ [_1307939, _1307941, _1307943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1307939), _1307941)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1307939), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1307941), _1307943)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1307939), _1307941)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1307941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1307941), _1307943))))], (29342 ^ _779308) ^ [_1308100, _1308102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1308100), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1308102), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1308102), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1308100))))), -(_1308100 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1308102), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1308102), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1308100))))], (29348 ^ _779308) ^ [_1308247, _1308249, _1308251] : [class_Groups_Oordered__ab__group__add(_1308247), -(hAPP(c_Set_Oimage(_1308247, _1308247, c_Groups_Ouminus__class_Ouminus(_1308247)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1308247, _1308249, _1308251)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1308247, hAPP(c_Groups_Ouminus__class_Ouminus(_1308247), _1308251)), hAPP(c_Groups_Ouminus__class_Ouminus(_1308247), _1308249)))], (29354 ^ _779308) ^ [_1308382, _1308384, _1308386] : [class_Groups_Oordered__ab__group__add(_1308382), -(hAPP(c_Set_Oimage(_1308382, _1308382, c_Groups_Ouminus__class_Ouminus(_1308382)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1308382, _1308384), _1308386)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1308382, hAPP(c_Groups_Ouminus__class_Ouminus(_1308382), _1308386), hAPP(c_Groups_Ouminus__class_Ouminus(_1308382), _1308384)))], (29360 ^ _779308) ^ [_1308526, _1308528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1308526), _1308528)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1308526), hAPP(c_Nat_OSuc, _1308528)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1308528), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1308526), _1308528)))], (29366 ^ _779308) ^ [_1308649, _1308651] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1308649), _1308651))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1308649), hAPP(c_Nat_OSuc, _1308651)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (29372 ^ _779308) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (29374 ^ _779308) ^ [_1308719, _1308721, _1308723] : [class_Orderings_Olinorder(_1308719), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308719), _1308721), _1308723)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308719, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1308719), _1308721)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1308719, _1308721, _1308723)) = hAPP(c_SetInterval_Oord__class_OatMost(_1308719), _1308723))], (29384 ^ _779308) ^ [_1308914, _1308916, _1308918, _1308920] : [class_Orderings_Olinorder(_1308914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1308914), _1308916), _1308918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308914), _1308918), _1308920)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308914, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1308914, _1308916, _1308918)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1308914, _1308918), _1308920)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1308914, _1308916, _1308920))], (29398 ^ _779308) ^ [_1309183, _1309185, _1309187] : [class_Orderings_Olinorder(_1309183), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309183), _1309185), _1309187)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309183, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1309183, _1309185), _1309187)), hAPP(hAPP(c_Set_Oinsert(_1309183), _1309187), c_Orderings_Obot__class_Obot(tc_fun(_1309183, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1309183, _1309185, _1309187))], (29408 ^ _779308) ^ [_1309396, _1309398, _1309400] : [class_Orderings_Olinorder(_1309396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309396), _1309398), _1309400)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309396, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1309396), _1309398), c_Orderings_Obot__class_Obot(tc_fun(_1309396, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1309396, _1309398, _1309400)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1309396, _1309398), _1309400))], (29418 ^ _779308) ^ [_1309609, _1309611, _1309613, _1309615] : [class_Orderings_Olinorder(_1309609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309609), _1309611), _1309613)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309609), _1309613), _1309615)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309609, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1309609, _1309611, _1309613)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1309609, _1309613, _1309615)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1309609, _1309611), _1309615))], (29432 ^ _779308) ^ [_1309878, _1309880, _1309882] : [class_Orderings_Olinorder(_1309878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309878), _1309880), _1309882)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309878, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1309878), _1309880)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1309878, _1309880, _1309882)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1309878), _1309882))], (29442 ^ _779308) ^ [_1310073, _1310075, _1310077] : [class_Orderings_Olinorder(_1310073), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310073), _1310075), _1310077)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310073, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1310073), _1310075)), c_SetInterval_Oord__class_OatLeastAtMost(_1310073, _1310075, _1310077)) = hAPP(c_SetInterval_Oord__class_OatMost(_1310073), _1310077))], (29452 ^ _779308) ^ [_1310268, _1310270] : [class_Orderings_Olinorder(_1310268), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310268, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1310268), _1310270)), hAPP(hAPP(c_Set_Oinsert(_1310268), _1310270), c_Orderings_Obot__class_Obot(tc_fun(_1310268, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1310268), _1310270))], (29458 ^ _779308) ^ [_1310411, _1310413, _1310415, _1310417, _1310419] : [class_Groups_Ocomm__monoid__mult(_1310411), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310413), _1310415)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310413), _1310417)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310413, tc_HOL_Obool)), _1310415), _1310417) = c_Orderings_Obot__class_Obot(tc_fun(_1310413, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1310411, _1310413, c_Groups_Otimes__class_Otimes(_1310411)), _1310419), c_Groups_Oone__class_Oone(_1310411)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310413, tc_HOL_Obool)), _1310415), _1310417)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1310411), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1310411, _1310413, c_Groups_Otimes__class_Otimes(_1310411)), _1310419), c_Groups_Oone__class_Oone(_1310411)), _1310415)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1310411, _1310413, c_Groups_Otimes__class_Otimes(_1310411)), _1310419), c_Groups_Oone__class_Oone(_1310411)), _1310417)))], (29476 ^ _779308) ^ [_1310854, _1310856, _1310858, _1310860] : [hBOOL(hAPP(_1310854, _1310856)), hBOOL(hAPP(_1310858, _1310856)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310860, tc_HOL_Obool)), _1310854), _1310858), _1310856)))], (29486 ^ _779308) ^ [_1311025, _1311027, _1311029, _1311031] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311025, tc_HOL_Obool)), _1311027), _1311029), _1311031)), 29489 ^ _779308 : [(29490 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1311027, _1311031)))], (29492 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1311029, _1311031)))]]], (29494 ^ _779308) ^ [_1311170] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1311170))))], (29496 ^ _779308) ^ [_1311198, _1311200] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1311198), _1311200))))], (29498 ^ _779308) ^ [_1311231, _1311233, _1311235, _1311237] : [hBOOL(hAPP(hAPP(c_member(_1311231), _1311233), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311231, tc_HOL_Obool)), _1311235), _1311237))), 29501 ^ _779308 : [(29502 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1311231), _1311233), _1311235)))], (29504 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1311231), _1311233), _1311237)))]]], (29506 ^ _779308) ^ [_1311406, _1311408, _1311410, _1311412] : [hBOOL(hAPP(hAPP(c_member(_1311406), _1311408), _1311410)), hBOOL(hAPP(hAPP(c_member(_1311406), _1311408), _1311412)), -(hBOOL(hAPP(hAPP(c_member(_1311406), _1311408), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311406, tc_HOL_Obool)), _1311410), _1311412))))], (29516 ^ _779308) ^ [_1311607, _1311609, _1311611] : [29517 ^ _779308 : [(29518 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1311607), _1311609))], (29520 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1311607), _1311611))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1311607), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311607, tc_HOL_Obool)), _1311609), _1311611))))], (29524 ^ _779308) ^ [_1311770, _1311772, _1311774] : [class_Orderings_Oorder(_1311770), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311770, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1311770), _1311772)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1311770, _1311772), _1311774)) = c_Orderings_Obot__class_Obot(tc_fun(_1311770, tc_HOL_Obool)))], (29530 ^ _779308) ^ [_1311901, _1311903, _1311905] : [-(hAPP(c_Set_OPow(_1311901), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311901, tc_HOL_Obool)), _1311903), _1311905)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1311901, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1311901), _1311903)), hAPP(c_Set_OPow(_1311901), _1311905)))], (29532 ^ _779308) ^ [_1311968, _1311970] : [c_Nat__Transfer_Onat__set(_1311968), c_Nat__Transfer_Onat__set(_1311970), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1311968), _1311970)))], (29542 ^ _779308) ^ [_1312103, _1312105, _1312107, _1312109, _1312111] : [c_Fun_Oinj__on(_1312103, _1312105, _1312107, _1312109), c_Fun_Oinj__on(_1312103, _1312105, _1312107, _1312111), -(c_Fun_Oinj__on(_1312103, _1312105, _1312107, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312103, tc_HOL_Obool)), _1312109), _1312111)))], (29552 ^ _779308) ^ [_1312278, _1312280, _1312282, _1312284, _1312286] : [class_Lattices_Olattice(_1312278), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312280, _1312278)), _1312282), _1312284), _1312286) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1312278), hAPP(_1312282, _1312286)), hAPP(_1312284, _1312286)))], (29558 ^ _779308) ^ [_1312415, _1312417, _1312419, _1312421] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312415, tc_HOL_Obool)), _1312417), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312415, tc_HOL_Obool)), _1312419), _1312421)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312415, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312415, tc_HOL_Obool)), _1312417), _1312419)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312415, tc_HOL_Obool)), _1312417), _1312421)))], (29560 ^ _779308) ^ [_1312499, _1312501, _1312503, _1312505] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312499, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312499, tc_HOL_Obool)), _1312501), _1312503)), _1312505) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312499, tc_HOL_Obool)), _1312501), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312499, tc_HOL_Obool)), _1312503), _1312505)))], (29562 ^ _779308) ^ [_1312572, _1312574, _1312576, _1312578] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312572, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312572, tc_HOL_Obool)), _1312574), _1312576)), _1312578) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312572, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312572, tc_HOL_Obool)), _1312574), _1312578)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312572, tc_HOL_Obool)), _1312576), _1312578)))], (29564 ^ _779308) ^ [_1312656, _1312658, _1312660, _1312662] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312656, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312656, tc_HOL_Obool)), _1312658), _1312660)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312656, tc_HOL_Obool)), _1312662), _1312660)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1312656, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312656, tc_HOL_Obool)), _1312658), _1312660)), _1312662))], (29566 ^ _779308) ^ [_1312740] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1312740) = c_Orderings_Oord__class_Omin(_1312740)), class_Lattices_Osemilattice__inf(_1312740), class_Orderings_Olinorder(_1312740)], (29576 ^ _779308) ^ [_1312869, _1312871, _1312873, _1312875] : [class_Lattices_Osemilattice__inf(_1312869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312869), _1312871), _1312873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1312869), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1312869), _1312875), _1312871)), _1312873)))], (29586 ^ _779308) ^ [_1313048, _1313050, _1313052, _1313054] : [class_Lattices_Osemilattice__inf(_1313048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1313048), _1313050), _1313052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1313048), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313048), _1313050), _1313054)), _1313052)))], (29596 ^ _779308) ^ [_1313227, _1313229] : [class_Lattices_Olattice(_1313227), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313227), _1313229), _1313229) = _1313229)], (29602 ^ _779308) ^ [_1313318, _1313320] : [class_Lattices_Osemilattice__inf(_1313318), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313318), _1313320), _1313320) = _1313320)], (29608 ^ _779308) ^ [_1313409, _1313411] : [class_Lattices_Osemilattice__inf(_1313409), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313409), _1313411), _1313411) = _1313411)], (29614 ^ _779308) ^ [_1313500, _1313502, _1313504] : [class_Lattices_Osemilattice__inf(_1313500), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313500), _1313502), _1313504) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313500), _1313504), _1313502))], (29620 ^ _779308) ^ [_1313609, _1313611, _1313613] : [class_Lattices_Olattice(_1313609), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313609), _1313611), _1313613) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313609), _1313613), _1313611))], (29626 ^ _779308) ^ [_1313718, _1313720, _1313722] : [class_Lattices_Osemilattice__inf(_1313718), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313718), _1313720), _1313722) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313718), _1313722), _1313720))], (29632 ^ _779308) ^ [_1313827, _1313829, _1313831] : [class_Lattices_Osemilattice__inf(_1313827), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313827), _1313829), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313827), _1313829), _1313831)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313827), _1313829), _1313831))], (29638 ^ _779308) ^ [_1313952, _1313954, _1313956] : [class_Lattices_Olattice(_1313952), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313952), _1313954), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313952), _1313954), _1313956)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313952), _1313954), _1313956))], (29644 ^ _779308) ^ [_1314077, _1314079, _1314081] : [class_Lattices_Osemilattice__inf(_1314077), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314077), _1314079), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314077), _1314079), _1314081)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314077), _1314079), _1314081))], (29650 ^ _779308) ^ [_1314202, _1314204, _1314206, _1314208] : [class_Lattices_Osemilattice__inf(_1314202), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314202), _1314204), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314202), _1314206), _1314208)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314202), _1314206), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314202), _1314204), _1314208)))], (29656 ^ _779308) ^ [_1314345, _1314347, _1314349, _1314351] : [class_Lattices_Olattice(_1314345), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314345), _1314347), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314345), _1314349), _1314351)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314345), _1314349), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314345), _1314347), _1314351)))], (29662 ^ _779308) ^ [_1314488, _1314490, _1314492, _1314494] : [class_Lattices_Osemilattice__inf(_1314488), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314488), _1314490), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314488), _1314492), _1314494)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314488), _1314492), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314488), _1314490), _1314494)))], (29668 ^ _779308) ^ [_1314631, _1314633, _1314635, _1314637] : [class_Lattices_Osemilattice__inf(_1314631), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314631), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314631), _1314633), _1314635)), _1314637) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314631), _1314633), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314631), _1314635), _1314637)))], (29674 ^ _779308) ^ [_1314774, _1314776, _1314778, _1314780] : [class_Lattices_Olattice(_1314774), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314774), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314774), _1314776), _1314778)), _1314780) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314774), _1314776), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314774), _1314778), _1314780)))], (29680 ^ _779308) ^ [_1314917, _1314919, _1314921, _1314923] : [class_Lattices_Osemilattice__inf(_1314917), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314917), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314917), _1314919), _1314921)), _1314923) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314917), _1314919), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1314917), _1314921), _1314923)))], (29686 ^ _779308) ^ [_1315060, _1315062, _1315064, _1315066, _1315068] : [class_Lattices_Olattice(_1315060), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315062, _1315060)), _1315064), _1315066), _1315068) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1315060), hAPP(_1315064, _1315068)), hAPP(_1315066, _1315068)))], (29692 ^ _779308) ^ [_1315197, _1315199] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315197, tc_HOL_Obool)), _1315199), _1315199) = _1315199)], (29694 ^ _779308) ^ [_1315233, _1315235, _1315237] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315233, tc_HOL_Obool)), _1315235), _1315237) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315233, tc_HOL_Obool)), _1315237), _1315235))], (29696 ^ _779308) ^ [_1315282, _1315284, _1315286] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315282, tc_HOL_Obool)), _1315284), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315282, tc_HOL_Obool)), _1315284), _1315286)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315282, tc_HOL_Obool)), _1315284), _1315286))], (29698 ^ _779308) ^ [_1315342, _1315344, _1315346, _1315348] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315342, tc_HOL_Obool)), _1315344), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315342, tc_HOL_Obool)), _1315346), _1315348)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315342, tc_HOL_Obool)), _1315346), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315342, tc_HOL_Obool)), _1315344), _1315348)))], (29700 ^ _779308) ^ [_1315415, _1315417, _1315419, _1315421] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315415, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315415, tc_HOL_Obool)), _1315417), _1315419)), _1315421) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315415, tc_HOL_Obool)), _1315417), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315415, tc_HOL_Obool)), _1315419), _1315421)))], (29702 ^ _779308) ^ [_1315488, _1315490, _1315492, _1315494] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315488, tc_HOL_Obool)), _1315490), _1315492), _1315494)), -(hBOOL(hAPP(_1315490, _1315494)))], (29708 ^ _779308) ^ [_1315599, _1315601, _1315603, _1315605] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315599, tc_HOL_Obool)), _1315601), _1315603), _1315605)), -(hBOOL(hAPP(_1315603, _1315605)))], (29714 ^ _779308) ^ [_1315710, _1315712, _1315714] : [class_Orderings_Olinorder(_1315710), 29717 ^ _779308 : [(29718 ^ _779308) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1315710), _1315712) = hAPP(c_SetInterval_Oord__class_OlessThan(_1315710), _1315714), -(_1315712 = _1315714)], (29724 ^ _779308) ^ [] : [_1315712 = _1315714, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1315710), _1315712) = hAPP(c_SetInterval_Oord__class_OlessThan(_1315710), _1315714))]]], (29730 ^ _779308) ^ [_1315951, _1315953, _1315955] : [class_Lattices_Olattice(_1315951), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1315951), _1315953), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1315951), _1315953), _1315955)) = _1315953)], (29736 ^ _779308) ^ [_1316060, _1316062, _1316064] : [class_Lattices_Olattice(_1316060), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316060), _1316062), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316060), _1316062), _1316064)) = _1316062)], (29742 ^ _779308) ^ [_1316169, _1316171, _1316173, _1316175] : [class_Lattices_Odistrib__lattice(_1316169), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316169), _1316171), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316169), _1316173), _1316175)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316169), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316169), _1316171), _1316173)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316169), _1316171), _1316175)))], (29748 ^ _779308) ^ [_1316328, _1316330, _1316332, _1316334] : [class_Lattices_Odistrib__lattice(_1316328), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316328), _1316330), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316328), _1316332), _1316334)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316328), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316328), _1316330), _1316332)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316328), _1316330), _1316334)))], (29754 ^ _779308) ^ [_1316487, _1316489, _1316491, _1316493] : [class_Lattices_Odistrib__lattice(_1316487), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316487), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316487), _1316489), _1316491)), _1316493) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316487), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316487), _1316489), _1316493)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316487), _1316491), _1316493)))], (29760 ^ _779308) ^ [_1316646, _1316648, _1316650, _1316652] : [class_Lattices_Odistrib__lattice(_1316646), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316646), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316646), _1316648), _1316650)), _1316652) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1316646), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316646), _1316648), _1316652)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1316646), _1316650), _1316652)))], (29766 ^ _779308) ^ [_1316805, _1316807, _1316809, _1316811] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316805, tc_HOL_Obool)), _1316807), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316805, tc_HOL_Obool)), _1316809), _1316811)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316805, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316805, tc_HOL_Obool)), _1316807), _1316809)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316805, tc_HOL_Obool)), _1316807), _1316811)))], (29768 ^ _779308) ^ [_1316889, _1316891, _1316893, _1316895] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316889, tc_HOL_Obool)), _1316891), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316889, tc_HOL_Obool)), _1316893), _1316895)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316889, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316889, tc_HOL_Obool)), _1316891), _1316893)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316889, tc_HOL_Obool)), _1316891), _1316895)))], (29770 ^ _779308) ^ [_1316973, _1316975, _1316977, _1316979] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316973, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316973, tc_HOL_Obool)), _1316975), _1316977)), _1316979) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316973, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316973, tc_HOL_Obool)), _1316975), _1316979)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316973, tc_HOL_Obool)), _1316977), _1316979)))], (29772 ^ _779308) ^ [_1317057, _1317059, _1317061, _1317063] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317057, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317057, tc_HOL_Obool)), _1317059), _1317061)), _1317063) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317057, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317057, tc_HOL_Obool)), _1317059), _1317063)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317057, tc_HOL_Obool)), _1317061), _1317063)))], (29774 ^ _779308) ^ [_1317141, _1317143, _1317145, _1317147] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317141, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317141, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317141, tc_HOL_Obool)), _1317143), _1317145)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317141, tc_HOL_Obool)), _1317145), _1317147))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317141, tc_HOL_Obool)), _1317147), _1317143)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317141, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317141, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317141, tc_HOL_Obool)), _1317143), _1317145)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317141, tc_HOL_Obool)), _1317145), _1317147))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317141, tc_HOL_Obool)), _1317147), _1317143)))], (29776 ^ _779308) ^ [_1317280, _1317282, _1317284, _1317286] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317280, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1317280), _1317282), _1317284)), hAPP(hAPP(c_Set_Oinsert(_1317280), _1317282), _1317286)) = hAPP(hAPP(c_Set_Oinsert(_1317280), _1317282), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317280, tc_HOL_Obool)), _1317284), _1317286)))], (29778 ^ _779308) ^ [_1317355, _1317357] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317355, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1317355, tc_HOL_Obool))), _1317357) = c_Orderings_Obot__class_Obot(tc_fun(_1317355, tc_HOL_Obool)))], (29780 ^ _779308) ^ [_1317401, _1317403] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317401, tc_HOL_Obool)), _1317403), c_Orderings_Obot__class_Obot(tc_fun(_1317401, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1317401, tc_HOL_Obool)))], (29796 ^ _779308) ^ [_1317779, _1317781, _1317783] : [29798 ^ _779308 : [(29799 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1317779), 29797 ^ [_1317779, _1317781, _1317783]), _1317781)))], (29802 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1317779), 29800 ^ [_1317779, _1317781, _1317783]), _1317783)))], (29804 ^ _779308) ^ [] : [-(29797 ^ [_1317779, _1317781, _1317783] = 29800 ^ [_1317779, _1317781, _1317783])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317779, tc_HOL_Obool)), _1317781), _1317783) = c_Orderings_Obot__class_Obot(tc_fun(_1317779, tc_HOL_Obool)))], (29782 ^ _779308) ^ [_1317465, _1317467, _1317469] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317465, tc_HOL_Obool)), _1317467), _1317469) = c_Orderings_Obot__class_Obot(tc_fun(_1317465, tc_HOL_Obool)), 29785 ^ _779308 : [(29786 ^ _779308) ^ [_1317589] : [hBOOL(hAPP(hAPP(c_member(_1317465), _1317589), _1317467)), 29789 ^ _779308 : [(29790 ^ _779308) ^ [_1317679] : [hBOOL(hAPP(hAPP(c_member(_1317465), _1317679), _1317469)), _1317589 = _1317679]]]]], (29808 ^ _779308) ^ [_1317940, _1317942] : [class_Lattices_Obounded__lattice__bot(_1317940), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1317940), c_Orderings_Obot__class_Obot(_1317940)), _1317942) = c_Orderings_Obot__class_Obot(_1317940))], (29814 ^ _779308) ^ [_1318039, _1318041] : [class_Lattices_Obounded__lattice__bot(_1318039), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1318039), _1318041), c_Orderings_Obot__class_Obot(_1318039)) = c_Orderings_Obot__class_Obot(_1318039))], (29820 ^ _779308) ^ [_1318138, _1318140, _1318142] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318138, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318138, tc_HOL_Obool)), _1318140), _1318142)), _1318140)))], (29822 ^ _779308) ^ [_1318186, _1318188, _1318190] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318186, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318186, tc_HOL_Obool)), _1318188), _1318190)), _1318190)))], (29824 ^ _779308) ^ [_1318234, _1318236, _1318238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318234, tc_HOL_Obool)), _1318236), _1318238)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318234, tc_HOL_Obool)), _1318236), _1318238) = _1318236)], (29830 ^ _779308) ^ [_1318355, _1318357, _1318359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318355, tc_HOL_Obool)), _1318357), _1318359)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318355, tc_HOL_Obool)), _1318359), _1318357) = _1318357)], (29836 ^ _779308) ^ [_1318476, _1318478, _1318480, _1318482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318476, tc_HOL_Obool)), _1318478), _1318480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318476, tc_HOL_Obool)), _1318478), _1318482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318476, tc_HOL_Obool)), _1318478), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318476, tc_HOL_Obool)), _1318480), _1318482))))], (29846 ^ _779308) ^ [_1318695, _1318697, _1318699, _1318701, _1318703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318695, tc_HOL_Obool)), _1318697), _1318699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318695, tc_HOL_Obool)), _1318701), _1318703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318695, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318695, tc_HOL_Obool)), _1318697), _1318701)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318695, tc_HOL_Obool)), _1318699), _1318703))))], (29856 ^ _779308) ^ [_1318940, _1318942, _1318944, _1318946] : [class_Lattices_Osemilattice__inf(_1318940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318940), _1318942), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1318940), _1318944), _1318946))), 29863 ^ _779308 : [(29864 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318940), _1318942), _1318944)))], (29866 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318940), _1318942), _1318946)))]]], (29868 ^ _779308) ^ [_1319163, _1319165, _1319167, _1319169, _1319171] : [class_Lattices_Osemilattice__inf(_1319163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319163), _1319165), _1319167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319163), _1319169), _1319171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319163), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319163), _1319165), _1319169)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319163), _1319167), _1319171))))], (29882 ^ _779308) ^ [_1319434, _1319436, _1319438, _1319440] : [class_Lattices_Osemilattice__inf(_1319434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319434), _1319436), _1319438)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319434), _1319436), _1319440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319434), _1319436), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319434), _1319438), _1319440))))], (29896 ^ _779308) ^ [_1319683, _1319685, _1319687, _1319689] : [class_Lattices_Osemilattice__inf(_1319683), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319683), _1319685), _1319687)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319683), _1319685), _1319689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319683), _1319685), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319683), _1319687), _1319689))))], (29910 ^ _779308) ^ [_1319932, _1319934, _1319936] : [class_Lattices_Osemilattice__inf(_1319932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319932), _1319934), _1319936)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1319932), _1319936), _1319934) = _1319934)], (29920 ^ _779308) ^ [_1320093, _1320095, _1320097] : [class_Lattices_Osemilattice__inf(_1320093), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320093), _1320095), _1320097)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320093), _1320095), _1320097) = _1320095)], (29930 ^ _779308) ^ [_1320254, _1320256, _1320258, _1320260] : [class_Lattices_Osemilattice__inf(_1320254), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320254), _1320256), _1320258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320254), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320254), _1320260), _1320256)), _1320258)))], (29940 ^ _779308) ^ [_1320433, _1320435, _1320437, _1320439] : [class_Lattices_Osemilattice__inf(_1320433), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320433), _1320435), _1320437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320433), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320433), _1320435), _1320439)), _1320437)))], (29950 ^ _779308) ^ [_1320612, _1320614, _1320616, _1320618] : [class_Lattices_Osemilattice__inf(_1320612), 29953 ^ _779308 : [(29954 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320612), _1320614), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320612), _1320616), _1320618))), 29957 ^ _779308 : [(29958 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320612), _1320614), _1320616)))], (29960 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320612), _1320614), _1320618)))]]], (29962 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320612), _1320614), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320612), _1320616), _1320618)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320612), _1320614), _1320616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320612), _1320614), _1320618))]]], (29972 ^ _779308) ^ [_1320992, _1320994, _1320996] : [class_Lattices_Osemilattice__inf(_1320992), 29975 ^ _779308 : [(29976 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320992), _1320994), _1320996)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320992), _1320994), _1320996) = _1320994)], (29982 ^ _779308) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1320992), _1320994), _1320996) = _1320994, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1320992), _1320994), _1320996)))]]], (29988 ^ _779308) ^ [_1321248, _1321250, _1321252] : [class_Lattices_Osemilattice__inf(_1321248), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321248), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321248), _1321250), _1321252)), _1321252)))], (29994 ^ _779308) ^ [_1321355, _1321357, _1321359] : [class_Lattices_Olattice(_1321355), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321355), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321355), _1321357), _1321359)), _1321359)))], (30000 ^ _779308) ^ [_1321462, _1321464, _1321466] : [class_Lattices_Osemilattice__inf(_1321462), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321462), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321462), _1321464), _1321466)), _1321464)))], (30006 ^ _779308) ^ [_1321569, _1321571, _1321573] : [class_Lattices_Olattice(_1321569), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321569), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1321569), _1321571), _1321573)), _1321571)))], (30012 ^ _779308) ^ [_1321676, _1321678, _1321680, _1321682] : [hBOOL(hAPP(hAPP(c_member(_1321676), _1321678), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321676, tc_HOL_Obool)), _1321680), _1321682))), -(hBOOL(hAPP(hAPP(c_member(_1321676), _1321678), _1321682)))], (30018 ^ _779308) ^ [_1321807, _1321809, _1321811, _1321813] : [hBOOL(hAPP(hAPP(c_member(_1321807), _1321809), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321807, tc_HOL_Obool)), _1321811), _1321813))), -(hBOOL(hAPP(hAPP(c_member(_1321807), _1321809), _1321811)))], (30024 ^ _779308) ^ [_1321959, _1321961, _1321963, _1321965] : [hBOOL(hAPP(hAPP(c_member(_1321959), _1321961), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321959, tc_HOL_Obool)), _1321963), _1321965))), 30027 ^ _779308 : [(30028 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1321959), _1321961), _1321963)))], (30030 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1321959), _1321961), _1321965)))]]], (30032 ^ _779308) ^ [_1322126, _1322128, _1322130, _1322132] : [-(hBOOL(hAPP(hAPP(c_member(_1322126), _1322128), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322126, tc_HOL_Obool)), _1322130), _1322132)))), hBOOL(hAPP(hAPP(c_member(_1322126), _1322128), _1322130)), hBOOL(hAPP(hAPP(c_member(_1322126), _1322128), _1322132))], (30042 ^ _779308) ^ [_1322329, _1322331, _1322333] : [class_Orderings_Oorder(_1322329), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322329, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1322329), _1322331)), c_SetInterval_Oord__class_OatLeastAtMost(_1322329, _1322331, _1322333)) = c_Orderings_Obot__class_Obot(tc_fun(_1322329, tc_HOL_Obool)))], (30048 ^ _779308) ^ [_1322456] : [class_Lattices_Osemilattice__inf(_1322456), -(c_Finite__Set_Ofun__left__comm__idem(_1322456, _1322456, c_Lattices_Osemilattice__inf__class_Oinf(_1322456)))], (30054 ^ _779308) ^ [_1322556, _1322558, _1322560, _1322562] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322556, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1322556, tc_fun(_1322556, tc_HOL_Obool), tc_HOL_Obool), c_member(_1322556)), _1322558)), hAPP(hAPP(c_COMBC(_1322556, tc_fun(_1322556, tc_HOL_Obool), tc_HOL_Obool), c_member(_1322556)), _1322560)), _1322562)), -(hBOOL(hAPP(hAPP(c_member(_1322556), _1322562), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322556, tc_HOL_Obool)), _1322558), _1322560))))], (30060 ^ _779308) ^ [_1322755, _1322757, _1322759, _1322761] : [hBOOL(hAPP(hAPP(c_member(_1322755), _1322761), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322755, tc_HOL_Obool)), _1322757), _1322759))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322755, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1322755, tc_fun(_1322755, tc_HOL_Obool), tc_HOL_Obool), c_member(_1322755)), _1322757)), hAPP(hAPP(c_COMBC(_1322755, tc_fun(_1322755, tc_HOL_Obool), tc_HOL_Obool), c_member(_1322755)), _1322759)), _1322761)))], (30066 ^ _779308) ^ [_1322960] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1322960)) = _1322960)], (30068 ^ _779308) ^ [_1322989, _1322991, _1322993, _1322995] : [class_Lattices_Olattice(_1322989), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1322989), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1322989), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1322989), _1322991), _1322993)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1322989), _1322991), _1322995))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1322989), _1322991), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1322989), _1322993), _1322995)))))], (30074 ^ _779308) ^ [_1323162, _1323164, _1323166, _1323168] : [class_Lattices_Olattice(_1323162), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323162), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1323162), _1323164), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323162), _1323166), _1323168))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323162), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1323162), _1323164), _1323166)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1323162), _1323164), _1323168)))))], (30080 ^ _779308) ^ [_1323335, _1323337] : [class_Lattices_Oboolean__algebra(_1323335), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323335), hAPP(c_Groups_Ouminus__class_Ouminus(_1323335), _1323337)), _1323337) = c_Orderings_Obot__class_Obot(_1323335))], (30086 ^ _779308) ^ [_1323440, _1323442] : [class_Lattices_Oboolean__algebra(_1323440), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323440), _1323442), hAPP(c_Groups_Ouminus__class_Ouminus(_1323440), _1323442)) = c_Orderings_Obot__class_Obot(_1323440))], (30092 ^ _779308) ^ [_1323545, _1323547, _1323549] : [class_Lattices_Oboolean__algebra(_1323545), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1323545), _1323547), _1323549) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323545), _1323547), hAPP(c_Groups_Ouminus__class_Ouminus(_1323545), _1323549)))], (30098 ^ _779308) ^ [_1323664, _1323666, _1323668] : [class_Lattices_Oboolean__algebra(_1323664), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1323664), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1323664), _1323666), _1323668)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323664), hAPP(c_Groups_Ouminus__class_Ouminus(_1323664), _1323666)), hAPP(c_Groups_Ouminus__class_Ouminus(_1323664), _1323668)))], (30104 ^ _779308) ^ [_1323803, _1323805, _1323807] : [class_Lattices_Oboolean__algebra(_1323803), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1323803), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1323803), _1323805), _1323807)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1323803), hAPP(c_Groups_Ouminus__class_Ouminus(_1323803), _1323805)), hAPP(c_Groups_Ouminus__class_Ouminus(_1323803), _1323807)))], (30110 ^ _779308) ^ [_1323957, _1323959, _1323961, _1323963] : [hBOOL(hAPP(hAPP(c_member(_1323957), _1323959), _1323961)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323957, tc_HOL_Obool)), _1323961), hAPP(hAPP(c_Set_Oinsert(_1323957), _1323959), _1323963)) = hAPP(hAPP(c_Set_Oinsert(_1323957), _1323959), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323957, tc_HOL_Obool)), _1323961), _1323963)))], (30116 ^ _779308) ^ [_1324122, _1324124, _1324126, _1324128] : [-(hBOOL(hAPP(hAPP(c_member(_1324122), _1324124), _1324126))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324122, tc_HOL_Obool)), _1324126), hAPP(hAPP(c_Set_Oinsert(_1324122), _1324124), _1324128)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324122, tc_HOL_Obool)), _1324126), _1324128))], (30122 ^ _779308) ^ [_1324216, _1324218, _1324220, _1324222] : [hBOOL(hAPP(hAPP(c_member(_1324216), _1324218), _1324220)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324216, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1324216), _1324218), _1324222)), _1324220) = hAPP(hAPP(c_Set_Oinsert(_1324216), _1324218), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324216, tc_HOL_Obool)), _1324222), _1324220)))], (30128 ^ _779308) ^ [_1324381, _1324383, _1324385, _1324387] : [-(hBOOL(hAPP(hAPP(c_member(_1324381), _1324383), _1324385))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324381, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1324381), _1324383), _1324387)), _1324385) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324381, tc_HOL_Obool)), _1324387), _1324385))], (30134 ^ _779308) ^ [_1324456, _1324458, _1324460, _1324462] : [-(hBOOL(hAPP(hAPP(c_member(_1324456), _1324458), _1324460))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324456, tc_HOL_Obool)), _1324460), hAPP(hAPP(c_Set_Oinsert(_1324456), _1324458), _1324462)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324456, tc_HOL_Obool)), _1324460), _1324462))], (30140 ^ _779308) ^ [_1324529, _1324531, _1324533, _1324535] : [-(hBOOL(hAPP(hAPP(c_member(_1324529), _1324531), _1324533))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324529, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1324529), _1324531), _1324535)), _1324533) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324529, tc_HOL_Obool)), _1324535), _1324533))], (30146 ^ _779308) ^ [_1324606, _1324608, _1324610, _1324612] : [hBOOL(hAPP(hAPP(c_member(_1324606), _1324608), _1324610)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324606, tc_HOL_Obool)), _1324610), hAPP(hAPP(c_Set_Oinsert(_1324606), _1324608), _1324612)) = hAPP(hAPP(c_Set_Oinsert(_1324606), _1324608), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324606, tc_HOL_Obool)), _1324610), _1324612)))], (30152 ^ _779308) ^ [_1324777, _1324779, _1324781, _1324783] : [hBOOL(hAPP(hAPP(c_member(_1324777), _1324779), _1324781)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324777, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1324777), _1324779), _1324783)), _1324781) = hAPP(hAPP(c_Set_Oinsert(_1324777), _1324779), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324777, tc_HOL_Obool)), _1324783), _1324781)))], (30158 ^ _779308) ^ [_1324948, _1324950, _1324952, _1324954, _1324956] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1324948, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1324950, _1324948, _1324952), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324950, tc_HOL_Obool)), _1324954), _1324956))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324948, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1324950, _1324948, _1324952), _1324954)), hAPP(c_Set_Oimage(_1324950, _1324948, _1324952), _1324956)))))], (30160 ^ _779308) ^ [_1325032, _1325034, _1325036] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325032, tc_HOL_Obool)), _1325034), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325032, tc_HOL_Obool)), _1325036), _1325034)) = c_Orderings_Obot__class_Obot(tc_fun(_1325032, tc_HOL_Obool)))], (30162 ^ _779308) ^ [_1325086, _1325088, _1325090] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325086, tc_HOL_Obool)), _1325088), _1325090) = c_Orderings_Obot__class_Obot(tc_fun(_1325086, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325086, tc_HOL_Obool)), _1325088), _1325090) = _1325088)], (30168 ^ _779308) ^ [_1325240, _1325242, _1325244, _1325246] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325240, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325240, tc_HOL_Obool)), _1325242), _1325244)), _1325246) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325240, tc_HOL_Obool)), _1325242), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325240, tc_HOL_Obool)), _1325244), _1325246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1325240, tc_HOL_Obool)), _1325246), _1325242)))], (30174 ^ _779308) ^ [_1325425, _1325427, _1325429, _1325431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1325425, tc_HOL_Obool)), _1325431), _1325427)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325425, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325425, tc_HOL_Obool)), _1325427), _1325429)), _1325431) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325425, tc_HOL_Obool)), _1325427), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325425, tc_HOL_Obool)), _1325429), _1325431)))], (30180 ^ _779308) ^ [_1325616, _1325618, _1325620, _1325622] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325616, tc_HOL_Obool)), _1325618), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325616, tc_HOL_Obool)), _1325620), _1325622)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325616, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325616, tc_HOL_Obool)), _1325618), _1325620)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325616, tc_HOL_Obool)), _1325618), _1325622)))], (30182 ^ _779308) ^ [_1325700, _1325702, _1325704, _1325706] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325700, tc_HOL_Obool)), _1325702), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325700, tc_HOL_Obool)), _1325704), _1325706)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325700, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325700, tc_HOL_Obool)), _1325702), _1325704)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325700, tc_HOL_Obool)), _1325702), _1325706)))], (30184 ^ _779308) ^ [_1325784, _1325786, _1325788] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325784, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1325784, tc_HOL_Obool)), _1325786), _1325788)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325784, tc_HOL_Obool)), _1325786), _1325788)) = _1325786)], (30186 ^ _779308) ^ [_1325844, _1325846, _1325848, _1325850] : [class_Orderings_Oorder(_1325844), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325844, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1325844, _1325846), _1325848)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1325844, _1325848), _1325850)) = c_Orderings_Obot__class_Obot(tc_fun(_1325844, tc_HOL_Obool)))], (30192 ^ _779308) ^ [_1325979, _1325981] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1325979), _1325981) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1325979)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1325981))))], (30194 ^ _779308) ^ [_1326025, _1326027] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326025, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326025, tc_HOL_Obool)), _1326027)), _1326027) = c_Orderings_Obot__class_Obot(tc_fun(_1326025, tc_HOL_Obool)))], (30196 ^ _779308) ^ [_1326074, _1326076] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326074, tc_HOL_Obool)), _1326076), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326074, tc_HOL_Obool)), _1326076)) = c_Orderings_Obot__class_Obot(tc_fun(_1326074, tc_HOL_Obool)))], (30198 ^ _779308) ^ [_1326123, _1326125, _1326127, _1326129, _1326131] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326123, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1326125, _1326123, _1326127), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326125, tc_HOL_Obool)), _1326129), _1326131))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326123, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1326125, _1326123, _1326127), _1326129)), hAPP(c_Relation_OImage(_1326125, _1326123, _1326127), _1326131)))))], (30200 ^ _779308) ^ [_1326207, _1326209, _1326211] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326207, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326207, tc_HOL_Obool)), _1326209), _1326211)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326207, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326207, tc_HOL_Obool)), _1326209)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326207, tc_HOL_Obool)), _1326211)))], (30202 ^ _779308) ^ [_1326280, _1326282, _1326284] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326280, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326280, tc_HOL_Obool)), _1326282), _1326284)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326280, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326280, tc_HOL_Obool)), _1326282)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326280, tc_HOL_Obool)), _1326284)))], (30204 ^ _779308) ^ [_1326353, _1326355, _1326357] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326353, tc_HOL_Obool)), _1326355), _1326357) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326353, tc_HOL_Obool)), _1326355), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326353, tc_HOL_Obool)), _1326357)))], (30206 ^ _779308) ^ [_1326410, _1326412, _1326414] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326410, tc_HOL_Obool)), _1326412), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1326410, tc_HOL_Obool)), _1326414)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326410, tc_HOL_Obool)), _1326412), _1326414))], (30208 ^ _779308) ^ [_1326467, _1326469, _1326471, _1326473] : [class_Orderings_Oorder(_1326467), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326467, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1326467, _1326469, _1326471)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1326467, _1326471, _1326473)) = c_Orderings_Obot__class_Obot(tc_fun(_1326467, tc_HOL_Obool)))], (30214 ^ _779308) ^ [_1326594] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1326594) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1326594))], (30216 ^ _779308) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (30218 ^ _779308) ^ [_1326641, _1326643] : [c_Nat__Transfer_Onat__set(_1326641), c_Nat__Transfer_Onat__set(_1326643), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1326641), _1326643) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1326641)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1326643))))], (30228 ^ _779308) ^ [_1326808] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1326808)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1326808), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1326808)))], (30230 ^ _779308) ^ [_1326846] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1326846)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1326846))], (30232 ^ _779308) ^ [_1326878] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1326878))))], (30234 ^ _779308) ^ [_1326906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1326906)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1326906) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Int_Onat, _1326906))))], (30240 ^ _779308) ^ [_1327009, _1327011, _1327013] : [class_Orderings_Oord(_1327009), 30243 ^ _779308 : [(30244 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1327009), _1327011), hAPP(c_SetInterval_Oord__class_OlessThan(_1327009), _1327013))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327009), _1327011), _1327013)))], (30250 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1327009), _1327011), _1327013)), -(hBOOL(hAPP(hAPP(c_member(_1327009), _1327011), hAPP(c_SetInterval_Oord__class_OlessThan(_1327009), _1327013))))]]], (30256 ^ _779308) ^ [_1327277, _1327279, _1327281] : [class_Lattices_Olattice(_1327277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327277), _1327279)), hBOOL(hAPP(hAPP(c_member(_1327277), _1327281), _1327279)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1327277), _1327281), c_Big__Operators_Olattice__class_OSup__fin(_1327277, _1327279)) = _1327281)], (30270 ^ _779308) ^ [_1327506, _1327508, _1327510] : [class_Orderings_Olinorder(_1327506), 30273 ^ _779308 : [(30274 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327506, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1327506), _1327508)), hAPP(c_SetInterval_Oord__class_OlessThan(_1327506), _1327510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327506), _1327508), _1327510)))], (30280 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327506), _1327508), _1327510)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327506, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1327506), _1327508)), hAPP(c_SetInterval_Oord__class_OlessThan(_1327506), _1327510))))]]], (30286 ^ _779308) ^ [_1327798, _1327800, _1327802, _1327804, _1327806, _1327808] : [c_Fun_Oinj__on(_1327798, _1327800, _1327802, _1327804), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327798, tc_HOL_Obool)), _1327806), _1327804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327798, tc_HOL_Obool)), _1327808), _1327804)), -(hAPP(c_Set_Oimage(_1327798, _1327800, _1327802), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327798, tc_HOL_Obool)), _1327806), _1327808)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327800, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1327798, _1327800, _1327802), _1327806)), hAPP(c_Set_Oimage(_1327798, _1327800, _1327802), _1327808)))], (30300 ^ _779308) ^ [_1328151, _1328153, _1328155] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328151, tc_HOL_Obool)), _1328153), _1328155) = c_Orderings_Obot__class_Obot(tc_fun(_1328151, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328151, tc_HOL_Obool)), _1328153), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328151, tc_HOL_Obool)), _1328155))))], (30306 ^ _779308) ^ [_1328294, _1328296, _1328298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1328294, tc_HOL_Obool)), _1328296), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1328294, tc_HOL_Obool)), _1328298))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328294, tc_HOL_Obool)), _1328296), _1328298) = c_Orderings_Obot__class_Obot(tc_fun(_1328294, tc_HOL_Obool)))], (30312 ^ _779308) ^ [_1328443, _1328445, _1328447, _1328449] : [class_Orderings_Oorder(_1328443), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328443, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1328443, _1328445), _1328447)), c_SetInterval_Oord__class_OatLeastAtMost(_1328443, _1328447, _1328449)) = c_Orderings_Obot__class_Obot(tc_fun(_1328443, tc_HOL_Obool)))], (30318 ^ _779308) ^ [_1328574, _1328576, _1328578, _1328580, _1328582] : [class_Orderings_Olinorder(_1328574), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328574, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1328574, _1328576, _1328578)), c_SetInterval_Oord__class_OatLeastAtMost(_1328574, _1328580, _1328582)) = c_SetInterval_Oord__class_OatLeastAtMost(_1328574, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1328574), _1328576), _1328580), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1328574), _1328578), _1328582)))], (30324 ^ _779308) ^ [_1328733, _1328735, _1328737, _1328739, _1328741] : [class_Orderings_Olinorder(_1328733), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328733, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1328733, _1328735), _1328737)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1328733, _1328739), _1328741)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1328733, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1328733), _1328735), _1328739)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1328733), _1328737), _1328741)))], (30330 ^ _779308) ^ [_1328904, _1328906, _1328908] : [class_Orderings_Olinorder(_1328904), 30333 ^ _779308 : [(30334 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1328904, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1328904), _1328906)), hAPP(c_SetInterval_Oord__class_OlessThan(_1328904), _1328908))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328904), _1328906), _1328908)))], (30340 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328904), _1328906), _1328908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1328904, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1328904), _1328906)), hAPP(c_SetInterval_Oord__class_OlessThan(_1328904), _1328908))))]]], (30346 ^ _779308) ^ [_1329196, _1329198, _1329200, _1329202] : [class_Orderings_Oorder(_1329196), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329196, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1329196, _1329198, _1329200)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1329196, _1329200, _1329202)) = c_Orderings_Obot__class_Obot(tc_fun(_1329196, tc_HOL_Obool)))], (30352 ^ _779308) ^ [_1329323, _1329325, _1329327, _1329329] : [class_Orderings_Oorder(_1329323), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329323, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1329323, _1329325, _1329327)), c_SetInterval_Oord__class_OatLeastAtMost(_1329323, _1329327, _1329329)) = c_Orderings_Obot__class_Obot(tc_fun(_1329323, tc_HOL_Obool)))], (30358 ^ _779308) ^ [_1329450, _1329452, _1329454, _1329456] : [class_Orderings_Oorder(_1329450), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329450, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1329450, _1329452, _1329454)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1329450, _1329454, _1329456)) = c_Orderings_Obot__class_Obot(tc_fun(_1329450, tc_HOL_Obool)))], (30364 ^ _779308) ^ [_1329577, _1329579, _1329581, _1329583, _1329585] : [class_Orderings_Olinorder(_1329577), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329577, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1329577, _1329579, _1329581)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1329577, _1329583, _1329585)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1329577, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1329577), _1329579), _1329583), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1329577), _1329581), _1329585)))], (30370 ^ _779308) ^ [_1329736, _1329738, _1329740, _1329742] : [class_Orderings_Oorder(_1329736), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329736, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1329736, _1329738, _1329740)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1329736, _1329740), _1329742)) = c_Orderings_Obot__class_Obot(tc_fun(_1329736, tc_HOL_Obool)))], (30376 ^ _779308) ^ [_1329867, _1329869, _1329871, _1329873, _1329875] : [class_Orderings_Olinorder(_1329867), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329867, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1329867, _1329869, _1329871)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1329867, _1329873, _1329875)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1329867, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1329867), _1329869), _1329873), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1329867), _1329871), _1329875)))], (30382 ^ _779308) ^ [_1330026, _1330028, _1330030, _1330032] : [class_Orderings_Olinorder(_1330026), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330026, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1330026), _1330028)), c_SetInterval_Oord__class_OatLeastAtMost(_1330026, _1330030, _1330032)) = c_SetInterval_Oord__class_OatLeastAtMost(_1330026, _1330030, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1330026), _1330028), _1330032)))], (30388 ^ _779308) ^ [_1330169, _1330171, _1330173, _1330175] : [class_Orderings_Olinorder(_1330169), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330169, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1330169, _1330171, _1330173)), hAPP(c_SetInterval_Oord__class_OatMost(_1330169), _1330175)) = c_SetInterval_Oord__class_OatLeastAtMost(_1330169, _1330171, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1330169), _1330173), _1330175)))], (30394 ^ _779308) ^ [_1330312, _1330314, _1330316] : [class_Orderings_Oorder(_1330312), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330312, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1330312), _1330314)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1330312, _1330314, _1330316)) = c_Orderings_Obot__class_Obot(tc_fun(_1330312, tc_HOL_Obool)))], (30400 ^ _779308) ^ [_1330439, _1330441, _1330443, _1330445] : [class_Orderings_Oorder(_1330439), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330439, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1330439, _1330441, _1330443)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1330439, _1330443, _1330445)) = c_Orderings_Obot__class_Obot(tc_fun(_1330439, tc_HOL_Obool)))], (30406 ^ _779308) ^ [_1330566, _1330568, _1330570] : [class_Orderings_Oorder(_1330566), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330566, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1330566), _1330568)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1330566, _1330568, _1330570)) = c_Orderings_Obot__class_Obot(tc_fun(_1330566, tc_HOL_Obool)))], (30412 ^ _779308) ^ [_1330693, _1330695, _1330697, _1330699, _1330701, _1330703, _1330705, _1330707] : [c_Finite__Set_Ofolding__image__simple(_1330693, _1330695, _1330697, _1330699, _1330701, _1330703), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330695), _1330705)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330695), _1330707)), -(hAPP(hAPP(_1330697, hAPP(_1330703, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330695, tc_HOL_Obool)), _1330705), _1330707))), hAPP(_1330703, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330695, tc_HOL_Obool)), _1330705), _1330707))) = hAPP(hAPP(_1330697, hAPP(_1330703, _1330705)), hAPP(_1330703, _1330707)))], (30426 ^ _779308) ^ [_1331026, _1331028] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1331026), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1331028), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1331026, _1331028))], (30428 ^ _779308) ^ [_1331067, _1331069, _1331071] : [class_Lattices_Osemilattice__inf(_1331067), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331067), _1331069)), hBOOL(hAPP(hAPP(c_member(_1331067), _1331071), _1331069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331067), hAPP(c_Finite__Set_Ofold1(_1331067, c_Lattices_Osemilattice__inf__class_Oinf(_1331067)), _1331069)), _1331071)))], (30442 ^ _779308) ^ [_1331304, _1331306] : [-(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Int_Oint, hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint)), _1331304)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1331306), _1331304))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1331304), _1331306))], (30444 ^ _779308) ^ [_1331354, _1331356, _1331358] : [class_Lattices_Osemilattice__inf(_1331354), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331354), _1331356)), -(_1331356 = c_Orderings_Obot__class_Obot(tc_fun(_1331354, tc_HOL_Obool))), 30455 ^ _779308 : [(30466 ^ _779308) ^ [] : [30468 ^ _779308 : [(30469 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331354), 30467 ^ [_1331354, _1331356, _1331358]), _1331356)))], (30471 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331354), _1331358), 30467 ^ [_1331354, _1331356, _1331358]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331354), _1331358), hAPP(c_Finite__Set_Ofold1(_1331354, c_Lattices_Osemilattice__inf__class_Oinf(_1331354)), _1331356))))], (30456 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331354), _1331358), hAPP(c_Finite__Set_Ofold1(_1331354, c_Lattices_Osemilattice__inf__class_Oinf(_1331354)), _1331356))), 30459 ^ _779308 : [(30460 ^ _779308) ^ [_1331647] : [hBOOL(hAPP(hAPP(c_member(_1331354), _1331647), _1331356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1331354), _1331358), _1331647)))]]]]], (30475 ^ _779308) ^ [_1331932] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331932)) = hAPP(c_Int_Onat, _1331932))], (30477 ^ _779308) ^ [_1331964, _1331966] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1331964), _1331966)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1331966), _1331964)))], (30479 ^ _779308) ^ [_1332007, _1332009, _1332011, _1332013, _1332015] : [class_Groups_Ocomm__monoid__mult(_1332007), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332009), _1332011)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332009), _1332013)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332007), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332009, _1332007), _1332015), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332009, tc_HOL_Obool)), _1332011), _1332013))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332009, _1332007), _1332015), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332009, tc_HOL_Obool)), _1332011), _1332013))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332007), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332009, _1332007), _1332015), _1332011)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332009, _1332007), _1332015), _1332013)))], (30493 ^ _779308) ^ [_1332368, _1332370, _1332372, _1332374, _1332376] : [class_Groups_Ocomm__monoid__mult(_1332368), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332370), _1332372)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332370), _1332374)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332368), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332370, _1332368), _1332376), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332370, tc_HOL_Obool)), _1332372), _1332374))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332370, _1332368), _1332376), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332370, tc_HOL_Obool)), _1332372), _1332374))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332368), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332370, _1332368), _1332376), _1332372)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1332370, _1332368), _1332376), _1332374)))], (30507 ^ _779308) ^ [_1332729, _1332731, _1332733] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332729), _1332731)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332729), _1332733)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1332729), _1332731)), hAPP(c_Finite__Set_Ocard(_1332729), _1332733)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1332729), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332729, tc_HOL_Obool)), _1332731), _1332733))), hAPP(c_Finite__Set_Ocard(_1332729), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332729, tc_HOL_Obool)), _1332731), _1332733))))], (30517 ^ _779308) ^ [_1332986, _1332988, _1332990] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1332986), _1332988)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332986), _1332990)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1332986), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332986, tc_HOL_Obool)), _1332988), _1332990))), hAPP(c_Finite__Set_Ocard(_1332986), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1332986, tc_HOL_Obool)), _1332988), _1332990))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1332986), _1332988)), hAPP(c_Finite__Set_Ocard(_1332986), _1332990)))], (30527 ^ _779308) ^ [_1333243, _1333245, _1333247] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1333243), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333243, tc_HOL_Obool)), _1333245), _1333247))), -(hAPP(c_Finite__Set_Ocard(_1333243), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333243, tc_HOL_Obool)), _1333245), _1333247)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1333243), _1333245)), hAPP(c_Finite__Set_Ocard(_1333243), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333243, tc_HOL_Obool)), _1333245), _1333247))))], (30533 ^ _779308) ^ [_1333438, _1333440] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1333438), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1333440) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1333438, _1333440))], (30535 ^ _779308) ^ [_1333479, _1333481, _1333483, _1333485, _1333487] : [c_Finite__Set_Ofolding__one(_1333479, _1333481, _1333483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333479), _1333485)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333479), _1333487)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333479, tc_HOL_Obool)), _1333485), _1333487) = c_Orderings_Obot__class_Obot(tc_fun(_1333479, tc_HOL_Obool))), -(hAPP(hAPP(_1333481, hAPP(_1333483, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333479, tc_HOL_Obool)), _1333485), _1333487))), hAPP(_1333483, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333479, tc_HOL_Obool)), _1333485), _1333487))) = hAPP(hAPP(_1333481, hAPP(_1333483, _1333485)), hAPP(_1333483, _1333487)))], (30553 ^ _779308) ^ [_1333835, _1333837, _1333839, _1333841, _1333843] : [c_Finite__Set_Ofolding__one(_1333835, _1333837, _1333839), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333835), _1333841)), -(_1333841 = c_Orderings_Obot__class_Obot(tc_fun(_1333835, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333835), _1333843)), -(_1333843 = c_Orderings_Obot__class_Obot(tc_fun(_1333835, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333835, tc_HOL_Obool)), _1333841), _1333843) = c_Orderings_Obot__class_Obot(tc_fun(_1333835, tc_HOL_Obool)), -(hAPP(_1333839, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333835, tc_HOL_Obool)), _1333841), _1333843)) = hAPP(hAPP(_1333837, hAPP(_1333839, _1333841)), hAPP(_1333839, _1333843)))], (30579 ^ _779308) ^ [_1334336, _1334338, _1334340, _1334342, _1334344, _1334346, _1334348, _1334350] : [c_Finite__Set_Ofolding__image__simple(_1334336, _1334338, _1334340, _1334342, _1334344, _1334346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334338), _1334348)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334338), _1334350)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334338, tc_HOL_Obool)), _1334348), _1334350) = c_Orderings_Obot__class_Obot(tc_fun(_1334338, tc_HOL_Obool)), -(hAPP(_1334346, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334338, tc_HOL_Obool)), _1334348), _1334350)) = hAPP(hAPP(_1334340, hAPP(_1334346, _1334348)), hAPP(_1334346, _1334350)))], (30597 ^ _779308) ^ [_1334725, _1334727] : [class_Orderings_Oorder(_1334725), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1334725, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1334725), _1334727), c_Orderings_Obot__class_Obot(tc_fun(_1334725, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1334725), _1334727)) = hAPP(hAPP(c_Set_Oinsert(_1334725), _1334727), c_Orderings_Obot__class_Obot(tc_fun(_1334725, tc_HOL_Obool))))], (30603 ^ _779308) ^ [_1334884, _1334886, _1334888] : [class_Orderings_Olinorder(_1334884), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334884), _1334886), _1334888)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334884, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1334884), _1334886)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1334884, _1334886), _1334888)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1334884), _1334888))], (30613 ^ _779308) ^ [_1335083, _1335085, _1335087, _1335089, _1335091] : [class_Groups_Ocomm__monoid__mult(_1335083), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335085), _1335087)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335085), _1335089)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335085, tc_HOL_Obool)), _1335087), _1335089) = c_Orderings_Obot__class_Obot(tc_fun(_1335085, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335085, _1335083), _1335091), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1335085, tc_HOL_Obool)), _1335087), _1335089)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335083), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335085, _1335083), _1335091), _1335087)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335085, _1335083), _1335091), _1335089)))], (30631 ^ _779308) ^ [_1335478, _1335480, _1335482, _1335484, _1335486] : [class_Groups_Ocomm__monoid__mult(_1335478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335480), _1335482)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335480), _1335484)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335480, tc_HOL_Obool)), _1335482), _1335484) = c_Orderings_Obot__class_Obot(tc_fun(_1335480, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335480, _1335478), _1335486), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1335480, tc_HOL_Obool)), _1335482), _1335484)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1335478), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335480, _1335478), _1335486), _1335482)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335480, _1335478), _1335486), _1335484)))], (30649 ^ _779308) ^ [_1335873, _1335875, _1335877] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1335873), _1335875)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335873), _1335877)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335873, tc_HOL_Obool)), _1335875), _1335877) = c_Orderings_Obot__class_Obot(tc_fun(_1335873, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1335873), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1335873, tc_HOL_Obool)), _1335875), _1335877)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1335873), _1335875)), hAPP(c_Finite__Set_Ocard(_1335873), _1335877)))], (30663 ^ _779308) ^ [_1336196, _1336198, _1336200, _1336202, _1336204] : [c_Fun_Oinj__on(_1336196, _1336198, _1336200, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1336196, tc_HOL_Obool)), _1336202), _1336204)), 30666 ^ _779308 : [(30667 ^ _779308) ^ [] : [-(c_Fun_Oinj__on(_1336196, _1336198, _1336200, _1336202))], (30669 ^ _779308) ^ [] : [-(c_Fun_Oinj__on(_1336196, _1336198, _1336200, _1336204))], (30671 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336198, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1336196, _1336198, _1336200), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336196, tc_HOL_Obool)), _1336202), _1336204))), hAPP(c_Set_Oimage(_1336196, _1336198, _1336200), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336196, tc_HOL_Obool)), _1336204), _1336202))) = c_Orderings_Obot__class_Obot(tc_fun(_1336198, tc_HOL_Obool)))]]], (30673 ^ _779308) ^ [_1336463, _1336465, _1336467, _1336469, _1336471] : [-(c_Fun_Oinj__on(_1336463, _1336465, _1336467, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1336463, tc_HOL_Obool)), _1336469), _1336471))), c_Fun_Oinj__on(_1336463, _1336465, _1336467, _1336469), c_Fun_Oinj__on(_1336463, _1336465, _1336467, _1336471), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336465, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1336463, _1336465, _1336467), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336463, tc_HOL_Obool)), _1336469), _1336471))), hAPP(c_Set_Oimage(_1336463, _1336465, _1336467), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336463, tc_HOL_Obool)), _1336471), _1336469))) = c_Orderings_Obot__class_Obot(tc_fun(_1336465, tc_HOL_Obool))], (30687 ^ _779308) ^ [_1336802, _1336804, _1336806, _1336808, _1336810] : [class_Groups_Ocomm__monoid__mult(_1336802), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336804), _1336806)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336804), _1336808)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336802), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1336802, _1336804, c_Groups_Otimes__class_Otimes(_1336802)), _1336810), c_Groups_Oone__class_Oone(_1336802)), _1336806)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1336802, _1336804, c_Groups_Otimes__class_Otimes(_1336802)), _1336810), c_Groups_Oone__class_Oone(_1336802)), _1336808)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336802), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1336802, _1336804, c_Groups_Otimes__class_Otimes(_1336802)), _1336810), c_Groups_Oone__class_Oone(_1336802)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1336804, tc_HOL_Obool)), _1336806), _1336808))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1336802, _1336804, c_Groups_Otimes__class_Otimes(_1336802)), _1336810), c_Groups_Oone__class_Oone(_1336802)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336804, tc_HOL_Obool)), _1336806), _1336808))))], (30701 ^ _779308) ^ [_1337227, _1337229, _1337231] : [class_Groups_Oab__semigroup__mult(_1337227), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337227), _1337229)), -(_1337229 = c_Orderings_Obot__class_Obot(tc_fun(_1337227, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337227), _1337231)), -(_1337231 = c_Orderings_Obot__class_Obot(tc_fun(_1337227, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337227, tc_HOL_Obool)), _1337229), _1337231) = c_Orderings_Obot__class_Obot(tc_fun(_1337227, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1337227, c_Groups_Otimes__class_Otimes(_1337227)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337227, tc_HOL_Obool)), _1337229), _1337231)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337227), hAPP(c_Finite__Set_Ofold1(_1337227, c_Groups_Otimes__class_Otimes(_1337227)), _1337229)), hAPP(c_Finite__Set_Ofold1(_1337227, c_Groups_Otimes__class_Otimes(_1337227)), _1337231)))], (30727 ^ _779308) ^ [_1337734, _1337736, _1337738] : [class_Lattices_Olattice(_1337734), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337734), _1337736)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337734), _1337738)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337734, tc_HOL_Obool)), _1337736), _1337738) = c_Orderings_Obot__class_Obot(tc_fun(_1337734, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1337734), c_Big__Operators_Olattice__class_OSup__fin(_1337734, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1337734, tc_HOL_Obool)), _1337736), _1337738))), c_Big__Operators_Olattice__class_OSup__fin(_1337734, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1337734, tc_HOL_Obool)), _1337736), _1337738))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1337734), c_Big__Operators_Olattice__class_OSup__fin(_1337734, _1337736)), c_Big__Operators_Olattice__class_OSup__fin(_1337734, _1337738)))], (30745 ^ _779308) ^ [_1338082, _1338084, _1338086] : [class_Lattices_Olattice(_1338082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338082), _1338084)), -(_1338084 = c_Orderings_Obot__class_Obot(tc_fun(_1338082, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338082), _1338086)), -(_1338086 = c_Orderings_Obot__class_Obot(tc_fun(_1338082, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338082, tc_HOL_Obool)), _1338084), _1338086) = c_Orderings_Obot__class_Obot(tc_fun(_1338082, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1338082, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338082, tc_HOL_Obool)), _1338084), _1338086)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1338082), c_Big__Operators_Olattice__class_OSup__fin(_1338082, _1338084)), c_Big__Operators_Olattice__class_OSup__fin(_1338082, _1338086)))], (30771 ^ _779308) ^ [_1338559, _1338561, _1338563] : [class_Orderings_Olinorder(_1338559), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338559), _1338561)), -(_1338561 = c_Orderings_Obot__class_Obot(tc_fun(_1338559, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338559), _1338563)), -(_1338563 = c_Orderings_Obot__class_Obot(tc_fun(_1338559, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338559, tc_HOL_Obool)), _1338561), _1338563) = c_Orderings_Obot__class_Obot(tc_fun(_1338559, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1338559, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338559, tc_HOL_Obool)), _1338561), _1338563)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1338559), c_Big__Operators_Olinorder__class_OMin(_1338559, _1338561)), c_Big__Operators_Olinorder__class_OMin(_1338559, _1338563)))], (30797 ^ _779308) ^ [_1339036, _1339038, _1339040] : [class_Orderings_Olinorder(_1339036), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339036), _1339038)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339036), _1339040)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339036, tc_HOL_Obool)), _1339038), _1339040) = c_Orderings_Obot__class_Obot(tc_fun(_1339036, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1339036), c_Big__Operators_Olinorder__class_OMin(_1339036, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339036, tc_HOL_Obool)), _1339038), _1339040))), c_Big__Operators_Olinorder__class_OMin(_1339036, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339036, tc_HOL_Obool)), _1339038), _1339040))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1339036), c_Big__Operators_Olinorder__class_OMin(_1339036, _1339038)), c_Big__Operators_Olinorder__class_OMin(_1339036, _1339040)))], (30815 ^ _779308) ^ [_1339384, _1339386, _1339388] : [class_Orderings_Olinorder(_1339384), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339384), _1339386)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339384), _1339388)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339384, tc_HOL_Obool)), _1339386), _1339388) = c_Orderings_Obot__class_Obot(tc_fun(_1339384, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339384), c_Big__Operators_Olinorder__class_OMax(_1339384, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339384, tc_HOL_Obool)), _1339386), _1339388))), c_Big__Operators_Olinorder__class_OMax(_1339384, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339384, tc_HOL_Obool)), _1339386), _1339388))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339384), c_Big__Operators_Olinorder__class_OMax(_1339384, _1339386)), c_Big__Operators_Olinorder__class_OMax(_1339384, _1339388)))], (30833 ^ _779308) ^ [_1339732, _1339734, _1339736] : [class_Orderings_Olinorder(_1339732), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339732), _1339734)), -(_1339734 = c_Orderings_Obot__class_Obot(tc_fun(_1339732, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339732), _1339736)), -(_1339736 = c_Orderings_Obot__class_Obot(tc_fun(_1339732, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339732, tc_HOL_Obool)), _1339734), _1339736) = c_Orderings_Obot__class_Obot(tc_fun(_1339732, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1339732, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339732, tc_HOL_Obool)), _1339734), _1339736)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1339732), c_Big__Operators_Olinorder__class_OMax(_1339732, _1339734)), c_Big__Operators_Olinorder__class_OMax(_1339732, _1339736)))], (30859 ^ _779308) ^ [_1340209, _1340211, _1340213] : [class_Orderings_Olinorder(_1340209), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340209), _1340211)), -(_1340211 = c_Orderings_Obot__class_Obot(tc_fun(_1340209, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340209), _1340213)), -(_1340213 = c_Orderings_Obot__class_Obot(tc_fun(_1340209, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340209, tc_HOL_Obool)), _1340211), _1340213) = c_Orderings_Obot__class_Obot(tc_fun(_1340209, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1340209, c_Orderings_Oord__class_Omin(_1340209), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340209, tc_HOL_Obool)), _1340211), _1340213)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1340209), c_Big__Operators_Olattice_OInf__fin(_1340209, c_Orderings_Oord__class_Omin(_1340209), _1340211)), c_Big__Operators_Olattice_OInf__fin(_1340209, c_Orderings_Oord__class_Omin(_1340209), _1340213)))], (30885 ^ _779308) ^ [_1340704, _1340706, _1340708] : [class_Orderings_Olinorder(_1340704), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340704), _1340706)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340704), _1340708)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340704, tc_HOL_Obool)), _1340706), _1340708) = c_Orderings_Obot__class_Obot(tc_fun(_1340704, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1340704), c_Big__Operators_Olattice_OInf__fin(_1340704, c_Orderings_Oord__class_Omin(_1340704), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340704, tc_HOL_Obool)), _1340706), _1340708))), c_Big__Operators_Olattice_OInf__fin(_1340704, c_Orderings_Oord__class_Omin(_1340704), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340704, tc_HOL_Obool)), _1340706), _1340708))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1340704), c_Big__Operators_Olattice_OInf__fin(_1340704, c_Orderings_Oord__class_Omin(_1340704), _1340706)), c_Big__Operators_Olattice_OInf__fin(_1340704, c_Orderings_Oord__class_Omin(_1340704), _1340708)))], (30903 ^ _779308) ^ [_1341076, _1341078, _1341080] : [class_Orderings_Olinorder(_1341076), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341076), _1341078)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341076), _1341080)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341076, tc_HOL_Obool)), _1341078), _1341080) = c_Orderings_Obot__class_Obot(tc_fun(_1341076, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341076), c_Big__Operators_Olattice_OSup__fin(_1341076, c_Orderings_Oord__class_Omax(_1341076), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341076, tc_HOL_Obool)), _1341078), _1341080))), c_Big__Operators_Olattice_OSup__fin(_1341076, c_Orderings_Oord__class_Omax(_1341076), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341076, tc_HOL_Obool)), _1341078), _1341080))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341076), c_Big__Operators_Olattice_OSup__fin(_1341076, c_Orderings_Oord__class_Omax(_1341076), _1341078)), c_Big__Operators_Olattice_OSup__fin(_1341076, c_Orderings_Oord__class_Omax(_1341076), _1341080)))], (30921 ^ _779308) ^ [_1341448, _1341450, _1341452] : [class_Orderings_Olinorder(_1341448), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341448), _1341450)), -(_1341450 = c_Orderings_Obot__class_Obot(tc_fun(_1341448, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341448), _1341452)), -(_1341452 = c_Orderings_Obot__class_Obot(tc_fun(_1341448, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341448, tc_HOL_Obool)), _1341450), _1341452) = c_Orderings_Obot__class_Obot(tc_fun(_1341448, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1341448, c_Orderings_Oord__class_Omax(_1341448), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341448, tc_HOL_Obool)), _1341450), _1341452)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1341448), c_Big__Operators_Olattice_OSup__fin(_1341448, c_Orderings_Oord__class_Omax(_1341448), _1341450)), c_Big__Operators_Olattice_OSup__fin(_1341448, c_Orderings_Oord__class_Omax(_1341448), _1341452)))], (30947 ^ _779308) ^ [_1341943] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1341943)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1341943))))], (30949 ^ _779308) ^ [_1341981, _1341983, _1341985] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Int_Oint, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1341981)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Int_Oint)), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), _1341983))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1341985))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1341985)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1341981), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1341981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1341985), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1341983)))))], (30951 ^ _779308) ^ [_1342068, _1342070, _1342072] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1342068), _1342070)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342068), _1342072)), 30961 ^ _779308 : [(30962 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1342068), 30960 ^ [_1342068, _1342070, _1342072]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342068, tc_HOL_Obool)), _1342070), _1342072))))], (30964 ^ _779308) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1342068), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342068, tc_HOL_Obool)), _1342070), _1342072)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1342068), _1342070)), hAPP(c_Finite__Set_Ocard(_1342068), _1342072)))], (30968 ^ _779308) ^ [_1342412, _1342414, _1342416, _1342418, _1342420] : [class_Fields_Ofield(_1342412), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342414), _1342416)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342414), _1342418)), 30982 ^ _779308 : [(30983 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1342414), 30981 ^ [_1342412, _1342414, _1342416, _1342418, _1342420]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342414, tc_HOL_Obool)), _1342416), _1342418))))], (30985 ^ _779308) ^ [] : [-(hAPP(_1342420, 30981 ^ [_1342412, _1342414, _1342416, _1342418, _1342420]) = c_Groups_Ozero__class_Ozero(_1342412))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342414, _1342412), _1342420), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342414, tc_HOL_Obool)), _1342416), _1342418)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1342412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342412), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342414, _1342412), _1342420), _1342416)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342414, _1342412), _1342420), _1342418))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342414, _1342412), _1342420), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342414, tc_HOL_Obool)), _1342416), _1342418))))], (30989 ^ _779308) ^ [_1342908, _1342910, _1342912, _1342914, _1342916] : [class_Groups_Ocomm__monoid__mult(_1342908), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342910), _1342912)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342910), _1342914)), 31003 ^ _779308 : [(31004 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1342910), 31002 ^ [_1342908, _1342910, _1342912, _1342914, _1342916]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342910, tc_HOL_Obool)), _1342912), _1342914))))], (31006 ^ _779308) ^ [] : [hAPP(_1342916, 31002 ^ [_1342908, _1342910, _1342912, _1342914, _1342916]) = c_Groups_Oone__class_Oone(_1342908)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1342908, _1342910, c_Groups_Otimes__class_Otimes(_1342908)), _1342916), c_Groups_Oone__class_Oone(_1342908)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1342910, tc_HOL_Obool)), _1342912), _1342914)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342908), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1342908, _1342910, c_Groups_Otimes__class_Otimes(_1342908)), _1342916), c_Groups_Oone__class_Oone(_1342908)), _1342912)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1342908, _1342910, c_Groups_Otimes__class_Otimes(_1342908)), _1342916), c_Groups_Oone__class_Oone(_1342908)), _1342914)))], (31010 ^ _779308) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (31012 ^ _779308) ^ [_1343469, _1343471, _1343473, _1343475] : [class_Groups_Oab__group__add(_1343469), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343471, _1343469), hAPP(hAPP(c_COMBB(_1343469, _1343469, _1343471), c_Groups_Ouminus__class_Ouminus(_1343469)), _1343473)), _1343475) = hAPP(c_Groups_Ouminus__class_Ouminus(_1343469), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343471, _1343469), _1343473), _1343475)))], (31018 ^ _779308) ^ [_1343618, _1343620, _1343622] : [class_Groups_Ocomm__monoid__add(_1343618), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343620, _1343618), hAPP(c_COMBK(_1343618, _1343620), c_Groups_Ozero__class_Ozero(_1343618))), _1343622) = c_Groups_Ozero__class_Ozero(_1343618))], (31024 ^ _779308) ^ [_1343733, _1343735, _1343737, _1343739, _1343741] : [class_Groups_Ocomm__monoid__add(_1343733), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343735, _1343733), hAPP(hAPP(c_COMBS(_1343735, _1343733, _1343733), hAPP(hAPP(c_COMBB(_1343733, tc_fun(_1343733, _1343733), _1343735), c_Groups_Oplus__class_Oplus(_1343733)), _1343737)), _1343739)), _1343741) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1343733), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343735, _1343733), _1343737), _1343741)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343735, _1343733), _1343739), _1343741)))], (31030 ^ _779308) ^ [_1343934, _1343936, _1343938, _1343940, _1343942, _1343944, _1343946] : [class_Rings_Osemiring__0(_1343934), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343934), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343936, _1343934), _1343938), _1343940)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343942, _1343934), _1343944), _1343946)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343936, _1343934), hAPP(hAPP(c_COMBC(_1343936, tc_fun(_1343942, tc_HOL_Obool), _1343934), hAPP(hAPP(c_COMBB(tc_fun(_1343942, _1343934), tc_fun(tc_fun(_1343942, tc_HOL_Obool), _1343934), _1343936), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343942, _1343934)), hAPP(hAPP(c_COMBC(_1343936, tc_fun(_1343942, _1343934), tc_fun(_1343942, _1343934)), hAPP(hAPP(c_COMBB(tc_fun(_1343934, _1343934), tc_fun(tc_fun(_1343942, _1343934), tc_fun(_1343942, _1343934)), _1343936), c_COMBB(_1343934, _1343934, _1343942)), hAPP(hAPP(c_COMBB(_1343934, tc_fun(_1343934, _1343934), _1343936), c_Groups_Otimes__class_Otimes(_1343934)), _1343938))), _1343944))), _1343946)), _1343940))], (31036 ^ _779308) ^ [_1344273, _1344275, _1344277, _1344279, _1344281] : [class_Rings_Osemiring__0(_1344273), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1344273), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344275, _1344273), _1344277), _1344279)), _1344281) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344275, _1344273), hAPP(hAPP(c_COMBC(_1344275, _1344273, _1344273), hAPP(hAPP(c_COMBB(_1344273, tc_fun(_1344273, _1344273), _1344275), c_Groups_Otimes__class_Otimes(_1344273)), _1344277)), _1344281)), _1344279))], (31042 ^ _779308) ^ [_1344456, _1344458, _1344460, _1344462, _1344464] : [class_Rings_Osemiring__0(_1344456), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1344456), _1344458), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344460, _1344456), _1344462), _1344464)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344460, _1344456), hAPP(hAPP(c_COMBB(_1344456, _1344456, _1344460), hAPP(c_Groups_Otimes__class_Otimes(_1344456), _1344458)), _1344462)), _1344464))], (31048 ^ _779308) ^ [_1344619, _1344621, _1344623, _1344625, _1344627, _1344629] : [class_Groups_Ocomm__monoid__add(_1344619), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344621, _1344619), hAPP(hAPP(c_COMBC(_1344621, tc_fun(_1344623, tc_HOL_Obool), _1344619), hAPP(hAPP(c_COMBB(tc_fun(_1344623, _1344619), tc_fun(tc_fun(_1344623, tc_HOL_Obool), _1344619), _1344621), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344623, _1344619)), _1344625)), _1344627)), _1344629) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344623, _1344619), hAPP(hAPP(c_COMBC(_1344623, tc_fun(_1344621, tc_HOL_Obool), _1344619), hAPP(hAPP(c_COMBB(tc_fun(_1344621, _1344619), tc_fun(tc_fun(_1344621, tc_HOL_Obool), _1344619), _1344623), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344621, _1344619)), hAPP(c_COMBC(_1344621, _1344623, _1344619), _1344625))), _1344629)), _1344627))], (31054 ^ _779308) ^ [_1344892, _1344894, _1344896, _1344898] : [class_Rings_Osemiring__1(_1344892), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1344892), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344894, tc_Nat_Onat), _1344896), _1344898)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1344894, _1344892), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1344892, _1344894), c_Nat_Osemiring__1__class_Oof__nat(_1344892)), _1344896)), _1344898))], (31060 ^ _779308) ^ [_1345041, _1345043, _1345045, _1345047] : [class_Rings_Oring__1(_1345041), -(hAPP(c_Int_Oring__1__class_Oof__int(_1345041), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345043, tc_Int_Oint), _1345045), _1345047)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345043, _1345041), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1345041, _1345043), c_Int_Oring__1__class_Oof__int(_1345041)), _1345045)), _1345047))], (31066 ^ _779308) ^ [_1345190, _1345192, _1345194, _1345196, _1345198] : [class_Groups_Oab__group__add(_1345190), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345192, _1345190), hAPP(hAPP(c_COMBS(_1345192, _1345190, _1345190), hAPP(hAPP(c_COMBB(_1345190, tc_fun(_1345190, _1345190), _1345192), c_Groups_Ominus__class_Ominus(_1345190)), _1345194)), _1345196)), _1345198) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1345190), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345192, _1345190), _1345194), _1345198)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345192, _1345190), _1345196), _1345198)))], (31072 ^ _779308) ^ [_1345391, _1345393, _1345395, _1345397, _1345399] : [class_Fields_Ofield(_1345391), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1345391), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345393, _1345391), _1345395), _1345397)), _1345399) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345393, _1345391), hAPP(hAPP(c_COMBC(_1345393, _1345391, _1345391), hAPP(hAPP(c_COMBB(_1345391, tc_fun(_1345391, _1345391), _1345393), c_Rings_Oinverse__class_Odivide(_1345391)), _1345395)), _1345399)), _1345397))], (31078 ^ _779308) ^ [_1345574, _1345576, _1345578] : [class_Groups_Ocomm__monoid__add(_1345574), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345576, _1345574), _1345578), c_Orderings_Obot__class_Obot(tc_fun(_1345576, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1345574))], (31084 ^ _779308) ^ [_1345683, _1345685, _1345687] : [class_Groups_Ocomm__monoid__add(_1345683), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345685, _1345683), _1345687), c_Orderings_Obot__class_Obot(tc_fun(_1345685, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1345683))], (31090 ^ _779308) ^ [_1345792, _1345794, _1345796, _1345798] : [class_Groups_Ocomm__monoid__add(_1345792), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1345794), _1345796))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345794, _1345792), _1345798), _1345796) = c_Groups_Ozero__class_Ozero(_1345792))], (31100 ^ _779308) ^ [_1345916, _1345918, _1345920, _1345922] : [class_Groups_Ocomm__monoid__add(_1345916), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1345918), _1345920))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1345918, _1345916), _1345922), _1345920) = c_Groups_Ozero__class_Ozero(_1345916))], (31110 ^ _779308) ^ [_1346067, _1346069, _1346071, _1346073, _1346075, _1346077] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346067, tc_fun(_1346069, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1346067, tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_fun(_1346069, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346069, tc_fun(tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_fun(_1346069, tc_HOL_Obool)), _1346067), c_COMBC(_1346069, tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346069, tc_prod(_1346067, _1346069)), tc_fun(_1346069, tc_fun(tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_HOL_Obool)), _1346067), hAPP(c_COMBB(tc_prod(_1346067, _1346069), tc_fun(tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_HOL_Obool), _1346069), c_member(tc_prod(_1346067, _1346069)))), c_Product__Type_OPair(_1346067, _1346069)))), _1346071)), hAPP(hAPP(c_COMBC(_1346067, tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_fun(_1346069, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346069, tc_fun(tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_fun(_1346069, tc_HOL_Obool)), _1346067), c_COMBC(_1346069, tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346069, tc_prod(_1346067, _1346069)), tc_fun(_1346069, tc_fun(tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_HOL_Obool)), _1346067), hAPP(c_COMBB(tc_prod(_1346067, _1346069), tc_fun(tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool), tc_HOL_Obool), _1346069), c_member(tc_prod(_1346067, _1346069)))), c_Product__Type_OPair(_1346067, _1346069)))), _1346073)), _1346075), _1346077)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1346067, _1346069)), hAPP(hAPP(c_Product__Type_OPair(_1346067, _1346069), _1346075), _1346077)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1346067, _1346069), tc_HOL_Obool)), _1346071), _1346073))))], (31116 ^ _779308) ^ [_1346724, _1346726, _1346728, _1346730, _1346732, _1346734] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1346724, _1346726)), hAPP(hAPP(c_Product__Type_OPair(_1346724, _1346726), _1346732), _1346734)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool)), _1346728), _1346730))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346724, tc_fun(_1346726, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1346724, tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_fun(_1346726, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346726, tc_fun(tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_fun(_1346726, tc_HOL_Obool)), _1346724), c_COMBC(_1346726, tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346726, tc_prod(_1346724, _1346726)), tc_fun(_1346726, tc_fun(tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_HOL_Obool)), _1346724), hAPP(c_COMBB(tc_prod(_1346724, _1346726), tc_fun(tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_HOL_Obool), _1346726), c_member(tc_prod(_1346724, _1346726)))), c_Product__Type_OPair(_1346724, _1346726)))), _1346728)), hAPP(hAPP(c_COMBC(_1346724, tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_fun(_1346726, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346726, tc_fun(tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_fun(_1346726, tc_HOL_Obool)), _1346724), c_COMBC(_1346726, tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1346726, tc_prod(_1346724, _1346726)), tc_fun(_1346726, tc_fun(tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_HOL_Obool)), _1346724), hAPP(c_COMBB(tc_prod(_1346724, _1346726), tc_fun(tc_fun(tc_prod(_1346724, _1346726), tc_HOL_Obool), tc_HOL_Obool), _1346726), c_member(tc_prod(_1346724, _1346726)))), c_Product__Type_OPair(_1346724, _1346726)))), _1346730)), _1346732), _1346734)))], (31122 ^ _779308) ^ [_1347387, _1347389, _1347391, _1347393, _1347395] : [class_Groups_Ocomm__monoid__add(_1347387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347389), _1347391)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1347389, _1347387), hAPP(hAPP(c_COMBS(_1347389, _1347387, _1347387), hAPP(hAPP(c_COMBB(_1347387, tc_fun(_1347387, _1347387), _1347389), c_Groups_Oplus__class_Oplus(_1347387)), _1347393)), _1347395)), _1347391) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347387), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1347389, _1347387), _1347393), _1347391)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1347389, _1347387), _1347395), _1347391)))], (31132 ^ _779308) ^ [_1347654, _1347656, _1347658] : [class_Groups_Ocomm__monoid__add(_1347654), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347654), _1347656), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1347658))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347654), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347654), _1347656), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1347658))), hAPP(_1347656, _1347658)))], (31138 ^ _779308) ^ [_1347807, _1347809, _1347811, _1347813] : [class_Groups_Ocomm__monoid__add(_1347807), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347807), _1347809), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1347811)), hAPP(c_Nat_OSuc, _1347813))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347807), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1347807, tc_Nat_Onat), _1347809), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1347811), _1347813)))], (31144 ^ _779308) ^ [_1347978, _1347980, _1347982, _1347984, _1347986] : [class_Groups_Ocomm__monoid__add(_1347978), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347978), _1347980), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1347982), _1347984)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1347986), _1347984))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1347978), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1347978, tc_Nat_Onat), _1347980), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1347984))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1347982), _1347986)))], (31150 ^ _779308) ^ [_1348169, _1348171, _1348173, _1348175] : [class_Groups_Ocomm__monoid__add(_1348169), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348169), _1348171), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1348173), hAPP(c_Nat_OSuc, _1348175))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348169), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1348169, tc_Nat_Onat), _1348171), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1348173, _1348175)))], (31156 ^ _779308) ^ [_1348332, _1348334, _1348336, _1348338, _1348340] : [class_Groups_Ocomm__monoid__add(_1348332), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348332), _1348334), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1348336), _1348338), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1348340), _1348338))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348332), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1348332, tc_Nat_Onat), _1348334), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1348338))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1348336, _1348340)))], (31162 ^ _779308) ^ [_1348515, _1348517, _1348519, _1348521, _1348523] : [class_Groups_Ocomm__monoid__add(_1348515), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1348517), _1348519)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1348519), _1348521)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348515), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348515), _1348523), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348517), _1348519))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348515), _1348523), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348519), _1348521))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348515), _1348523), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348517), _1348521)))], (31176 ^ _779308) ^ [_1348838, _1348840, _1348842, _1348844, _1348846] : [class_Groups_Oab__group__add(_1348838), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1348840), _1348842)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1348842), _1348844)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1348838), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348838), _1348846), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348840), _1348844))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348838), _1348846), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348840), _1348842))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348838), _1348846), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1348842), _1348844)))], (31190 ^ _779308) ^ [_1349161, _1349163, _1349165, _1349167, _1349169] : [class_Groups_Ocomm__monoid__add(_1349161), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349163), _1349165)), 31197 ^ _779308 : [(31198 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1349163), _1349167), _1349165)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349163, _1349161), hAPP(hAPP(c_COMBC(_1349163, _1349161, _1349161), hAPP(hAPP(c_COMBS(_1349163, _1349161, tc_fun(_1349161, _1349161)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1349161, tc_fun(_1349161, _1349161)), _1349163), c_If(_1349161)), hAPP(hAPP(c_COMBC(_1349163, _1349163, tc_HOL_Obool), c_fequal), _1349167))), _1349169)), c_Groups_Ozero__class_Ozero(_1349161))), _1349165) = hAPP(_1349169, _1349167))], (31204 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1349163), _1349167), _1349165))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349163, _1349161), hAPP(hAPP(c_COMBC(_1349163, _1349161, _1349161), hAPP(hAPP(c_COMBS(_1349163, _1349161, tc_fun(_1349161, _1349161)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1349161, tc_fun(_1349161, _1349161)), _1349163), c_If(_1349161)), hAPP(hAPP(c_COMBC(_1349163, _1349163, tc_HOL_Obool), c_fequal), _1349167))), _1349169)), c_Groups_Ozero__class_Ozero(_1349161))), _1349165) = c_Groups_Ozero__class_Ozero(_1349161))]]], (31210 ^ _779308) ^ [_1349699, _1349701, _1349703, _1349705, _1349707] : [class_Groups_Ocomm__monoid__add(_1349699), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349701), _1349703)), 31217 ^ _779308 : [(31218 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1349701), _1349705), _1349703)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349701, _1349699), hAPP(hAPP(c_COMBC(_1349701, _1349699, _1349699), hAPP(hAPP(c_COMBS(_1349701, _1349699, tc_fun(_1349699, _1349699)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1349699, tc_fun(_1349699, _1349699)), _1349701), c_If(_1349699)), hAPP(c_fequal, _1349705))), _1349707)), c_Groups_Ozero__class_Ozero(_1349699))), _1349703) = hAPP(_1349707, _1349705))], (31224 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1349701), _1349705), _1349703))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349701, _1349699), hAPP(hAPP(c_COMBC(_1349701, _1349699, _1349699), hAPP(hAPP(c_COMBS(_1349701, _1349699, tc_fun(_1349699, _1349699)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1349699, tc_fun(_1349699, _1349699)), _1349701), c_If(_1349699)), hAPP(c_fequal, _1349705))), _1349707)), c_Groups_Ozero__class_Ozero(_1349699))), _1349703) = c_Groups_Ozero__class_Ozero(_1349699))]]], (31230 ^ _779308) ^ [_1350209, _1350211, _1350213, _1350215] : [class_Rings_Osemiring__1(_1350209), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350211, _1350209), hAPP(c_COMBK(_1350209, _1350211), _1350213)), _1350215) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350209), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1350209), hAPP(c_Finite__Set_Ocard(_1350211), _1350215))), _1350213))], (31236 ^ _779308) ^ [_1350354, _1350356, _1350358] : [class_Groups_Ocomm__monoid__add(_1350354), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1350354), _1350356), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1350358))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1350354), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1350354), _1350356), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1350358))), hAPP(_1350356, hAPP(c_Nat_OSuc, _1350358))))], (31242 ^ _779308) ^ [_1350513, _1350515, _1350517, _1350519, _1350521] : [class_Groups_Ocomm__monoid__add(_1350513), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350515), _1350517)), -(hBOOL(hAPP(hAPP(c_member(_1350515), _1350519), _1350517))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350515, _1350513), _1350521), hAPP(hAPP(c_Set_Oinsert(_1350515), _1350519), _1350517)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1350513), hAPP(_1350521, _1350519)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350515, _1350513), _1350521), _1350517)))], (31256 ^ _779308) ^ [_1350763, _1350765, _1350767, _1350769, _1350771] : [class_Groups_Ocomm__monoid__add(_1350763), hBOOL(hAPP(c_Finite__Set_Ofinite(_1350765), _1350767)), -(hBOOL(hAPP(hAPP(c_member(_1350765), _1350769), _1350767))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350765, _1350763), _1350771), hAPP(hAPP(c_Set_Oinsert(_1350765), _1350769), _1350767)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1350763), hAPP(_1350771, _1350769)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350765, _1350763), _1350771), _1350767)))], (31270 ^ _779308) ^ [_1351013, _1351015, _1351017, _1351019, _1351021] : [class_Groups_Ocomm__monoid__add(_1351013), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351015), _1351017)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351015), _1351019)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351013), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351015, _1351013), _1351021), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1351015, tc_HOL_Obool)), _1351017), _1351019))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351015, _1351013), _1351021), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1351015, tc_HOL_Obool)), _1351017), _1351019))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351013), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351015, _1351013), _1351021), _1351017)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351015, _1351013), _1351021), _1351019)))], (31284 ^ _779308) ^ [_1351374, _1351376, _1351378, _1351380, _1351382] : [class_Groups_Oab__group__add(_1351374), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351376), _1351378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1351376, tc_HOL_Obool)), _1351380), _1351378)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351376, _1351374), _1351382), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351376, tc_HOL_Obool)), _1351378), _1351380)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351374), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351376, _1351374), _1351382), _1351378)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351376, _1351374), _1351382), _1351380)))], (31298 ^ _779308) ^ [_1351691, _1351693, _1351695, _1351697] : [class_Groups_Ocomm__monoid__add(_1351691), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351693), _1351695)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351693, _1351691), _1351697), _1351695) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1351691, _1351693, c_Groups_Oplus__class_Oplus(_1351691)), _1351697), c_Groups_Ozero__class_Ozero(_1351691)), _1351695))], (31308 ^ _779308) ^ [_1351886, _1351888, _1351890, _1351892] : [class_Groups_Ocomm__monoid__add(_1351886), 31311 ^ _779308 : [(31312 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1351888), _1351890)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351888, _1351886), _1351892), _1351890) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1351886, _1351888, c_Groups_Oplus__class_Oplus(_1351886)), _1351892), c_Groups_Ozero__class_Ozero(_1351886)), _1351890))], (31318 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1351888), _1351890))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351888, _1351886), _1351892), _1351890) = c_Groups_Ozero__class_Ozero(_1351886))]]], (31324 ^ _779308) ^ [_1352158, _1352160, _1352162] : [class_Groups_Ocomm__monoid__add(_1352158), hAPP(_1352160, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1352158), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352158), _1352160), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1352162)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352158), _1352160), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1352162)))], (31334 ^ _779308) ^ [_1352347, _1352349, _1352351, _1352353] : [class_Groups_Ocomm__monoid__add(_1352347), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1352349), _1352351)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352347), _1352353), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1352349), _1352351)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352347), hAPP(_1352353, _1352349)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352347), _1352353), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1352349)), _1352351))))], (31344 ^ _779308) ^ [_1352580, _1352582, _1352584, _1352586] : [class_Groups_Ocomm__monoid__add(_1352580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1352582), _1352584)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352580), _1352586), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1352582, _1352584)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1352580), hAPP(_1352586, _1352582)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1352580), _1352586), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1352582), _1352584))))], (31354 ^ _779308) ^ [_1352805, _1352807, _1352809, _1352811, _1352813] : [class_Groups_Ocomm__monoid__add(_1352805), hBOOL(hAPP(c_Finite__Set_Ofinite(_1352807), _1352809)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352807, _1352805), _1352811), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1352807, tc_HOL_Obool)), _1352809), _1352813)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352807, _1352805), hAPP(hAPP(c_COMBC(_1352807, _1352805, _1352805), hAPP(hAPP(c_COMBS(_1352807, _1352805, tc_fun(_1352805, _1352805)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1352805, tc_fun(_1352805, _1352805)), _1352807), c_If(_1352805)), hAPP(hAPP(c_COMBC(_1352807, tc_fun(_1352807, tc_HOL_Obool), tc_HOL_Obool), c_member(_1352807)), _1352813))), _1352811)), c_Groups_Ozero__class_Ozero(_1352805))), _1352809))], (31364 ^ _779308) ^ [_1353126, _1353128, _1353130, _1353132, _1353134] : [class_Groups_Ocomm__monoid__add(_1353126), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353128), _1353130)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353128, _1353126), _1353132), hAPP(hAPP(c_Set_Oinsert(_1353128), _1353134), _1353130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353126), hAPP(_1353132, _1353134)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353128, _1353126), _1353132), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1353128, tc_HOL_Obool)), _1353130), hAPP(hAPP(c_Set_Oinsert(_1353128), _1353134), c_Orderings_Obot__class_Obot(tc_fun(_1353128, tc_HOL_Obool)))))))], (31374 ^ _779308) ^ [_1353395, _1353397, _1353399, _1353401, _1353403] : [class_Groups_Ocomm__monoid__add(_1353395), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353397), _1353399)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353397), _1353401)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1353397, tc_HOL_Obool)), _1353399), _1353401) = c_Orderings_Obot__class_Obot(tc_fun(_1353397, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353397, _1353395), _1353403), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353397, tc_HOL_Obool)), _1353399), _1353401)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353395), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353397, _1353395), _1353403), _1353399)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353397, _1353395), _1353403), _1353401)))], (31392 ^ _779308) ^ [_1353790, _1353792, _1353794, _1353796, _1353798] : [class_Groups_Oab__group__add(_1353790), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353792), _1353794)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1353792), _1353796)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353792, _1353790), _1353798), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353792, tc_HOL_Obool)), _1353794), _1353796)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1353790), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1353790), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353792, _1353790), _1353798), _1353794)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353792, _1353790), _1353798), _1353796))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353792, _1353790), _1353798), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1353792, tc_HOL_Obool)), _1353794), _1353796))))], (31406 ^ _779308) ^ [_1354151, _1354153, _1354155, _1354157] : [class_Groups_Ocomm__monoid__add(_1354151), 31409 ^ _779308 : [(31410 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1354153), _1354155)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354151), _1354157), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1354155), hAPP(c_Nat_OSuc, _1354153))) = c_Groups_Ozero__class_Ozero(_1354151))], (31416 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1354153), _1354155))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354151), _1354157), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1354155), hAPP(c_Nat_OSuc, _1354153))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354151), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354151), _1354157), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1354155), _1354153))), hAPP(_1354157, _1354153)))]]], (31422 ^ _779308) ^ [_1354481, _1354483, _1354485, _1354487] : [class_Groups_Ocomm__monoid__add(_1354481), 31425 ^ _779308 : [(31426 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1354483)), _1354485)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354481), _1354487), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1354485, hAPP(c_Nat_OSuc, _1354483))) = c_Groups_Ozero__class_Ozero(_1354481))], (31432 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1354483)), _1354485))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354481), _1354487), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1354485, hAPP(c_Nat_OSuc, _1354483))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354481), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354481), _1354487), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1354485, _1354483))), hAPP(_1354487, hAPP(c_Nat_OSuc, _1354483))))]]], (31438 ^ _779308) ^ [_1354817, _1354819, _1354821, _1354823] : [class_Groups_Ocomm__monoid__add(_1354817), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1354819), _1354821)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354817), _1354823), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1354819, _1354821)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354817), hAPP(_1354823, _1354819)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1354817), _1354823), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1354819, _1354821))))], (31448 ^ _779308) ^ [_1355036, _1355038, _1355040, _1355042, _1355044] : [class_Groups_Ocomm__monoid__add(_1355036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1355038), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1355040), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355036), _1355042), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1355038, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1355040), _1355044))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355036), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355036), _1355042), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1355038, _1355040))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1355036), _1355042), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1355040), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1355040), _1355044)))))], (31458 ^ _779308) ^ [_1355327, _1355329, _1355331, _1355333, _1355335] : [class_Groups_Ocomm__monoid__add(_1355327), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355329), _1355331)), hBOOL(hAPP(hAPP(c_member(_1355329), _1355333), _1355331)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355329, _1355327), _1355335), _1355331) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355327), hAPP(_1355335, _1355333)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355329, _1355327), _1355335), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355329, tc_HOL_Obool)), _1355331), hAPP(hAPP(c_Set_Oinsert(_1355329), _1355333), c_Orderings_Obot__class_Obot(tc_fun(_1355329, tc_HOL_Obool)))))))], (31472 ^ _779308) ^ [_1355652, _1355654, _1355656, _1355658, _1355660] : [class_Groups_Ocomm__monoid__add(_1355652), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355654), _1355656)), hBOOL(hAPP(hAPP(c_member(_1355654), _1355658), _1355656)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355654, _1355652), _1355660), _1355656) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1355652), hAPP(_1355660, _1355658)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355654, _1355652), _1355660), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355654, tc_HOL_Obool)), _1355656), hAPP(hAPP(c_Set_Oinsert(_1355654), _1355658), c_Orderings_Obot__class_Obot(tc_fun(_1355654, tc_HOL_Obool)))))))], (31486 ^ _779308) ^ [_1355977, _1355979, _1355981, _1355983, _1355985] : [class_Rings_Oring(_1355977), hBOOL(hAPP(c_Finite__Set_Ofinite(_1355979), _1355981)), hBOOL(hAPP(hAPP(c_member(_1355979), _1355983), _1355981)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355979, _1355977), _1355985), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1355979, tc_HOL_Obool)), _1355981), hAPP(hAPP(c_Set_Oinsert(_1355979), _1355983), c_Orderings_Obot__class_Obot(tc_fun(_1355979, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1355977), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1355979, _1355977), _1355985), _1355981)), hAPP(_1355985, _1355983)))], (31500 ^ _779308) ^ [_1356302, _1356304, _1356306, _1356308, _1356310] : [class_Groups_Oab__group__add(_1356302), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356304), _1356306)), 31507 ^ _779308 : [(31508 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1356304), _1356308), _1356306)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356304, _1356302), _1356310), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356304, tc_HOL_Obool)), _1356306), hAPP(hAPP(c_Set_Oinsert(_1356304), _1356308), c_Orderings_Obot__class_Obot(tc_fun(_1356304, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1356302), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356304, _1356302), _1356310), _1356306)), hAPP(_1356310, _1356308)))], (31514 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1356304), _1356308), _1356306))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356304, _1356302), _1356310), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1356304, tc_HOL_Obool)), _1356306), hAPP(hAPP(c_Set_Oinsert(_1356304), _1356308), c_Orderings_Obot__class_Obot(tc_fun(_1356304, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356304, _1356302), _1356310), _1356306))]]], (31520 ^ _779308) ^ [_1356772, _1356774, _1356776, _1356778] : [class_Rings_Ocomm__semiring__1(_1356772), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356772), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356772), c_Groups_Oone__class_Oone(_1356772)), c_Groups_Oone__class_Oone(_1356772))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1356772), hAPP(hAPP(c_COMBB(_1356772, _1356772, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1356772), _1356774)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1356772, _1356772), hAPP(hAPP(c_COMBB(_1356772, tc_fun(_1356772, _1356772), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1356772)), c_Nat_Osemiring__1__class_Oof__nat(_1356772))), _1356776))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1356778))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356772), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1356772), _1356778)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356772), _1356774), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1356772), _1356774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356772), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1356772), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1356778), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1356776)))))], (31526 ^ _779308) ^ [_1357095, _1357097, _1357099] : [class_Fields_Ofield(_1357095), -(_1357097 = c_Groups_Oone__class_Oone(_1357095)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1357095), hAPP(c_Power_Opower__class_Opower(_1357095), _1357097)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1357099)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357095), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357095), hAPP(hAPP(c_Power_Opower__class_Opower(_1357095), _1357097), _1357099)), c_Groups_Oone__class_Oone(_1357095))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357095), _1357097), c_Groups_Oone__class_Oone(_1357095))))], (31536 ^ _779308) ^ [_1357297, _1357299] : [class_Rings_Ocomm__semiring__1(_1357297), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357297), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357297), c_Groups_Oone__class_Oone(_1357297)), c_Groups_Oone__class_Oone(_1357297))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1357297), c_Nat_Osemiring__1__class_Oof__nat(_1357297)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1357299))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357297), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1357297), _1357299)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1357297), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1357297), _1357299)), c_Groups_Oone__class_Oone(_1357297))))], (31542 ^ _779308) ^ [_1357498, _1357500, _1357502, _1357504] : [class_Groups_Oab__group__add(_1357498), 31545 ^ _779308 : [(31546 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1357500), _1357502)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1357498), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1357498, _1357498), hAPP(hAPP(c_COMBB(_1357498, tc_fun(_1357498, _1357498), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1357498)), _1357504)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1357498, tc_Nat_Onat), _1357504), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1357500, _1357502)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1357498), hAPP(_1357504, _1357500)), hAPP(_1357504, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1357502), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (31552 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1357500), _1357502))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1357498), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1357498, _1357498), hAPP(hAPP(c_COMBB(_1357498, tc_fun(_1357498, _1357498), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1357498)), _1357504)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1357498, tc_Nat_Onat), _1357504), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1357500, _1357502)) = c_Groups_Ozero__class_Ozero(_1357498))]]], (31558 ^ _779308) ^ [_1357936, _1357938, _1357940, _1357942, _1357944] : [class_Groups_Oordered__comm__monoid__add(_1357936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357938), _1357940)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1357938, tc_HOL_Obool)), _1357942), _1357940)), 31572 ^ _779308 : [(31573 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1357938), 31571 ^ [_1357936, _1357938, _1357940, _1357942, _1357944]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1357938, tc_HOL_Obool)), _1357940), _1357942))))], (31575 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357936), c_Groups_Ozero__class_Ozero(_1357936)), hAPP(_1357944, 31571 ^ [_1357936, _1357938, _1357940, _1357942, _1357944])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357936), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357938, _1357936), _1357944), _1357942)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357938, _1357936), _1357944), _1357940))))], (31579 ^ _779308) ^ [_1358422, _1358424, _1358426, _1358428, _1358430] : [class_Groups_Ocomm__monoid__mult(_1358422), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358424), _1358426)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358424), _1358428)), 31593 ^ _779308 : [(31594 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358424), 31592 ^ [_1358422, _1358424, _1358426, _1358428, _1358430]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1358424, tc_HOL_Obool)), _1358426), _1358428))))], (31596 ^ _779308) ^ [] : [hAPP(_1358430, 31592 ^ [_1358422, _1358424, _1358426, _1358428, _1358430]) = c_Groups_Oone__class_Oone(_1358422)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358424, _1358422), _1358430), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1358424, tc_HOL_Obool)), _1358426), _1358428)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358422), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358424, _1358422), _1358430), _1358426)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358424, _1358422), _1358430), _1358428)))], (31600 ^ _779308) ^ [_1358917, _1358919, _1358921, _1358923, _1358925] : [class_Groups_Ocomm__monoid__mult(_1358917), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358919), _1358921)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358919), _1358923)), 31614 ^ _779308 : [(31615 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358919), 31613 ^ [_1358917, _1358919, _1358921, _1358923, _1358925]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1358919, tc_HOL_Obool)), _1358921), _1358923))))], (31617 ^ _779308) ^ [] : [hAPP(_1358925, 31613 ^ [_1358917, _1358919, _1358921, _1358923, _1358925]) = c_Groups_Oone__class_Oone(_1358917)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358919, _1358917), _1358925), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1358919, tc_HOL_Obool)), _1358921), _1358923)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358917), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358919, _1358917), _1358925), _1358921)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358919, _1358917), _1358925), _1358923)))], (31621 ^ _779308) ^ [_1359412, _1359414, _1359416, _1359418, _1359420] : [class_Groups_Oordered__ab__semigroup__add(_1359412), class_Rings_Osemiring__1(_1359412), 31631 ^ _779308 : [(31632 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1359414), 31630 ^ [_1359412, _1359414, _1359416, _1359418, _1359420]), _1359416)))], (31634 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359412), hAPP(_1359418, 31630 ^ [_1359412, _1359414, _1359416, _1359418, _1359420])), _1359420))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1359412), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359414, _1359412), _1359418), _1359416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359412), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1359412), hAPP(c_Finite__Set_Ocard(_1359414), _1359416))), _1359420))))], (31638 ^ _779308) ^ [_1359802, _1359804, _1359806, _1359808, _1359810, _1359812] : [hBOOL(hAPP(hAPP(_1359802, _1359804), _1359806)), hBOOL(hAPP(hAPP(_1359808, _1359804), _1359806)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1359810, tc_fun(_1359812, tc_HOL_Obool))), _1359802), _1359808), _1359804), _1359806)))], (31648 ^ _779308) ^ [_1360005, _1360007, _1360009, _1360011, _1360013, _1360015] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360005, tc_fun(_1360007, tc_HOL_Obool))), _1360009), _1360011), _1360013), _1360015)), 31651 ^ _779308 : [(31652 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1360009, _1360013), _1360015)))], (31654 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1360011, _1360013), _1360015)))]]], (31656 ^ _779308) ^ [_1360178, _1360180, _1360182, _1360184, _1360186, _1360188] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360178, tc_fun(_1360180, tc_HOL_Obool))), _1360182), _1360184), _1360186), _1360188)), -(hBOOL(hAPP(hAPP(_1360182, _1360186), _1360188)))], (31662 ^ _779308) ^ [_1360311, _1360313, _1360315, _1360317, _1360319, _1360321] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360311, tc_fun(_1360313, tc_HOL_Obool))), _1360315), _1360317), _1360319), _1360321)), -(hBOOL(hAPP(hAPP(_1360317, _1360319), _1360321)))], (31668 ^ _779308) ^ [_1360444, _1360446, _1360448] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1360444), _1360446)), 31671 ^ _779308 : [(31682 ^ _779308) ^ [] : [31684 ^ _779308 : [(31685 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1360444), 31683 ^ [_1360444, _1360446, _1360448]), _1360446)))], (31687 ^ _779308) ^ [] : [hAPP(_1360448, 31683 ^ [_1360444, _1360446, _1360448]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360444, tc_Nat_Onat), _1360448), _1360446) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31672 ^ _779308) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360444, tc_Nat_Onat), _1360448), _1360446) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 31675 ^ _779308 : [(31676 ^ _779308) ^ [_1360606] : [hBOOL(hAPP(hAPP(c_member(_1360444), _1360606), _1360446)), -(hAPP(_1360448, _1360606) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (31691 ^ _779308) ^ [_1360864, _1360866] : [-(hAPP(c_Finite__Set_Ocard(_1360864), _1360866) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360864, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1360864), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1360866))], (31693 ^ _779308) ^ [_1360909, _1360911, _1360913] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360909, tc_Nat_Onat), _1360911), _1360913)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360909, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1360909), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1360911)), _1360913))], (31695 ^ _779308) ^ [_1360967, _1360969, _1360971] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1360967), _1360969)), 31698 ^ _779308 : [(31699 ^ _779308) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1360967, tc_Nat_Onat), _1360971), _1360969) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31703 ^ _779308 : [(31704 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1360967), 31702 ^ [_1360967, _1360969, _1360971]), _1360969)))], (31706 ^ _779308) ^ [] : [-(hAPP(_1360971, 31702 ^ [_1360967, _1360969, _1360971]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31708 ^ _779308) ^ [_1361287] : [hBOOL(hAPP(hAPP(c_member(_1360967), _1361287), _1360969)), -(31702 ^ [_1360967, _1360969, _1360971] = _1361287), -(hAPP(_1360971, 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[hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361801, tc_Nat_Onat), _1361805), _1361803) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 31745 ^ _779308 : [(31746 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1361801), 31744 ^ [_1361801, _1361803, _1361805]), _1361803)))], (31748 ^ _779308) ^ [] : [-(hAPP(_1361805, 31744 ^ [_1361801, _1361803, _1361805]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (31750 ^ _779308) ^ [_1362121] : [hBOOL(hAPP(hAPP(c_member(_1361801), _1362121), _1361803)), -(31744 ^ [_1361801, _1361803, _1361805] = _1362121), -(hAPP(_1361805, _1362121) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (31760 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361801, tc_Nat_Onat), _1361805), _1361803) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 31761 ^ _779308 : [(31762 ^ _779308) ^ [_1362282] : [hBOOL(hAPP(hAPP(c_member(_1361801), _1362282), _1361803)), hAPP(_1361805, _1362282) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 31770 ^ 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hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362816, tc_Nat_Onat), _1362822), _1362818)))], (31797 ^ _779308) ^ [_1363069, _1363071, _1363073] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363069), _1363071), _1363073) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1363069), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1363069, tc_Int_Oint), _1363071), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1363073))), class_Groups_Ocomm__monoid__add(_1363069), class_Groups_Ocomm__monoid__mult(_1363069)], (31807 ^ _779308) ^ [_1363275, _1363277, _1363279, _1363281] : [hBOOL(hAPP(hAPP(c_member(_1363275), _1363277), _1363279)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363275, tc_Nat_Onat), _1363281), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363275, tc_HOL_Obool)), _1363279), hAPP(hAPP(c_Set_Oinsert(_1363275), _1363277), c_Orderings_Obot__class_Obot(tc_fun(_1363275, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363275, tc_Nat_Onat), _1363281), _1363279)), hAPP(_1363281, _1363277)))], (31813 ^ _779308) ^ [_1363466, _1363468, _1363470, _1363472] : [-(hBOOL(hAPP(hAPP(c_member(_1363466), _1363468), _1363470))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363466, tc_Nat_Onat), _1363472), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363466, tc_HOL_Obool)), _1363470), hAPP(hAPP(c_Set_Oinsert(_1363466), _1363468), c_Orderings_Obot__class_Obot(tc_fun(_1363466, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363466, tc_Nat_Onat), _1363472), _1363470))], (31819 ^ _779308) ^ [_1363557, _1363559, _1363561, _1363563] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1363557), _1363559)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363557), _1363561)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363557, tc_Nat_Onat), _1363563), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363557, tc_HOL_Obool)), _1363559), _1363561)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363557, tc_Nat_Onat), _1363563), _1363559)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363557, tc_Nat_Onat), _1363563), _1363561))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363557, tc_Nat_Onat), _1363563), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1363557, tc_HOL_Obool)), _1363559), _1363561))))], (31829 ^ _779308) ^ [_1363850, _1363852, _1363854] : [class_Groups_Ocomm__monoid__add(_1363850), class_Groups_Ocomm__monoid__mult(_1363850), c_Nat__Transfer_Onat__set(_1363852), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1363850), _1363854), _1363852) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363850), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1363850, tc_Nat_Onat), _1363854), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1363852)))], (31843 ^ _779308) ^ [_1364095, _1364097, _1364099] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1364095)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1364097))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1364099))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1364099), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1364095), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1364095), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1364099), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1364097)))))], (31845 ^ _779308) ^ [_1364176, _1364178, _1364180] : [31847 ^ _779308 : [(31848 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364176), 31846 ^ [_1364176, _1364178, _1364180]), _1364178)))], (31850 ^ _779308) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1364180, 31846 ^ [_1364176, _1364178, _1364180]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364176, tc_Int_Oint), _1364180), _1364178) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364176, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1364176), c_Int_Onat), _1364180)), _1364178)))], (31854 ^ _779308) ^ [_1364406, _1364408, _1364410, _1364412, _1364414] : [class_Groups_Ocomm__monoid__add(_1364406), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364408), _1364410)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364408), _1364412)), 31868 ^ _779308 : [(31869 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364408), 31867 ^ [_1364406, _1364408, _1364410, _1364412, _1364414]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364408, tc_HOL_Obool)), _1364410), _1364412))))], (31871 ^ _779308) ^ [] : [hAPP(_1364414, 31867 ^ [_1364406, _1364408, _1364410, _1364412, _1364414]) = c_Groups_Ozero__class_Ozero(_1364406)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364408, _1364406), _1364414), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364408, tc_HOL_Obool)), _1364410), _1364412)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364406), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364408, _1364406), _1364414), _1364410)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364408, _1364406), _1364414), _1364412)))], (31875 ^ _779308) ^ [_1364901, _1364903, _1364905, _1364907, _1364909] : [class_Groups_Ocomm__monoid__add(_1364901), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364903), _1364905)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364903), _1364907)), 31889 ^ _779308 : [(31890 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1364903), 31888 ^ [_1364901, _1364903, _1364905, _1364907, _1364909]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364903, tc_HOL_Obool)), _1364905), _1364907))))], (31892 ^ _779308) ^ [] : [hAPP(_1364909, 31888 ^ [_1364901, _1364903, _1364905, _1364907, _1364909]) = c_Groups_Ozero__class_Ozero(_1364901)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364903, _1364901), _1364909), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364903, tc_HOL_Obool)), _1364905), _1364907)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364901), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364903, _1364901), _1364909), _1364905)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364903, _1364901), _1364909), _1364907)))], (31896 ^ _779308) ^ [_1365396, _1365398, _1365400, _1365402, _1365404] : [class_Groups_Ocomm__monoid__add(_1365396), class_Groups_Oordered__ab__semigroup__add(_1365396), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365398), _1365400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1365398, tc_HOL_Obool)), _1365402), _1365400)), 31914 ^ _779308 : [(31915 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1365398), 31913 ^ [_1365396, _1365398, _1365400, _1365402, _1365404]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365398, tc_HOL_Obool)), _1365400), _1365402))))], (31917 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365396), c_Groups_Ozero__class_Ozero(_1365396)), hAPP(_1365404, 31913 ^ [_1365396, _1365398, _1365400, _1365402, _1365404])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365396), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365398, _1365396), _1365404), _1365402)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365398, _1365396), _1365404), _1365400))))], (31921 ^ _779308) ^ [_1365940, _1365942, _1365944] : [class_Lattices_Olattice(_1365940), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365940), _1365942)), hBOOL(hAPP(hAPP(c_member(_1365940), _1365944), _1365942)), 31932 ^ _779308 : [(31933 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365940, tc_HOL_Obool)), _1365942), hAPP(hAPP(c_Set_Oinsert(_1365940), _1365944), c_Orderings_Obot__class_Obot(tc_fun(_1365940, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1365940, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1365940, _1365942) = _1365944)], (31939 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365940, tc_HOL_Obool)), _1365942), hAPP(hAPP(c_Set_Oinsert(_1365940), _1365944), c_Orderings_Obot__class_Obot(tc_fun(_1365940, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1365940, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1365940, _1365942) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1365940), _1365944), c_Big__Operators_Olattice__class_OInf__fin(_1365940, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1365940, tc_HOL_Obool)), _1365942), hAPP(hAPP(c_Set_Oinsert(_1365940), _1365944), c_Orderings_Obot__class_Obot(tc_fun(_1365940, tc_HOL_Obool)))))))]]], (31945 ^ _779308) ^ [_1366446, _1366448, _1366450, _1366452, _1366454, _1366456] : [class_Groups_Oordered__ab__group__add(_1366446), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366448), _1366450)), 31955 ^ _779308 : [(31956 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366448), 31954 ^ [_1366446, _1366448, _1366450, _1366452, _1366454, _1366456]), _1366450)))], (31958 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366446), c_Groups_Ozero__class_Ozero(_1366446)), hAPP(_1366452, 31954 ^ [_1366446, _1366448, _1366450, _1366452, _1366454, _1366456])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1366448, _1366446), _1366452), _1366450) = _1366454, hBOOL(hAPP(hAPP(c_member(_1366448), _1366456), _1366450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366446), hAPP(_1366452, _1366456)), _1366454)))], (31970 ^ _779308) ^ [_1366966, _1366968, _1366970, _1366972, _1366974] : [class_Groups_Oordered__ab__group__add(_1366966), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366968), _1366970)), 31980 ^ _779308 : [(31981 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366968), 31979 ^ [_1366966, _1366968, _1366970, _1366972, _1366974]), _1366970)))], (31983 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366966), c_Groups_Ozero__class_Ozero(_1366966)), hAPP(_1366972, 31979 ^ [_1366966, _1366968, _1366970, _1366972, _1366974])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1366968, _1366966), _1366972), _1366970) = c_Groups_Ozero__class_Ozero(_1366966), hBOOL(hAPP(hAPP(c_member(_1366968), _1366974), _1366970)), -(hAPP(_1366972, _1366974) = c_Groups_Ozero__class_Ozero(_1366966))], (31995 ^ _779308) ^ [_1367464, _1367466, _1367468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1367464, 31996 ^ [_1367464, _1367466, _1367468])), hAPP(_1367466, 31996 ^ [_1367464, _1367466, _1367468]))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1367466), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1367468))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1367464), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1367468))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), _1367466)), _1367464)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1367468)))], (32002 ^ _779308) ^ [_1367697, _1367699] : [class_Lattices_Olattice(_1367697), -(c_Big__Operators_Olattice__class_OInf__fin(_1367697, hAPP(hAPP(c_Set_Oinsert(_1367697), _1367699), c_Orderings_Obot__class_Obot(tc_fun(_1367697, tc_HOL_Obool)))) = _1367699)], (32008 ^ _779308) ^ [_1367804, _1367806, _1367808] : [class_Lattices_Olattice(_1367804), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367804), _1367806)), hBOOL(hAPP(hAPP(c_member(_1367804), _1367808), _1367806)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1367804), _1367808), c_Big__Operators_Olattice__class_OInf__fin(_1367804, _1367806)) = _1367808)], (32022 ^ _779308) ^ [_1368033, _1368035, _1368037] : [class_Lattices_Olattice(_1368033), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368033), _1368035)), hBOOL(hAPP(hAPP(c_member(_1368033), _1368037), _1368035)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1368033), _1368037), c_Big__Operators_Olattice__class_OInf__fin(_1368033, _1368035)) = c_Big__Operators_Olattice__class_OInf__fin(_1368033, _1368035))], (32036 ^ _779308) ^ [_1368268, _1368270] : [class_Lattices_Olattice(_1368268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368268), _1368270)), -(c_Big__Operators_Olattice__class_OInf__fin(_1368268, _1368270) = hAPP(c_Finite__Set_Ofold1(_1368268, c_Lattices_Osemilattice__inf__class_Oinf(_1368268)), _1368270))], (32046 ^ _779308) ^ [_1368425, _1368427, _1368429] : [class_Lattices_Olattice(_1368425), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368425), _1368427)), -(_1368427 = c_Orderings_Obot__class_Obot(tc_fun(_1368425, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1368425, hAPP(hAPP(c_Set_Oinsert(_1368425), _1368429), _1368427)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1368425), _1368429), c_Big__Operators_Olattice__class_OInf__fin(_1368425, _1368427)))], (32060 ^ _779308) ^ [_1368633, _1368635, _1368637] : [class_Lattices_Olattice(_1368633), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368633), _1368635)), -(_1368637 = c_Orderings_Obot__class_Obot(tc_fun(_1368633, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1368633, tc_HOL_Obool)), _1368637), _1368635)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1368633), c_Big__Operators_Olattice__class_OInf__fin(_1368633, _1368637)), c_Big__Operators_Olattice__class_OInf__fin(_1368633, _1368635)) = c_Big__Operators_Olattice__class_OInf__fin(_1368633, _1368635))], (32078 ^ _779308) ^ [_1368947, _1368949, _1368951] : [class_Lattices_Olattice(_1368947), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368947), _1368949)), -(_1368949 = c_Orderings_Obot__class_Obot(tc_fun(_1368947, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1368947), _1368951)), -(_1368951 = c_Orderings_Obot__class_Obot(tc_fun(_1368947, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1368947, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1368947, tc_HOL_Obool)), _1368949), _1368951)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1368947), c_Big__Operators_Olattice__class_OInf__fin(_1368947, _1368949)), c_Big__Operators_Olattice__class_OInf__fin(_1368947, _1368951)))], (32100 ^ _779308) ^ [_1369296, _1369298] : [class_Lattices_Olattice(_1369296), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369296), _1369298)), -(_1369298 = c_Orderings_Obot__class_Obot(tc_fun(_1369296, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369296), c_Big__Operators_Olattice__class_OInf__fin(_1369296, _1369298)), c_Big__Operators_Olattice__class_OSup__fin(_1369296, _1369298))))], (32114 ^ _779308) ^ [_1369482, _1369484, _1369486] : [class_Lattices_Olattice(_1369482), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369482), _1369484)), -(hBOOL(hAPP(hAPP(c_member(_1369482), _1369486), _1369484))), -(_1369484 = c_Orderings_Obot__class_Obot(tc_fun(_1369482, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1369482, hAPP(hAPP(c_Set_Oinsert(_1369482), _1369486), _1369484)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1369482), _1369486), c_Big__Operators_Olattice__class_OInf__fin(_1369482, _1369484)))], (32132 ^ _779308) ^ [_1369719, _1369721, _1369723] : [class_Lattices_Olattice(_1369719), hBOOL(hAPP(c_Finite__Set_Ofinite(_1369719), _1369721)), 32139 ^ _779308 : [(32140 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369719, tc_HOL_Obool)), _1369721), hAPP(hAPP(c_Set_Oinsert(_1369719), _1369723), c_Orderings_Obot__class_Obot(tc_fun(_1369719, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1369719, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1369719, hAPP(hAPP(c_Set_Oinsert(_1369719), _1369723), _1369721)) = _1369723)], (32146 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369719, tc_HOL_Obool)), _1369721), hAPP(hAPP(c_Set_Oinsert(_1369719), _1369723), c_Orderings_Obot__class_Obot(tc_fun(_1369719, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1369719, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1369719, hAPP(hAPP(c_Set_Oinsert(_1369719), _1369723), _1369721)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1369719), _1369723), c_Big__Operators_Olattice__class_OInf__fin(_1369719, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1369719, tc_HOL_Obool)), _1369721), hAPP(hAPP(c_Set_Oinsert(_1369719), _1369723), c_Orderings_Obot__class_Obot(tc_fun(_1369719, tc_HOL_Obool)))))))]]], (32152 ^ _779308) ^ [_1370189, _1370191, _1370193] : [class_Lattices_Olattice(_1370189), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370189), _1370191)), -(_1370191 = c_Orderings_Obot__class_Obot(tc_fun(_1370189, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370189), _1370193)), -(_1370193 = c_Orderings_Obot__class_Obot(tc_fun(_1370189, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370189, tc_HOL_Obool)), _1370191), _1370193) = c_Orderings_Obot__class_Obot(tc_fun(_1370189, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1370189, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1370189, tc_HOL_Obool)), _1370191), _1370193)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1370189), c_Big__Operators_Olattice__class_OInf__fin(_1370189, _1370191)), c_Big__Operators_Olattice__class_OInf__fin(_1370189, _1370193)))], (32178 ^ _779308) ^ [_1370666, _1370668, _1370670] : [class_Lattices_Olattice(_1370666), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370666), _1370668)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370666), _1370670)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370666, tc_HOL_Obool)), _1370668), _1370670) = c_Orderings_Obot__class_Obot(tc_fun(_1370666, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1370666), c_Big__Operators_Olattice__class_OInf__fin(_1370666, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1370666, tc_HOL_Obool)), _1370668), _1370670))), c_Big__Operators_Olattice__class_OInf__fin(_1370666, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1370666, tc_HOL_Obool)), _1370668), _1370670))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1370666), c_Big__Operators_Olattice__class_OInf__fin(_1370666, _1370668)), c_Big__Operators_Olattice__class_OInf__fin(_1370666, _1370670)))], (32196 ^ _779308) ^ [_1371014, _1371016] : [class_Lattices_Olattice(_1371014), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371014), _1371016)), -(_1371016 = c_Orderings_Obot__class_Obot(tc_fun(_1371014, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1371014), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371014), 32209 ^ [_1371014, _1371016]), 32210 ^ [_1371014, _1371016])), hAPP(hAPP(c_Set_Oinsert(_1371014), 32209 ^ [_1371014, _1371016]), hAPP(hAPP(c_Set_Oinsert(_1371014), 32210 ^ [_1371014, _1371016]), c_Orderings_Obot__class_Obot(tc_fun(_1371014, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1371014), c_Big__Operators_Olattice__class_OInf__fin(_1371014, _1371016)), _1371016)))], (32216 ^ _779308) ^ [_1371458, _1371460, _1371462] : [class_Lattices_Olattice(_1371458), hAPP(_1371460, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371458), 32221 ^ [_1371458, _1371460, _1371462]), 32222 ^ [_1371458, _1371460, _1371462])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1371458), hAPP(_1371460, 32221 ^ [_1371458, _1371460, _1371462])), hAPP(_1371460, 32222 ^ [_1371458, _1371460, _1371462])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371458), _1371462)), -(_1371462 = c_Orderings_Obot__class_Obot(tc_fun(_1371458, tc_HOL_Obool))), -(hAPP(_1371460, c_Big__Operators_Olattice__class_OInf__fin(_1371458, _1371462)) = c_Big__Operators_Olattice__class_OInf__fin(_1371458, hAPP(c_Set_Oimage(_1371458, _1371458, _1371460), _1371462)))], (32236 ^ _779308) ^ [_1371861, _1371863, _1371865, _1371867, _1371869] : [class_Groups_Ocomm__monoid__add(_1371861), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371863), _1371865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1371863, tc_HOL_Obool)), _1371867), _1371865)), 32250 ^ _779308 : [(32251 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1371863), 32249 ^ [_1371861, _1371863, _1371865, _1371867, _1371869]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1371863, tc_HOL_Obool)), _1371865), _1371867))))], (32253 ^ _779308) ^ [] : [hAPP(_1371869, 32249 ^ [_1371861, _1371863, _1371865, _1371867, _1371869]) = c_Groups_Ozero__class_Ozero(_1371861)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371863, _1371861), _1371869), _1371865) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1371863, _1371861), _1371869), _1371867))], (32257 ^ _779308) ^ [_1372312, _1372314, _1372316, _1372318, _1372320] : [class_Groups_Ocomm__monoid__add(_1372312), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372314), _1372316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1372314, tc_HOL_Obool)), _1372318), _1372316)), 32271 ^ _779308 : [(32272 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372314), 32270 ^ [_1372312, _1372314, _1372316, _1372318, _1372320]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1372314, tc_HOL_Obool)), _1372316), _1372318))))], (32274 ^ _779308) ^ [] : [hAPP(_1372320, 32270 ^ [_1372312, _1372314, _1372316, _1372318, _1372320]) = c_Groups_Ozero__class_Ozero(_1372312)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372314, _1372312), _1372320), _1372318) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372314, _1372312), _1372320), _1372316))], (32278 ^ _779308) ^ [_1372763, _1372765, _1372767, _1372769, _1372771] : [class_Groups_Ocomm__monoid__add(_1372763), class_Groups_Oordered__cancel__ab__semigroup__add(_1372763), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372765), _1372767)), -(_1372767 = c_Orderings_Obot__class_Obot(tc_fun(_1372765, tc_HOL_Obool))), 32296 ^ _779308 : [(32297 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1372765), 32295 ^ [_1372763, _1372765, _1372767, _1372769, _1372771]), _1372767)))], (32299 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372763), hAPP(_1372769, 32295 ^ [_1372763, _1372765, _1372767, _1372769, _1372771])), hAPP(_1372771, 32295 ^ [_1372763, _1372765, _1372767, _1372769, _1372771])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372763), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372765, _1372763), _1372769), _1372767)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1372765, _1372763), _1372771), _1372767))))], (32303 ^ _779308) ^ [_1373294, _1373296] : [class_Orderings_Oorder(_1373294), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1373294, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1373294), _1373296)), hAPP(c_SetInterval_Oord__class_OatLeast(_1373294), _1373296)) = hAPP(hAPP(c_Set_Oinsert(_1373294), _1373296), c_Orderings_Obot__class_Obot(tc_fun(_1373294, tc_HOL_Obool))))], (32309 ^ _779308) ^ [_1373437, _1373439, _1373441] : [class_Fields_Olinordered__field__inverse__zero(_1373437), 32315 ^ _779308 : [(32316 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373437), c_Groups_Ozero__class_Ozero(_1373437)), 32314 ^ [_1373437, _1373439, _1373441])))], (32318 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373437), 32314 ^ [_1373437, _1373439, _1373441]), c_Groups_Oone__class_Oone(_1373437))))], (32320 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1373437), 32314 ^ [_1373437, _1373439, _1373441]), _1373439)), _1373441))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1373437), _1373439), _1373441)))], (32324 ^ _779308) ^ [_1373786, _1373788, _1373790, _1373792, _1373794] : [class_Groups_Ocomm__monoid__add(_1373786), class_Groups_Ocomm__monoid__mult(_1373786), _1373788 = _1373790, c_Nat__Transfer_Onat__set(_1373790), 32342 ^ _779308 : [(32343 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32341 ^ [_1373786, _1373788, _1373790, _1373792, _1373794])))], (32345 ^ _779308) ^ [] : [hAPP(_1373792, 32341 ^ [_1373786, _1373788, _1373790, _1373792, _1373794]) = hAPP(_1373794, 32341 ^ [_1373786, _1373788, _1373790, _1373792, _1373794])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1373786), _1373792), _1373788) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1373786), _1373794), _1373790))], (32349 ^ _779308) ^ [_1374249, _1374251, _1374253] : [class_Orderings_Olinorder(_1374249), 32352 ^ _779308 : [(32353 ^ _779308) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1374249), _1374251) = hAPP(c_SetInterval_Oord__class_OatLeast(_1374249), _1374253), -(_1374251 = _1374253)], (32359 ^ _779308) ^ [] : [_1374251 = _1374253, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1374249), _1374251) = hAPP(c_SetInterval_Oord__class_OatLeast(_1374249), _1374253))]]], (32365 ^ _779308) ^ [_1374490, _1374492, _1374494] : [class_Orderings_Oord(_1374490), 32368 ^ _779308 : [(32369 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1374490), _1374492), hAPP(c_SetInterval_Oord__class_OatLeast(_1374490), _1374494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374490), _1374494), _1374492)))], (32375 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374490), _1374494), _1374492)), -(hBOOL(hAPP(hAPP(c_member(_1374490), _1374492), hAPP(c_SetInterval_Oord__class_OatLeast(_1374490), _1374494))))]]], (32381 ^ _779308) ^ [_1374758, _1374760, _1374762] : [class_Orderings_Oorder(_1374758), 32384 ^ _779308 : [(32385 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1374758, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1374758), _1374760)), hAPP(c_SetInterval_Oord__class_OatLeast(_1374758), _1374762))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374758), _1374762), _1374760)))], (32391 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1374758), _1374762), _1374760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1374758, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1374758), _1374760)), hAPP(c_SetInterval_Oord__class_OatLeast(_1374758), _1374762))))]]], (32397 ^ _779308) ^ [_1375050, _1375052] : [class_Orderings_Olinorder(_1375050), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1375050, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1375050), _1375052)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1375050), _1375052))], (32403 ^ _779308) ^ [_1375161, _1375163] : [class_Orderings_Olinorder(_1375161), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1375161, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1375161), _1375163)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1375161), _1375163))], (32409 ^ _779308) ^ [_1375272, _1375274, _1375276] : [class_Orderings_Olinorder(_1375272), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375272), _1375274), _1375276)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1375272, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1375272, _1375274), _1375276)), hAPP(c_SetInterval_Oord__class_OatLeast(_1375272), _1375276)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1375272), _1375274))], (32419 ^ _779308) ^ [_1375471, _1375473, _1375475] : [class_Orderings_Oorder(_1375471), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1375471, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1375471, _1375473), _1375475)), hAPP(c_SetInterval_Oord__class_OatLeast(_1375471), _1375475)) = c_Orderings_Obot__class_Obot(tc_fun(_1375471, tc_HOL_Obool)))], (32425 ^ _779308) ^ [_1375602, _1375604, _1375606, _1375608] : [class_Orderings_Olinorder(_1375602), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1375602, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1375602), _1375604)), c_SetInterval_Oord__class_OatLeastAtMost(_1375602, _1375606, _1375608)) = c_SetInterval_Oord__class_OatLeastAtMost(_1375602, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1375602), _1375604), _1375606), _1375608))], (32431 ^ _779308) ^ [_1375745, _1375747, _1375749, _1375751] : [class_Orderings_Olinorder(_1375745), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1375745, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1375745, _1375747, _1375749)), hAPP(c_SetInterval_Oord__class_OatLeast(_1375745), _1375751)) = c_SetInterval_Oord__class_OatLeastAtMost(_1375745, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1375745), _1375747), _1375751), _1375749))], (32437 ^ _779308) ^ [_1375888, _1375890, _1375892] : [class_Orderings_Oorder(_1375888), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1375888, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1375888, _1375890, _1375892)), hAPP(c_SetInterval_Oord__class_OatLeast(_1375888), _1375892)) = c_Orderings_Obot__class_Obot(tc_fun(_1375888, tc_HOL_Obool)))], (32443 ^ _779308) ^ [_1376015, _1376017] : [class_Groups_Oordered__ab__group__add(_1376015), -(hAPP(c_Set_Oimage(_1376015, _1376015, c_Groups_Ouminus__class_Ouminus(_1376015)), hAPP(c_SetInterval_Oord__class_OatMost(_1376015), _1376017)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1376015), hAPP(c_Groups_Ouminus__class_Ouminus(_1376015), _1376017)))], (32449 ^ _779308) ^ [_1376138, _1376140] : [class_Groups_Oordered__ab__group__add(_1376138), -(hAPP(c_Set_Oimage(_1376138, _1376138, c_Groups_Ouminus__class_Ouminus(_1376138)), hAPP(c_SetInterval_Oord__class_OatLeast(_1376138), _1376140)) = hAPP(c_SetInterval_Oord__class_OatMost(_1376138), hAPP(c_Groups_Ouminus__class_Ouminus(_1376138), _1376140)))], (32455 ^ _779308) ^ [_1376261] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1376261)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1376261)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1376261), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (32457 ^ _779308) ^ [_1376305, _1376307, _1376309] : [class_Orderings_Olinorder(_1376305), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376305), _1376307), _1376309)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1376305, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1376305, _1376307, _1376309)), hAPP(c_SetInterval_Oord__class_OatLeast(_1376305), _1376309)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1376305), _1376307))], (32467 ^ _779308) ^ [_1376500, _1376502, _1376504] : [class_Orderings_Olinorder(_1376500), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376500), _1376502), _1376504)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1376500, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1376500, _1376502, _1376504)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1376500), _1376504)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1376500), _1376502))], (32477 ^ _779308) ^ [_1376695, _1376697] : [class_Orderings_Olinorder(_1376695), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1376695, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1376695), _1376697), c_Orderings_Obot__class_Obot(tc_fun(_1376695, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1376695), _1376697)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1376695), _1376697))], (32483 ^ _779308) ^ [_1376838, _1376840] : [class_Groups_Osgn__if(_1376838), 32486 ^ _779308 : [(32487 ^ _779308) ^ [] : [_1376840 = c_Groups_Ozero__class_Ozero(_1376838), -(c_Groups_Osgn__class_Osgn(_1376838, _1376840) = c_Groups_Ozero__class_Ozero(_1376838))], (32493 ^ _779308) ^ [] : [-(_1376840 = c_Groups_Ozero__class_Ozero(_1376838)), 32496 ^ _779308 : [(32497 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376838), c_Groups_Ozero__class_Ozero(_1376838)), _1376840)), -(c_Groups_Osgn__class_Osgn(_1376838, _1376840) = c_Groups_Oone__class_Oone(_1376838))], (32503 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376838), c_Groups_Ozero__class_Ozero(_1376838)), _1376840))), -(c_Groups_Osgn__class_Osgn(_1376838, _1376840) = hAPP(c_Groups_Ouminus__class_Ouminus(_1376838), c_Groups_Oone__class_Oone(_1376838)))]]]]], (32509 ^ _779308) ^ [_1377235, _1377237, _1377239] : [class_Orderings_Olinorder(_1377235), 32512 ^ _779308 : [(32513 ^ _779308) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1377235), _1377237) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1377235), _1377239), -(_1377237 = _1377239)], (32519 ^ _779308) ^ [] : [_1377237 = _1377239, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1377235), _1377237) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1377235), _1377239))]]], (32525 ^ _779308) ^ [_1377476, _1377478] : [class_Rings_Olinordered__idom(_1377476), -(c_Groups_Osgn__class_Osgn(_1377476, c_Groups_Osgn__class_Osgn(_1377476, _1377478)) = c_Groups_Osgn__class_Osgn(_1377476, _1377478))], (32531 ^ _779308) ^ [_1377569] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1377569)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1377569))], (32533 ^ _779308) ^ [_1377601, _1377603] : [class_Rings_Olinordered__idom(_1377601), 32536 ^ _779308 : [(32537 ^ _779308) ^ [] : [c_Groups_Osgn__class_Osgn(_1377601, _1377603) = c_Groups_Ozero__class_Ozero(_1377601), -(_1377603 = c_Groups_Ozero__class_Ozero(_1377601))], (32543 ^ _779308) ^ [] : [_1377603 = c_Groups_Ozero__class_Ozero(_1377601), -(c_Groups_Osgn__class_Osgn(_1377601, _1377603) = c_Groups_Ozero__class_Ozero(_1377601))]]], (32549 ^ _779308) ^ [_1377827] : [class_Groups_Osgn__if(_1377827), -(c_Groups_Osgn__class_Osgn(_1377827, c_Groups_Ozero__class_Ozero(_1377827)) = c_Groups_Ozero__class_Ozero(_1377827))], (32555 ^ _779308) ^ [_1377914, _1377916, _1377918] : [class_Rings_Olinordered__idom(_1377914), -(c_Groups_Osgn__class_Osgn(_1377914, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377914), _1377916), _1377918)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377914), c_Groups_Osgn__class_Osgn(_1377914, _1377916)), c_Groups_Osgn__class_Osgn(_1377914, _1377918)))], (32561 ^ _779308) ^ [_1378041, _1378043] : [class_Rings_Olinordered__idom(_1378041), 32564 ^ _779308 : [(32565 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378041), c_Groups_Osgn__class_Osgn(_1378041, _1378043)), c_Groups_Ozero__class_Ozero(_1378041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378041), _1378043), c_Groups_Ozero__class_Ozero(_1378041))))], (32571 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378041), _1378043), c_Groups_Ozero__class_Ozero(_1378041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378041), c_Groups_Osgn__class_Osgn(_1378041, _1378043)), c_Groups_Ozero__class_Ozero(_1378041))))]]], (32577 ^ _779308) ^ [_1378309, _1378311] : [class_Rings_Olinordered__idom(_1378309), 32580 ^ _779308 : [(32581 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378309), c_Groups_Ozero__class_Ozero(_1378309)), c_Groups_Osgn__class_Osgn(_1378309, _1378311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378309), c_Groups_Ozero__class_Ozero(_1378309)), _1378311)))], (32587 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378309), c_Groups_Ozero__class_Ozero(_1378309)), _1378311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378309), c_Groups_Ozero__class_Ozero(_1378309)), c_Groups_Osgn__class_Osgn(_1378309, _1378311))))]]], (32593 ^ _779308) ^ [_1378577, _1378579, _1378581] : [class_Orderings_Oord(_1378577), 32596 ^ _779308 : [(32597 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1378577), _1378579), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1378577), _1378581))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378577), _1378581), _1378579)))], (32603 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378577), _1378581), _1378579)), -(hBOOL(hAPP(hAPP(c_member(_1378577), _1378579), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1378577), _1378581))))]]], (32609 ^ _779308) ^ [_1378845, _1378847, _1378849] : [class_Orderings_Olinorder(_1378845), 32612 ^ _779308 : [(32613 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1378845, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1378845), _1378847)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1378845), _1378849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1378845), _1378849), _1378847)))], (32619 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1378845), _1378849), _1378847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1378845, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1378845), _1378847)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1378845), _1378849))))]]], (32625 ^ _779308) ^ [_1379137, _1379139] : [class_Orderings_Olinorder(_1379137), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1379137, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1379137), _1379139)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379137), _1379139))], (32631 ^ _779308) ^ [_1379248, _1379250] : [class_Orderings_Olinorder(_1379248), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1379248, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379248), _1379250)) = hAPP(c_SetInterval_Oord__class_OatMost(_1379248), _1379250))], (32637 ^ _779308) ^ [_1379359, _1379361] : [class_Rings_Olinordered__idom(_1379359), 32640 ^ _779308 : [(32641 ^ _779308) ^ [] : [c_Groups_Osgn__class_Osgn(_1379359, _1379361) = c_Groups_Oone__class_Oone(_1379359), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379359), c_Groups_Ozero__class_Ozero(_1379359)), _1379361)))], (32647 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379359), c_Groups_Ozero__class_Ozero(_1379359)), _1379361)), -(c_Groups_Osgn__class_Osgn(_1379359, _1379361) = c_Groups_Oone__class_Oone(_1379359))]]], (32653 ^ _779308) ^ [_1379606, _1379608] : [class_Rings_Olinordered__idom(_1379606), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379606), c_Groups_Ozero__class_Ozero(_1379606)), _1379608)), -(c_Groups_Osgn__class_Osgn(_1379606, _1379608) = c_Groups_Oone__class_Oone(_1379606))], (32663 ^ _779308) ^ [_1379761, _1379763, _1379765] : [class_Orderings_Oorder(_1379761), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1379761, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1379761, _1379763, _1379765)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379761), _1379765)) = c_Orderings_Obot__class_Obot(tc_fun(_1379761, tc_HOL_Obool)))], (32669 ^ _779308) ^ [_1379888, _1379890, _1379892] : [class_Orderings_Olinorder(_1379888), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1379888), _1379890), _1379892)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1379888, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1379888, _1379890, _1379892)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379888), _1379892)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1379888), _1379890))], (32679 ^ _779308) ^ [_1380083, _1380085] : [class_Groups_Oordered__ab__group__add(_1380083), -(hAPP(c_Set_Oimage(_1380083, _1380083, c_Groups_Ouminus__class_Ouminus(_1380083)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1380083), _1380085)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1380083), hAPP(c_Groups_Ouminus__class_Ouminus(_1380083), _1380085)))], (32685 ^ _779308) ^ [_1380206, _1380208] : [class_Groups_Oordered__ab__group__add(_1380206), -(hAPP(c_Set_Oimage(_1380206, _1380206, c_Groups_Ouminus__class_Ouminus(_1380206)), hAPP(c_SetInterval_Oord__class_OlessThan(_1380206), _1380208)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1380206), hAPP(c_Groups_Ouminus__class_Ouminus(_1380206), _1380208)))], (32691 ^ _779308) ^ [_1380329, _1380331, _1380333] : [class_Orderings_Oorder(_1380329), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380329, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1380329, _1380331, _1380333)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1380329), _1380333)) = c_Orderings_Obot__class_Obot(tc_fun(_1380329, tc_HOL_Obool)))], (32697 ^ _779308) ^ [_1380456] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1380456)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1380456)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1380456)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (32699 ^ _779308) ^ [_1380509] : [_1380509 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1380509) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32705 ^ _779308) ^ [_1380585] : [-(_1380585 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32708 ^ _779308 : [(32709 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380585)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1380585) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (32715 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380585))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1380585) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (32721 ^ _779308) ^ [_1380777, _1380779] : [class_Rings_Olinordered__idom(_1380777), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380777), _1380779), c_Groups_Ozero__class_Ozero(_1380777))), -(c_Groups_Osgn__class_Osgn(_1380777, _1380779) = hAPP(c_Groups_Ouminus__class_Ouminus(_1380777), c_Groups_Oone__class_Oone(_1380777)))], (32731 ^ _779308) ^ [_1380942, _1380944] : [class_Rings_Olinordered__idom(_1380942), 32734 ^ _779308 : [(32735 ^ _779308) ^ [] : [c_Groups_Osgn__class_Osgn(_1380942, _1380944) = hAPP(c_Groups_Ouminus__class_Ouminus(_1380942), c_Groups_Oone__class_Oone(_1380942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380942), _1380944), c_Groups_Ozero__class_Ozero(_1380942))))], (32741 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380942), _1380944), c_Groups_Ozero__class_Ozero(_1380942))), -(c_Groups_Osgn__class_Osgn(_1380942, _1380944) = hAPP(c_Groups_Ouminus__class_Ouminus(_1380942), c_Groups_Oone__class_Oone(_1380942)))]]], (32747 ^ _779308) ^ [_1381204, _1381206, _1381208, _1381210, _1381212, _1381214] : [c_Equiv__Relations_Oequiv(_1381204, _1381206, _1381208), hBOOL(hAPP(hAPP(c_member(_1381204), _1381210), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1381204, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1381204, _1381204, _1381208), hAPP(hAPP(c_Set_Oinsert(_1381204), _1381212), c_Orderings_Obot__class_Obot(tc_fun(_1381204, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1381204, _1381204, _1381208), hAPP(hAPP(c_Set_Oinsert(_1381204), _1381214), c_Orderings_Obot__class_Obot(tc_fun(_1381204, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1381204, _1381204)), hAPP(hAPP(c_Product__Type_OPair(_1381204, _1381204), _1381212), _1381214)), _1381208)))], (32757 ^ _779308) ^ [_1381505, _1381507, _1381509, _1381511, _1381513] : [c_Equiv__Relations_Oequiv(_1381505, _1381507, _1381509), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1381505, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1381505, _1381505, _1381509), hAPP(hAPP(c_Set_Oinsert(_1381505), _1381511), c_Orderings_Obot__class_Obot(tc_fun(_1381505, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1381505, _1381505, _1381509), hAPP(hAPP(c_Set_Oinsert(_1381505), _1381513), c_Orderings_Obot__class_Obot(tc_fun(_1381505, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1381505), _1381511), _1381507)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1381505, _1381505)), hAPP(hAPP(c_Product__Type_OPair(_1381505, _1381505), _1381513), _1381511)), _1381509)))], (32771 ^ _779308) ^ [_1381858, _1381860, _1381862, _1381864] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1381858, _1381860, _1381862, c_Code__Numeral_OSuc__code__numeral(_1381864)) = hAPP(_1381862, _1381864))], (32773 ^ _779308) ^ [_1381897, _1381899, _1381901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1381897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1381899), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1381899), _1381901))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1381897))), _1381901)))], (32779 ^ _779308) ^ [_1382044, _1382046, _1382048, _1382050] : [class_Groups_Oordered__ab__group__add__abs(_1382044), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382044), hAPP(c_Groups_Oabs__class_Oabs(_1382044), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382046, _1382044), _1382048), _1382050))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382046, _1382044), hAPP(hAPP(c_COMBB(_1382044, _1382044, _1382046), c_Groups_Oabs__class_Oabs(_1382044)), _1382048)), _1382050))))], (32785 ^ _779308) ^ [_1382207, _1382209, _1382211, _1382213] : [class_Groups_Oordered__ab__group__add__abs(_1382207), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1382207), c_Groups_Ozero__class_Ozero(_1382207)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382209, _1382207), hAPP(hAPP(c_COMBB(_1382207, _1382207, _1382209), c_Groups_Oabs__class_Oabs(_1382207)), _1382211)), _1382213))))], (32791 ^ _779308) ^ [_1382346, _1382348, _1382350] : [class_Groups_Oordered__ab__group__add__abs(_1382346), -(hAPP(c_Groups_Oabs__class_Oabs(_1382346), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382346), _1382348), _1382350)) = hAPP(c_Groups_Oabs__class_Oabs(_1382346), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382346), _1382350), _1382348)))], (32797 ^ _779308) ^ [_1382475, _1382477, _1382479, _1382481] : [class_Groups_Oordered__ab__group__add__abs(_1382475), -(hAPP(c_Groups_Oabs__class_Oabs(_1382475), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382477, _1382475), hAPP(hAPP(c_COMBB(_1382475, _1382475, _1382477), c_Groups_Oabs__class_Oabs(_1382475)), _1382479)), _1382481)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1382477, _1382475), hAPP(hAPP(c_COMBB(_1382475, _1382475, _1382477), c_Groups_Oabs__class_Oabs(_1382475)), _1382479)), _1382481))], (32803 ^ _779308) ^ [_1382648, _1382650, _1382652, _1382654] : [class_Fields_Olinordered__field(_1382648), -(hAPP(c_Groups_Oabs__class_Oabs(_1382648), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382650, _1382648), _1382652), _1382654)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382650, _1382648), hAPP(hAPP(c_COMBB(_1382648, _1382648, _1382650), c_Groups_Oabs__class_Oabs(_1382648)), _1382652)), _1382654))], (32809 ^ _779308) ^ [_1382797, _1382799, _1382801] : [class_Fields_Olinordered__field__inverse__zero(_1382797), -(hAPP(c_Groups_Oabs__class_Oabs(_1382797), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382797), _1382799), _1382801)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382797), hAPP(c_Groups_Oabs__class_Oabs(_1382797), _1382799)), hAPP(c_Groups_Oabs__class_Oabs(_1382797), _1382801)))], (32815 ^ _779308) ^ [_1382936] : [class_Rings_Olinordered__idom(_1382936), -(hAPP(c_Groups_Oabs__class_Oabs(_1382936), c_Groups_Oone__class_Oone(_1382936)) = c_Groups_Oone__class_Oone(_1382936))], (32821 ^ _779308) ^ [_1383027, _1383029] : [class_Groups_Oordered__ab__group__add__abs(_1383027), -(hAPP(c_Groups_Oabs__class_Oabs(_1383027), hAPP(c_Groups_Ouminus__class_Ouminus(_1383027), _1383029)) = hAPP(c_Groups_Oabs__class_Oabs(_1383027), _1383029))], (32827 ^ _779308) ^ [_1383132, _1383134] : [class_Groups_Oordered__ab__group__add__abs(_1383132), 32830 ^ _779308 : [(32831 ^ _779308) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1383132), _1383134) = c_Groups_Ozero__class_Ozero(_1383132), -(_1383134 = c_Groups_Ozero__class_Ozero(_1383132))], (32837 ^ _779308) ^ [] : [_1383134 = c_Groups_Ozero__class_Ozero(_1383132), -(hAPP(c_Groups_Oabs__class_Oabs(_1383132), _1383134) = c_Groups_Ozero__class_Ozero(_1383132))]]], (32843 ^ _779308) ^ [_1383364] : [class_Groups_Oordered__ab__group__add__abs(_1383364), -(hAPP(c_Groups_Oabs__class_Oabs(_1383364), c_Groups_Ozero__class_Ozero(_1383364)) = c_Groups_Ozero__class_Ozero(_1383364))], (32849 ^ _779308) ^ [_1383455, _1383457] : [class_Groups_Oordered__ab__group__add__abs(_1383455), -(hAPP(c_Groups_Oabs__class_Oabs(_1383455), hAPP(c_Groups_Oabs__class_Oabs(_1383455), _1383457)) = hAPP(c_Groups_Oabs__class_Oabs(_1383455), _1383457))], (32855 ^ _779308) ^ [_1383560, _1383562] : [class_Rings_Olinordered__idom(_1383560), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383560), hAPP(c_Groups_Oabs__class_Oabs(_1383560), _1383562)), hAPP(c_Groups_Oabs__class_Oabs(_1383560), _1383562)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383560), _1383562), _1383562))], (32861 ^ _779308) ^ [_1383687, _1383689, _1383691] : [class_Rings_Olinordered__idom(_1383687), -(hAPP(c_Groups_Oabs__class_Oabs(_1383687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383687), _1383689), _1383691)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383687), hAPP(c_Groups_Oabs__class_Oabs(_1383687), _1383689)), hAPP(c_Groups_Oabs__class_Oabs(_1383687), _1383691)))], (32867 ^ _779308) ^ [_1383826, _1383828, _1383830] : [class_Groups_Oordered__ab__group__add__abs(_1383826), -(hAPP(c_Groups_Oabs__class_Oabs(_1383826), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1383826), hAPP(c_Groups_Oabs__class_Oabs(_1383826), _1383828)), hAPP(c_Groups_Oabs__class_Oabs(_1383826), _1383830))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1383826), hAPP(c_Groups_Oabs__class_Oabs(_1383826), _1383828)), hAPP(c_Groups_Oabs__class_Oabs(_1383826), _1383830)))], (32873 ^ _779308) ^ [_1383985, _1383987, _1383989] : [class_Rings_Olinordered__idom(_1383985), -(hAPP(c_Groups_Oabs__class_Oabs(_1383985), hAPP(hAPP(c_Power_Opower__class_Opower(_1383985), _1383987), _1383989)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1383985), hAPP(c_Groups_Oabs__class_Oabs(_1383985), _1383987)), _1383989))], (32879 ^ _779308) ^ [_1384114, _1384116] : [class_Rings_Olinordered__idom(_1384114), -(hAPP(c_Groups_Oabs__class_Oabs(_1384114), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1384114), _1384116)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1384114), _1384116))], (32885 ^ _779308) ^ [_1384219] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1384219)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1384219))], (32887 ^ _779308) ^ [_1384251, _1384253, _1384255] : [class_Groups_Oordered__ab__group__add__abs(_1384251), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384251), hAPP(c_Groups_Oabs__class_Oabs(_1384251), _1384253)), _1384255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384251), _1384253), _1384255)))], (32897 ^ _779308) ^ [_1384420, _1384422] : [class_Groups_Oordered__ab__group__add__abs(_1384420), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384420), _1384422), hAPP(c_Groups_Oabs__class_Oabs(_1384420), _1384422))))], (32903 ^ _779308) ^ [_1384519, _1384521] : [class_Groups_Oordered__ab__group__add__abs(_1384519), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384519), c_Groups_Ozero__class_Ozero(_1384519)), hAPP(c_Groups_Oabs__class_Oabs(_1384519), _1384521))))], (32909 ^ _779308) ^ [_1384622, _1384624] : [class_Groups_Oordered__ab__group__add__abs(_1384622), 32912 ^ _779308 : [(32913 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384622), hAPP(c_Groups_Oabs__class_Oabs(_1384622), _1384624)), c_Groups_Ozero__class_Ozero(_1384622))), -(_1384624 = c_Groups_Ozero__class_Ozero(_1384622))], (32919 ^ _779308) ^ [] : [_1384624 = c_Groups_Ozero__class_Ozero(_1384622), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384622), hAPP(c_Groups_Oabs__class_Oabs(_1384622), _1384624)), c_Groups_Ozero__class_Ozero(_1384622))))]]], (32925 ^ _779308) ^ [_1384875, _1384877] : [class_Groups_Oordered__ab__group__add__abs(_1384875), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384875), c_Groups_Ozero__class_Ozero(_1384875)), _1384877)), -(hAPP(c_Groups_Oabs__class_Oabs(_1384875), _1384877) = _1384877)], (32935 ^ _779308) ^ [_1385030, _1385032] : [class_Groups_Oordered__ab__group__add__abs(_1385030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385030), c_Groups_Ozero__class_Ozero(_1385030)), _1385032)), -(hAPP(c_Groups_Oabs__class_Oabs(_1385030), _1385032) = _1385032)], (32945 ^ _779308) ^ [_1385185, _1385187] : [class_Groups_Oordered__ab__group__add__abs(_1385185), 32948 ^ _779308 : [(32949 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385185), c_Groups_Ozero__class_Ozero(_1385185)), hAPP(c_Groups_Oabs__class_Oabs(_1385185), _1385187))), _1385187 = c_Groups_Ozero__class_Ozero(_1385185)], (32955 ^ _779308) ^ [] : [-(_1385187 = c_Groups_Ozero__class_Ozero(_1385185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385185), c_Groups_Ozero__class_Ozero(_1385185)), hAPP(c_Groups_Oabs__class_Oabs(_1385185), _1385187))))]]], (32961 ^ _779308) ^ [_1385400, _1385402] : [class_Groups_Oordered__ab__group__add__abs(_1385400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385400), hAPP(c_Groups_Oabs__class_Oabs(_1385400), _1385402)), c_Groups_Ozero__class_Ozero(_1385400)))], (32967 ^ _779308) ^ [_1385504, _1385506, _1385508] : [class_Groups_Oordered__ab__group__add__abs(_1385504), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385504), hAPP(c_Groups_Oabs__class_Oabs(_1385504), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385504), _1385506), _1385508))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385504), hAPP(c_Groups_Oabs__class_Oabs(_1385504), _1385506)), hAPP(c_Groups_Oabs__class_Oabs(_1385504), _1385508)))))], (32973 ^ _779308) ^ [_1385657, _1385659, _1385661, _1385663, _1385665] : [class_Rings_Olinordered__idom(_1385657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385657), hAPP(c_Groups_Oabs__class_Oabs(_1385657), _1385659)), _1385661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385657), hAPP(c_Groups_Oabs__class_Oabs(_1385657), _1385663)), _1385665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385657), hAPP(c_Groups_Oabs__class_Oabs(_1385657), _1385659)), hAPP(c_Groups_Oabs__class_Oabs(_1385657), _1385663))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385657), _1385661), _1385665))))], (32987 ^ _779308) ^ [_1385968, _1385970, _1385972] : [class_Groups_Oordered__ab__group__add__abs(_1385968), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385968), hAPP(c_Groups_Oabs__class_Oabs(_1385968), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1385968), hAPP(c_Groups_Oabs__class_Oabs(_1385968), _1385970)), hAPP(c_Groups_Oabs__class_Oabs(_1385968), _1385972)))), hAPP(c_Groups_Oabs__class_Oabs(_1385968), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1385968), _1385970), _1385972)))))], (32993 ^ _779308) ^ [_1386131, _1386133, _1386135] : [class_Groups_Oordered__ab__group__add__abs(_1386131), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386131), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1386131), hAPP(c_Groups_Oabs__class_Oabs(_1386131), _1386133)), hAPP(c_Groups_Oabs__class_Oabs(_1386131), _1386135))), hAPP(c_Groups_Oabs__class_Oabs(_1386131), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1386131), _1386133), _1386135)))))], (32999 ^ _779308) ^ [_1386284, _1386286, _1386288] : [class_Groups_Oordered__ab__group__add__abs(_1386284), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386284), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1386284), hAPP(c_Groups_Oabs__class_Oabs(_1386284), _1386286)), hAPP(c_Groups_Oabs__class_Oabs(_1386284), _1386288))), hAPP(c_Groups_Oabs__class_Oabs(_1386284), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1386284), _1386288), _1386286)))))], (33005 ^ _779308) ^ [_1386437, _1386439] : [class_Groups_Oordered__ab__group__add__abs(_1386437), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386437), hAPP(c_Groups_Ouminus__class_Ouminus(_1386437), _1386439)), hAPP(c_Groups_Oabs__class_Oabs(_1386437), _1386439))))], (33011 ^ _779308) ^ [_1386546, _1386548, _1386550] : [class_Groups_Oordered__ab__group__add__abs(_1386546), 33014 ^ _779308 : [(33015 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386546), hAPP(c_Groups_Oabs__class_Oabs(_1386546), _1386548)), _1386550)), 33018 ^ _779308 : [(33019 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386546), _1386548), _1386550)))], (33021 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386546), hAPP(c_Groups_Ouminus__class_Ouminus(_1386546), _1386548)), _1386550)))]]], (33023 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386546), hAPP(c_Groups_Oabs__class_Oabs(_1386546), _1386548)), _1386550))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386546), _1386548), _1386550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386546), hAPP(c_Groups_Ouminus__class_Ouminus(_1386546), _1386548)), _1386550))]]], (33033 ^ _779308) ^ [_1386924, _1386926, _1386928] : [class_Groups_Oordered__ab__group__add__abs(_1386924), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386924), _1386926), _1386928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386924), hAPP(c_Groups_Ouminus__class_Ouminus(_1386924), _1386926)), _1386928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386924), hAPP(c_Groups_Oabs__class_Oabs(_1386924), _1386926)), _1386928)))], (33047 ^ _779308) ^ [_1387171, _1387173, _1387175] : [class_Groups_Oordered__ab__group__add__abs(_1387171), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387171), hAPP(c_Groups_Oabs__class_Oabs(_1387171), _1387173)), _1387175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387171), hAPP(c_Groups_Ouminus__class_Ouminus(_1387171), _1387173)), _1387175)))], (33057 ^ _779308) ^ [_1387350, _1387352, _1387354] : [class_Rings_Olinordered__idom(_1387350), 33060 ^ _779308 : [(33061 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387350), hAPP(c_Groups_Oabs__class_Oabs(_1387350), _1387352)), _1387354)), 33064 ^ _779308 : [(33065 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387350), _1387352), _1387354)))], (33067 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387350), hAPP(c_Groups_Ouminus__class_Ouminus(_1387350), _1387352)), _1387354)))]]], (33069 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387350), hAPP(c_Groups_Oabs__class_Oabs(_1387350), _1387352)), _1387354))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387350), _1387352), _1387354)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387350), hAPP(c_Groups_Ouminus__class_Ouminus(_1387350), _1387352)), _1387354))]]], (33079 ^ _779308) ^ [_1387728, _1387730, _1387732] : [class_Fields_Olinordered__field(_1387728), -(_1387730 = c_Groups_Ozero__class_Ozero(_1387728)), -(hAPP(c_Groups_Oabs__class_Oabs(_1387728), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387728), _1387732), _1387730)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387728), hAPP(c_Groups_Oabs__class_Oabs(_1387728), _1387732)), hAPP(c_Groups_Oabs__class_Oabs(_1387728), _1387730)))], (33089 ^ _779308) ^ [_1387886, _1387888, _1387890] : [class_Rings_Olinordered__idom(_1387886), -(hAPP(c_Groups_Oabs__class_Oabs(_1387886), hAPP(hAPP(c_Power_Opower__class_Opower(_1387886), hAPP(c_Groups_Ouminus__class_Ouminus(_1387886), _1387888)), _1387890)) = hAPP(c_Groups_Oabs__class_Oabs(_1387886), hAPP(hAPP(c_Power_Opower__class_Opower(_1387886), _1387888), _1387890)))], (33095 ^ _779308) ^ [_1388025, _1388027] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1388025), _1388027)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1388025) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (33101 ^ _779308) ^ [_1388126, _1388128] : [class_Rings_Olinordered__idom(_1388126), -(hAPP(c_Groups_Oabs__class_Oabs(_1388126), _1388128) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388126), _1388128), c_Groups_Osgn__class_Osgn(_1388126, _1388128)))], (33107 ^ _779308) ^ [_1388233, _1388235] : [class_Rings_Olinordered__idom(_1388233), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388233), c_Groups_Osgn__class_Osgn(_1388233, _1388235)), hAPP(c_Groups_Oabs__class_Oabs(_1388233), _1388235)) = _1388235)], (33113 ^ _779308) ^ [_1388340, _1388342, _1388344] : [class_Rings_Olinordered__idom(_1388340), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388340), c_Groups_Ozero__class_Ozero(_1388340)), _1388342)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388340), hAPP(c_Groups_Oabs__class_Oabs(_1388340), _1388344)), _1388342) = hAPP(c_Groups_Oabs__class_Oabs(_1388340), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388340), _1388344), _1388342)))], (33123 ^ _779308) ^ [_1388541, _1388543, _1388545] : [class_Rings_Oordered__ring__abs(_1388541), -(hAPP(c_Groups_Oabs__class_Oabs(_1388541), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388541), _1388543), _1388545)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388541), hAPP(c_Groups_Oabs__class_Oabs(_1388541), _1388543)), hAPP(c_Groups_Oabs__class_Oabs(_1388541), _1388545))), 33130 ^ _779308 : [(33131 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388541), c_Groups_Ozero__class_Ozero(_1388541)), _1388543))], (33133 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388541), _1388543), c_Groups_Ozero__class_Ozero(_1388541)))]], 33134 ^ _779308 : [(33135 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388541), c_Groups_Ozero__class_Ozero(_1388541)), _1388545))], (33137 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388541), _1388545), c_Groups_Ozero__class_Ozero(_1388541)))]]], (33141 ^ _779308) ^ [_1388936, _1388938, _1388940] : [class_Groups_Oordered__ab__group__add__abs(_1388936), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388936), hAPP(c_Groups_Oabs__class_Oabs(_1388936), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388936), _1388938), _1388940))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1388936), hAPP(c_Groups_Oabs__class_Oabs(_1388936), _1388938)), hAPP(c_Groups_Oabs__class_Oabs(_1388936), _1388940)))))], (33147 ^ _779308) ^ [_1389089, _1389091, _1389093, _1389095, _1389097] : [class_Groups_Oordered__ab__group__add__abs(_1389089), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389089), hAPP(c_Groups_Oabs__class_Oabs(_1389089), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1389089), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389089), _1389091), _1389093)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389089), _1389095), _1389097)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389089), hAPP(c_Groups_Oabs__class_Oabs(_1389089), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1389089), _1389091), _1389095))), hAPP(c_Groups_Oabs__class_Oabs(_1389089), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1389089), _1389093), _1389097))))))], (33153 ^ _779308) ^ [_1389310, _1389312] : [class_Groups_Oordered__ab__group__add__abs(_1389310), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389310), hAPP(c_Groups_Ouminus__class_Ouminus(_1389310), hAPP(c_Groups_Oabs__class_Oabs(_1389310), _1389312))), c_Groups_Ozero__class_Ozero(_1389310))))], (33159 ^ _779308) ^ [_1389423, _1389425] : [class_Groups_Oordered__ab__group__add__abs(_1389423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389423), _1389425), c_Groups_Ozero__class_Ozero(_1389423))), -(hAPP(c_Groups_Oabs__class_Oabs(_1389423), _1389425) = hAPP(c_Groups_Ouminus__class_Ouminus(_1389423), _1389425))], (33169 ^ _779308) ^ [_1389588, _1389590] : [class_Groups_Oordered__ab__group__add__abs(_1389588), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389588), _1389590), c_Groups_Ozero__class_Ozero(_1389588))), -(hAPP(c_Groups_Oabs__class_Oabs(_1389588), _1389590) = hAPP(c_Groups_Ouminus__class_Ouminus(_1389588), _1389590))], (33179 ^ _779308) ^ [_1389753, _1389755] : [class_Groups_Oabs__if(_1389753), 33182 ^ _779308 : [(33183 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389753), _1389755), c_Groups_Ozero__class_Ozero(_1389753))), -(hAPP(c_Groups_Oabs__class_Oabs(_1389753), _1389755) = hAPP(c_Groups_Ouminus__class_Ouminus(_1389753), _1389755))], (33189 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389753), _1389755), c_Groups_Ozero__class_Ozero(_1389753)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1389753), _1389755) = _1389755)]]], (33195 ^ _779308) ^ [_1389993, _1389995, _1389997] : [class_Rings_Olinordered__idom(_1389993), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389993), c_Groups_Ozero__class_Ozero(_1389993)), hAPP(hAPP(c_Power_Opower__class_Opower(_1389993), hAPP(c_Groups_Oabs__class_Oabs(_1389993), _1389995)), _1389997))))], (33201 ^ _779308) ^ [_1390114, _1390116, _1390118] : [class_Fields_Olinordered__field__inverse__zero(_1390114), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390114), c_Groups_Ozero__class_Ozero(_1390114)), _1390116)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1390114), hAPP(c_Groups_Oabs__class_Oabs(_1390114), _1390118)), _1390116) = hAPP(c_Groups_Oabs__class_Oabs(_1390114), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1390114), _1390118), _1390116)))], (33211 ^ _779308) ^ [_1390315] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1390315), hAPP(c_Int_Onumber__class_Onumber__of(_1390315), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1390315)), class_Int_Onumber__ring(_1390315), class_Rings_Olinordered__idom(_1390315)], (33221 ^ _779308) ^ [_1390472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1390472)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1390472 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33227 ^ _779308) ^ [_1390559] : [_1390559 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1390559)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (33233 ^ _779308) ^ [_1390658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1390658), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1390658) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1390658))], (33239 ^ _779308) ^ [_1390749] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1390749), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1390749) = _1390749)], (33245 ^ _779308) ^ [_1390793, _1390795] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390793), _1390795))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1390793))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1390795))))], (33247 ^ _779308) ^ [_1390848, _1390850] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1390848)), _1390850))))], (33249 ^ _779308) ^ [_1390884, _1390886, _1390888, _1390890] : [c_Equiv__Relations_Oequiv(_1390884, _1390886, _1390888), hBOOL(hAPP(hAPP(c_member(_1390884), _1390890), _1390886)), -(hBOOL(hAPP(hAPP(c_member(_1390884), _1390890), hAPP(c_Relation_OImage(_1390884, _1390884, _1390888), hAPP(hAPP(c_Set_Oinsert(_1390884), _1390890), c_Orderings_Obot__class_Obot(tc_fun(_1390884, tc_HOL_Obool)))))))], (33259 ^ _779308) ^ [_1391091, _1391093] : [class_Int_Onumber__ring(_1391091), class_Rings_Olinordered__idom(_1391091), 33266 ^ _779308 : [(33267 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391091), hAPP(c_Int_Onumber__class_Onumber__of(_1391091), _1391093)), c_Groups_Ozero__class_Ozero(_1391091))), -(hAPP(c_Groups_Oabs__class_Oabs(_1391091), hAPP(c_Int_Onumber__class_Onumber__of(_1391091), _1391093)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1391091), hAPP(c_Int_Onumber__class_Onumber__of(_1391091), _1391093)))], (33273 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391091), hAPP(c_Int_Onumber__class_Onumber__of(_1391091), _1391093)), c_Groups_Ozero__class_Ozero(_1391091)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1391091), hAPP(c_Int_Onumber__class_Onumber__of(_1391091), _1391093)) = hAPP(c_Int_Onumber__class_Onumber__of(_1391091), _1391093))]]], (33279 ^ _779308) ^ [_1391443, _1391445] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1391443), hAPP(hAPP(c_Power_Opower__class_Opower(_1391443), hAPP(c_Int_Onumber__class_Onumber__of(_1391443), c_Int_OMin)), _1391445)) = c_Groups_Oone__class_Oone(_1391443)), class_Int_Onumber__ring(_1391443), class_Rings_Olinordered__idom(_1391443)], (33299 ^ _779308) ^ [_1391772, _1391774] : [33300 ^ _779308 : [(33301 ^ _779308) ^ [] : [-(_1391772 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33303 ^ _779308) ^ [] : [_1391774 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1391772)), _1391774))))], (33289 ^ _779308) ^ [_1391623, _1391625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1391623)), _1391625))), _1391623 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1391625 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33307 ^ _779308) ^ [_1391908, _1391910, _1391912, _1391914, _1391916] : [c_Equiv__Relations_Oequiv(_1391908, _1391910, _1391912), hBOOL(hAPP(hAPP(c_member(tc_prod(_1391908, _1391908)), hAPP(hAPP(c_Product__Type_OPair(_1391908, _1391908), _1391914), _1391916)), _1391912)), -(hAPP(c_Relation_OImage(_1391908, _1391908, _1391912), hAPP(hAPP(c_Set_Oinsert(_1391908), _1391914), c_Orderings_Obot__class_Obot(tc_fun(_1391908, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1391908, _1391908, _1391912), hAPP(hAPP(c_Set_Oinsert(_1391908), _1391916), c_Orderings_Obot__class_Obot(tc_fun(_1391908, tc_HOL_Obool)))))], (33317 ^ _779308) ^ [_1392169, _1392171] : [class_Rings_Olinordered__idom(_1392169), -(hAPP(c_Groups_Oabs__class_Oabs(_1392169), hAPP(hAPP(c_Power_Opower__class_Opower(_1392169), _1392171), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(_1392169), _1392171), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (33323 ^ _779308) ^ [_1392286, _1392288] : [class_Rings_Olinordered__idom(_1392286), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1392286), hAPP(c_Groups_Oabs__class_Oabs(_1392286), _1392288)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_1392286), _1392288), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (33329 ^ _779308) ^ [_1392403, _1392405, _1392407, _1392409, _1392411] : [c_Equiv__Relations_Oequiv(_1392403, _1392405, _1392407), 33332 ^ _779308 : [(33333 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1392403, _1392403)), hAPP(hAPP(c_Product__Type_OPair(_1392403, _1392403), _1392409), _1392411)), _1392407)), 33336 ^ _779308 : [(33337 ^ _779308) ^ [] : [-(hAPP(c_Relation_OImage(_1392403, _1392403, _1392407), hAPP(hAPP(c_Set_Oinsert(_1392403), _1392409), c_Orderings_Obot__class_Obot(tc_fun(_1392403, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1392403, _1392403, _1392407), hAPP(hAPP(c_Set_Oinsert(_1392403), _1392411), c_Orderings_Obot__class_Obot(tc_fun(_1392403, tc_HOL_Obool)))))], (33339 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1392403), _1392409), _1392405)))], (33341 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1392403), _1392411), _1392405)))]]], (33343 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1392403, _1392403)), hAPP(hAPP(c_Product__Type_OPair(_1392403, _1392403), _1392409), _1392411)), _1392407))), hAPP(c_Relation_OImage(_1392403, _1392403, _1392407), hAPP(hAPP(c_Set_Oinsert(_1392403), _1392409), c_Orderings_Obot__class_Obot(tc_fun(_1392403, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1392403, _1392403, _1392407), hAPP(hAPP(c_Set_Oinsert(_1392403), _1392411), c_Orderings_Obot__class_Obot(tc_fun(_1392403, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1392403), _1392409), _1392405)), hBOOL(hAPP(hAPP(c_member(_1392403), _1392411), _1392405))]]], (33357 ^ _779308) ^ [_1393003, _1393005, _1393007, _1393009, _1393011] : [hAPP(c_Relation_OImage(_1393003, _1393003, _1393005), hAPP(hAPP(c_Set_Oinsert(_1393003), _1393007), c_Orderings_Obot__class_Obot(tc_fun(_1393003, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1393003, _1393003, _1393005), hAPP(hAPP(c_Set_Oinsert(_1393003), _1393009), c_Orderings_Obot__class_Obot(tc_fun(_1393003, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1393003, _1393011, _1393005), hBOOL(hAPP(hAPP(c_member(_1393003), _1393009), _1393011)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1393003, _1393003)), hAPP(hAPP(c_Product__Type_OPair(_1393003, _1393003), _1393007), _1393009)), _1393005)))], (33371 ^ _779308) ^ [_1393336, _1393338, _1393340, _1393342, _1393344] : [c_Equiv__Relations_Oequiv(_1393336, _1393338, _1393340), hBOOL(hAPP(hAPP(c_member(_1393336), _1393342), _1393338)), hBOOL(hAPP(hAPP(c_member(_1393336), _1393344), _1393338)), 33382 ^ _779308 : [(33383 ^ _779308) ^ [] : [hAPP(c_Relation_OImage(_1393336, _1393336, _1393340), hAPP(hAPP(c_Set_Oinsert(_1393336), _1393342), c_Orderings_Obot__class_Obot(tc_fun(_1393336, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1393336, _1393336, _1393340), hAPP(hAPP(c_Set_Oinsert(_1393336), _1393344), c_Orderings_Obot__class_Obot(tc_fun(_1393336, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1393336, _1393336)), hAPP(hAPP(c_Product__Type_OPair(_1393336, _1393336), _1393342), _1393344)), _1393340)))], (33389 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1393336, _1393336)), hAPP(hAPP(c_Product__Type_OPair(_1393336, _1393336), _1393342), _1393344)), _1393340)), -(hAPP(c_Relation_OImage(_1393336, _1393336, _1393340), hAPP(hAPP(c_Set_Oinsert(_1393336), _1393342), c_Orderings_Obot__class_Obot(tc_fun(_1393336, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1393336, _1393336, _1393340), hAPP(hAPP(c_Set_Oinsert(_1393336), _1393344), c_Orderings_Obot__class_Obot(tc_fun(_1393336, tc_HOL_Obool)))))]]], (33395 ^ _779308) ^ [_1393884, _1393886, _1393888, _1393890, _1393892] : [c_Equiv__Relations_Oequiv(_1393884, _1393886, _1393888), hBOOL(hAPP(hAPP(c_member(tc_prod(_1393884, _1393884)), hAPP(hAPP(c_Product__Type_OPair(_1393884, _1393884), _1393890), _1393892)), _1393888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1393884, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1393884, _1393884, _1393888), hAPP(hAPP(c_Set_Oinsert(_1393884), _1393890), c_Orderings_Obot__class_Obot(tc_fun(_1393884, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1393884, _1393884, _1393888), hAPP(hAPP(c_Set_Oinsert(_1393884), _1393892), c_Orderings_Obot__class_Obot(tc_fun(_1393884, tc_HOL_Obool)))))))], (33405 ^ _779308) ^ [_1394165, _1394167, _1394169] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1394165, _1394167, _1394169, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1394167)], (33407 ^ _779308) ^ [_1394197, _1394199, _1394201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1394197)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394199), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1394201), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1394201), _1394199))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1394197)))))], (33413 ^ _779308) ^ [_1394353, _1394355] : [_1394353 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1394353, _1394355) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33419 ^ _779308) ^ [_1394431, _1394433] : [-(_1394431 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 33422 ^ _779308 : [(33423 ^ _779308) ^ [] : [_1394433 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1394431, _1394433) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1394431))], (33429 ^ _779308) ^ [] : [-(_1394433 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1394431, _1394433) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1394433))), hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_fdisj, hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1394433)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1394431))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394433), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394431), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1394431, _1394433)), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_fun(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), hAPP(c_COMBC(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_If(tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), c_fequal), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBB(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint)), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1394433))))), c_Divides_Opdivmod(_1394431, _1394433)))))]]], (33435 ^ _779308) ^ [_1394791, _1394793] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1394791), _1394793) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nitpick_Onat__gcd(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1394791)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1394793)))))], (33437 ^ _779308) ^ [_1394849, _1394851] : [_1394849 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1394849, _1394851) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33443 ^ _779308) ^ [_1394927, _1394929] : [-(_1394927 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 33446 ^ _779308 : [(33447 ^ _779308) ^ [] : [_1394929 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1394927, _1394929) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1394927))], (33453 ^ _779308) ^ [] : [-(_1394929 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1394927, _1394929) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1394929))), hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_fequal, c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1394927)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1394929))), c_Divides_Opdivmod(_1394927, _1394929)), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_fun(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBS(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), hAPP(c_COMBC(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_If(tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), c_fequal), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_fun(tc_fun(tc_Int_Oint, tc_Int_Oint), tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint))), tc_Int_Oint), c_COMBB(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), tc_Int_Oint), c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint)), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1394929))))), c_Divides_Opdivmod(_1394927, _1394929)))))]]], (33459 ^ _779308) ^ [_1395248, _1395250] : [_1395248 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1395250, _1395248) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1395250)))], (33465 ^ _779308) ^ [_1395337, _1395339] : [-(_1395337 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1395339, _1395337) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1395339), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1395337)))], (33471 ^ _779308) ^ [_1395387, _1395389, _1395391, _1395393, _1395395, _1395397] : [-(hAPP(c_Product__Type_Oapsnd(_1395387, _1395389, _1395391, _1395393), hAPP(hAPP(c_Product__Type_OPair(_1395391, _1395387), _1395395), _1395397)) = hAPP(hAPP(c_Product__Type_OPair(_1395391, _1395389), _1395395), hAPP(_1395393, _1395397)))], (33473 ^ _779308) ^ [_1395449, _1395451, _1395453, _1395455, _1395457] : [-(hAPP(c_Product__Type_Ofst(_1395449, _1395451), hAPP(c_Product__Type_Oapsnd(_1395453, _1395451, _1395449, _1395455), _1395457)) = hAPP(c_Product__Type_Ofst(_1395449, _1395453), _1395457))], (33475 ^ _779308) ^ [_1395527, _1395529, _1395531, _1395533, _1395535, _1395537] : [hAPP(c_Product__Type_Oapsnd(_1395527, _1395529, _1395531, _1395533), _1395535) = hAPP(c_Product__Type_Oapsnd(_1395527, _1395529, _1395531, _1395537), _1395535), -(hAPP(_1395533, hAPP(c_Product__Type_Osnd(_1395531, _1395527), _1395535)) = hAPP(_1395537, hAPP(c_Product__Type_Osnd(_1395531, _1395527), _1395535)))], (33481 ^ _779308) ^ [_1395676, _1395678, _1395680, _1395682, _1395684, _1395686] : [hAPP(_1395682, hAPP(c_Product__Type_Osnd(_1395680, _1395676), _1395684)) = hAPP(_1395686, hAPP(c_Product__Type_Osnd(_1395680, _1395676), _1395684)), -(hAPP(c_Product__Type_Oapsnd(_1395676, _1395678, _1395680, _1395682), _1395684) = hAPP(c_Product__Type_Oapsnd(_1395676, _1395678, _1395680, _1395686), _1395684))], (33487 ^ _779308) ^ [_1395831, _1395833, _1395835, _1395837, _1395839] : [-(hAPP(c_Product__Type_Osnd(_1395831, _1395833), hAPP(c_Product__Type_Oapsnd(_1395835, _1395833, _1395831, _1395837), _1395839)) = hAPP(_1395837, hAPP(c_Product__Type_Osnd(_1395831, _1395835), _1395839)))], (33489 ^ _779308) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (33491 ^ _779308) ^ [_1395912, _1395914] : [_1395912 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1395914, _1395912) = _1395914)], (33497 ^ _779308) ^ [_1395989, _1395991] : [-(_1395989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1395991, _1395989) = c_Nitpick_Onat__gcd(_1395989, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1395991, _1395989)))], (33503 ^ _779308) ^ [_1396037, _1396039] : [-(c_Divides_Opdivmod(_1396037, _1396039) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1396037)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1396039))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1396037), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1396039))))], (33505 ^ _779308) ^ [_1396093, _1396095] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Nitpick_Onat__gcd__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1396093), _1396095))), 33508 ^ _779308 : [(33509 ^ _779308) ^ [] : [_1396095 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1396093, _1396095) = _1396093)], (33515 ^ _779308) ^ [] : [-(_1396095 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1396093, _1396095) = c_Nitpick_Onat__gcd(_1396095, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1396093, _1396095)))]]], (33521 ^ _779308) ^ [_1396311, _1396313] : [-(c_Nitpick_Onat__lcm(_1396311, _1396313) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1396311), _1396313)), c_Nitpick_Onat__gcd(_1396311, _1396313)))], (33523 ^ _779308) ^ [_1396354, _1396356, _1396358] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1396354), _1396356)), c_Fun_Oinj__on(_1396354, tc_fun(tc_fun(_1396354, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1396354, tc_fun(tc_prod(_1396354, _1396354), tc_HOL_Obool), tc_fun(tc_fun(_1396354, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1396354, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1396354, _1396354), tc_HOL_Obool), tc_fun(tc_fun(_1396354, tc_HOL_Obool), tc_HOL_Obool)), _1396354), c_Equiv__Relations_Oquotient(_1396354)), hAPP(hAPP(c_COMBC(_1396354, tc_fun(_1396354, tc_HOL_Obool), tc_fun(_1396354, tc_HOL_Obool)), c_Set_Oinsert(_1396354)), c_Orderings_Obot__class_Obot(tc_fun(_1396354, tc_HOL_Obool))))), _1396358), _1396356), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1396354, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1396354), _1396356), _1396358)) = hAPP(c_Finite__Set_Ocard(_1396354), _1396356))], (33533 ^ _779308) ^ [_1396703, _1396705, _1396707, _1396709, _1396711] : [c_Equiv__Relations_Oequiv(_1396703, _1396705, _1396707), hBOOL(hAPP(hAPP(c_member(_1396703), _1396709), _1396705)), hBOOL(hAPP(hAPP(c_member(_1396703), _1396711), _1396705)), 33544 ^ _779308 : [(33545 ^ _779308) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1396703), hAPP(hAPP(c_Set_Oinsert(_1396703), _1396709), c_Orderings_Obot__class_Obot(tc_fun(_1396703, tc_HOL_Obool)))), _1396707) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1396703), hAPP(hAPP(c_Set_Oinsert(_1396703), _1396711), c_Orderings_Obot__class_Obot(tc_fun(_1396703, tc_HOL_Obool)))), _1396707), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1396703, _1396703)), hAPP(hAPP(c_Product__Type_OPair(_1396703, _1396703), _1396709), _1396711)), _1396707)))], (33551 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1396703, _1396703)), hAPP(hAPP(c_Product__Type_OPair(_1396703, _1396703), _1396709), _1396711)), _1396707)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1396703), hAPP(hAPP(c_Set_Oinsert(_1396703), _1396709), c_Orderings_Obot__class_Obot(tc_fun(_1396703, tc_HOL_Obool)))), _1396707) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1396703), hAPP(hAPP(c_Set_Oinsert(_1396703), _1396711), c_Orderings_Obot__class_Obot(tc_fun(_1396703, tc_HOL_Obool)))), _1396707))]]], (33557 ^ _779308) ^ [_1397275, _1397277, _1397279] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397275), _1397277), _1397279) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1397275, tc_HOL_Obool), tc_HOL_Obool)), -(_1397277 = c_Orderings_Obot__class_Obot(tc_fun(_1397275, tc_HOL_Obool)))], (33563 ^ _779308) ^ [_1397392, _1397394, _1397396] : [_1397394 = c_Orderings_Obot__class_Obot(tc_fun(_1397392, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397392), _1397394), _1397396) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1397392, tc_HOL_Obool), tc_HOL_Obool)))], (33569 ^ _779308) ^ [_1397533, _1397535, _1397537] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1397533, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397533), _1397535), _1397537), -(_1397535 = c_Orderings_Obot__class_Obot(tc_fun(_1397533, tc_HOL_Obool)))], (33575 ^ _779308) ^ [_1397650, _1397652, _1397654] : [_1397652 = c_Orderings_Obot__class_Obot(tc_fun(_1397650, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1397650, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397650), _1397652), _1397654))], (33581 ^ _779308) ^ [_1397773, _1397775] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397773), c_Orderings_Obot__class_Obot(tc_fun(_1397773, tc_HOL_Obool))), _1397775) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1397773, tc_HOL_Obool), tc_HOL_Obool)))], (33583 ^ _779308) ^ [_1397819, _1397821, _1397823, _1397825, _1397827] : [c_Equiv__Relations_Oequiv(_1397819, _1397821, _1397823), hBOOL(hAPP(hAPP(c_member(tc_fun(_1397819, tc_HOL_Obool)), _1397825), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397819), _1397821), _1397823))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1397819, tc_HOL_Obool)), _1397827), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1397819), _1397821), _1397823))), -(_1397825 = _1397827), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397819, tc_HOL_Obool)), _1397825), _1397827) = c_Orderings_Obot__class_Obot(tc_fun(_1397819, tc_HOL_Obool)))], (33601 ^ _779308) ^ [_1398137, _1398139, _1398141, _1398143] : [c_Fun_Oinj__on(_1398137, tc_fun(tc_fun(_1398137, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1398137, tc_fun(tc_prod(_1398137, _1398137), tc_HOL_Obool), tc_fun(tc_fun(_1398137, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1398137, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1398137, _1398137), tc_HOL_Obool), tc_fun(tc_fun(_1398137, tc_HOL_Obool), tc_HOL_Obool)), _1398137), c_Equiv__Relations_Oquotient(_1398137)), hAPP(hAPP(c_COMBC(_1398137, tc_fun(_1398137, tc_HOL_Obool), tc_fun(_1398137, tc_HOL_Obool)), c_Set_Oinsert(_1398137)), c_Orderings_Obot__class_Obot(tc_fun(_1398137, tc_HOL_Obool))))), _1398139), _1398141), hBOOL(hAPP(hAPP(c_member(_1398137), _1398143), _1398141)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398137), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1398137, tc_HOL_Obool)), _1398141), hAPP(hAPP(c_Set_Oinsert(_1398137), _1398143), c_Orderings_Obot__class_Obot(tc_fun(_1398137, tc_HOL_Obool))))), _1398139) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1398137, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398137), _1398141), _1398139)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398137), hAPP(hAPP(c_Set_Oinsert(_1398137), _1398143), c_Orderings_Obot__class_Obot(tc_fun(_1398137, tc_HOL_Obool)))), _1398139)))], (33611 ^ _779308) ^ [_1398604, _1398606, _1398608, _1398610] : [hBOOL(hAPP(hAPP(c_member(_1398604), _1398606), _1398608)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1398604, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1398604, _1398604, _1398610), hAPP(hAPP(c_Set_Oinsert(_1398604), _1398606), c_Orderings_Obot__class_Obot(tc_fun(_1398604, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398604), _1398608), _1398610))))], (33617 ^ _779308) ^ [_1398775, _1398777, _1398779, _1398781, _1398783, _1398785, _1398787] : [c_Equiv__Relations_Oequiv(_1398775, _1398777, _1398779), hBOOL(hAPP(hAPP(c_member(tc_fun(_1398775, tc_HOL_Obool)), _1398781), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398775), _1398777), _1398779))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1398775, tc_HOL_Obool)), _1398783), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398775), _1398777), _1398779))), hBOOL(hAPP(hAPP(c_member(_1398775), _1398785), _1398781)), hBOOL(hAPP(hAPP(c_member(_1398775), _1398787), _1398783)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1398775, _1398775)), hAPP(hAPP(c_Product__Type_OPair(_1398775, _1398775), _1398785), _1398787)), _1398779)), -(_1398781 = _1398783)], (33643 ^ _779308) ^ [_1399312, _1399314, _1399316, _1399318, _1399320, _1399322, _1399324] : [c_Equiv__Relations_Oequiv(_1399312, _1399314, _1399316), hBOOL(hAPP(hAPP(c_member(tc_fun(_1399312, tc_HOL_Obool)), _1399318), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399312), _1399314), _1399316))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1399312, tc_HOL_Obool)), _1399320), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399312), _1399314), _1399316))), hBOOL(hAPP(hAPP(c_member(_1399312), _1399322), _1399318)), hBOOL(hAPP(hAPP(c_member(_1399312), _1399324), _1399320)), 33662 ^ _779308 : [(33663 ^ _779308) ^ [] : [_1399318 = _1399320, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1399312, _1399312)), hAPP(hAPP(c_Product__Type_OPair(_1399312, _1399312), _1399322), _1399324)), _1399316)))], (33669 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1399312, _1399312)), hAPP(hAPP(c_Product__Type_OPair(_1399312, _1399312), _1399322), _1399324)), _1399316)), -(_1399318 = _1399320)]]], (33675 ^ _779308) ^ [_1399956, _1399958, _1399960] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399956), hAPP(hAPP(c_Set_Oinsert(_1399956), _1399958), c_Orderings_Obot__class_Obot(tc_fun(_1399956, tc_HOL_Obool)))), _1399960) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1399956, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1399956, _1399956, _1399960), hAPP(hAPP(c_Set_Oinsert(_1399956), _1399958), c_Orderings_Obot__class_Obot(tc_fun(_1399956, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399956, tc_HOL_Obool), tc_HOL_Obool))))], (33677 ^ _779308) ^ [_1400043, _1400045] : [-(c_Nitpick_Oint__lcm(_1400043, _1400045) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Nitpick_Onat__lcm(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1400043)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1400045)))))], (33679 ^ _779308) ^ [_1400089, _1400091, _1400093] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Nitpick_Onat__gcd__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1400089), _1400091))), -(hBOOL(hAPP(hAPP(_1400093, _1400089), _1400091))), 33686 ^ _779308 : [(33687 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Nitpick_Onat__gcd__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), 33684 ^ [_1400089, _1400091, _1400093]), 33685 ^ [_1400089, _1400091, _1400093]))))], (33695 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1400093, 33684 ^ [_1400089, _1400091, _1400093]), 33685 ^ [_1400089, _1400091, _1400093]))], (33689 ^ _779308) ^ [] : [-(33685 ^ [_1400089, _1400091, _1400093] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1400093, 33685 ^ [_1400089, _1400091, _1400093]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 33684 ^ [_1400089, _1400091, _1400093], 33685 ^ [_1400089, _1400091, _1400093]))))]]], (33699 ^ _779308) ^ [_1400511, _1400513, _1400515, _1400517] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1400511, tc_HOL_Obool)), _1400513), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400511), _1400515), _1400517))), 33703 ^ _779308 : [(33704 ^ _779308) ^ [] : [-(_1400513 = hAPP(c_Relation_OImage(_1400511, _1400511, _1400517), hAPP(hAPP(c_Set_Oinsert(_1400511), 33702 ^ [_1400511, _1400513, _1400515, _1400517]), c_Orderings_Obot__class_Obot(tc_fun(_1400511, tc_HOL_Obool)))))], (33706 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1400511), 33702 ^ [_1400511, _1400513, _1400515, _1400517]), _1400515)))]]], (33708 ^ _779308) ^ [_1400739, _1400741, _1400743] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1400739), _1400741), _1400743) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400739, tc_fun(tc_fun(_1400739, tc_HOL_Obool), tc_HOL_Obool)), _1400741), hAPP(hAPP(c_COMBC(_1400739, tc_fun(tc_fun(_1400739, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1400739, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1400739, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1400739, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1400739, tc_HOL_Obool), tc_HOL_Obool)), _1400739), c_Set_Oinsert(tc_fun(_1400739, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1400739, tc_HOL_Obool), tc_fun(_1400739, tc_HOL_Obool), _1400739), c_Relation_OImage(_1400739, _1400739, _1400743)), hAPP(hAPP(c_COMBC(_1400739, tc_fun(_1400739, tc_HOL_Obool), tc_fun(_1400739, tc_HOL_Obool)), c_Set_Oinsert(_1400739)), c_Orderings_Obot__class_Obot(tc_fun(_1400739, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1400739, tc_HOL_Obool), tc_HOL_Obool)))))], (33710 ^ _779308) ^ [_1400895, _1400897, _1400899, _1400901, _1400903, _1400905] : [hBOOL(hAPP(hAPP(c_member(_1400895), _1400897), _1400899)), hBOOL(hAPP(hAPP(_1400901, _1400897), _1400903)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1400895, tc_fun(_1400905, tc_HOL_Obool)), _1400899), _1400901), _1400903)))], (33720 ^ _779308) ^ [_1401092, _1401094, _1401096, _1401098] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1401092), _1401094)), 33723 ^ _779308 : [(33734 ^ _779308) ^ [] : [33736 ^ _779308 : [(33737 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401092), 33735 ^ [_1401092, _1401094, _1401096, _1401098]), _1401094)))], (33739 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1401096), hAPP(_1401098, 33735 ^ [_1401092, _1401094, _1401096, _1401098])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1401096), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401092, tc_fun(_1401096, tc_HOL_Obool)), _1401094), _1401098))))], (33724 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1401096), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401092, tc_fun(_1401096, tc_HOL_Obool)), _1401094), _1401098))), 33727 ^ _779308 : [(33728 ^ _779308) ^ [_1401276] : [hBOOL(hAPP(hAPP(c_member(_1401092), _1401276), _1401094)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1401096), hAPP(_1401098, _1401276))))]]]]], (33743 ^ _779308) ^ [_1401591, _1401593, _1401595, _1401597, _1401599] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401591, tc_fun(_1401593, tc_HOL_Obool)), _1401595), _1401597), _1401599)), 33747 ^ _779308 : [(33748 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1401591), 33746 ^ [_1401591, _1401593, _1401595, _1401597, _1401599]), _1401595)))], (33750 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1401597, 33746 ^ [_1401591, _1401593, _1401595, _1401597, _1401599]), _1401599)))]]], (33752 ^ _779308) ^ [_1401779, _1401781, _1401783, _1401785, _1401787] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1401779, tc_fun(_1401781, tc_HOL_Obool)), _1401783), _1401785), _1401787))), 33753 ^ _779308 : [(33754 ^ _779308) ^ [_1401851] : [hBOOL(hAPP(hAPP(c_member(_1401779), _1401851), _1401783)), hBOOL(hAPP(hAPP(_1401785, _1401851), _1401787))]]], (33762 ^ _779308) ^ [_1402003, _1402005, _1402007, _1402009, _1402011, _1402013] : [-(hAPP(c_Relation_OImage(_1402003, _1402005, _1402007), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402009, tc_fun(_1402003, tc_HOL_Obool)), _1402011), _1402013)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402009, tc_fun(_1402005, tc_HOL_Obool)), _1402011), hAPP(hAPP(c_COMBB(tc_fun(_1402003, tc_HOL_Obool), tc_fun(_1402005, tc_HOL_Obool), _1402009), c_Relation_OImage(_1402003, _1402005, _1402007)), _1402013)))], (33764 ^ _779308) ^ [_1402087, _1402089, _1402091, _1402093] : [-(hAPP(c_Relation_OImage(_1402087, _1402089, _1402091), _1402093) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402087, tc_fun(_1402089, tc_HOL_Obool)), _1402093), hAPP(hAPP(c_COMBB(tc_fun(_1402087, tc_HOL_Obool), tc_fun(_1402089, tc_HOL_Obool), _1402087), c_Relation_OImage(_1402087, _1402089, _1402091)), hAPP(hAPP(c_COMBC(_1402087, tc_fun(_1402087, tc_HOL_Obool), tc_fun(_1402087, tc_HOL_Obool)), c_Set_Oinsert(_1402087)), c_Orderings_Obot__class_Obot(tc_fun(_1402087, tc_HOL_Obool))))))], (33766 ^ _779308) ^ [_1402178, _1402180, _1402182, _1402184, _1402186, _1402188] : [hBOOL(hAPP(hAPP(c_member(_1402178), _1402180), _1402182)), hBOOL(hAPP(hAPP(c_member(_1402184), _1402186), hAPP(_1402188, _1402180))), -(hBOOL(hAPP(hAPP(c_member(_1402184), _1402186), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402178, tc_fun(_1402184, tc_HOL_Obool)), _1402182), _1402188))))], (33776 ^ _779308) ^ [_1402395, _1402397, _1402399, _1402401] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1402395, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402397, tc_fun(tc_fun(_1402395, tc_HOL_Obool), tc_HOL_Obool)), _1402399), hAPP(hAPP(c_COMBB(tc_fun(_1402395, tc_HOL_Obool), tc_fun(tc_fun(_1402395, tc_HOL_Obool), tc_HOL_Obool), _1402397), c_Set_OPow(_1402395)), _1402401))), hAPP(c_Set_OPow(_1402395), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402397, tc_fun(_1402395, tc_HOL_Obool)), _1402399), _1402401)))))], (33778 ^ _779308) ^ [_1402490, _1402492, _1402494, _1402496] : [-(hAPP(c_Set_Oimage(_1402490, _1402492, _1402494), _1402496) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402490, tc_fun(_1402492, tc_HOL_Obool)), _1402496), hAPP(hAPP(c_COMBC(_1402490, tc_fun(_1402492, tc_HOL_Obool), tc_fun(_1402492, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1402492, tc_fun(tc_fun(_1402492, tc_HOL_Obool), tc_fun(_1402492, tc_HOL_Obool)), _1402490), c_Set_Oinsert(_1402492)), _1402494)), c_Orderings_Obot__class_Obot(tc_fun(_1402492, tc_HOL_Obool)))))], (33780 ^ _779308) ^ [_1402580, _1402582, _1402584, _1402586, _1402588, _1402590, _1402592, _1402594, _1402596, _1402598] : [c_Equiv__Relations_Oequiv(_1402580, _1402582, _1402584), c_Equiv__Relations_Oequiv(_1402586, _1402588, _1402590), c_Equiv__Relations_Ocongruent2(_1402580, _1402586, tc_fun(_1402592, tc_HOL_Obool), _1402584, _1402590, _1402594), hBOOL(hAPP(hAPP(c_member(_1402580), _1402596), _1402582)), hBOOL(hAPP(hAPP(c_member(_1402586), _1402598), _1402588)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402580, tc_fun(_1402592, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1402580, _1402580, _1402584), hAPP(hAPP(c_Set_Oinsert(_1402580), _1402596), c_Orderings_Obot__class_Obot(tc_fun(_1402580, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1402586, tc_fun(_1402592, tc_HOL_Obool)), tc_fun(_1402592, tc_HOL_Obool), _1402580), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1402586, tc_fun(_1402592, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1402586, _1402586, _1402590), hAPP(hAPP(c_Set_Oinsert(_1402586), _1402598), c_Orderings_Obot__class_Obot(tc_fun(_1402586, tc_HOL_Obool)))))), _1402594)) = hAPP(hAPP(_1402594, _1402596), _1402598))], (33819 ^ _779308) ^ [_1403623, _1403625, _1403627, _1403629, _1403631] : [33821 ^ _779308 : [(33822 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403625), 33820 ^ [_1403623, _1403625, _1403627, _1403629, _1403631]), _1403627)))], (33825 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403623), 33823 ^ [_1403623, _1403625, _1403627, _1403629, _1403631]), hAPP(_1403629, 33820 ^ [_1403623, _1403625, _1403627, _1403629, _1403631]))))], (33827 ^ _779308) ^ [] : [hBOOL(hAPP(_1403631, 33823 ^ [_1403623, _1403625, _1403627, _1403629, _1403631]))]], 33828 ^ _779308 : [(33829 ^ _779308) ^ [_1403933] : [hBOOL(hAPP(hAPP(c_member(_1403623), _1403933), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403625, tc_fun(_1403623, tc_HOL_Obool)), _1403627), _1403629))), -(hBOOL(hAPP(_1403631, _1403933)))]]], (33802 ^ _779308) ^ [_1403187, _1403189, _1403191, _1403193, _1403195] : [33804 ^ _779308 : [(33805 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403187), 33803 ^ [_1403187, _1403189, _1403191, _1403193, _1403195]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403189, tc_fun(_1403187, tc_HOL_Obool)), _1403191), _1403193))))], (33807 ^ _779308) ^ [] : [hBOOL(hAPP(_1403195, 33803 ^ [_1403187, _1403189, _1403191, _1403193, _1403195]))]], 33808 ^ _779308 : [(33809 ^ _779308) ^ [_1403409] : [hBOOL(hAPP(hAPP(c_member(_1403189), _1403409), _1403191)), 33812 ^ _779308 : [(33813 ^ _779308) ^ [_1403506] : [hBOOL(hAPP(hAPP(c_member(_1403187), _1403506), hAPP(_1403193, _1403409))), -(hBOOL(hAPP(_1403195, _1403506)))]]]]], (33835 ^ _779308) ^ [_1404068, _1404070, _1404072, _1404074] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1404068, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1404070)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1404068, tc_HOL_Obool), tc_Nat_Onat), _1404072), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1404074))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1404068, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1404074, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1404070), _1404074))), _1404072))], (33837 ^ _779308) ^ [_1404150, _1404152, _1404154, _1404156, _1404158, _1404160] : [class_Complete__Lattice_Ocomplete__lattice(_1404150), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404152, _1404150), _1404154), hAPP(hAPP(c_COMBB(tc_fun(_1404156, _1404150), _1404150, _1404152), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404156, _1404150), _1404158)), _1404160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404156, _1404150), _1404158), hAPP(hAPP(c_COMBB(tc_fun(_1404152, _1404150), _1404150, _1404156), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404152, _1404150), _1404154)), hAPP(c_COMBC(_1404152, _1404156, _1404150), _1404160))))], (33843 ^ _779308) ^ [_1404359, _1404361, _1404363, _1404365, _1404367, _1404369] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404359, tc_fun(_1404361, tc_HOL_Obool)), _1404363), hAPP(hAPP(c_COMBC(_1404359, tc_fun(_1404365, tc_fun(_1404361, tc_HOL_Obool)), tc_fun(_1404361, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404365, tc_HOL_Obool), tc_fun(tc_fun(_1404365, tc_fun(_1404361, tc_HOL_Obool)), tc_fun(_1404361, tc_HOL_Obool)), _1404359), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404365, tc_fun(_1404361, tc_HOL_Obool))), _1404367)), _1404369)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404365, tc_fun(_1404361, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404359, tc_fun(_1404365, tc_HOL_Obool)), _1404363), _1404367)), _1404369))], (33845 ^ _779308) ^ [_1404478, _1404480, _1404482, _1404484, _1404486, _1404488] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404478, tc_fun(_1404480, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404482, tc_fun(_1404478, tc_HOL_Obool)), _1404484), _1404486)), _1404488) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404482, tc_fun(_1404480, tc_HOL_Obool)), _1404484), hAPP(hAPP(c_COMBC(_1404482, tc_fun(_1404478, tc_fun(_1404480, tc_HOL_Obool)), tc_fun(_1404480, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404478, tc_HOL_Obool), tc_fun(tc_fun(_1404478, tc_fun(_1404480, tc_HOL_Obool)), tc_fun(_1404480, tc_HOL_Obool)), _1404482), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404478, tc_fun(_1404480, tc_HOL_Obool))), _1404486)), _1404488)))], (33847 ^ _779308) ^ [_1404597, _1404599, _1404601, _1404603, _1404605, _1404607] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404597, tc_fun(_1404599, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404601, tc_fun(_1404597, tc_HOL_Obool)), _1404603), _1404605)), _1404607) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404601, tc_fun(_1404599, tc_HOL_Obool)), _1404603), hAPP(hAPP(c_COMBC(_1404601, tc_fun(_1404597, tc_fun(_1404599, tc_HOL_Obool)), tc_fun(_1404599, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1404597, tc_HOL_Obool), tc_fun(tc_fun(_1404597, tc_fun(_1404599, tc_HOL_Obool)), tc_fun(_1404599, tc_HOL_Obool)), _1404601), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404597, tc_fun(_1404599, tc_HOL_Obool))), _1404605)), _1404607)))], (33849 ^ _779308) ^ [_1404716, _1404718, _1404720, _1404722, _1404724, _1404726, _1404728, _1404730, _1404732, _1404734] : [c_Equiv__Relations_Ocongruent2(_1404716, _1404718, _1404720, _1404722, _1404724, _1404726), hBOOL(hAPP(hAPP(c_member(tc_prod(_1404716, _1404716)), hAPP(hAPP(c_Product__Type_OPair(_1404716, _1404716), _1404728), _1404730)), _1404722)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1404718, _1404718)), hAPP(hAPP(c_Product__Type_OPair(_1404718, _1404718), _1404732), _1404734)), _1404724)), -(hAPP(hAPP(_1404726, _1404728), _1404732) = hAPP(hAPP(_1404726, _1404730), _1404734))], (33863 ^ _779308) ^ [_1405053, _1405055, _1405057] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1405053, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1405055)), _1405057) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1405053, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1405053, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1405055)), _1405057)), hAPP(_1405057, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (33865 ^ _779308) ^ [_1405125, _1405127, _1405129, _1405131, _1405133] : [class_Complete__Lattice_Ocomplete__lattice(_1405125), 33868 ^ _779308 : [(33879 ^ _779308) ^ [] : [33881 ^ _779308 : [(33882 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405127), 33880 ^ [_1405125, _1405127, _1405129, _1405131, _1405133]), _1405129)))], (33884 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405125), hAPP(_1405131, 33880 ^ [_1405125, _1405127, _1405129, _1405131, _1405133])), _1405133))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405125), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405127, _1405125), _1405129), _1405131)), _1405133)))], (33869 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405125), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405127, _1405125), _1405129), _1405131)), _1405133)), 33872 ^ _779308 : [(33873 ^ _779308) ^ [_1405306] : [hBOOL(hAPP(hAPP(c_member(_1405127), _1405306), _1405129)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405125), hAPP(_1405131, _1405306)), _1405133)))]]]]], (33888 ^ _779308) ^ [_1405619, _1405621, _1405623, _1405625, _1405627] : [class_Complete__Lattice_Ocomplete__lattice(_1405619), class_Orderings_Olinorder(_1405619), 33895 ^ _779308 : [(33896 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405619), _1405621), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405623, _1405619), _1405625), _1405627))), 33900 ^ _779308 : [(33901 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405623), 33899 ^ [_1405619, _1405621, _1405623, _1405625, _1405627]), _1405625)))], (33903 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405619), _1405621), hAPP(_1405627, 33899 ^ [_1405619, _1405621, _1405623, _1405625, _1405627]))))]]], (33905 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405619), _1405621), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1405623, _1405619), _1405625), _1405627)))), 33906 ^ _779308 : [(33907 ^ _779308) ^ [_1405967] : [hBOOL(hAPP(hAPP(c_member(_1405623), _1405967), _1405625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1405619), _1405621), hAPP(_1405627, _1405967)))]]]]], (33915 ^ _779308) ^ [_1406161, _1406163, _1406165, _1406167, _1406169] : [hBOOL(hAPP(hAPP(c_member(_1406161), _1406163), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406165, tc_fun(_1406161, tc_HOL_Obool)), _1406167), _1406169))), 33919 ^ _779308 : [(33920 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406165), 33918 ^ [_1406161, _1406163, _1406165, _1406167, _1406169]), _1406167)))], (33922 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406161), _1406163), hAPP(_1406169, 33918 ^ [_1406161, _1406163, _1406165, _1406167, _1406169]))))]]], (33924 ^ _779308) ^ [_1406369, _1406371, _1406373, _1406375, _1406377] : [-(hBOOL(hAPP(hAPP(c_member(_1406369), _1406371), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406373, tc_fun(_1406369, tc_HOL_Obool)), _1406375), _1406377)))), 33925 ^ _779308 : [(33926 ^ _779308) ^ [_1406451] : [hBOOL(hAPP(hAPP(c_member(_1406373), _1406451), _1406375)), hBOOL(hAPP(hAPP(c_member(_1406369), _1406371), hAPP(_1406377, _1406451)))]]], (33934 ^ _779308) ^ [_1406618, _1406620, _1406622, _1406624] : [class_Complete__Lattice_Ocomplete__lattice(_1406618), -(_1406620 = c_Orderings_Obot__class_Obot(tc_fun(_1406622, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406622, _1406618), _1406620), hAPP(c_COMBK(_1406618, _1406622), _1406624)) = _1406624)], (33954 ^ _779308) ^ [_1407002, _1407004, _1407006, _1407008] : [33956 ^ _779308 : [(33957 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1407002), 33955 ^ [_1407002, _1407004, _1407006, _1407008]), _1407006)))], (33959 ^ _779308) ^ [] : [hAPP(_1407008, 33955 ^ [_1407002, _1407004, _1407006, _1407008]) = c_Orderings_Obot__class_Obot(tc_fun(_1407004, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407002, tc_fun(_1407004, tc_HOL_Obool)), _1407006), _1407008) = c_Orderings_Obot__class_Obot(tc_fun(_1407004, tc_HOL_Obool)))], (33944 ^ _779308) ^ [_1406773, _1406775, _1406777, _1406779] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406773, tc_fun(_1406775, tc_HOL_Obool)), _1406777), _1406779) = c_Orderings_Obot__class_Obot(tc_fun(_1406775, tc_HOL_Obool)), 33947 ^ _779308 : [(33948 ^ _779308) ^ [_1406889] : [hBOOL(hAPP(hAPP(c_member(_1406773), _1406889), _1406777)), -(hAPP(_1406779, _1406889) = c_Orderings_Obot__class_Obot(tc_fun(_1406775, tc_HOL_Obool)))]]], (33963 ^ _779308) ^ [_1407247, _1407249, _1407251, _1407253] : [_1407247 = c_Orderings_Obot__class_Obot(tc_fun(_1407249, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407249, tc_fun(_1407251, tc_HOL_Obool)), _1407247), hAPP(c_COMBK(tc_fun(_1407251, tc_HOL_Obool), _1407249), _1407253)) = c_Orderings_Obot__class_Obot(tc_fun(_1407251, tc_HOL_Obool)))], (33969 ^ _779308) ^ [_1407384, _1407386, _1407388, _1407390] : [-(_1407384 = c_Orderings_Obot__class_Obot(tc_fun(_1407386, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407386, tc_fun(_1407388, tc_HOL_Obool)), _1407384), hAPP(c_COMBK(tc_fun(_1407388, tc_HOL_Obool), _1407386), _1407390)) = _1407390)], (33975 ^ _779308) ^ [_1407452, _1407454, _1407456] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407452, tc_fun(_1407454, tc_HOL_Obool)), _1407456), hAPP(c_COMBK(tc_fun(_1407454, tc_HOL_Obool), _1407452), c_Orderings_Obot__class_Obot(tc_fun(_1407454, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1407454, tc_HOL_Obool)))], (33987 ^ _779308) ^ [_1407760, _1407762, _1407764, _1407766] : [33989 ^ _779308 : [(33990 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1407762), 33988 ^ [_1407760, _1407762, _1407764, _1407766]), _1407764)))], (33992 ^ _779308) ^ [] : [hAPP(_1407766, 33988 ^ [_1407760, _1407762, _1407764, _1407766]) = c_Orderings_Obot__class_Obot(tc_fun(_1407760, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1407760, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407762, tc_fun(_1407760, tc_HOL_Obool)), _1407764), _1407766))], (33977 ^ _779308) ^ [_1407531, _1407533, _1407535, _1407537] : [c_Orderings_Obot__class_Obot(tc_fun(_1407531, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407533, tc_fun(_1407531, tc_HOL_Obool)), _1407535), _1407537), 33980 ^ _779308 : [(33981 ^ _779308) ^ [_1407647] : [hBOOL(hAPP(hAPP(c_member(_1407533), _1407647), _1407535)), -(hAPP(_1407537, _1407647) = c_Orderings_Obot__class_Obot(tc_fun(_1407531, tc_HOL_Obool)))]]], (34006 ^ _779308) ^ [_1408272, _1408274, _1408276, _1408278, _1408280] : [34008 ^ _779308 : [(34009 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1408274), 34007 ^ [_1408272, _1408274, _1408276, _1408278, _1408280]), _1408276)))], (34011 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1408272, tc_HOL_Obool)), hAPP(_1408278, 34007 ^ [_1408272, _1408274, _1408276, _1408278, _1408280])), _1408280))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1408272, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408274, tc_fun(_1408272, tc_HOL_Obool)), _1408276), _1408278)), _1408280)))], (33996 ^ _779308) ^ [_1408014, _1408016, _1408018, _1408020, _1408022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1408014, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408016, tc_fun(_1408014, tc_HOL_Obool)), _1408018), _1408020)), _1408022)), 33999 ^ _779308 : [(34000 ^ _779308) ^ [_1408147] : [hBOOL(hAPP(hAPP(c_member(_1408016), _1408147), _1408018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1408014, tc_HOL_Obool)), hAPP(_1408020, _1408147)), _1408022)))]]], (34015 ^ _779308) ^ [_1408535, _1408537, _1408539, _1408541, _1408543, _1408545] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408535, tc_fun(_1408537, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1408539, _1408535, _1408541), _1408543)), _1408545) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408539, tc_fun(_1408537, tc_HOL_Obool)), _1408543), hAPP(hAPP(c_COMBB(_1408535, tc_fun(_1408537, tc_HOL_Obool), _1408539), _1408545), _1408541)))], (34017 ^ _779308) ^ [_1408612, _1408614, _1408616, _1408618, _1408620, _1408622] : [-(hAPP(c_Set_Oimage(_1408612, _1408614, _1408616), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408618, tc_fun(_1408612, tc_HOL_Obool)), _1408620), _1408622)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408618, tc_fun(_1408614, tc_HOL_Obool)), _1408620), hAPP(hAPP(c_COMBB(tc_fun(_1408612, tc_HOL_Obool), tc_fun(_1408614, tc_HOL_Obool), _1408618), c_Set_Oimage(_1408612, _1408614, _1408616)), _1408622)))], (34019 ^ _779308) ^ [_1408696, _1408698, _1408700, _1408702, _1408704, _1408706] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408696, tc_fun(_1408698, tc_HOL_Obool)), _1408700), hAPP(hAPP(c_COMBB(_1408702, tc_fun(_1408698, tc_HOL_Obool), _1408696), _1408704), _1408706)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408702, tc_fun(_1408698, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1408696, _1408702, _1408706), _1408700)), _1408704))], (34021 ^ _779308) ^ [_1408773, _1408775, _1408777, _1408779, _1408781] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408773, tc_fun(_1408775, tc_HOL_Obool)), _1408777), hAPP(hAPP(c_COMBS(_1408773, tc_fun(_1408775, tc_HOL_Obool), tc_fun(_1408775, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1408775, tc_HOL_Obool), tc_fun(tc_fun(_1408775, tc_HOL_Obool), tc_fun(_1408775, tc_HOL_Obool)), _1408773), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408775, tc_HOL_Obool))), _1408779)), _1408781)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408775, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408773, tc_fun(_1408775, tc_HOL_Obool)), _1408777), _1408779)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408773, tc_fun(_1408775, tc_HOL_Obool)), _1408777), _1408781)))], (34023 ^ _779308) ^ [_1408894, _1408896, _1408898, _1408900, _1408902] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408894, tc_fun(_1408896, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408894, tc_HOL_Obool)), _1408898), _1408900)), _1408902) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1408896, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408894, tc_fun(_1408896, tc_HOL_Obool)), _1408898), _1408902)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408894, tc_fun(_1408896, tc_HOL_Obool)), _1408900), _1408902)))], (34025 ^ _779308) ^ [_1408983, _1408985, _1408987, _1408989, _1408991, _1408993, _1408995] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408983, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408985, tc_fun(_1408983, tc_HOL_Obool)), _1408987), _1408989)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408991, tc_fun(_1408983, tc_HOL_Obool)), _1408993), _1408995)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408985, tc_fun(_1408983, tc_HOL_Obool)), _1408987), hAPP(hAPP(c_COMBB(tc_fun(_1408991, tc_fun(_1408983, tc_HOL_Obool)), tc_fun(_1408983, tc_HOL_Obool), _1408985), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408991, tc_fun(_1408983, tc_HOL_Obool)), _1408993)), hAPP(hAPP(c_COMBC(_1408985, tc_fun(_1408991, tc_fun(_1408983, tc_HOL_Obool)), tc_fun(_1408991, tc_fun(_1408983, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1408983, tc_HOL_Obool), tc_fun(_1408983, tc_HOL_Obool)), tc_fun(tc_fun(_1408991, tc_fun(_1408983, tc_HOL_Obool)), tc_fun(_1408991, tc_fun(_1408983, tc_HOL_Obool))), _1408985), c_COMBB(tc_fun(_1408983, tc_HOL_Obool), tc_fun(_1408983, tc_HOL_Obool), _1408991)), hAPP(hAPP(c_COMBB(tc_fun(_1408983, tc_HOL_Obool), tc_fun(tc_fun(_1408983, tc_HOL_Obool), tc_fun(_1408983, tc_HOL_Obool)), _1408985), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1408983, tc_HOL_Obool))), _1408989))), _1408995))))], (34027 ^ _779308) ^ [_1409186, _1409188, _1409190, _1409192, _1409194] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409186, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409188, tc_fun(_1409186, tc_HOL_Obool)), _1409190), _1409192)), _1409194) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409188, tc_fun(_1409186, tc_HOL_Obool)), _1409190), hAPP(hAPP(c_COMBC(_1409188, tc_fun(_1409186, tc_HOL_Obool), tc_fun(_1409186, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409186, tc_HOL_Obool), tc_fun(tc_fun(_1409186, tc_HOL_Obool), tc_fun(_1409186, tc_HOL_Obool)), _1409188), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409186, tc_HOL_Obool))), _1409192)), _1409194)))], (34029 ^ _779308) ^ [_1409295, _1409297, _1409299, _1409301, _1409303] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409295, tc_HOL_Obool)), _1409297), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409299, tc_fun(_1409295, tc_HOL_Obool)), _1409301), _1409303)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409299, tc_fun(_1409295, tc_HOL_Obool)), _1409301), hAPP(hAPP(c_COMBB(tc_fun(_1409295, tc_HOL_Obool), tc_fun(_1409295, tc_HOL_Obool), _1409299), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409295, tc_HOL_Obool)), _1409297)), _1409303)))], (34031 ^ _779308) ^ [_1409385, _1409387, _1409389, _1409391, _1409393] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409385, tc_HOL_Obool)), _1409387), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409389, tc_fun(_1409385, tc_HOL_Obool)), _1409391), _1409393)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409389, tc_fun(_1409385, tc_HOL_Obool)), _1409391), hAPP(hAPP(c_COMBB(tc_fun(_1409385, tc_HOL_Obool), tc_fun(_1409385, tc_HOL_Obool), _1409389), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409385, tc_HOL_Obool)), _1409387)), _1409393)))], (34033 ^ _779308) ^ [_1409475, _1409477, _1409479, _1409481, _1409483] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409475, tc_fun(_1409477, tc_HOL_Obool)), _1409479), hAPP(hAPP(c_COMBC(_1409475, tc_fun(_1409477, tc_HOL_Obool), tc_fun(_1409477, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409477, tc_HOL_Obool), tc_fun(tc_fun(_1409477, tc_HOL_Obool), tc_fun(_1409477, tc_HOL_Obool)), _1409475), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409477, tc_HOL_Obool))), _1409481)), _1409483)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409477, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409475, tc_fun(_1409477, tc_HOL_Obool)), _1409479), _1409481)), _1409483))], (34035 ^ _779308) ^ [_1409584, _1409586, _1409588, _1409590, _1409592] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409584, tc_fun(_1409586, tc_HOL_Obool)), _1409588), hAPP(hAPP(c_COMBB(tc_fun(_1409586, tc_HOL_Obool), tc_fun(_1409586, tc_HOL_Obool), _1409584), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409586, tc_HOL_Obool)), _1409590)), _1409592)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409586, tc_HOL_Obool)), _1409590), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409584, tc_fun(_1409586, tc_HOL_Obool)), _1409588), _1409592)))], (34037 ^ _779308) ^ [_1409674, _1409676, _1409678, _1409680, _1409682, _1409684] : [class_Complete__Lattice_Ocomplete__lattice(_1409674), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409676, tc_fun(_1409678, _1409674)), _1409680), _1409682), _1409684) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409676, _1409674), _1409680), hAPP(hAPP(c_COMBC(_1409676, _1409678, _1409674), _1409682), _1409684)))], (34043 ^ _779308) ^ [_1409825, _1409827, _1409829, _1409831, _1409833] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409825, tc_fun(_1409827, tc_HOL_Obool)), _1409829), hAPP(hAPP(c_COMBC(_1409825, tc_fun(_1409827, tc_HOL_Obool), tc_fun(_1409827, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409827, tc_HOL_Obool), tc_fun(tc_fun(_1409827, tc_HOL_Obool), tc_fun(_1409827, tc_HOL_Obool)), _1409825), c_Groups_Ominus__class_Ominus(tc_fun(_1409827, tc_HOL_Obool))), _1409831)), _1409833)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1409827, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409825, tc_fun(_1409827, tc_HOL_Obool)), _1409829), _1409831)), _1409833))], (34045 ^ _779308) ^ [_1409934, _1409936, _1409938, _1409940, _1409942] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1409934, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409936, tc_fun(_1409934, tc_HOL_Obool)), _1409938), _1409940)), _1409942) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409936, tc_fun(_1409934, tc_HOL_Obool)), _1409938), hAPP(hAPP(c_COMBC(_1409936, tc_fun(_1409934, tc_HOL_Obool), tc_fun(_1409934, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409934, tc_HOL_Obool), tc_fun(tc_fun(_1409934, tc_HOL_Obool), tc_fun(_1409934, tc_HOL_Obool)), _1409936), c_Groups_Ominus__class_Ominus(tc_fun(_1409934, tc_HOL_Obool))), _1409940)), _1409942)))], (34047 ^ _779308) ^ [_1410043, _1410045, _1410047, _1410049, _1410051] : [class_Complete__Lattice_Ocomplete__lattice(_1410043), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1410045, tc_HOL_Obool)), _1410047), _1410049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410043), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410045, _1410043), _1410047), _1410051)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410045, _1410043), _1410049), _1410051))))], (34057 ^ _779308) ^ [_1410252, _1410254, _1410256, _1410258, _1410260] : [class_Complete__Lattice_Ocomplete__lattice(_1410252), hBOOL(hAPP(hAPP(c_member(_1410254), _1410256), _1410258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410252), hAPP(_1410260, _1410256)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410254, _1410252), _1410258), _1410260))))], (34067 ^ _779308) ^ [_1410443, _1410445, _1410447, _1410449, _1410451, _1410453] : [hBOOL(hAPP(hAPP(c_member(_1410443), _1410445), _1410447)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410443, tc_fun(_1410449, tc_HOL_Obool)), _1410447), hAPP(hAPP(c_COMBB(tc_fun(_1410449, tc_HOL_Obool), tc_fun(_1410449, tc_HOL_Obool), _1410443), hAPP(c_Set_Oinsert(_1410449), _1410451)), _1410453)) = hAPP(hAPP(c_Set_Oinsert(_1410449), _1410451), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410443, tc_fun(_1410449, tc_HOL_Obool)), _1410447), _1410453)))], (34073 ^ _779308) ^ [_1410648, _1410650, _1410652, _1410654, _1410656] : [hBOOL(hAPP(hAPP(c_member(_1410648), _1410650), _1410652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1410654, tc_HOL_Obool)), hAPP(_1410656, _1410650)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410648, tc_fun(_1410654, tc_HOL_Obool)), _1410652), _1410656))))], (34079 ^ _779308) ^ [_1410795, _1410797, _1410799, _1410801, _1410803] : [hBOOL(hAPP(hAPP(c_member(_1410795), _1410797), _1410799)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410801, tc_HOL_Obool)), hAPP(_1410803, _1410797)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410795, tc_fun(_1410801, tc_HOL_Obool)), _1410799), _1410803)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410795, tc_fun(_1410801, tc_HOL_Obool)), _1410799), _1410803))], (34085 ^ _779308) ^ [_1410986, _1410988, _1410990, _1410992, _1410994] : [_1410986 = c_Orderings_Obot__class_Obot(tc_fun(_1410988, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410988, tc_fun(_1410990, tc_HOL_Obool)), _1410986), hAPP(hAPP(c_COMBB(tc_fun(_1410990, tc_HOL_Obool), tc_fun(_1410990, tc_HOL_Obool), _1410988), hAPP(c_Set_Oinsert(_1410990), _1410992)), _1410994)) = c_Orderings_Obot__class_Obot(tc_fun(_1410990, tc_HOL_Obool)))], (34091 ^ _779308) ^ [_1411149, _1411151, _1411153, _1411155, _1411157] : [-(_1411149 = c_Orderings_Obot__class_Obot(tc_fun(_1411151, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411151, tc_fun(_1411153, tc_HOL_Obool)), _1411149), hAPP(hAPP(c_COMBB(tc_fun(_1411153, tc_HOL_Obool), tc_fun(_1411153, tc_HOL_Obool), _1411151), hAPP(c_Set_Oinsert(_1411153), _1411155)), _1411157)) = hAPP(hAPP(c_Set_Oinsert(_1411153), _1411155), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411151, tc_fun(_1411153, tc_HOL_Obool)), _1411149), _1411157)))], (34097 ^ _779308) ^ [_1411251, _1411253] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411251, tc_fun(_1411251, tc_HOL_Obool)), _1411253), hAPP(hAPP(c_COMBC(_1411251, tc_fun(_1411251, tc_HOL_Obool), tc_fun(_1411251, tc_HOL_Obool)), c_Set_Oinsert(_1411251)), c_Orderings_Obot__class_Obot(tc_fun(_1411251, tc_HOL_Obool)))) = _1411253)], (34099 ^ _779308) ^ [_1411329, _1411331, _1411333, _1411335, _1411337] : [_1411329 = c_Orderings_Obot__class_Obot(tc_fun(_1411331, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1411333), _1411335), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411331, tc_fun(_1411333, tc_HOL_Obool)), _1411329), _1411337)) = hAPP(hAPP(c_Set_Oinsert(_1411333), _1411335), c_Orderings_Obot__class_Obot(tc_fun(_1411333, tc_HOL_Obool))))], (34105 ^ _779308) ^ [_1411482, _1411484, _1411486, _1411488, _1411490] : [-(_1411482 = c_Orderings_Obot__class_Obot(tc_fun(_1411484, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1411486), _1411488), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411484, tc_fun(_1411486, tc_HOL_Obool)), _1411482), _1411490)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411484, tc_fun(_1411486, tc_HOL_Obool)), _1411482), hAPP(hAPP(c_COMBB(tc_fun(_1411486, tc_HOL_Obool), tc_fun(_1411486, tc_HOL_Obool), _1411484), hAPP(c_Set_Oinsert(_1411486), _1411488)), _1411490)))], (34111 ^ _779308) ^ [_1411602, _1411604, _1411606, _1411608, _1411610] : [_1411602 = c_Orderings_Obot__class_Obot(tc_fun(_1411604, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411604, tc_fun(_1411606, tc_HOL_Obool)), _1411602), hAPP(hAPP(c_COMBB(tc_fun(_1411606, tc_HOL_Obool), tc_fun(_1411606, tc_HOL_Obool), _1411604), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411606, tc_HOL_Obool)), _1411608)), _1411610)) = c_Orderings_Obot__class_Obot(tc_fun(_1411606, tc_HOL_Obool)))], (34117 ^ _779308) ^ [_1411771, _1411773, _1411775, _1411777, _1411779] : [-(_1411771 = c_Orderings_Obot__class_Obot(tc_fun(_1411773, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411773, tc_fun(_1411775, tc_HOL_Obool)), _1411771), hAPP(hAPP(c_COMBB(tc_fun(_1411775, tc_HOL_Obool), tc_fun(_1411775, tc_HOL_Obool), _1411773), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411775, tc_HOL_Obool)), _1411777)), _1411779)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411775, tc_HOL_Obool)), _1411777), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411773, tc_fun(_1411775, tc_HOL_Obool)), _1411771), _1411779)))], (34123 ^ _779308) ^ [_1411897, _1411899, _1411901, _1411903, _1411905] : [_1411897 = c_Orderings_Obot__class_Obot(tc_fun(_1411899, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411899, tc_fun(_1411901, tc_HOL_Obool)), _1411897), hAPP(hAPP(c_COMBC(_1411899, tc_fun(_1411901, tc_HOL_Obool), tc_fun(_1411901, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411901, tc_HOL_Obool), tc_fun(tc_fun(_1411901, tc_HOL_Obool), tc_fun(_1411901, tc_HOL_Obool)), _1411899), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411901, tc_HOL_Obool))), _1411903)), _1411905)) = c_Orderings_Obot__class_Obot(tc_fun(_1411901, tc_HOL_Obool)))], (34129 ^ _779308) ^ [_1412104, _1412106, _1412108, _1412110, _1412112] : [-(_1412104 = c_Orderings_Obot__class_Obot(tc_fun(_1412106, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412106, tc_fun(_1412108, tc_HOL_Obool)), _1412104), hAPP(hAPP(c_COMBC(_1412106, tc_fun(_1412108, tc_HOL_Obool), tc_fun(_1412108, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1412108, tc_HOL_Obool), tc_fun(tc_fun(_1412108, tc_HOL_Obool), tc_fun(_1412108, tc_HOL_Obool)), _1412106), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412108, tc_HOL_Obool))), _1412110)), _1412112)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412108, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412106, tc_fun(_1412108, tc_HOL_Obool)), _1412104), _1412110)), _1412112))], (34135 ^ _779308) ^ [_1412249, _1412251, _1412253, _1412255, _1412257] : [_1412249 = c_Orderings_Obot__class_Obot(tc_fun(_1412251, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412253, tc_HOL_Obool)), _1412255), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412251, tc_fun(_1412253, tc_HOL_Obool)), _1412249), _1412257)) = _1412255)], (34141 ^ _779308) ^ [_1412382, _1412384, _1412386, _1412388, _1412390] : [-(_1412382 = c_Orderings_Obot__class_Obot(tc_fun(_1412384, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412386, tc_HOL_Obool)), _1412388), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412384, tc_fun(_1412386, tc_HOL_Obool)), _1412382), _1412390)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412384, tc_fun(_1412386, tc_HOL_Obool)), _1412382), hAPP(hAPP(c_COMBB(tc_fun(_1412386, tc_HOL_Obool), tc_fun(_1412386, tc_HOL_Obool), _1412384), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412386, tc_HOL_Obool)), _1412388)), _1412390)))], (34147 ^ _779308) ^ [_1412508, _1412510, _1412512, _1412514, _1412516] : [_1412508 = c_Orderings_Obot__class_Obot(tc_fun(_1412510, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412512, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412510, tc_fun(_1412512, tc_HOL_Obool)), _1412508), _1412514)), _1412516) = _1412516)], (34153 ^ _779308) ^ [_1412641, _1412643, _1412645, _1412647, _1412649] : [-(_1412641 = c_Orderings_Obot__class_Obot(tc_fun(_1412643, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412645, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412643, tc_fun(_1412645, tc_HOL_Obool)), _1412641), _1412647)), _1412649) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412643, tc_fun(_1412645, tc_HOL_Obool)), _1412641), hAPP(hAPP(c_COMBC(_1412643, tc_fun(_1412645, tc_HOL_Obool), tc_fun(_1412645, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1412645, tc_HOL_Obool), tc_fun(tc_fun(_1412645, tc_HOL_Obool), tc_fun(_1412645, tc_HOL_Obool)), _1412643), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412645, tc_HOL_Obool))), _1412647)), _1412649)))], (34159 ^ _779308) ^ [_1412768, _1412770, _1412772, _1412774, _1412776] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412768, tc_fun(_1412770, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1412768), _1412772), _1412774)), _1412776) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412770, tc_HOL_Obool)), hAPP(_1412776, _1412772)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412768, tc_fun(_1412770, tc_HOL_Obool)), _1412774), _1412776)))], (34161 ^ _779308) ^ [_1412845, _1412847, _1412849, _1412851, _1412853, _1412855, _1412857, _1412859, _1412861] : [c_Equiv__Relations_Oequiv(_1412845, _1412847, _1412849), c_Equiv__Relations_Oequiv(_1412851, _1412853, _1412855), c_Equiv__Relations_Ocongruent2(_1412845, _1412851, tc_fun(_1412857, tc_HOL_Obool), _1412849, _1412855, _1412859), hBOOL(hAPP(hAPP(c_member(_1412851), _1412861), _1412853)), -(c_Equiv__Relations_Ocongruent(_1412845, tc_fun(_1412857, tc_HOL_Obool), _1412849, hAPP(hAPP(c_COMBB(tc_fun(_1412851, tc_fun(_1412857, tc_HOL_Obool)), tc_fun(_1412857, tc_HOL_Obool), _1412845), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412851, tc_fun(_1412857, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1412851, _1412851, _1412855), hAPP(hAPP(c_Set_Oinsert(_1412851), _1412861), c_Orderings_Obot__class_Obot(tc_fun(_1412851, tc_HOL_Obool)))))), _1412859)))], (34179 ^ _779308) ^ [_1413272] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1413272) = hAPP(c_Int_OAbs__Integ, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1413272)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat, tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_fun(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_Nat_Onat), c_Relation_OImage(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Int_Ointrel))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), tc_Nat_Onat), c_COMBC(tc_Nat_Onat, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_prod(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), tc_Nat_Onat), hAPP(c_COMBB(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), tc_Nat_Onat), c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)))), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_prod(tc_Nat_Onat, tc_Nat_Onat)), c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat))))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (34181 ^ _779308) ^ [_1413310, _1413312, _1413314, _1413316, _1413318, _1413320] : [c_Equiv__Relations_Oequiv(_1413310, _1413312, _1413314), c_Equiv__Relations_Ocongruent(_1413310, tc_fun(_1413316, tc_HOL_Obool), _1413314, _1413318), hBOOL(hAPP(hAPP(c_member(_1413310), _1413320), _1413312)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413310, tc_fun(_1413316, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1413310, _1413310, _1413314), hAPP(hAPP(c_Set_Oinsert(_1413310), _1413320), c_Orderings_Obot__class_Obot(tc_fun(_1413310, tc_HOL_Obool))))), _1413318) = hAPP(_1413318, _1413320))], (34195 ^ _779308) ^ [_1413611, _1413613, _1413615, _1413617, _1413619, _1413621, _1413623, _1413625] : [hBOOL(hAPP(hAPP(c_member(_1413611), _1413613), _1413615)), hBOOL(hAPP(hAPP(hAPP(_1413617, _1413613), _1413619), _1413621)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413611, tc_fun(_1413623, tc_fun(_1413625, tc_HOL_Obool))), _1413615), _1413617), _1413619), _1413621)))], (34205 ^ _779308) ^ [_1413849, _1413851] : [hAPP(c_Int_ORep__Integ, _1413849) = hAPP(c_Int_ORep__Integ, _1413851), -(_1413849 = _1413851)], (34211 ^ _779308) ^ [_1413934, _1413936] : [_1413934 = _1413936, -(hAPP(c_Int_ORep__Integ, _1413934) = hAPP(c_Int_ORep__Integ, _1413936))], (34217 ^ _779308) ^ [_1414025] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1414025)) = _1414025)], (34219 ^ _779308) ^ [_1414054, _1414056, _1414058, _1414060, _1414062, _1414064] : [c_Equiv__Relations_Ocongruent(_1414054, _1414056, _1414058, _1414060), hBOOL(hAPP(hAPP(c_member(tc_prod(_1414054, _1414054)), hAPP(hAPP(c_Product__Type_OPair(_1414054, _1414054), _1414062), _1414064)), _1414058)), -(hAPP(_1414060, _1414062) = hAPP(_1414060, _1414064))], (34229 ^ _779308) ^ [_1414253] : [-(hAPP(c_Int_Onat, _1414253) = c_Set_Othe__elem(tc_Nat_Onat, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1414253)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat, tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool))), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool))), tc_Nat_Onat), c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool))), tc_Nat_Onat), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_Set_Oinsert(tc_Nat_Onat))), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))))], (34231 ^ _779308) ^ [_1414291, _1414293, _1414295, _1414297, _1414299, _1414301, _1414303, _1414305] : [c_Equiv__Relations_Oequiv(_1414291, _1414293, _1414295), c_Equiv__Relations_Ocongruent2(_1414291, _1414297, _1414299, _1414295, _1414301, _1414303), hBOOL(hAPP(hAPP(c_member(_1414291), _1414305), _1414293)), -(c_Equiv__Relations_Ocongruent(_1414297, _1414299, _1414301, hAPP(_1414303, _1414305)))], (34245 ^ _779308) ^ [_1414542, _1414544, _1414546, _1414548, _1414550, _1414552, _1414554] : [c_Equiv__Relations_Oequiv(_1414542, _1414544, _1414546), c_Equiv__Relations_Ocongruent(_1414542, tc_fun(_1414548, tc_HOL_Obool), _1414546, _1414550), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414542, tc_fun(_1414548, tc_HOL_Obool)), _1414552), _1414550) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414542, tc_fun(_1414548, tc_HOL_Obool)), _1414554), _1414550), hBOOL(hAPP(hAPP(c_member(tc_fun(_1414542, tc_HOL_Obool)), _1414552), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1414542), _1414544), _1414546))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1414542, tc_HOL_Obool)), _1414554), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1414542), _1414544), _1414546))), 34267 ^ _779308 : [(34268 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1414542), 34266 ^ [_1414542, _1414544, _1414546, _1414548, _1414550, _1414552, _1414554]), _1414544)))], (34271 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1414542), 34269 ^ [_1414542, _1414544, _1414546, _1414548, _1414550, _1414552, _1414554]), _1414544)))], (34273 ^ _779308) ^ [] : [-(hAPP(_1414550, 34266 ^ [_1414542, _1414544, _1414546, _1414548, _1414550, _1414552, _1414554]) = hAPP(_1414550, 34269 ^ [_1414542, _1414544, _1414546, _1414548, _1414550, _1414552, _1414554]))], (34275 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1414542, _1414542)), hAPP(hAPP(c_Product__Type_OPair(_1414542, _1414542), 34266 ^ [_1414542, _1414544, _1414546, _1414548, _1414550, _1414552, _1414554]), 34269 ^ [_1414542, _1414544, _1414546, _1414548, _1414550, _1414552, _1414554])), _1414546))]], -(_1414552 = _1414554)], (34279 ^ _779308) ^ [_1415512, _1415514, _1415516, _1415518, _1415520, _1415522, _1415524, _1415526, _1415528, _1415530, _1415532] : [c_Equiv__Relations_Oequiv(_1415512, _1415514, _1415516), c_Equiv__Relations_Oequiv(_1415518, _1415520, _1415522), c_Equiv__Relations_Ocongruent2(_1415512, _1415518, tc_fun(_1415524, tc_HOL_Obool), _1415516, _1415522, _1415526), hBOOL(hAPP(hAPP(c_member(tc_fun(_1415512, tc_HOL_Obool)), _1415528), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1415512), _1415514), _1415516))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1415518, tc_HOL_Obool)), _1415530), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1415518), _1415520), _1415522))), 34301 ^ _779308 : [(34302 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415512), 34300 ^ [_1415512, _1415514, _1415516, _1415518, _1415520, _1415522, _1415524, _1415526, _1415528, _1415530, _1415532]), _1415514)))], (34305 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1415518), 34303 ^ [_1415512, _1415514, _1415516, _1415518, _1415520, _1415522, _1415524, _1415526, _1415528, _1415530, _1415532]), _1415520)))], (34307 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1415524, tc_HOL_Obool)), hAPP(hAPP(_1415526, 34300 ^ [_1415512, _1415514, _1415516, _1415518, _1415520, _1415522, _1415524, _1415526, _1415528, _1415530, _1415532]), 34303 ^ [_1415512, _1415514, _1415516, _1415518, _1415520, _1415522, _1415524, _1415526, _1415528, _1415530, _1415532])), _1415532))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1415524, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415512, tc_fun(_1415524, tc_HOL_Obool)), _1415528), hAPP(hAPP(c_COMBB(tc_fun(_1415518, tc_fun(_1415524, tc_HOL_Obool)), tc_fun(_1415524, tc_HOL_Obool), _1415512), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415518, tc_fun(_1415524, tc_HOL_Obool)), _1415530)), _1415526))), _1415532)))], (34311 ^ _779308) ^ [_1416514, _1416516, _1416518, _1416520, _1416522, _1416524, _1416526] : [c_Equiv__Relations_Oequiv(_1416514, _1416516, _1416518), c_Equiv__Relations_Ocongruent(_1416514, tc_fun(_1416520, tc_HOL_Obool), _1416518, _1416522), hBOOL(hAPP(hAPP(c_member(tc_fun(_1416514, tc_HOL_Obool)), _1416524), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1416514), _1416516), _1416518))), 34325 ^ _779308 : [(34326 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416514), 34324 ^ [_1416514, _1416516, _1416518, _1416520, _1416522, _1416524, _1416526]), _1416516)))], (34328 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1416520, tc_HOL_Obool)), hAPP(_1416522, 34324 ^ [_1416514, _1416516, _1416518, _1416520, _1416522, _1416524, _1416526])), _1416526))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1416520, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416514, tc_fun(_1416520, tc_HOL_Obool)), _1416524), _1416522)), _1416526)))], (34332 ^ _779308) ^ [_1417055, _1417057, _1417059, _1417061, _1417063, _1417065, _1417067] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417055, tc_fun(_1417057, tc_fun(_1417059, tc_HOL_Obool))), _1417061), _1417063), _1417065), _1417067)), 34336 ^ _779308 : [(34337 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417055), 34335 ^ [_1417055, _1417057, _1417059, _1417061, _1417063, _1417065, _1417067]), _1417061)))], (34339 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1417063, 34335 ^ [_1417055, _1417057, _1417059, _1417061, _1417063, _1417065, _1417067]), _1417065), _1417067)))]]], (34341 ^ _779308) ^ [_1417273, _1417275, _1417277, _1417279, _1417281, _1417283, _1417285] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417273, tc_fun(_1417275, tc_fun(_1417277, tc_HOL_Obool))), _1417279), _1417281), _1417283), _1417285))), 34342 ^ _779308 : [(34343 ^ _779308) ^ [_1417358] : [hBOOL(hAPP(hAPP(c_member(_1417273), _1417358), _1417279)), hBOOL(hAPP(hAPP(hAPP(_1417281, _1417358), _1417283), _1417285))]]], (34351 ^ _779308) ^ [_1417526, _1417528] : [-(c_Relation_OId__on(_1417526, _1417528) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417526, tc_fun(tc_prod(_1417526, _1417526), tc_HOL_Obool)), _1417528), hAPP(hAPP(c_COMBC(_1417526, tc_fun(tc_prod(_1417526, _1417526), tc_HOL_Obool), tc_fun(tc_prod(_1417526, _1417526), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1417526, _1417526), tc_fun(tc_fun(tc_prod(_1417526, _1417526), tc_HOL_Obool), tc_fun(tc_prod(_1417526, _1417526), tc_HOL_Obool)), _1417526), c_Set_Oinsert(tc_prod(_1417526, _1417526))), hAPP(hAPP(c_COMBS(_1417526, _1417526, tc_prod(_1417526, _1417526)), c_Product__Type_OPair(_1417526, _1417526)), c_COMBI(_1417526)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1417526, _1417526), tc_HOL_Obool)))))], (34353 ^ _779308) ^ [_1417650, _1417652, _1417654, _1417656, _1417658, _1417660, _1417662] : [-(hAPP(c_Product__Type_Oapfst(_1417650, _1417652, _1417654, _1417656), hAPP(c_Product__Type_Oapsnd(_1417658, _1417654, _1417650, _1417660), _1417662)) = hAPP(hAPP(c_Product__Type_OPair(_1417652, _1417654), hAPP(_1417656, hAPP(c_Product__Type_Ofst(_1417650, _1417658), _1417662))), hAPP(_1417660, hAPP(c_Product__Type_Osnd(_1417650, _1417658), _1417662))))], (34355 ^ _779308) ^ [_1417728, _1417730, _1417732, _1417734, _1417736, _1417738, _1417740] : [-(hAPP(c_Product__Type_Oapsnd(_1417728, _1417730, _1417732, _1417734), hAPP(c_Product__Type_Oapfst(_1417736, _1417732, _1417728, _1417738), _1417740)) = hAPP(hAPP(c_Product__Type_OPair(_1417732, _1417730), hAPP(_1417738, hAPP(c_Product__Type_Ofst(_1417736, _1417728), _1417740))), hAPP(_1417734, hAPP(c_Product__Type_Osnd(_1417736, _1417728), _1417740))))], (34357 ^ _779308) ^ [_1417806, _1417808, _1417810, _1417812, _1417814, _1417816] : [-(hAPP(c_Product__Type_Oapfst(_1417806, _1417808, _1417810, _1417812), hAPP(hAPP(c_Product__Type_OPair(_1417806, _1417810), _1417814), _1417816)) = hAPP(hAPP(c_Product__Type_OPair(_1417808, _1417810), hAPP(_1417812, _1417814)), _1417816))], (34359 ^ _779308) ^ [_1417895, _1417897, _1417899, _1417901, _1417903, _1417905] : [hAPP(c_Product__Type_Oapfst(_1417895, _1417897, _1417899, _1417901), _1417903) = hAPP(c_Product__Type_Oapfst(_1417895, _1417897, _1417899, _1417905), _1417903), -(hAPP(_1417901, hAPP(c_Product__Type_Ofst(_1417895, _1417899), _1417903)) = hAPP(_1417905, hAPP(c_Product__Type_Ofst(_1417895, _1417899), _1417903)))], (34365 ^ _779308) ^ [_1418044, _1418046, _1418048, _1418050, _1418052, _1418054] : [hAPP(_1418050, hAPP(c_Product__Type_Ofst(_1418044, _1418048), _1418052)) = hAPP(_1418054, hAPP(c_Product__Type_Ofst(_1418044, _1418048), _1418052)), -(hAPP(c_Product__Type_Oapfst(_1418044, _1418046, _1418048, _1418050), _1418052) = hAPP(c_Product__Type_Oapfst(_1418044, _1418046, _1418048, _1418054), _1418052))], (34371 ^ _779308) ^ [_1418199, _1418201, _1418203, _1418205, _1418207] : [-(hAPP(c_Product__Type_Ofst(_1418199, _1418201), hAPP(c_Product__Type_Oapfst(_1418203, _1418199, _1418201, _1418205), _1418207)) = hAPP(_1418205, hAPP(c_Product__Type_Ofst(_1418203, _1418201), _1418207)))], (34373 ^ _779308) ^ [_1418253, _1418255, _1418257, _1418259, _1418261] : [-(hAPP(c_Product__Type_Osnd(_1418253, _1418255), hAPP(c_Product__Type_Oapfst(_1418257, _1418253, _1418255, _1418259), _1418261)) = hAPP(c_Product__Type_Osnd(_1418257, _1418255), _1418261))], (34375 ^ _779308) ^ [_1418304, _1418306, _1418308, _1418310, _1418312, _1418314, _1418316] : [-(hAPP(c_Product__Type_Oapsnd(_1418304, _1418306, _1418308, _1418310), hAPP(c_Product__Type_Oapfst(_1418312, _1418308, _1418304, _1418314), _1418316)) = hAPP(c_Product__Type_Oapfst(_1418312, _1418308, _1418306, _1418314), hAPP(c_Product__Type_Oapsnd(_1418304, _1418306, _1418312, _1418310), _1418316)))], (34377 ^ _779308) ^ [_1418371, _1418373] : [-(c_Relation_OId__on(_1418371, _1418373) = hAPP(c_Product__Type_Oprod_Oprod__case(_1418371, _1418371, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1418371, tc_HOL_Obool, tc_fun(_1418371, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1418371, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1418371, tc_HOL_Obool)), _1418371), c_COMBC(_1418371, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1418371, tc_HOL_Obool), tc_fun(_1418371, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1418371), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1418371), c_fconj)), c_fequal))), _1418373)))], (34379 ^ _779308) ^ [_1418465] : [-(c_Relation_OId__on(_1418465, c_Orderings_Obot__class_Obot(tc_fun(_1418465, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1418465, _1418465), tc_HOL_Obool)))], (34381 ^ _779308) ^ [_1418504, _1418506, _1418508] : [-(hAPP(c_Relation_OImage(_1418504, _1418504, c_Relation_OId__on(_1418504, _1418506)), _1418508) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418504, tc_HOL_Obool)), _1418506), _1418508))], (34383 ^ _779308) ^ [_1418573, _1418575, _1418577, _1418579] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1418573, _1418573)), hAPP(hAPP(c_Product__Type_OPair(_1418573, _1418573), _1418575), _1418577)), c_Relation_OId__on(_1418573, _1418579))), 34386 ^ _779308 : [(34387 ^ _779308) ^ [] : [-(_1418575 = _1418577)], (34389 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418573), _1418575), _1418579)))]]], (34391 ^ _779308) ^ [_1418734, _1418736, _1418738, _1418740] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1418734, _1418734)), hAPP(hAPP(c_Product__Type_OPair(_1418734, _1418734), _1418736), _1418738)), c_Relation_OId__on(_1418734, _1418740)))), _1418736 = _1418738, hBOOL(hAPP(hAPP(c_member(_1418734), _1418736), _1418740))], (34401 ^ _779308) ^ [_1418931, _1418933, _1418935, _1418937] : [_1418931 = _1418933, hBOOL(hAPP(hAPP(c_member(_1418935), _1418931), _1418937)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1418935, _1418935)), hAPP(hAPP(c_Product__Type_OPair(_1418935, _1418935), _1418931), _1418933)), c_Relation_OId__on(_1418935, _1418937))))], (34411 ^ _779308) ^ [_1419126, _1419128, _1419130] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1419126, _1419126)), _1419128), c_Relation_OId__on(_1419126, _1419130))), 34415 ^ _779308 : [(34416 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1419126), 34414 ^ [_1419126, _1419128, _1419130]), _1419130)))], (34418 ^ _779308) ^ [] : [-(_1419128 = hAPP(hAPP(c_Product__Type_OPair(_1419126, _1419126), 34414 ^ [_1419126, _1419128, _1419130]), 34414 ^ [_1419126, _1419128, _1419130]))]]], (34420 ^ _779308) ^ [_1419325, _1419327, _1419329] : [class_Lattices_Oboolean__algebra(_1419325), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1419325), _1419327), _1419329) = c_Orderings_Obot__class_Obot(_1419325), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1419325), _1419327), _1419329) = c_Orderings_Otop__class_Otop(_1419325), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1419325), _1419327) = _1419329)], (34434 ^ _779308) ^ [_1419560, _1419562, _1419564, _1419566, _1419568] : [class_Groups_Ocomm__monoid__add(_1419560), class_Groups_Ocomm__monoid__mult(_1419560), _1419562 = _1419564, c_Nat__Transfer_Onat__set(_1419564), 34452 ^ _779308 : [(34453 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34451 ^ [_1419560, _1419562, _1419564, _1419566, _1419568])))], (34455 ^ _779308) ^ [] : [hAPP(_1419566, 34451 ^ [_1419560, _1419562, _1419564, _1419566, _1419568]) = hAPP(_1419568, 34451 ^ [_1419560, _1419562, _1419564, _1419566, _1419568])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1419560), _1419566), _1419562) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1419560), _1419568), _1419564))], (34459 ^ _779308) ^ [_1420023, _1420025] : [-(hBOOL(hAPP(hAPP(c_member(_1420023), _1420025), c_Orderings_Otop__class_Otop(tc_fun(_1420023, tc_HOL_Obool)))))], (34461 ^ _779308) ^ [_1420060, _1420062] : [class_Orderings_Otop(_1420060), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420060), _1420062), c_Orderings_Otop__class_Otop(_1420060))))], (34467 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (34469 ^ _779308) ^ [_1420177] : [-(hAPP(c_Set_OPow(_1420177), c_Orderings_Otop__class_Otop(tc_fun(_1420177, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1420177, tc_HOL_Obool), tc_HOL_Obool)))], (34471 ^ _779308) ^ [] : [-(hAPP(c_Finite__Set_Ocard(tc_Product__Type_Ounit), c_Orderings_Otop__class_Otop(tc_fun(tc_Product__Type_Ounit, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34473 ^ _779308) ^ [_1420236, _1420238] : [-(c_Sum__Type_OPlus(_1420236, _1420238, c_Orderings_Otop__class_Otop(tc_fun(_1420236, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1420238, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1420236, _1420238), tc_HOL_Obool)))], (34475 ^ _779308) ^ [_1420284, _1420286, _1420288] : [class_Orderings_Otop(_1420284), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1420286, _1420284)), _1420288) = c_Orderings_Otop__class_Otop(_1420284))], (34481 ^ _779308) ^ [_1420381, _1420383] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420381, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1420381, tc_HOL_Obool))), _1420383) = c_Orderings_Otop__class_Otop(tc_fun(_1420381, tc_HOL_Obool)))], (34483 ^ _779308) ^ [_1420427, _1420429] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420427, tc_HOL_Obool)), _1420429), c_Orderings_Otop__class_Otop(tc_fun(_1420427, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1420427, tc_HOL_Obool)))], (34485 ^ _779308) ^ [_1420482] : [c_Orderings_Otop__class_Otop(tc_fun(_1420482, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1420482, tc_HOL_Obool))], (34487 ^ _779308) ^ [_1420515, _1420517] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1420515, tc_HOL_Obool)), _1420517), c_Orderings_Otop__class_Otop(tc_fun(_1420515, tc_HOL_Obool)))))], (34489 ^ _779308) ^ [_1420555, _1420557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1420555, _1420557)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1420555, _1420557), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1420557), c_Orderings_Otop__class_Otop(tc_fun(_1420557, tc_HOL_Obool)))))], (34495 ^ _779308) ^ [_1420692] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1420692)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1420692), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1420692), c_Orderings_Otop__class_Otop(tc_fun(_1420692, tc_HOL_Obool)))))], (34501 ^ _779308) ^ [_1420807] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1420807), c_Orderings_Otop__class_Otop(tc_fun(_1420807, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1420807)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1420807), tc_HOL_Obool)))))], (34507 ^ _779308) ^ [_1420928, _1420930] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1420928), c_Orderings_Otop__class_Otop(tc_fun(_1420928, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1420930), c_Orderings_Otop__class_Otop(tc_fun(_1420930, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1420928, _1420930)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1420928, _1420930), tc_HOL_Obool)))))], (34517 ^ _779308) ^ [_1421123] : [class_Finite__Set_Ofinite(_1421123), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1421123), c_Orderings_Otop__class_Otop(tc_fun(_1421123, tc_HOL_Obool)))))], (34523 ^ _779308) ^ [_1421229, _1421231] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1421229, _1421231)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1421229, _1421231), tc_HOL_Obool)))), 34526 ^ _779308 : [(34527 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1421229), c_Orderings_Otop__class_Otop(tc_fun(_1421229, tc_HOL_Obool)))))], (34529 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1421231), c_Orderings_Otop__class_Otop(tc_fun(_1421231, tc_HOL_Obool)))))]]], (34531 ^ _779308) ^ [_1421394, _1421396] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1421394, _1421396)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1421394, _1421396), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421394), c_Orderings_Otop__class_Otop(tc_fun(_1421394, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1421396), c_Orderings_Otop__class_Otop(tc_fun(_1421396, tc_HOL_Obool))))], (34541 ^ _779308) ^ [_1421591, _1421593] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421591, tc_HOL_Obool)), _1421593), c_Orderings_Otop__class_Otop(tc_fun(_1421591, tc_HOL_Obool))) = _1421593)], (34543 ^ _779308) ^ [_1421632, _1421634] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1421632, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1421632, tc_HOL_Obool))), _1421634) = _1421634)], (34545 ^ _779308) ^ [_1421673, _1421675, _1421677, _1421679, _1421681] : [-(hAPP(c_Set_Oimage(_1421673, _1421675, hAPP(hAPP(c_COMBB(_1421677, _1421675, _1421673), _1421679), _1421681)), c_Orderings_Otop__class_Otop(tc_fun(_1421673, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1421677, _1421675, _1421679), hAPP(c_Set_Oimage(_1421673, _1421677, _1421681), c_Orderings_Otop__class_Otop(tc_fun(_1421673, tc_HOL_Obool)))))], (34547 ^ _779308) ^ [] : [-(c_Equiv__Relations_Oequiv(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), c_Int_Ointrel))], (34549 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (34551 ^ _779308) ^ [] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (34553 ^ _779308) ^ [_1421805, _1421807, _1421809, _1421811, _1421813] : [c_Fun_Oinj__on(_1421805, _1421807, _1421809, c_Orderings_Otop__class_Otop(tc_fun(_1421805, tc_HOL_Obool))), hAPP(_1421809, _1421811) = hAPP(_1421809, _1421813), -(_1421811 = _1421813)], (34563 ^ _779308) ^ [_1421972, _1421974, _1421976, _1421978, _1421980] : [c_Fun_Oinj__on(_1421972, _1421974, _1421976, c_Orderings_Otop__class_Otop(tc_fun(_1421972, tc_HOL_Obool))), 34566 ^ _779308 : [(34567 ^ _779308) ^ [] : [hAPP(_1421976, _1421978) = hAPP(_1421976, _1421980), -(_1421978 = _1421980)], (34573 ^ _779308) ^ [] : [_1421978 = _1421980, -(hAPP(_1421976, _1421978) = hAPP(_1421976, _1421980))]]], (34579 ^ _779308) ^ [_1422229, _1422231] : [class_Lattices_Obounded__lattice__top(_1422229), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1422229), c_Orderings_Otop__class_Otop(_1422229)), _1422231) = c_Orderings_Otop__class_Otop(_1422229))], (34585 ^ _779308) ^ [_1422328, _1422330] : [class_Lattices_Obounded__lattice__top(_1422328), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1422328), _1422330), c_Orderings_Otop__class_Otop(_1422328)) = c_Orderings_Otop__class_Otop(_1422328))], (34591 ^ _779308) ^ [_1422427, _1422429] : [class_Lattices_Obounded__lattice__top(_1422427), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1422427), c_Orderings_Otop__class_Otop(_1422427)), _1422429) = _1422429)], (34597 ^ _779308) ^ [_1422522, _1422524] : [class_Lattices_Obounded__lattice__top(_1422522), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1422522), _1422524), c_Orderings_Otop__class_Otop(_1422522)) = _1422524)], (34603 ^ _779308) ^ [_1422617, _1422619, _1422621] : [class_Lattices_Obounded__lattice__top(_1422617), 34606 ^ _779308 : [(34607 ^ _779308) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1422617), _1422619), _1422621) = c_Orderings_Otop__class_Otop(_1422617), 34610 ^ _779308 : [(34611 ^ _779308) ^ [] : [-(_1422619 = c_Orderings_Otop__class_Otop(_1422617))], (34613 ^ _779308) ^ [] : [-(_1422621 = c_Orderings_Otop__class_Otop(_1422617))]]], (34615 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1422617), _1422619), _1422621) = c_Orderings_Otop__class_Otop(_1422617)), _1422619 = c_Orderings_Otop__class_Otop(_1422617), _1422621 = c_Orderings_Otop__class_Otop(_1422617)]]], (34625 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34627 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_SetInterval_Oord__class_OatMost(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34629 ^ _779308) ^ [_1422980, _1422982, _1422984, _1422986] : [-(hBOOL(hAPP(hAPP(c_member(_1422980), hAPP(_1422982, _1422984)), hAPP(c_Set_Oimage(_1422986, _1422980, _1422982), c_Orderings_Otop__class_Otop(tc_fun(_1422986, tc_HOL_Obool))))))], (34631 ^ _779308) ^ [_1423031, _1423033, _1423035, _1423037, _1423039] : [_1423031 = hAPP(_1423033, _1423035), -(hBOOL(hAPP(hAPP(c_member(_1423037), _1423031), hAPP(c_Set_Oimage(_1423039, _1423037, _1423033), c_Orderings_Otop__class_Otop(tc_fun(_1423039, tc_HOL_Obool))))))], (34637 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34639 ^ _779308) ^ [_1423176, _1423178] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1423176, tc_HOL_Obool)), _1423178), c_Orderings_Otop__class_Otop(tc_fun(_1423176, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1423176, tc_HOL_Obool)))], (34641 ^ _779308) ^ [_1423222, _1423224] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1423222), c_Orderings_Otop__class_Otop(tc_fun(_1423222, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1423222), _1423224) = hAPP(c_Finite__Set_Ocard(_1423222), c_Orderings_Otop__class_Otop(tc_fun(_1423222, tc_HOL_Obool))), -(_1423224 = c_Orderings_Otop__class_Otop(tc_fun(_1423222, tc_HOL_Obool)))], (34651 ^ _779308) ^ [_1423409, _1423411, _1423413, _1423415, _1423417] : [c_Fun_Oinj__on(_1423409, _1423411, _1423413, c_Orderings_Otop__class_Otop(tc_fun(_1423409, tc_HOL_Obool))), 34654 ^ _779308 : [(34655 ^ _779308) ^ [] : [hAPP(c_Set_Oimage(_1423409, _1423411, _1423413), _1423415) = hAPP(c_Set_Oimage(_1423409, _1423411, _1423413), _1423417), -(_1423415 = _1423417)], (34661 ^ _779308) ^ [] : [_1423415 = _1423417, -(hAPP(c_Set_Oimage(_1423409, _1423411, _1423413), _1423415) = hAPP(c_Set_Oimage(_1423409, _1423411, _1423413), _1423417))]]], (34667 ^ _779308) ^ [_1423690] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1423690, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1423690, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1423690, tc_HOL_Obool)))], (34669 ^ _779308) ^ [_1423731] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1423731, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1423731, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1423731, tc_HOL_Obool)))], (34671 ^ _779308) ^ [_1423772, _1423774] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1423772), _1423774)), 34674 ^ _779308 : [(34675 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1423772), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1423772, tc_HOL_Obool)), _1423774))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1423772), c_Orderings_Otop__class_Otop(tc_fun(_1423772, tc_HOL_Obool)))))], (34681 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1423772), c_Orderings_Otop__class_Otop(tc_fun(_1423772, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1423772), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1423772, tc_HOL_Obool)), _1423774))))]]], (34687 ^ _779308) ^ [_1424050, _1424052] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1424050, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1424050, tc_HOL_Obool)), _1424052)), _1424052) = c_Orderings_Otop__class_Otop(tc_fun(_1424050, tc_HOL_Obool)))], (34689 ^ _779308) ^ [_1424099, _1424101] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1424099, tc_HOL_Obool)), _1424101), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1424099, tc_HOL_Obool)), _1424101)) = c_Orderings_Otop__class_Otop(tc_fun(_1424099, tc_HOL_Obool)))], (34691 ^ _779308) ^ [_1424148, _1424150] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1424148, tc_HOL_Obool)), _1424150) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1424148, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1424148, tc_HOL_Obool))), _1424150))], (34693 ^ _779308) ^ [_1424218, _1424220, _1424222, _1424224] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1424218, tc_fun(_1424220, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1424218, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1424220, tc_HOL_Obool), tc_fun(_1424220, tc_HOL_Obool), _1424218), hAPP(c_COMBC(_1424220, tc_fun(_1424220, tc_HOL_Obool), tc_HOL_Obool), c_member(_1424220))), _1424222)), _1424224)), -(hBOOL(hAPP(hAPP(c_member(_1424220), _1424224), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1424218, tc_fun(_1424220, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1424218, tc_HOL_Obool))), _1424222))))], (34699 ^ _779308) ^ [_1424437, _1424439, _1424441, _1424443] : [hBOOL(hAPP(hAPP(c_member(_1424439), _1424443), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1424437, tc_fun(_1424439, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1424437, tc_HOL_Obool))), _1424441))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1424437, tc_fun(_1424439, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1424437, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1424439, tc_HOL_Obool), tc_fun(_1424439, tc_HOL_Obool), _1424437), hAPP(c_COMBC(_1424439, tc_fun(_1424439, tc_HOL_Obool), tc_HOL_Obool), c_member(_1424439))), _1424441)), _1424443)))], (34705 ^ _779308) ^ [_1424662, _1424664, _1424666, _1424668, _1424670] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1424662), hAPP(c_Set_Oimage(_1424664, _1424662, _1424666), c_Orderings_Otop__class_Otop(tc_fun(_1424664, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1424668), hAPP(c_Set_Oimage(_1424664, _1424668, hAPP(hAPP(c_COMBB(_1424662, _1424668, _1424664), _1424670), _1424666)), c_Orderings_Otop__class_Otop(tc_fun(_1424664, tc_HOL_Obool))))))], (34711 ^ _779308) ^ [_1424829, _1424831, _1424833, _1424835] : [c_Fun_Oinj__on(_1424829, _1424831, _1424833, c_Orderings_Otop__class_Otop(tc_fun(_1424829, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1424829, _1424831, c_Orderings_Otop__class_Otop(tc_fun(_1424829, tc_HOL_Obool)), _1424833), hAPP(_1424833, _1424835)) = _1424835)], (34717 ^ _779308) ^ [_1424956, _1424958] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1424956, _1424958)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1424956, _1424958), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1424958), c_Orderings_Otop__class_Otop(tc_fun(_1424958, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1424956), c_Orderings_Otop__class_Otop(tc_fun(_1424956, tc_HOL_Obool)))))], (34727 ^ _779308) ^ [_1425116] : [class_Nat_Osemiring__char__0(_1425116), -(c_Fun_Oinj__on(tc_Nat_Onat, _1425116, c_Nat_Osemiring__1__class_Oof__nat(_1425116), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (34733 ^ _779308) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (34735 ^ _779308) ^ [_1425215, _1425217, _1425219, _1425221] : [c_Fun_Oinj__on(_1425215, _1425217, _1425219, c_Orderings_Otop__class_Otop(tc_fun(_1425215, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1425215, tc_fun(_1425221, _1425217), hAPP(hAPP(c_COMBB(_1425217, tc_fun(_1425221, _1425217), _1425215), c_COMBK(_1425217, _1425221)), _1425219), c_Orderings_Otop__class_Otop(tc_fun(_1425215, tc_HOL_Obool))))], (34741 ^ _779308) ^ [_1425362] : [class_Lattices_Oboolean__algebra(_1425362), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1425362), c_Orderings_Otop__class_Otop(_1425362)) = c_Orderings_Obot__class_Obot(_1425362))], (34747 ^ _779308) ^ [_1425453] : [class_Lattices_Oboolean__algebra(_1425453), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1425453), c_Orderings_Obot__class_Obot(_1425453)) = c_Orderings_Otop__class_Otop(_1425453))], (34753 ^ _779308) ^ [_1425544, _1425546] : [class_Lattices_Oboolean__algebra(_1425544), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1425544), hAPP(c_Groups_Ouminus__class_Ouminus(_1425544), _1425546)), _1425546) = c_Orderings_Otop__class_Otop(_1425544))], (34759 ^ _779308) ^ [_1425649, _1425651] : [class_Lattices_Oboolean__algebra(_1425649), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1425649), _1425651), hAPP(c_Groups_Ouminus__class_Ouminus(_1425649), _1425651)) = c_Orderings_Otop__class_Otop(_1425649))], (34765 ^ _779308) ^ [_1425754, _1425756, _1425758, _1425760] : [c_Fun_Oinj__on(_1425754, _1425756, _1425758, c_Orderings_Otop__class_Otop(tc_fun(_1425754, tc_HOL_Obool))), 34768 ^ _779308 : [(34769 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1425756), _1425760), hAPP(c_Set_Oimage(_1425754, _1425756, _1425758), c_Orderings_Otop__class_Otop(tc_fun(_1425754, tc_HOL_Obool))))), 34773 ^ _779308 : [(34774 ^ _779308) ^ [] : [-(_1425760 = hAPP(_1425758, 34772 ^ [_1425754, _1425756, _1425758, _1425760]))], (34776 ^ _779308) ^ [_1426019] : [_1425760 = hAPP(_1425758, _1426019), -(_1426019 = 34772 ^ [_1425754, _1425756, _1425758, _1425760])]]], (34782 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1425756), _1425760), hAPP(c_Set_Oimage(_1425754, _1425756, _1425758), c_Orderings_Otop__class_Otop(tc_fun(_1425754, tc_HOL_Obool)))))), 34783 ^ _779308 : [(34784 ^ _779308) ^ [_1426157] : [_1425760 = hAPP(_1425758, _1426157), 34788 ^ _779308 : [(34789 ^ _779308) ^ [] : [-(_1425760 = hAPP(_1425758, 34787 ^ [_1425754, _1425756, _1425758, _1425760, _1426157]))], (34791 ^ _779308) ^ [] : [34787 ^ [_1425754, _1425756, _1425758, _1425760, _1426157] = _1426157]]]]]]], (34795 ^ _779308) ^ [_1426385, _1426387, _1426389, _1426391, _1426393] : [c_Fun_Oinj__on(_1426385, _1426387, _1426389, c_Orderings_Otop__class_Otop(tc_fun(_1426385, tc_HOL_Obool))), 34798 ^ _779308 : [(34799 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1426387), hAPP(_1426389, _1426391)), hAPP(c_Set_Oimage(_1426385, _1426387, _1426389), _1426393))), -(hBOOL(hAPP(hAPP(c_member(_1426385), _1426391), _1426393)))], (34805 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1426385), _1426391), _1426393)), -(hBOOL(hAPP(hAPP(c_member(_1426387), hAPP(_1426389, _1426391)), hAPP(c_Set_Oimage(_1426385, _1426387, _1426389), _1426393))))]]], (34811 ^ _779308) ^ [_1426696, _1426698] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1426696), c_Orderings_Otop__class_Otop(tc_fun(_1426696, tc_HOL_Obool)))), c_Fun_Oinj__on(_1426696, _1426696, _1426698, c_Orderings_Otop__class_Otop(tc_fun(_1426696, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1426696, _1426696, _1426698), c_Orderings_Otop__class_Otop(tc_fun(_1426696, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1426696, tc_HOL_Obool)))], (34821 ^ _779308) ^ [_1426891, _1426893] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1426891), c_Orderings_Otop__class_Otop(tc_fun(_1426891, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1426891, _1426891, _1426893), c_Orderings_Otop__class_Otop(tc_fun(_1426891, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1426891, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1426891, _1426891, _1426893, c_Orderings_Otop__class_Otop(tc_fun(_1426891, tc_HOL_Obool))))], (34831 ^ _779308) ^ [_1427086, _1427088, _1427090, _1427092, _1427094] : [c_Fun_Oinj__on(_1427086, _1427088, _1427090, c_Orderings_Otop__class_Otop(tc_fun(_1427086, tc_HOL_Obool))), 34834 ^ _779308 : [(34835 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427088, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1427086, _1427088, _1427090), _1427092)), hAPP(c_Set_Oimage(_1427086, _1427088, _1427090), _1427094))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427086, tc_HOL_Obool)), _1427092), _1427094)))], (34841 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427086, tc_HOL_Obool)), _1427092), _1427094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427088, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1427086, _1427088, _1427090), _1427092)), hAPP(c_Set_Oimage(_1427086, _1427088, _1427090), _1427094))))]]], (34847 ^ _779308) ^ [_1427427, _1427429, _1427431, _1427433, _1427435] : [c_Fun_Oinj__on(_1427427, _1427429, _1427431, c_Orderings_Otop__class_Otop(tc_fun(_1427427, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1427427, _1427429, _1427431), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427427, tc_HOL_Obool)), _1427433), _1427435)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1427429, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1427427, _1427429, _1427431), _1427433)), hAPP(c_Set_Oimage(_1427427, _1427429, _1427431), _1427435)))], (34853 ^ _779308) ^ [_1427610, _1427612, _1427614, _1427616, _1427618] : [c_Fun_Oinj__on(_1427610, _1427612, _1427614, c_Orderings_Otop__class_Otop(tc_fun(_1427610, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1427610, _1427612, _1427614), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1427610, tc_HOL_Obool)), _1427616), _1427618)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1427612, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1427610, _1427612, _1427614), _1427616)), hAPP(c_Set_Oimage(_1427610, _1427612, _1427614), _1427618)))], (34859 ^ _779308) ^ [_1427793, _1427795, _1427797, _1427799] : [hAPP(c_Set_Oimage(_1427793, _1427795, _1427797), c_Orderings_Otop__class_Otop(tc_fun(_1427793, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1427795, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1427795, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1427795, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1427793, _1427795, _1427797), _1427799))), hAPP(c_Set_Oimage(_1427793, _1427795, _1427797), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1427793, tc_HOL_Obool)), _1427799)))))], (34865 ^ _779308) ^ [_1427988, _1427990] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1427988, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_fun(_1427988, tc_HOL_Obool)), tc_fun(_1427988, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1427988, tc_HOL_Obool)), tc_fun(_1427988, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1427988, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1427990)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1427988, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1427990))], (34867 ^ _779308) ^ [_1428084] : [-(c_Fun_Oinj__on(_1428084, tc_fun(_1428084, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1428084, tc_fun(_1428084, tc_HOL_Obool), tc_fun(_1428084, tc_HOL_Obool)), c_Set_Oinsert(_1428084)), c_Orderings_Obot__class_Obot(tc_fun(_1428084, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1428084, tc_HOL_Obool))))], (34869 ^ _779308) ^ [_1428140] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1428140), c_Orderings_Otop__class_Otop(tc_fun(_1428140, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1428140), c_Orderings_Otop__class_Otop(tc_fun(_1428140, tc_HOL_Obool))))))], (34875 ^ _779308) ^ [] : [-(hAPP(c_Finite__Set_Ocard(tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_HOL_Obool, tc_HOL_Obool))) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (34877 ^ _779308) ^ [_1428275, _1428277, _1428279, _1428281] : [c_Fun_Oinj__on(_1428275, _1428277, _1428279, c_Orderings_Otop__class_Otop(tc_fun(_1428275, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428277, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1428275, _1428277, _1428279), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1428275, tc_HOL_Obool)), _1428281))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1428277, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1428275, _1428277, _1428279), _1428281)))))], (34883 ^ _779308) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (34885 ^ _779308) ^ [_1428495, _1428497, _1428499, _1428501, _1428503, _1428505] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428495, tc_fun(_1428497, tc_fun(_1428499, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1428495, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1428497, _1428499), tc_HOL_Obool), tc_fun(_1428497, tc_fun(_1428499, tc_HOL_Obool)), _1428495), hAPP(c_COMBC(_1428497, tc_fun(tc_prod(_1428497, _1428499), tc_HOL_Obool), tc_fun(_1428499, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428499, tc_fun(tc_fun(tc_prod(_1428497, _1428499), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1428497, _1428499), tc_HOL_Obool), tc_fun(_1428499, tc_HOL_Obool)), _1428497), c_COMBC(_1428499, tc_fun(tc_prod(_1428497, _1428499), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428499, tc_prod(_1428497, _1428499)), tc_fun(_1428499, tc_fun(tc_fun(tc_prod(_1428497, _1428499), tc_HOL_Obool), tc_HOL_Obool)), _1428497), hAPP(c_COMBB(tc_prod(_1428497, _1428499), tc_fun(tc_fun(tc_prod(_1428497, _1428499), tc_HOL_Obool), tc_HOL_Obool), _1428499), c_member(tc_prod(_1428497, _1428499)))), c_Product__Type_OPair(_1428497, _1428499))))), _1428501)), _1428503), _1428505)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1428497, _1428499)), hAPP(hAPP(c_Product__Type_OPair(_1428497, _1428499), _1428503), _1428505)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428495, tc_fun(tc_prod(_1428497, _1428499), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1428495, tc_HOL_Obool))), _1428501))))], (34891 ^ _779308) ^ [_1428978, _1428980, _1428982, _1428984, _1428986, _1428988] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1428980, _1428982)), hAPP(hAPP(c_Product__Type_OPair(_1428980, _1428982), _1428986), _1428988)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428978, tc_fun(tc_prod(_1428980, _1428982), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1428978, tc_HOL_Obool))), _1428984))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428978, tc_fun(_1428980, tc_fun(_1428982, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1428978, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1428980, _1428982), tc_HOL_Obool), tc_fun(_1428980, tc_fun(_1428982, tc_HOL_Obool)), _1428978), hAPP(c_COMBC(_1428980, tc_fun(tc_prod(_1428980, _1428982), tc_HOL_Obool), tc_fun(_1428982, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428982, tc_fun(tc_fun(tc_prod(_1428980, _1428982), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1428980, _1428982), tc_HOL_Obool), tc_fun(_1428982, tc_HOL_Obool)), _1428980), c_COMBC(_1428982, tc_fun(tc_prod(_1428980, _1428982), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1428982, tc_prod(_1428980, _1428982)), tc_fun(_1428982, tc_fun(tc_fun(tc_prod(_1428980, _1428982), tc_HOL_Obool), tc_HOL_Obool)), _1428980), hAPP(c_COMBB(tc_prod(_1428980, _1428982), tc_fun(tc_fun(tc_prod(_1428980, _1428982), tc_HOL_Obool), tc_HOL_Obool), _1428982), c_member(tc_prod(_1428980, _1428982)))), c_Product__Type_OPair(_1428980, _1428982))))), _1428984)), _1428986), _1428988)))], (34897 ^ _779308) ^ [_1429467, _1429469, _1429471, _1429473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429467, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1429467, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 34898 ^ [_1429467, _1429469, _1429471, _1429473])), _1429469)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1429467, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 34898 ^ [_1429467, _1429469, _1429471, _1429473]), _1429471))), _1429473))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1429467, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1429467, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1429469)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1429467, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1429473))))], (34904 ^ _779308) ^ [_1429797, _1429799, _1429801, _1429803] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1429797, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 34905 ^ [_1429797, _1429799, _1429801, _1429803])), _1429799) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1429797, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 34905 ^ [_1429797, _1429799, _1429801, _1429803]), _1429801))), _1429803), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1429797, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1429799) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1429797, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1429803))], (34911 ^ _779308) ^ [_1430077, _1430079, _1430081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430077, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430077, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 34912 ^ [_1430077, _1430079, _1430081])), _1430079)), _1430081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1430077, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430077, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1430079)), _1430081)))], (34918 ^ _779308) ^ [_1430303, _1430305] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1430303, tc_HOL_Obool)), _1430305)))], (34920 ^ _779308) ^ [] : [-(c_Int_OInteg = hAPP(hAPP(c_Equiv__Relations_Oquotient(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))), c_Int_Ointrel))], (34922 ^ _779308) ^ [_1430353, _1430355] : [-(hBOOL(hAPP(hAPP(c_member(_1430353), _1430355), c_Orderings_Otop__class_Otop(tc_fun(_1430353, tc_HOL_Obool)))))], (34924 ^ _779308) ^ [_1430405, _1430407] : [c_Equiv__Relations_Oequiv(_1430405, c_Orderings_Otop__class_Otop(tc_fun(_1430405, tc_HOL_Obool)), _1430407), -(c_Equiv__Relations_Oequivp(_1430405, hAPP(hAPP(c_COMBC(_1430405, tc_fun(tc_prod(_1430405, _1430405), tc_HOL_Obool), tc_fun(_1430405, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1430405, tc_fun(tc_fun(tc_prod(_1430405, _1430405), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1430405, _1430405), tc_HOL_Obool), tc_fun(_1430405, tc_HOL_Obool)), _1430405), c_COMBC(_1430405, tc_fun(tc_prod(_1430405, _1430405), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1430405, tc_prod(_1430405, _1430405)), tc_fun(_1430405, tc_fun(tc_fun(tc_prod(_1430405, _1430405), tc_HOL_Obool), tc_HOL_Obool)), _1430405), hAPP(c_COMBB(tc_prod(_1430405, _1430405), tc_fun(tc_fun(tc_prod(_1430405, _1430405), tc_HOL_Obool), tc_HOL_Obool), _1430405), c_member(tc_prod(_1430405, _1430405)))), c_Product__Type_OPair(_1430405, _1430405)))), _1430407)))], (34930 ^ _779308) ^ [_1430726, _1430728] : [c_Equiv__Relations_Oequivp(_1430726, hAPP(hAPP(c_COMBC(_1430726, tc_fun(tc_prod(_1430726, _1430726), tc_HOL_Obool), tc_fun(_1430726, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1430726, tc_fun(tc_fun(tc_prod(_1430726, _1430726), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1430726, _1430726), tc_HOL_Obool), tc_fun(_1430726, tc_HOL_Obool)), _1430726), c_COMBC(_1430726, tc_fun(tc_prod(_1430726, _1430726), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1430726, tc_prod(_1430726, _1430726)), tc_fun(_1430726, tc_fun(tc_fun(tc_prod(_1430726, _1430726), tc_HOL_Obool), tc_HOL_Obool)), _1430726), hAPP(c_COMBB(tc_prod(_1430726, _1430726), tc_fun(tc_fun(tc_prod(_1430726, _1430726), tc_HOL_Obool), tc_HOL_Obool), _1430726), c_member(tc_prod(_1430726, _1430726)))), c_Product__Type_OPair(_1430726, _1430726)))), _1430728)), -(c_Equiv__Relations_Oequiv(_1430726, c_Orderings_Otop__class_Otop(tc_fun(_1430726, tc_HOL_Obool)), _1430728))], (34936 ^ _779308) ^ [_1431053] : [-(c_Equiv__Relations_Oequivp(_1431053, c_fequal))], (34954 ^ _779308) ^ [_1431389, _1431391] : [-(c_Equiv__Relations_Oequivp(_1431389, _1431391)), 34959 ^ _779308 : [(34960 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1431391, 34955 ^ [_1431389, _1431391]), 34956 ^ [_1431389, _1431391])))], (34962 ^ _779308) ^ [] : [hAPP(_1431391, 34955 ^ [_1431389, _1431391]) = hAPP(_1431391, 34956 ^ [_1431389, _1431391])]], 34963 ^ _779308 : [(34964 ^ _779308) ^ [] : [-(hAPP(_1431391, 34955 ^ [_1431389, _1431391]) = hAPP(_1431391, 34956 ^ [_1431389, _1431391]))], (34966 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1431391, 34955 ^ [_1431389, _1431391]), 34956 ^ [_1431389, _1431391]))]]], (34938 ^ _779308) ^ [_1431091, _1431093] : [c_Equiv__Relations_Oequivp(_1431091, _1431093), 34941 ^ _779308 : [(34942 ^ _779308) ^ [_1431185, _1431187] : [hBOOL(hAPP(hAPP(_1431093, _1431187), _1431185)), -(hAPP(_1431093, _1431187) = hAPP(_1431093, _1431185))], (34948 ^ _779308) ^ [_1431284, _1431286] : [hAPP(_1431093, _1431286) = hAPP(_1431093, _1431284), -(hBOOL(hAPP(hAPP(_1431093, _1431286), _1431284)))]]], (34970 ^ _779308) ^ [_1431718, _1431720, _1431722] : [c_Equiv__Relations_Oequivp(_1431718, _1431720), -(hBOOL(hAPP(hAPP(_1431720, _1431722), _1431722)))], (34976 ^ _779308) ^ [_1431807, _1431809, _1431811, _1431813] : [c_Equiv__Relations_Oequivp(_1431807, _1431809), hBOOL(hAPP(hAPP(_1431809, _1431811), _1431813)), -(hBOOL(hAPP(hAPP(_1431809, _1431813), _1431811)))], (34986 ^ _779308) ^ [_1431964, _1431966, _1431968, _1431970, _1431972] : [c_Equiv__Relations_Oequivp(_1431964, _1431966), hBOOL(hAPP(hAPP(_1431966, _1431968), _1431970)), hBOOL(hAPP(hAPP(_1431966, _1431970), _1431972)), -(hBOOL(hAPP(hAPP(_1431966, _1431968), _1431972)))], (35000 ^ _779308) ^ [_1432193] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1432193)), c_Int_OInteg)))], (35002 ^ _779308) ^ [] : [-(c_Typedef_Otype__definition(tc_Int_Oint, tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool), c_Int_ORep__Integ, c_Int_OAbs__Integ, c_Int_OInteg))], (35004 ^ _779308) ^ [_1432242, _1432244, _1432246, _1432248] : [c_Fun_Oinj__on(_1432242, _1432244, _1432246, c_Orderings_Otop__class_Otop(tc_fun(_1432242, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1432242, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1432242, _1432244, _1432246), hAPP(hAPP(c_Set_Oinsert(_1432244), _1432248), c_Orderings_Obot__class_Obot(tc_fun(_1432244, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1432242), c_HOL_OThe(_1432242, hAPP(hAPP(c_COMBC(_1432242, _1432244, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1432244, tc_fun(_1432244, tc_HOL_Obool), _1432242), c_fequal), _1432246)), _1432248))), c_Orderings_Obot__class_Obot(tc_fun(_1432242, tc_HOL_Obool))))))], (35010 ^ _779308) ^ [_1432493, _1432495, _1432497] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1432493, hAPP(hAPP(c_COMBC(_1432493, tc_fun(tc_prod(_1432493, _1432493), tc_HOL_Obool), tc_fun(_1432493, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432493, tc_fun(tc_fun(tc_prod(_1432493, _1432493), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1432493, _1432493), tc_HOL_Obool), tc_fun(_1432493, tc_HOL_Obool)), _1432493), c_COMBC(_1432493, tc_fun(tc_prod(_1432493, _1432493), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432493, tc_prod(_1432493, _1432493)), tc_fun(_1432493, tc_fun(tc_fun(tc_prod(_1432493, _1432493), tc_HOL_Obool), tc_HOL_Obool)), _1432493), hAPP(c_COMBB(tc_prod(_1432493, _1432493), tc_fun(tc_fun(tc_prod(_1432493, _1432493), tc_HOL_Obool), tc_HOL_Obool), _1432493), c_member(tc_prod(_1432493, _1432493)))), c_Product__Type_OPair(_1432493, _1432493)))), _1432495)), _1432497)), -(hBOOL(hAPP(hAPP(c_member(_1432493), _1432497), c_Wellfounded_Oacc(_1432493, _1432495))))], (35016 ^ _779308) ^ [_1432834, _1432836, _1432838] : [hBOOL(hAPP(hAPP(c_member(_1432834), _1432838), c_Wellfounded_Oacc(_1432834, _1432836))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1432834, hAPP(hAPP(c_COMBC(_1432834, tc_fun(tc_prod(_1432834, _1432834), tc_HOL_Obool), tc_fun(_1432834, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432834, tc_fun(tc_fun(tc_prod(_1432834, _1432834), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1432834, _1432834), tc_HOL_Obool), tc_fun(_1432834, tc_HOL_Obool)), _1432834), c_COMBC(_1432834, tc_fun(tc_prod(_1432834, _1432834), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432834, tc_prod(_1432834, _1432834)), tc_fun(_1432834, tc_fun(tc_fun(tc_prod(_1432834, _1432834), tc_HOL_Obool), tc_HOL_Obool)), _1432834), hAPP(c_COMBB(tc_prod(_1432834, _1432834), tc_fun(tc_fun(tc_prod(_1432834, _1432834), tc_HOL_Obool), tc_HOL_Obool), _1432834), c_member(tc_prod(_1432834, _1432834)))), c_Product__Type_OPair(_1432834, _1432834)))), _1432836)), _1432838)))], (35022 ^ _779308) ^ [_1433181, _1433183, _1433185, _1433187, _1433189, _1433191] : [hAPP(_1433181, _1433183) = _1433185, hBOOL(hAPP(hAPP(c_member(_1433187), _1433185), _1433189)), -(hBOOL(hAPP(hAPP(c_member(_1433191), _1433183), hAPP(c_Set_Ovimage(_1433191, _1433187, _1433181), _1433189))))], (35032 ^ _779308) ^ [_1433374, _1433376, _1433378, _1433380, _1433382] : [-(hAPP(c_Set_Ovimage(_1433374, _1433376, _1433378), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1433376, tc_HOL_Obool)), _1433380), _1433382)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1433374, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1433374, _1433376, _1433378), _1433380)), hAPP(c_Set_Ovimage(_1433374, _1433376, _1433378), _1433382)))], (35034 ^ _779308) ^ [_1433472, _1433474, _1433476, _1433478, _1433480] : [hBOOL(hAPP(hAPP(c_member(_1433472), _1433474), hAPP(c_Set_Ovimage(_1433472, _1433476, _1433478), _1433480))), -(hBOOL(hAPP(hAPP(c_member(_1433476), hAPP(_1433478, _1433474)), _1433480)))], (35040 ^ _779308) ^ [_1433599, _1433601, _1433603, _1433605, _1433607] : [hBOOL(hAPP(hAPP(c_member(_1433603), hAPP(_1433605, _1433601)), _1433607)), -(hBOOL(hAPP(hAPP(c_member(_1433599), _1433601), hAPP(c_Set_Ovimage(_1433599, _1433603, _1433605), _1433607))))], (35046 ^ _779308) ^ [_1433732, _1433734, _1433736, _1433738, _1433740] : [hBOOL(hAPP(hAPP(c_member(_1433732), _1433734), hAPP(c_Set_Ovimage(_1433732, _1433736, _1433738), _1433740))), -(hBOOL(hAPP(hAPP(c_member(_1433736), hAPP(_1433738, _1433734)), _1433740)))], (35052 ^ _779308) ^ [_1433863, _1433865, _1433867, _1433869, _1433871] : [hBOOL(hAPP(hAPP(c_member(_1433863), hAPP(_1433865, _1433867)), _1433869)), -(hBOOL(hAPP(hAPP(c_member(_1433871), _1433867), hAPP(c_Set_Ovimage(_1433871, _1433863, _1433865), _1433869))))], (35058 ^ _779308) ^ [_1433994, _1433996, _1433998, _1434000, _1434002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1433994, tc_HOL_Obool)), _1433996), _1433998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1434000, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1434000, _1433994, _1434002), _1433996)), hAPP(c_Set_Ovimage(_1434000, _1433994, _1434002), _1433998))))], (35064 ^ _779308) ^ [_1434145, _1434147, _1434149] : [-(hAPP(c_Set_Ovimage(_1434145, _1434147, _1434149), c_Orderings_Obot__class_Obot(tc_fun(_1434147, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1434145, tc_HOL_Obool)))], (35066 ^ _779308) ^ [_1434189, _1434191, _1434193, _1434195, _1434197] : [-(hAPP(c_Set_Ovimage(_1434189, _1434191, _1434193), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1434191, tc_HOL_Obool)), _1434195), _1434197)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1434189, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1434189, _1434191, _1434193), _1434195)), hAPP(c_Set_Ovimage(_1434189, _1434191, _1434193), _1434197)))], (35068 ^ _779308) ^ [_1434287, _1434289, _1434291, _1434293, _1434295] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1434287, _1434289, _1434291), _1434293), _1434295)), -(hBOOL(hAPP(_1434293, hAPP(_1434291, _1434295))))], (35074 ^ _779308) ^ [_1434394, _1434396, _1434398, _1434400, _1434402] : [hBOOL(hAPP(_1434400, hAPP(_1434398, _1434402))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1434394, _1434396, _1434398), _1434400), _1434402)))], (35080 ^ _779308) ^ [_1434507, _1434509] : [-(hAPP(c_Set_Ovimage(_1434507, _1434507, c_COMBI(_1434507)), _1434509) = _1434509)], (35082 ^ _779308) ^ [_1434541, _1434543, _1434545, _1434547] : [-(hAPP(c_Set_Ovimage(_1434541, _1434543, _1434545), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1434543, tc_HOL_Obool)), _1434547)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1434541, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1434541, _1434543, _1434545), _1434547)))], (35084 ^ _779308) ^ [_1434600, _1434602, _1434604, _1434606, _1434608] : [-(hAPP(c_Set_Ovimage(_1434600, _1434602, _1434604), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1434602, tc_HOL_Obool)), _1434606), _1434608)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1434600, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1434600, _1434602, _1434604), _1434606)), hAPP(c_Set_Ovimage(_1434600, _1434602, _1434604), _1434608)))], (35086 ^ _779308) ^ [_1434674, _1434676, _1434678, _1434680, _1434682, _1434684] : [-(hAPP(c_Set_Ovimage(_1434674, _1434676, _1434678), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1434680, tc_fun(_1434676, tc_HOL_Obool)), _1434682), _1434684)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1434680, tc_fun(_1434674, tc_HOL_Obool)), _1434682), hAPP(hAPP(c_COMBB(tc_fun(_1434676, tc_HOL_Obool), tc_fun(_1434674, tc_HOL_Obool), _1434680), c_Set_Ovimage(_1434674, _1434676, _1434678)), _1434684)))], (35088 ^ _779308) ^ [_1434758, _1434760, _1434762] : [-(hAPP(c_Set_Ovimage(_1434758, _1434760, _1434762), c_Orderings_Otop__class_Otop(tc_fun(_1434760, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1434758, tc_HOL_Obool)))], (35090 ^ _779308) ^ [_1434802, _1434804, _1434806, _1434808] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1434802, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1434804, _1434802, _1434806), hAPP(c_Set_Ovimage(_1434804, _1434802, _1434806), _1434808))), _1434808)))], (35092 ^ _779308) ^ [_1434855, _1434857, _1434859, _1434861] : [hAPP(c_Set_Oimage(_1434855, _1434857, _1434859), c_Orderings_Otop__class_Otop(tc_fun(_1434855, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1434857, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1434855, _1434857, _1434859), hAPP(c_Set_Ovimage(_1434855, _1434857, _1434859), _1434861)) = _1434861)], (35098 ^ _779308) ^ [_1434998, _1435000, _1435002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1434998, _1434998), tc_HOL_Obool)), _1435000), _1435002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1434998, tc_HOL_Obool)), c_Wellfounded_Oacc(_1434998, _1435002)), c_Wellfounded_Oacc(_1434998, _1435000))))], (35104 ^ _779308) ^ [_1435159, _1435161, _1435163, _1435165, _1435167] : [hBOOL(hAPP(hAPP(c_member(_1435159), _1435161), hAPP(c_Set_Ovimage(_1435159, _1435163, _1435165), hAPP(hAPP(c_Set_Oinsert(_1435163), _1435167), c_Orderings_Obot__class_Obot(tc_fun(_1435163, tc_HOL_Obool)))))), -(hAPP(_1435165, _1435161) = _1435167)], (35110 ^ _779308) ^ [_1435298, _1435300, _1435302, _1435304, _1435306] : [hAPP(_1435304, _1435300) = _1435306, -(hBOOL(hAPP(hAPP(c_member(_1435298), _1435300), hAPP(c_Set_Ovimage(_1435298, _1435302, _1435304), hAPP(hAPP(c_Set_Oinsert(_1435302), _1435306), c_Orderings_Obot__class_Obot(tc_fun(_1435302, tc_HOL_Obool)))))))], (35116 ^ _779308) ^ [_1435443, _1435445, _1435447, _1435449, _1435451] : [-(hAPP(c_Set_Ovimage(_1435443, _1435445, _1435447), hAPP(hAPP(c_Set_Oinsert(_1435445), _1435449), _1435451)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1435443, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1435443, _1435445, _1435447), hAPP(hAPP(c_Set_Oinsert(_1435445), _1435449), c_Orderings_Obot__class_Obot(tc_fun(_1435445, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1435443, _1435445, _1435447), _1435451)))], (35118 ^ _779308) ^ [_1435527, _1435529, _1435531, _1435533] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1435527), hAPP(c_Set_Ovimage(_1435527, _1435529, _1435531), _1435533))), hAPP(c_Set_Oimage(_1435527, _1435529, _1435531), c_Orderings_Otop__class_Otop(tc_fun(_1435527, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1435529, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1435529), _1435533)))], (35128 ^ _779308) ^ [_1435728, _1435730, _1435732, _1435734, _1435736] : [hAPP(c_Set_Oimage(_1435728, _1435730, _1435732), c_Orderings_Otop__class_Otop(tc_fun(_1435728, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1435730, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1435728, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1435728, _1435730, _1435732), _1435734)), _1435736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1435730, tc_HOL_Obool)), _1435734), hAPP(c_Set_Oimage(_1435728, _1435730, _1435732), _1435736))))], (35138 ^ _779308) ^ [_1435971, _1435973, _1435975, _1435977] : [-(hAPP(c_Set_Oimage(_1435971, _1435973, _1435975), hAPP(c_Set_Ovimage(_1435971, _1435973, _1435975), _1435977)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1435973, tc_HOL_Obool)), _1435977), hAPP(c_Set_Oimage(_1435971, _1435973, _1435975), c_Orderings_Otop__class_Otop(tc_fun(_1435971, tc_HOL_Obool)))))], (35140 ^ _779308) ^ [_1436037, _1436039, _1436041, _1436043] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1436037), _1436039)), c_Fun_Oinj__on(_1436041, _1436037, _1436043, c_Orderings_Otop__class_Otop(tc_fun(_1436041, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1436041), hAPP(c_Set_Ovimage(_1436041, _1436037, _1436043), _1436039))))], (35150 ^ _779308) ^ [_1436218, _1436220, _1436222, _1436224] : [c_Fun_Oinj__on(_1436218, _1436220, _1436222, c_Orderings_Otop__class_Otop(tc_fun(_1436218, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1436218, _1436220, _1436222), hAPP(c_Set_Oimage(_1436218, _1436220, _1436222), _1436224)) = _1436224)], (35156 ^ _779308) ^ [_1436356, _1436358, _1436360, _1436362] : [hBOOL(hAPP(hAPP(c_member(_1436356), _1436358), _1436360)), -(hAPP(c_Set_Ovimage(_1436362, _1436356, hAPP(c_COMBK(_1436356, _1436362), _1436358)), _1436360) = c_Orderings_Otop__class_Otop(tc_fun(_1436362, tc_HOL_Obool)))], (35162 ^ _779308) ^ [_1436481, _1436483, _1436485, _1436487] : [-(hBOOL(hAPP(hAPP(c_member(_1436481), _1436483), _1436485))), -(hAPP(c_Set_Ovimage(_1436487, _1436481, hAPP(c_COMBK(_1436481, _1436487), _1436483)), _1436485) = c_Orderings_Obot__class_Obot(tc_fun(_1436487, tc_HOL_Obool)))], (35168 ^ _779308) ^ [_1436548, _1436550, _1436552, _1436554] : [-(hAPP(c_Set_Ovimage(_1436548, _1436550, _1436552), _1436554) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1436550, tc_fun(_1436548, tc_HOL_Obool)), _1436554), hAPP(hAPP(c_COMBB(tc_fun(_1436550, tc_HOL_Obool), tc_fun(_1436548, tc_HOL_Obool), _1436550), c_Set_Ovimage(_1436548, _1436550, _1436552)), hAPP(hAPP(c_COMBC(_1436550, tc_fun(_1436550, tc_HOL_Obool), tc_fun(_1436550, tc_HOL_Obool)), c_Set_Oinsert(_1436550)), c_Orderings_Obot__class_Obot(tc_fun(_1436550, tc_HOL_Obool))))))], (35180 ^ _779308) ^ [_1436910, _1436912, _1436914] : [35182 ^ _779308 : [(35183 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1436910, _1436910)), hAPP(hAPP(c_Product__Type_OPair(_1436910, _1436910), 35181 ^ [_1436910, _1436912, _1436914]), _1436912)), _1436914)))], (35185 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1436910), 35181 ^ [_1436910, _1436912, _1436914]), c_Wellfounded_Oacc(_1436910, _1436914)))]], -(hBOOL(hAPP(hAPP(c_member(_1436910), _1436912), c_Wellfounded_Oacc(_1436910, _1436914))))], (35170 ^ _779308) ^ [_1436657, _1436659, _1436661] : [hBOOL(hAPP(hAPP(c_member(_1436657), _1436659), c_Wellfounded_Oacc(_1436657, _1436661))), 35173 ^ _779308 : [(35174 ^ _779308) ^ [_1436771] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1436657, _1436657)), hAPP(hAPP(c_Product__Type_OPair(_1436657, _1436657), _1436771), _1436659)), _1436661)), -(hBOOL(hAPP(hAPP(c_member(_1436657), _1436771), c_Wellfounded_Oacc(_1436657, _1436661))))]]], (35189 ^ _779308) ^ [_1437150, _1437152, _1437154, _1437156] : [hBOOL(hAPP(hAPP(c_member(_1437150), _1437152), c_Wellfounded_Oacc(_1437150, _1437154))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1437150, _1437150)), hAPP(hAPP(c_Product__Type_OPair(_1437150, _1437150), _1437156), _1437152)), _1437154)), -(hBOOL(hAPP(hAPP(c_member(_1437150), _1437156), c_Wellfounded_Oacc(_1437150, _1437154))))], (35199 ^ _779308) ^ [_1437365, _1437367, _1437369, _1437371, _1437373] : [c_Fun_Oinj__on(_1437365, _1437367, _1437369, c_Orderings_Otop__class_Otop(tc_fun(_1437365, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437367, tc_HOL_Obool)), _1437371), hAPP(c_Set_Oimage(_1437365, _1437367, _1437369), _1437373))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437365, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1437365, _1437367, _1437369), _1437371)), _1437373)))], (35209 ^ _779308) ^ [_1437609, _1437611, _1437613, _1437615, _1437617, _1437619] : [hBOOL(hAPP(hAPP(c_member(_1437609), _1437611), _1437613)), 35212 ^ _779308 : [(35213 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1437609), _1437615), _1437613)), -(hAPP(c_Set_Ovimage(_1437617, _1437609, hAPP(hAPP(c_COMBC(_1437617, _1437609, _1437609), hAPP(hAPP(c_COMBC(_1437617, _1437609, tc_fun(_1437609, _1437609)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1437609, tc_fun(_1437609, _1437609)), _1437617), c_If(_1437609)), hAPP(hAPP(c_COMBC(_1437617, tc_fun(_1437617, tc_HOL_Obool), tc_HOL_Obool), c_member(_1437617)), _1437619))), _1437611)), _1437615)), _1437613) = c_Orderings_Otop__class_Otop(tc_fun(_1437617, tc_HOL_Obool)))], (35219 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1437609), _1437615), _1437613))), -(hAPP(c_Set_Ovimage(_1437617, _1437609, hAPP(hAPP(c_COMBC(_1437617, _1437609, _1437609), hAPP(hAPP(c_COMBC(_1437617, _1437609, tc_fun(_1437609, _1437609)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1437609, tc_fun(_1437609, _1437609)), _1437617), c_If(_1437609)), hAPP(hAPP(c_COMBC(_1437617, tc_fun(_1437617, tc_HOL_Obool), tc_HOL_Obool), c_member(_1437617)), _1437619))), _1437611)), _1437615)), _1437613) = _1437619)]]], (35225 ^ _779308) ^ [_1438100, _1438102, _1438104, _1438106, _1438108, _1438110] : [-(hBOOL(hAPP(hAPP(c_member(_1438100), _1438102), _1438104))), 35228 ^ _779308 : [(35229 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1438100), _1438106), _1438104)), -(hAPP(c_Set_Ovimage(_1438108, _1438100, hAPP(hAPP(c_COMBC(_1438108, _1438100, _1438100), hAPP(hAPP(c_COMBC(_1438108, _1438100, tc_fun(_1438100, _1438100)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1438100, tc_fun(_1438100, _1438100)), _1438108), c_If(_1438100)), hAPP(hAPP(c_COMBC(_1438108, tc_fun(_1438108, tc_HOL_Obool), tc_HOL_Obool), c_member(_1438108)), _1438110))), _1438102)), _1438106)), _1438104) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1438108, tc_HOL_Obool)), _1438110))], (35235 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1438100), _1438106), _1438104))), -(hAPP(c_Set_Ovimage(_1438108, _1438100, hAPP(hAPP(c_COMBC(_1438108, _1438100, _1438100), hAPP(hAPP(c_COMBC(_1438108, _1438100, tc_fun(_1438100, _1438100)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1438100, tc_fun(_1438100, _1438100)), _1438108), c_If(_1438100)), hAPP(hAPP(c_COMBC(_1438108, tc_fun(_1438108, tc_HOL_Obool), tc_HOL_Obool), c_member(_1438108)), _1438110))), _1438102)), _1438106)), _1438104) = c_Orderings_Obot__class_Obot(tc_fun(_1438108, tc_HOL_Obool)))]]], (35241 ^ _779308) ^ [_1438605, _1438607, _1438609, _1438611, _1438613] : [c_Typedef_Otype__definition(_1438605, _1438607, _1438609, _1438611, _1438613), -(hAPP(c_Set_Oimage(_1438607, _1438605, _1438611), _1438613) = c_Orderings_Otop__class_Otop(tc_fun(_1438605, tc_HOL_Obool)))], (35247 ^ _779308) ^ [_1438718, _1438720, _1438722, _1438724, _1438726] : [c_Typedef_Otype__definition(_1438718, _1438720, _1438722, _1438724, _1438726), -(hAPP(c_Set_Oimage(_1438718, _1438720, _1438722), c_Orderings_Otop__class_Otop(tc_fun(_1438718, tc_HOL_Obool))) = _1438726)], (35253 ^ _779308) ^ [_1438831, _1438833, _1438835, _1438837, _1438839, _1438841, _1438843] : [c_Typedef_Otype__definition(_1438831, _1438833, _1438835, _1438837, _1438839), hBOOL(hAPP(hAPP(c_member(_1438833), _1438841), _1438839)), hBOOL(hAPP(hAPP(c_member(_1438833), _1438843), _1438839)), 35264 ^ _779308 : [(35265 ^ _779308) ^ [] : [hAPP(_1438837, _1438841) = hAPP(_1438837, _1438843), -(_1438841 = _1438843)], (35271 ^ _779308) ^ [] : [_1438841 = _1438843, -(hAPP(_1438837, _1438841) = hAPP(_1438837, _1438843))]]], (35277 ^ _779308) ^ [_1439244, _1439246, _1439248, _1439250, _1439252, _1439254, _1439256] : [c_Typedef_Otype__definition(_1439244, _1439246, _1439248, _1439250, _1439252), 35280 ^ _779308 : [(35281 ^ _779308) ^ [] : [hAPP(_1439248, _1439254) = hAPP(_1439248, _1439256), -(_1439254 = _1439256)], (35287 ^ _779308) ^ [] : [_1439254 = _1439256, -(hAPP(_1439248, _1439254) = hAPP(_1439248, _1439256))]]], (35293 ^ _779308) ^ [_1439505, _1439507, _1439509, _1439511, _1439513, _1439515] : [c_Typedef_Otype__definition(_1439505, _1439507, _1439509, _1439511, _1439513), -(hAPP(_1439511, hAPP(_1439509, _1439515)) = _1439515)], (35299 ^ _779308) ^ [_1439608, _1439610, _1439612, _1439614, _1439616, _1439618] : [c_Typedef_Otype__definition(_1439608, _1439610, _1439612, _1439614, _1439616), -(hBOOL(hAPP(hAPP(c_member(_1439610), hAPP(_1439612, _1439618)), _1439616)))], (35305 ^ _779308) ^ [_1439719, _1439721, _1439723, _1439725, _1439727, _1439729] : [c_Typedef_Otype__definition(_1439719, _1439721, _1439723, _1439725, _1439727), hBOOL(hAPP(hAPP(c_member(_1439721), _1439729), _1439727)), -(hAPP(_1439723, hAPP(_1439725, _1439729)) = _1439729)], (35315 ^ _779308) ^ [_1439917, _1439919, _1439921, _1439923] : [c_Wellfounded_Omax__extp(_1439917, _1439919, _1439921, _1439923), 35318 ^ _779308 : [(35319 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1439917), _1439921)))], (35321 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1439917), _1439923)))], (35323 ^ _779308) ^ [] : [_1439923 = c_Orderings_Obot__class_Obot(tc_fun(_1439917, tc_HOL_Obool))], (35325 ^ _779308) ^ [_1440133] : [hBOOL(hAPP(hAPP(c_member(_1439917), _1440133), _1439921)), 35329 ^ _779308 : [(35330 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1439917), 35328 ^ [_1439917, _1439919, _1439921, _1439923, _1440133]), _1439923)))], (35332 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1439919, _1440133), 35328 ^ [_1439917, _1439919, _1439921, _1439923, _1440133])))]]]]], (35334 ^ _779308) ^ [_1440317, _1440319, _1440321, _1440323] : [-(c_Wellfounded_Omax__extp(_1440317, _1440319, _1440321, _1440323)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440317), _1440321)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440317), _1440323)), -(_1440323 = c_Orderings_Obot__class_Obot(tc_fun(_1440317, tc_HOL_Obool))), 35348 ^ _779308 : [(35349 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1440317), 35347 ^ [_1440317, _1440319, _1440321, _1440323]), _1440321)))], (35351 ^ _779308) ^ [_1440662] : [hBOOL(hAPP(hAPP(c_member(_1440317), _1440662), _1440323)), hBOOL(hAPP(hAPP(_1440319, 35347 ^ [_1440317, _1440319, _1440321, _1440323]), _1440662))]]], (35359 ^ _779308) ^ [_1440830, _1440832, _1440834, _1440836] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1440830), _1440832)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440830), _1440834)), -(_1440834 = c_Orderings_Obot__class_Obot(tc_fun(_1440830, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1440830, tc_HOL_Obool), tc_fun(_1440830, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1440830, tc_HOL_Obool), tc_fun(_1440830, tc_HOL_Obool)), _1440832), _1440834)), c_Wellfounded_Omax__ext(_1440830, _1440836)))), 35373 ^ _779308 : [(35374 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1440830), 35372 ^ [_1440830, _1440832, _1440834, _1440836]), _1440832)))], (35376 ^ _779308) ^ [_1441235] : [hBOOL(hAPP(hAPP(c_member(_1440830), _1441235), _1440834)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1440830, _1440830)), hAPP(hAPP(c_Product__Type_OPair(_1440830, _1440830), 35372 ^ [_1440830, _1440832, _1440834, _1440836]), _1441235)), _1440836))]]], (35384 ^ _779308) ^ [_1441461] : [-(c_Nitpick_Ozero__frac(_1441461) = c_Nitpick_OAbs__Frac(_1441461, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35386 ^ _779308) ^ [_1441489] : [-(c_Nitpick_Oone__frac(_1441489) = c_Nitpick_OAbs__Frac(_1441489, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35388 ^ _779308) ^ [_1441517, _1441519] : [-(c_Nitpick_Onumber__of__frac(_1441517, _1441519) = c_Nitpick_OAbs__Frac(_1441517, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1441519), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35390 ^ _779308) ^ [_1441554, _1441556, _1441558] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1441554), _1441556), _1441558) = c_Nitpick_OAbs__Frac(_1441554, c_Nitpick_Onorm__frac(_1441556, _1441558)))], (35392 ^ _779308) ^ [_1441595, _1441597, _1441599, _1441601, _1441603, _1441605] : [-(hAPP(c_Set_Oimage(_1441595, tc_prod(_1441597, _1441599), hAPP(hAPP(c_COMBS(_1441595, _1441599, tc_prod(_1441597, _1441599)), hAPP(hAPP(c_COMBB(_1441597, tc_fun(_1441599, tc_prod(_1441597, _1441599)), _1441595), c_Product__Type_OPair(_1441597, _1441599)), _1441601)), _1441603)), _1441605) = hAPP(hAPP(c_Product__Type_OSigma(_1441597, _1441599), hAPP(c_Set_Oimage(_1441595, _1441597, _1441601), _1441605)), hAPP(hAPP(c_COMBB(tc_fun(_1441595, tc_HOL_Obool), tc_fun(_1441599, tc_HOL_Obool), _1441597), c_Set_Oimage(_1441595, _1441599, _1441603)), hAPP(hAPP(c_COMBC(_1441597, tc_fun(_1441595, tc_HOL_Obool), tc_fun(_1441595, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1441595, tc_HOL_Obool), tc_fun(tc_fun(_1441595, tc_HOL_Obool), tc_fun(_1441595, tc_HOL_Obool)), _1441597), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441595, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1441597, tc_HOL_Obool), tc_fun(_1441595, tc_HOL_Obool), _1441597), c_Set_Ovimage(_1441595, _1441597, _1441601)), hAPP(hAPP(c_COMBC(_1441597, tc_fun(_1441597, tc_HOL_Obool), tc_fun(_1441597, tc_HOL_Obool)), c_Set_Oinsert(_1441597)), c_Orderings_Obot__class_Obot(tc_fun(_1441597, tc_HOL_Obool)))))), _1441605))))], (35394 ^ _779308) ^ [_1441792, _1441794, _1441796] : [35396 ^ _779308 : [(35397 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 35395 ^ [_1441792, _1441794, _1441796]), _1441792)))], (35399 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(_1441794, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 35395 ^ [_1441792, _1441794, _1441796]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1441794, 35395 ^ [_1441792, _1441794, _1441796])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1441794, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1441796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1441796), hAPP(_1441794, _1441792))), 35409 ^ _779308 : [(35410 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35408 ^ [_1441792, _1441794, _1441796]), _1441792)))], (35412 ^ _779308) ^ [] : [-(hAPP(_1441794, 35408 ^ [_1441792, _1441794, _1441796]) = _1441796)]]], (35414 ^ _779308) ^ [_1442242, _1442244, _1442246] : [35416 ^ _779308 : [(35417 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 35415 ^ [_1442242, _1442244, _1442246]), _1442242)))], (35419 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(_1442244, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 35415 ^ [_1442242, _1442244, _1442246]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1442244, 35415 ^ [_1442242, _1442244, _1442246])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1442244, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1442246)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1442246), hAPP(_1442244, _1442242))), 35429 ^ _779308 : [(35430 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 35428 ^ [_1442242, _1442244, _1442246]), _1442242)))], (35432 ^ _779308) ^ [] : [-(hAPP(_1442244, 35428 ^ [_1442242, _1442244, _1442246]) = _1442246)]]], (35434 ^ _779308) ^ [_1442692, _1442694, _1442696, _1442698, _1442700, _1442702] : [hBOOL(hAPP(hAPP(c_member(_1442692), _1442694), _1442696)), hBOOL(hAPP(hAPP(c_member(_1442698), _1442700), hAPP(_1442702, _1442694))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1442692, _1442698)), hAPP(hAPP(c_Product__Type_OPair(_1442692, _1442698), _1442694), _1442700)), hAPP(hAPP(c_Product__Type_OSigma(_1442692, _1442698), _1442696), _1442702))))], (35444 ^ _779308) ^ [_1442927, _1442929, _1442931, _1442933, _1442935] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1442927, _1442929), _1442931), hAPP(hAPP(c_COMBS(_1442927, tc_fun(_1442929, tc_HOL_Obool), tc_fun(_1442929, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1442929, tc_HOL_Obool), tc_fun(tc_fun(_1442929, tc_HOL_Obool), tc_fun(_1442929, tc_HOL_Obool)), _1442927), c_Groups_Ominus__class_Ominus(tc_fun(_1442929, tc_HOL_Obool))), _1442933)), _1442935)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1442927, _1442929), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1442927, _1442929), _1442931), _1442933)), hAPP(hAPP(c_Product__Type_OSigma(_1442927, _1442929), _1442931), _1442935)))], (35446 ^ _779308) ^ [_1443042, _1443044, _1443046, _1443048, _1443050] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1443042, _1443044), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443042, tc_HOL_Obool)), _1443046), _1443048)), hAPP(c_COMBK(tc_fun(_1443044, tc_HOL_Obool), _1443042), _1443050)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1443042, _1443044), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1443042, _1443044), _1443046), hAPP(c_COMBK(tc_fun(_1443044, tc_HOL_Obool), _1443042), _1443050))), hAPP(hAPP(c_Product__Type_OSigma(_1443042, _1443044), _1443048), hAPP(c_COMBK(tc_fun(_1443044, tc_HOL_Obool), _1443042), _1443050))))], (35448 ^ _779308) ^ [_1443152, _1443154, _1443156, _1443158, _1443160] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1443152, _1443154), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443152, tc_HOL_Obool)), _1443156), _1443158)), _1443160) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1443152, _1443154), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1443152, _1443154), _1443156), _1443160)), hAPP(hAPP(c_Product__Type_OSigma(_1443152, _1443154), _1443158), _1443160)))], (35450 ^ _779308) ^ [_1443235, _1443237, _1443239, _1443241, _1443243, _1443245] : [hBOOL(hAPP(hAPP(c_member(_1443235), _1443237), _1443239)), 35453 ^ _779308 : [(35454 ^ _779308) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1443241, _1443235), _1443243), hAPP(c_COMBK(tc_fun(_1443235, tc_HOL_Obool), _1443241), _1443239)) = hAPP(hAPP(c_Product__Type_OSigma(_1443241, _1443235), _1443245), hAPP(c_COMBK(tc_fun(_1443235, tc_HOL_Obool), _1443241), _1443239)), -(_1443243 = _1443245)], (35460 ^ _779308) ^ [] : [_1443243 = _1443245, -(hAPP(hAPP(c_Product__Type_OSigma(_1443241, _1443235), _1443243), hAPP(c_COMBK(tc_fun(_1443235, tc_HOL_Obool), _1443241), _1443239)) = hAPP(hAPP(c_Product__Type_OSigma(_1443241, _1443235), _1443245), hAPP(c_COMBK(tc_fun(_1443235, tc_HOL_Obool), _1443241), _1443239)))]]], (35466 ^ _779308) ^ [_1443588, _1443590, _1443592] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1443588, _1443590), c_Orderings_Obot__class_Obot(tc_fun(_1443588, tc_HOL_Obool))), _1443592) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1443588, _1443590), tc_HOL_Obool)))], (35468 ^ _779308) ^ [_1443637, _1443639, _1443641, _1443643] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1443637, _1443639)), hAPP(hAPP(c_Product__Type_OSigma(_1443637, _1443639), _1443641), hAPP(c_COMBK(tc_fun(_1443639, tc_HOL_Obool), _1443637), _1443643))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1443637), _1443641)), hAPP(c_Finite__Set_Ocard(_1443639), _1443643)))], (35470 ^ _779308) ^ [_1443708, _1443710, _1443712, _1443714, _1443716, _1443718] : [class_Groups_Ocomm__monoid__add(_1443708), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443710, _1443708), hAPP(hAPP(c_COMBC(_1443710, tc_fun(_1443712, tc_HOL_Obool), _1443708), hAPP(hAPP(c_COMBB(tc_fun(_1443712, _1443708), tc_fun(tc_fun(_1443712, tc_HOL_Obool), _1443708), _1443710), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443712, _1443708)), _1443714)), _1443716)), _1443718) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1443710, _1443712), _1443708), hAPP(c_Product__Type_Oprod_Oprod__case(_1443710, _1443712, _1443708), _1443714)), hAPP(hAPP(c_Product__Type_OSigma(_1443710, _1443712), _1443718), hAPP(c_COMBK(tc_fun(_1443712, tc_HOL_Obool), _1443710), _1443716))))], (35486 ^ _779308) ^ [_1444136, _1444138, _1444140, _1444142] : [35487 ^ _779308 : [(35488 ^ _779308) ^ [] : [_1444140 = c_Orderings_Obot__class_Obot(tc_fun(_1444136, tc_HOL_Obool))], (35490 ^ _779308) ^ [] : [_1444142 = c_Orderings_Obot__class_Obot(tc_fun(_1444138, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1444136, _1444138), _1444140), hAPP(c_COMBK(tc_fun(_1444138, tc_HOL_Obool), _1444136), _1444142)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1444136, _1444138), tc_HOL_Obool)))], (35476 ^ _779308) ^ [_1443974, _1443976, _1443978, _1443980] : [hAPP(hAPP(c_Product__Type_OSigma(_1443974, _1443976), _1443978), hAPP(c_COMBK(tc_fun(_1443976, tc_HOL_Obool), _1443974), _1443980)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1443974, _1443976), tc_HOL_Obool)), -(_1443978 = c_Orderings_Obot__class_Obot(tc_fun(_1443974, tc_HOL_Obool))), -(_1443980 = c_Orderings_Obot__class_Obot(tc_fun(_1443976, tc_HOL_Obool)))], (35494 ^ _779308) ^ [_1444329, _1444331, _1444333] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1444329, _1444331), _1444333), hAPP(c_COMBK(tc_fun(_1444331, tc_HOL_Obool), _1444329), c_Orderings_Obot__class_Obot(tc_fun(_1444331, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1444329, _1444331), tc_HOL_Obool)))], (35496 ^ _779308) ^ [_1444387, _1444389, _1444391] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1444387, _1444389), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1444387, _1444389), c_Orderings_Otop__class_Otop(tc_fun(_1444387, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1444389, tc_HOL_Obool), _1444387), _1444391))) = hAPP(hAPP(c_Product__Type_OSigma(_1444387, _1444389), c_Orderings_Otop__class_Otop(tc_fun(_1444387, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1444389, tc_HOL_Obool), _1444387), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1444389, tc_HOL_Obool)), _1444391))))], (35498 ^ _779308) ^ [_1444479, _1444481, _1444483] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1444479, _1444481), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1444479, _1444481), _1444483), hAPP(c_COMBK(tc_fun(_1444481, tc_HOL_Obool), _1444479), c_Orderings_Otop__class_Otop(tc_fun(_1444481, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1444479, _1444481), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1444479, tc_HOL_Obool)), _1444483)), hAPP(c_COMBK(tc_fun(_1444481, tc_HOL_Obool), _1444479), c_Orderings_Otop__class_Otop(tc_fun(_1444481, tc_HOL_Obool)))))], (35500 ^ _779308) ^ [_1444571, _1444573, _1444575, _1444577, _1444579, _1444581] : [class_Groups_Ocomm__monoid__mult(_1444571), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1444573, _1444571), hAPP(hAPP(c_COMBC(_1444573, tc_fun(_1444575, tc_HOL_Obool), _1444571), hAPP(hAPP(c_COMBB(tc_fun(_1444575, _1444571), tc_fun(tc_fun(_1444575, tc_HOL_Obool), _1444571), _1444573), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1444575, _1444571)), _1444577)), _1444579)), _1444581) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1444573, _1444575), _1444571), hAPP(c_Product__Type_Oprod_Oprod__case(_1444573, _1444575, _1444571), _1444577)), hAPP(hAPP(c_Product__Type_OSigma(_1444573, _1444575), _1444581), hAPP(c_COMBK(tc_fun(_1444575, tc_HOL_Obool), _1444573), _1444579))))], (35506 ^ _779308) ^ [_1444816, _1444818, _1444820, _1444822, _1444824] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1444816, _1444818), _1444820), hAPP(hAPP(c_COMBS(_1444816, tc_fun(_1444818, tc_HOL_Obool), tc_fun(_1444818, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1444818, tc_HOL_Obool), tc_fun(tc_fun(_1444818, tc_HOL_Obool), tc_fun(_1444818, tc_HOL_Obool)), _1444816), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1444818, tc_HOL_Obool))), _1444822)), _1444824)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1444816, _1444818), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1444816, _1444818), _1444820), _1444822)), hAPP(hAPP(c_Product__Type_OSigma(_1444816, _1444818), _1444820), _1444824)))], (35508 ^ _779308) ^ [_1444931, _1444933, _1444935, _1444937, _1444939] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1444931, _1444933), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1444931, tc_HOL_Obool)), _1444935), _1444937)), hAPP(c_COMBK(tc_fun(_1444933, tc_HOL_Obool), _1444931), _1444939)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1444931, _1444933), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1444931, _1444933), _1444935), hAPP(c_COMBK(tc_fun(_1444933, tc_HOL_Obool), _1444931), _1444939))), hAPP(hAPP(c_Product__Type_OSigma(_1444931, _1444933), _1444937), hAPP(c_COMBK(tc_fun(_1444933, tc_HOL_Obool), _1444931), _1444939))))], (35510 ^ _779308) ^ [_1445041, _1445043, _1445045, _1445047, _1445049] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1445041, _1445043), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445041, tc_HOL_Obool)), _1445045), _1445047)), _1445049) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1445041, _1445043), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1445041, _1445043), _1445045), _1445049)), hAPP(hAPP(c_Product__Type_OSigma(_1445041, _1445043), _1445047), _1445049)))], (35512 ^ _779308) ^ [_1445124, _1445126, _1445128, _1445130] : [-(hAPP(c_Set_Oimage(tc_prod(_1445124, _1445126), tc_prod(_1445126, _1445124), hAPP(c_Product__Type_Oprod_Oprod__case(_1445124, _1445126, tc_prod(_1445126, _1445124)), hAPP(c_COMBC(_1445126, _1445124, tc_prod(_1445126, _1445124)), c_Product__Type_OPair(_1445126, _1445124)))), hAPP(hAPP(c_Product__Type_OSigma(_1445124, _1445126), _1445128), hAPP(c_COMBK(tc_fun(_1445126, tc_HOL_Obool), _1445124), _1445130))) = hAPP(hAPP(c_Product__Type_OSigma(_1445126, _1445124), _1445130), hAPP(c_COMBK(tc_fun(_1445124, tc_HOL_Obool), _1445126), _1445128)))], (35514 ^ _779308) ^ [_1445225, _1445227, _1445229, _1445231] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1445225), _1445227)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1445229), _1445231)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1445225, _1445229)), hAPP(hAPP(c_Product__Type_OSigma(_1445225, _1445229), _1445227), hAPP(c_COMBK(tc_fun(_1445229, tc_HOL_Obool), _1445225), _1445231)))))], (35524 ^ _779308) ^ [_1445428, _1445430, _1445432] : [c_Equiv__Relations_Oequiv(_1445428, _1445430, _1445432), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1445428, _1445428), tc_HOL_Obool)), _1445432), hAPP(hAPP(c_Product__Type_OSigma(_1445428, _1445428), _1445430), hAPP(c_COMBK(tc_fun(_1445428, tc_HOL_Obool), _1445428), _1445430)))))], (35530 ^ _779308) ^ [_1445571, _1445573, _1445575, _1445577, _1445579] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1445571, _1445573), _1445575), hAPP(hAPP(c_COMBS(_1445571, tc_fun(_1445573, tc_HOL_Obool), tc_fun(_1445573, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445573, tc_HOL_Obool), tc_fun(tc_fun(_1445573, tc_HOL_Obool), tc_fun(_1445573, tc_HOL_Obool)), _1445571), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445573, tc_HOL_Obool))), _1445577)), _1445579)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1445571, _1445573), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1445571, _1445573), _1445575), _1445577)), hAPP(hAPP(c_Product__Type_OSigma(_1445571, _1445573), _1445575), _1445579)))], (35532 ^ _779308) ^ [_1445686, _1445688, _1445690, _1445692, _1445694] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1445686, _1445688), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445686, tc_HOL_Obool)), _1445690), _1445692)), hAPP(c_COMBK(tc_fun(_1445688, tc_HOL_Obool), _1445686), _1445694)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1445686, _1445688), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1445686, _1445688), _1445690), hAPP(c_COMBK(tc_fun(_1445688, tc_HOL_Obool), _1445686), _1445694))), hAPP(hAPP(c_Product__Type_OSigma(_1445686, _1445688), _1445692), hAPP(c_COMBK(tc_fun(_1445688, tc_HOL_Obool), _1445686), _1445694))))], (35534 ^ _779308) ^ [_1445796, _1445798, _1445800, _1445802, _1445804] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1445796, _1445798), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1445796, tc_HOL_Obool)), _1445800), _1445802)), _1445804) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1445796, _1445798), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1445796, _1445798), _1445800), _1445804)), hAPP(hAPP(c_Product__Type_OSigma(_1445796, _1445798), _1445802), _1445804)))], (35536 ^ _779308) ^ [_1445879, _1445881] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1445879, _1445879), tc_HOL_Obool)), c_Relation_OId__on(_1445879, _1445881)), hAPP(hAPP(c_Product__Type_OSigma(_1445879, _1445879), _1445881), hAPP(c_COMBK(tc_fun(_1445879, tc_HOL_Obool), _1445879), _1445881)))))], (35538 ^ _779308) ^ [_1445938, _1445940] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1445938, _1445940), c_Orderings_Otop__class_Otop(tc_fun(_1445938, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1445940, tc_HOL_Obool), _1445938), c_Orderings_Otop__class_Otop(tc_fun(_1445940, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1445938, _1445940), tc_HOL_Obool)))], (35540 ^ _779308) ^ [_1446026, _1446028, _1446030, _1446032, _1446034, _1446036] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1446026, _1446028)), hAPP(hAPP(c_Product__Type_OPair(_1446026, _1446028), _1446030), _1446032)), hAPP(hAPP(c_Product__Type_OSigma(_1446026, _1446028), _1446034), _1446036))), 35543 ^ _779308 : [(35544 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1446026), _1446030), _1446034)))], (35546 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1446028), _1446032), hAPP(_1446036, _1446030))))]]], (35548 ^ _779308) ^ [_1446223, _1446225, _1446227, _1446229, _1446231, _1446233] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446223, _1446225)), hAPP(hAPP(c_Product__Type_OPair(_1446223, _1446225), _1446227), _1446229)), hAPP(hAPP(c_Product__Type_OSigma(_1446223, _1446225), _1446231), _1446233)))), hBOOL(hAPP(hAPP(c_member(_1446223), _1446227), _1446231)), hBOOL(hAPP(hAPP(c_member(_1446225), _1446229), hAPP(_1446233, _1446227)))], (35558 ^ _779308) ^ [_1446460, _1446462, _1446464, _1446466, _1446468, _1446470] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1446460, _1446462)), hAPP(hAPP(c_Product__Type_OPair(_1446460, _1446462), _1446464), _1446466)), hAPP(hAPP(c_Product__Type_OSigma(_1446460, _1446462), _1446468), _1446470))), -(hBOOL(hAPP(hAPP(c_member(_1446460), _1446464), _1446468)))], (35564 ^ _779308) ^ [_1446615, _1446617, _1446619, _1446621, _1446623, _1446625] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1446615, _1446617)), hAPP(hAPP(c_Product__Type_OPair(_1446615, _1446617), _1446619), _1446621)), hAPP(hAPP(c_Product__Type_OSigma(_1446615, _1446617), _1446623), _1446625))), -(hBOOL(hAPP(hAPP(c_member(_1446617), _1446621), hAPP(_1446625, _1446619))))], (35570 ^ _779308) ^ [_1446776, _1446778, _1446780, _1446782, _1446784, _1446786] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1446776, _1446778)), hAPP(hAPP(c_Product__Type_OPair(_1446776, _1446778), _1446780), _1446782)), hAPP(hAPP(c_Product__Type_OSigma(_1446776, _1446778), _1446784), _1446786))), 35573 ^ _779308 : [(35574 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1446776), _1446780), _1446784)))], (35576 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1446778), _1446782), hAPP(_1446786, _1446780))))]]], (35578 ^ _779308) ^ [_1446981, _1446983, _1446985, _1446987] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1446981, _1446983)), hAPP(hAPP(c_Product__Type_OSigma(_1446981, _1446983), hAPP(hAPP(c_Set_Oinsert(_1446981), _1446985), c_Orderings_Obot__class_Obot(tc_fun(_1446981, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1446983, tc_HOL_Obool), _1446981), _1446987))) = hAPP(c_Finite__Set_Ocard(_1446983), _1446987))], (35580 ^ _779308) ^ [_1447054, _1447056, _1447058, _1447060, _1447062, _1447064] : [hBOOL(hAPP(hAPP(c_member(_1447054), _1447056), _1447058)), 35583 ^ _779308 : [(35584 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1447060, _1447054), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1447060, _1447054), _1447062), hAPP(c_COMBK(tc_fun(_1447054, tc_HOL_Obool), _1447060), _1447058))), hAPP(hAPP(c_Product__Type_OSigma(_1447060, _1447054), _1447064), hAPP(c_COMBK(tc_fun(_1447054, tc_HOL_Obool), _1447060), _1447058)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447060, tc_HOL_Obool)), _1447062), _1447064)))], (35590 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447060, tc_HOL_Obool)), _1447062), _1447064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1447060, _1447054), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1447060, _1447054), _1447062), hAPP(c_COMBK(tc_fun(_1447054, tc_HOL_Obool), _1447060), _1447058))), hAPP(hAPP(c_Product__Type_OSigma(_1447060, _1447054), _1447064), hAPP(c_COMBK(tc_fun(_1447054, tc_HOL_Obool), _1447060), _1447058)))))]]], (35596 ^ _779308) ^ [_1447476, _1447478, _1447480, _1447482, _1447484, _1447486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1447476, _1447478), tc_HOL_Obool)), _1447480), hAPP(hAPP(c_Product__Type_OSigma(_1447476, _1447478), _1447482), hAPP(c_COMBK(tc_fun(_1447478, tc_HOL_Obool), _1447476), _1447484)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1447478, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1447476, _1447478, _1447480), _1447486)), _1447484)))], (35602 ^ _779308) ^ [_1447657, _1447659, _1447661, _1447663] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1447657, _1447659)), hAPP(hAPP(c_Product__Type_OSigma(_1447657, _1447659), _1447661), hAPP(c_COMBK(tc_fun(_1447659, tc_HOL_Obool), _1447657), _1447663)))), -(_1447663 = c_Orderings_Obot__class_Obot(tc_fun(_1447659, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1447657), _1447661)))], (35612 ^ _779308) ^ [_1447821, _1447823, _1447825, _1447827] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1447821, _1447823)), hAPP(hAPP(c_Product__Type_OSigma(_1447821, _1447823), _1447825), hAPP(c_COMBK(tc_fun(_1447823, tc_HOL_Obool), _1447821), _1447827)))), -(_1447825 = c_Orderings_Obot__class_Obot(tc_fun(_1447821, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1447823), _1447827)))], (35622 ^ _779308) ^ [_1448000, _1448002, _1448004, _1448006] : [_1448000 = c_Orderings_Obot__class_Obot(tc_fun(_1448002, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1448004, _1448002), _1448004, c_Product__Type_Ofst(_1448004, _1448002)), hAPP(hAPP(c_Product__Type_OSigma(_1448004, _1448002), _1448006), hAPP(c_COMBK(tc_fun(_1448002, tc_HOL_Obool), _1448004), _1448000))) = c_Orderings_Obot__class_Obot(tc_fun(_1448004, tc_HOL_Obool)))], (35628 ^ _779308) ^ [_1448157, _1448159, _1448161, _1448163] : [-(_1448157 = c_Orderings_Obot__class_Obot(tc_fun(_1448159, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1448161, _1448159), _1448161, c_Product__Type_Ofst(_1448161, _1448159)), hAPP(hAPP(c_Product__Type_OSigma(_1448161, _1448159), _1448163), hAPP(c_COMBK(tc_fun(_1448159, tc_HOL_Obool), _1448161), _1448157))) = _1448163)], (35634 ^ _779308) ^ [_1448250, _1448252, _1448254, _1448256] : [_1448250 = c_Orderings_Obot__class_Obot(tc_fun(_1448252, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1448252, _1448254), _1448254, c_Product__Type_Osnd(_1448252, _1448254)), hAPP(hAPP(c_Product__Type_OSigma(_1448252, _1448254), _1448250), hAPP(c_COMBK(tc_fun(_1448254, tc_HOL_Obool), _1448252), _1448256))) = c_Orderings_Obot__class_Obot(tc_fun(_1448254, tc_HOL_Obool)))], (35640 ^ _779308) ^ [_1448407, _1448409, _1448411, _1448413] : [-(_1448407 = c_Orderings_Obot__class_Obot(tc_fun(_1448409, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1448409, _1448411), _1448411, c_Product__Type_Osnd(_1448409, _1448411)), hAPP(hAPP(c_Product__Type_OSigma(_1448409, _1448411), _1448407), hAPP(c_COMBK(tc_fun(_1448411, tc_HOL_Obool), _1448409), _1448413))) = _1448413)], (35646 ^ _779308) ^ [_1448485, _1448487, _1448489, _1448491, _1448493, _1448495] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1448485, _1448487), hAPP(hAPP(c_Set_Oinsert(_1448485), _1448489), _1448491)), hAPP(c_COMBK(tc_fun(_1448487, tc_HOL_Obool), _1448485), hAPP(hAPP(c_Set_Oinsert(_1448487), _1448493), _1448495))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1448485, _1448487)), hAPP(hAPP(c_Product__Type_OPair(_1448485, _1448487), _1448489), _1448493)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1448485, _1448487), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1448485, _1448487), _1448491), hAPP(c_COMBK(tc_fun(_1448487, tc_HOL_Obool), _1448485), hAPP(hAPP(c_Set_Oinsert(_1448487), _1448493), _1448495)))), hAPP(hAPP(c_Product__Type_OSigma(_1448485, _1448487), hAPP(hAPP(c_Set_Oinsert(_1448485), _1448489), _1448491)), hAPP(c_COMBK(tc_fun(_1448487, tc_HOL_Obool), _1448485), _1448495)))))], (35648 ^ _779308) ^ [_1448638, _1448640, _1448642, _1448644] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1448638), _1448640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1448638, _1448638), tc_HOL_Obool)), _1448642), hAPP(hAPP(c_Product__Type_OSigma(_1448638, _1448638), _1448640), hAPP(c_COMBK(tc_fun(_1448638, tc_HOL_Obool), _1448638), _1448640)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1448638, tc_HOL_Obool)), _1448644), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1448638), _1448640), _1448642))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1448638), _1448644)))], (35662 ^ _779308) ^ [_1448945, _1448947, _1448949, _1448951, _1448953, _1448955, _1448957, _1448959] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1448945, _1448947), tc_fun(tc_prod(_1448949, _1448951), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1448945, _1448947), _1448953), hAPP(c_COMBK(tc_fun(_1448947, tc_HOL_Obool), _1448945), _1448955))), hAPP(c_Product__Type_Oprod_Oprod__case(_1448945, _1448947, tc_fun(tc_prod(_1448949, _1448951), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1448945, tc_fun(_1448947, tc_fun(_1448949, tc_fun(_1448951, tc_HOL_Obool))), tc_fun(_1448947, tc_fun(tc_prod(_1448949, _1448951), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1448949, tc_fun(_1448951, tc_HOL_Obool)), tc_fun(tc_prod(_1448949, _1448951), tc_HOL_Obool)), tc_fun(tc_fun(_1448947, tc_fun(_1448949, tc_fun(_1448951, tc_HOL_Obool))), tc_fun(_1448947, tc_fun(tc_prod(_1448949, _1448951), tc_HOL_Obool))), _1448945), c_COMBB(tc_fun(_1448949, tc_fun(_1448951, tc_HOL_Obool)), tc_fun(tc_prod(_1448949, _1448951), tc_HOL_Obool), _1448947)), hAPP(hAPP(c_COMBB(tc_fun(_1448949, tc_HOL_Obool), tc_fun(tc_fun(_1448949, tc_fun(_1448951, tc_HOL_Obool)), tc_fun(tc_prod(_1448949, _1448951), tc_HOL_Obool)), _1448945), c_Product__Type_OSigma(_1448949, _1448951)), _1448957))), hAPP(hAPP(c_COMBB(tc_fun(_1448951, tc_HOL_Obool), tc_fun(_1448949, tc_fun(_1448951, tc_HOL_Obool)), _1448947), c_COMBK(tc_fun(_1448951, tc_HOL_Obool), _1448949)), _1448959)))) = hAPP(hAPP(c_Product__Type_OSigma(_1448949, _1448951), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1448945, tc_fun(_1448949, tc_HOL_Obool)), _1448953), _1448957)), hAPP(c_COMBK(tc_fun(_1448951, tc_HOL_Obool), _1448949), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1448947, tc_fun(_1448951, tc_HOL_Obool)), _1448955), _1448959))))], (35664 ^ _779308) ^ [_1449219, _1449221, _1449223, _1449225] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1449219, _1449221), _1449223), _1449225) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449219, tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool)), _1449223), hAPP(hAPP(c_COMBS(_1449219, tc_fun(_1449221, tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool)), tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449221, tc_HOL_Obool), tc_fun(tc_fun(_1449221, tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool)), tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool)), _1449219), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449221, tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool))), _1449225)), hAPP(hAPP(c_COMBC(_1449219, tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool), tc_fun(_1449221, tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1449221, tc_fun(tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool), tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool), tc_fun(_1449221, tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool))), _1449219), c_COMBC(_1449221, tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool), tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1449221, tc_prod(_1449219, _1449221)), tc_fun(_1449221, tc_fun(tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool), tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool))), _1449219), hAPP(c_COMBB(tc_prod(_1449219, _1449221), tc_fun(tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool), tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool)), _1449221), c_Set_Oinsert(tc_prod(_1449219, _1449221)))), c_Product__Type_OPair(_1449219, _1449221)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1449219, _1449221), tc_HOL_Obool))))))], (35666 ^ _779308) ^ [_1449499, _1449501, _1449503] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1449499), _1449501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1449499, _1449499), tc_HOL_Obool)), _1449503), hAPP(hAPP(c_Product__Type_OSigma(_1449499, _1449499), _1449501), hAPP(c_COMBK(tc_fun(_1449499, tc_HOL_Obool), _1449499), _1449501)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1449499, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449499), _1449501), _1449503))))], (35677 ^ _779308) ^ [_1449730, _1449732, _1449734, _1449736] : [-(c_Fun_Oinj__on(_1449730, tc_prod(_1449732, _1449730), 35675 ^ [_1449730, _1449732, _1449734, _1449736], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449732, tc_fun(_1449730, tc_HOL_Obool)), _1449734), _1449736)))], (35679 ^ _779308) ^ [_1449784, _1449786, _1449788, _1449790] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1449786, _1449784), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1449784, tc_prod(_1449786, _1449784), 35675 ^ [_1449784, _1449786, _1449788, _1449790]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449786, tc_fun(_1449784, tc_HOL_Obool)), _1449788), _1449790))), hAPP(hAPP(c_Product__Type_OSigma(_1449786, _1449784), _1449788), _1449790))))], (35681 ^ _779308) ^ [_1449870, _1449872, _1449874, _1449876, _1449878, _1449880] : [class_Groups_Ocomm__monoid__mult(_1449870), hBOOL(hAPP(c_Finite__Set_Ofinite(_1449872), _1449874)), 35691 ^ _779308 : [(35692 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1449872), 35690 ^ [_1449870, _1449872, _1449874, _1449876, _1449878, _1449880]), _1449874)))], (35694 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1449876), hAPP(_1449878, 35690 ^ [_1449870, _1449872, _1449874, _1449876, _1449878, _1449880])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1449870, _1449872, c_Groups_Otimes__class_Otimes(_1449870)), hAPP(hAPP(c_COMBS(_1449872, tc_fun(_1449876, tc_HOL_Obool), _1449870), hAPP(hAPP(c_COMBC(_1449872, _1449870, tc_fun(tc_fun(_1449876, tc_HOL_Obool), _1449870)), hAPP(hAPP(c_COMBB(tc_fun(_1449876, _1449870), tc_fun(_1449870, tc_fun(tc_fun(_1449876, tc_HOL_Obool), _1449870)), _1449872), c_Finite__Set_Ofold__image(_1449870, _1449876, c_Groups_Otimes__class_Otimes(_1449870))), _1449880)), c_Groups_Oone__class_Oone(_1449870))), _1449878)), c_Groups_Oone__class_Oone(_1449870)), _1449874) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1449870, tc_prod(_1449872, _1449876), c_Groups_Otimes__class_Otimes(_1449870)), hAPP(c_Product__Type_Oprod_Oprod__case(_1449872, _1449876, _1449870), _1449880)), c_Groups_Oone__class_Oone(_1449870)), hAPP(hAPP(c_Product__Type_OSigma(_1449872, _1449876), _1449874), _1449878)))], (35698 ^ _779308) ^ [_1450427, _1450429, _1450431, _1450433] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1450427), _1450429)), 35704 ^ _779308 : [(35705 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450427), 35703 ^ [_1450427, _1450429, _1450431, _1450433]), _1450429)))], (35707 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1450431), hAPP(_1450433, 35703 ^ [_1450427, _1450429, _1450431, _1450433])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1450427, _1450431)), hAPP(hAPP(c_Product__Type_OSigma(_1450427, _1450431), _1450429), _1450433))))], (35711 ^ _779308) ^ [_1450714, _1450716, _1450718, _1450720, _1450722, _1450724] : [class_Groups_Ocomm__monoid__mult(_1450714), hBOOL(hAPP(c_Finite__Set_Ofinite(_1450716), _1450718)), 35721 ^ _779308 : [(35722 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1450716), 35720 ^ [_1450714, _1450716, _1450718, _1450720, _1450722, _1450724]), _1450718)))], (35724 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1450720), hAPP(_1450722, 35720 ^ [_1450714, _1450716, _1450718, _1450720, _1450722, _1450724])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1450716, _1450714), hAPP(hAPP(c_COMBS(_1450716, tc_fun(_1450720, tc_HOL_Obool), _1450714), hAPP(hAPP(c_COMBB(tc_fun(_1450720, _1450714), tc_fun(tc_fun(_1450720, tc_HOL_Obool), _1450714), _1450716), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1450720, _1450714)), _1450724)), _1450722)), _1450718) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1450716, _1450720), _1450714), hAPP(c_Product__Type_Oprod_Oprod__case(_1450716, _1450720, _1450714), _1450724)), hAPP(hAPP(c_Product__Type_OSigma(_1450716, _1450720), _1450718), _1450722)))], (35728 ^ _779308) ^ [_1451191, _1451193, _1451195, _1451197, _1451199, _1451201] : [class_Groups_Ocomm__monoid__add(_1451191), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451193), _1451195)), 35738 ^ _779308 : [(35739 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451193), 35737 ^ [_1451191, _1451193, _1451195, _1451197, _1451199, _1451201]), _1451195)))], (35741 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1451197), hAPP(_1451199, 35737 ^ [_1451191, _1451193, _1451195, _1451197, _1451199, _1451201])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1451193, _1451191), hAPP(hAPP(c_COMBS(_1451193, tc_fun(_1451197, tc_HOL_Obool), _1451191), hAPP(hAPP(c_COMBB(tc_fun(_1451197, _1451191), tc_fun(tc_fun(_1451197, tc_HOL_Obool), _1451191), _1451193), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1451197, _1451191)), _1451201)), _1451199)), _1451195) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1451193, _1451197), _1451191), hAPP(c_Product__Type_Oprod_Oprod__case(_1451193, _1451197, _1451191), _1451201)), hAPP(hAPP(c_Product__Type_OSigma(_1451193, _1451197), _1451195), _1451199)))], (35745 ^ _779308) ^ [_1451668, _1451670, _1451672, _1451674] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1451668), _1451670)), 35751 ^ _779308 : [(35752 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451668), 35750 ^ [_1451668, _1451670, _1451672, _1451674]), _1451670)))], (35754 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1451672), hAPP(_1451674, 35750 ^ [_1451668, _1451670, _1451672, _1451674])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1451668, _1451672)), hAPP(hAPP(c_Product__Type_OSigma(_1451668, _1451672), _1451670), _1451674)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1451668, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1451672, tc_HOL_Obool), tc_Nat_Onat, _1451668), c_Finite__Set_Ocard(_1451672)), _1451674)), _1451670))], (35758 ^ _779308) ^ [_1452005, _1452007, _1452009, _1452011, _1452013] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1452005, _1452007)), _1452009), hAPP(hAPP(c_Product__Type_OSigma(_1452005, _1452007), _1452011), _1452013))), 35762 ^ _779308 : [(35763 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1452005), 35761 ^ [_1452005, _1452007, _1452009, _1452011, _1452013]), _1452011)))], (35766 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1452007), 35764 ^ [_1452005, _1452007, _1452009, _1452011, _1452013]), hAPP(_1452013, 35761 ^ [_1452005, _1452007, _1452009, _1452011, _1452013]))))], (35768 ^ _779308) ^ [] : [-(_1452009 = hAPP(hAPP(c_Product__Type_OPair(_1452005, _1452007), 35761 ^ [_1452005, _1452007, _1452009, _1452011, _1452013]), 35764 ^ [_1452005, _1452007, _1452009, _1452011, _1452013]))]]], (35770 ^ _779308) ^ [_1452307, _1452309, _1452311, _1452313, _1452315, _1452317] : [hAPP(c_Set_Oimage(_1452307, _1452309, _1452311), c_Orderings_Otop__class_Otop(tc_fun(_1452307, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1452309, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1452313, _1452315, _1452317), c_Orderings_Otop__class_Otop(tc_fun(_1452313, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1452315, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1452307, _1452313), tc_prod(_1452309, _1452315), c_Product__Type_Omap__pair(_1452307, _1452309, _1452313, _1452315, _1452311, _1452317)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1452307, _1452313), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1452309, _1452315), tc_HOL_Obool)))], (35780 ^ _779308) ^ [_1452592, _1452594, _1452596, _1452598, _1452600, _1452602, _1452604, _1452606] : [c_Fun_Oinj__on(_1452592, _1452594, _1452596, _1452598), c_Fun_Oinj__on(_1452600, _1452602, _1452604, _1452606), -(c_Fun_Oinj__on(tc_prod(_1452592, _1452600), tc_prod(_1452594, _1452602), c_Product__Type_Omap__pair(_1452592, _1452594, _1452600, _1452602, _1452596, _1452604), hAPP(hAPP(c_Product__Type_OSigma(_1452592, _1452600), _1452598), hAPP(c_COMBK(tc_fun(_1452600, tc_HOL_Obool), _1452592), _1452606))))], (35790 ^ _779308) ^ [_1452819, _1452821, _1452823, _1452825, _1452827, _1452829, _1452831, _1452833, _1452835] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1452819, _1452821)), hAPP(hAPP(c_Product__Type_OPair(_1452819, _1452821), _1452823), _1452825)), _1452827)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1452829, _1452831)), hAPP(hAPP(c_Product__Type_OPair(_1452829, _1452831), hAPP(_1452833, _1452823)), hAPP(_1452835, _1452825))), hAPP(c_Set_Oimage(tc_prod(_1452819, _1452821), tc_prod(_1452829, _1452831), c_Product__Type_Omap__pair(_1452819, _1452829, _1452821, _1452831, _1452833, _1452835)), _1452827))))], (35796 ^ _779308) ^ [_1453038, _1453040, _1453042, _1453044, _1453046, _1453048, _1453050] : [-(hAPP(c_Product__Type_Ofst(_1453038, _1453040), hAPP(c_Product__Type_Omap__pair(_1453042, _1453038, _1453044, _1453040, _1453046, _1453048), _1453050)) = hAPP(_1453046, hAPP(c_Product__Type_Ofst(_1453042, _1453044), _1453050)))], (35798 ^ _779308) ^ [_1453098, _1453100, _1453102, _1453104, _1453106, _1453108, _1453110, _1453112] : [-(hAPP(c_Product__Type_Omap__pair(_1453098, _1453100, _1453102, _1453104, _1453106, _1453108), hAPP(hAPP(c_Product__Type_OPair(_1453098, _1453102), _1453110), _1453112)) = hAPP(hAPP(c_Product__Type_OPair(_1453100, _1453104), hAPP(_1453106, _1453110)), hAPP(_1453108, _1453112)))], (35800 ^ _779308) ^ [_1453169, _1453171, _1453173] : [-(hAPP(c_Product__Type_Omap__pair(_1453169, _1453169, _1453171, _1453171, c_COMBI(_1453169), c_COMBI(_1453171)), _1453173) = _1453173)], (35802 ^ _779308) ^ [_1453210, _1453212, _1453214, _1453216, _1453218, _1453220, _1453222] : [-(hAPP(c_Product__Type_Osnd(_1453210, _1453212), hAPP(c_Product__Type_Omap__pair(_1453214, _1453210, _1453216, _1453212, _1453218, _1453220), _1453222)) = hAPP(_1453220, hAPP(c_Product__Type_Osnd(_1453214, _1453216), _1453222)))], (35804 ^ _779308) ^ [_1453270, _1453272, _1453274, _1453276, _1453278, _1453280] : [-(c_Product__Type_Omap__pair(_1453270, _1453272, _1453274, _1453276, _1453278, _1453280) = hAPP(c_Product__Type_Oprod_Oprod__case(_1453270, _1453274, tc_prod(_1453272, _1453276)), hAPP(hAPP(c_COMBC(_1453270, tc_fun(_1453274, _1453276), tc_fun(_1453274, tc_prod(_1453272, _1453276))), hAPP(hAPP(c_COMBB(tc_fun(_1453276, tc_prod(_1453272, _1453276)), tc_fun(tc_fun(_1453274, _1453276), tc_fun(_1453274, tc_prod(_1453272, _1453276))), _1453270), c_COMBB(_1453276, tc_prod(_1453272, _1453276), _1453274)), hAPP(hAPP(c_COMBB(_1453272, tc_fun(_1453276, tc_prod(_1453272, _1453276)), _1453270), c_Product__Type_OPair(_1453272, _1453276)), _1453278))), _1453280)))], (35806 ^ _779308) ^ [_1453393, _1453395, _1453397, _1453399, _1453401, _1453403, _1453405, _1453407, _1453409, _1453411] : [hAPP(c_Set_Oimage(_1453393, _1453395, _1453397), _1453399) = _1453401, hAPP(c_Set_Oimage(_1453403, _1453405, _1453407), _1453409) = _1453411, -(hAPP(c_Set_Oimage(tc_prod(_1453393, _1453403), tc_prod(_1453395, _1453405), c_Product__Type_Omap__pair(_1453393, _1453395, _1453403, _1453405, _1453397, _1453407)), hAPP(hAPP(c_Product__Type_OSigma(_1453393, _1453403), _1453399), hAPP(c_COMBK(tc_fun(_1453403, tc_HOL_Obool), _1453393), _1453409))) = hAPP(hAPP(c_Product__Type_OSigma(_1453395, _1453405), _1453401), hAPP(c_COMBK(tc_fun(_1453405, tc_HOL_Obool), _1453395), _1453411)))], (35816 ^ _779308) ^ [_1453694, _1453696, _1453698, _1453700, _1453702, _1453704, _1453706, _1453708] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1453694, _1453696)), _1453698), hAPP(c_Set_Oimage(tc_prod(_1453700, _1453702), tc_prod(_1453694, _1453696), c_Product__Type_Omap__pair(_1453700, _1453694, _1453702, _1453696, _1453704, _1453706)), _1453708))), 35821 ^ _779308 : [(35822 ^ _779308) ^ [] : [-(_1453698 = hAPP(hAPP(c_Product__Type_OPair(_1453694, _1453696), hAPP(_1453704, 35819 ^ [_1453694, _1453696, _1453698, _1453700, _1453702, _1453704, _1453706, _1453708])), hAPP(_1453706, 35820 ^ [_1453694, _1453696, _1453698, _1453700, _1453702, _1453704, _1453706, _1453708])))], (35824 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1453700, _1453702)), hAPP(hAPP(c_Product__Type_OPair(_1453700, _1453702), 35819 ^ [_1453694, _1453696, _1453698, _1453700, _1453702, _1453704, _1453706, _1453708]), 35820 ^ [_1453694, _1453696, _1453698, _1453700, _1453702, _1453704, _1453706, _1453708])), _1453708)))]]], (35826 ^ _779308) ^ [_1454045, _1454047, _1454049] : [c_Relation_Orefl__on(_1454045, _1454047, _1454049), 35829 ^ _779308 : [(35830 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1454045, _1454045), tc_HOL_Obool)), _1454049), hAPP(hAPP(c_Product__Type_OSigma(_1454045, _1454045), _1454047), hAPP(c_COMBK(tc_fun(_1454045, tc_HOL_Obool), _1454045), _1454047)))))], (35832 ^ _779308) ^ [_1454227] : [hBOOL(hAPP(hAPP(c_member(_1454045), _1454227), _1454047)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1454045, _1454045)), hAPP(hAPP(c_Product__Type_OPair(_1454045, _1454045), _1454227), _1454227)), _1454049)))]]], (35838 ^ _779308) ^ [_1454362, _1454364, _1454366] : [-(c_Relation_Orefl__on(_1454362, _1454364, _1454366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1454362, _1454362), tc_HOL_Obool)), _1454366), hAPP(hAPP(c_Product__Type_OSigma(_1454362, _1454362), _1454364), hAPP(c_COMBK(tc_fun(_1454362, tc_HOL_Obool), _1454362), _1454364)))), 35844 ^ _779308 : [(35845 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1454362), 35843 ^ [_1454362, _1454364, _1454366]), _1454364)))], (35847 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1454362, _1454362)), hAPP(hAPP(c_Product__Type_OPair(_1454362, _1454362), 35843 ^ [_1454362, _1454364, _1454366]), 35843 ^ [_1454362, _1454364, _1454366])), _1454366))]]], (35851 ^ _779308) ^ [_1454711, _1454713, _1454715] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1454711), _1454713)), 35857 ^ _779308 : [(35858 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1454711), 35856 ^ [_1454711, _1454713, _1454715]), _1454713)))], (35860 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1454715, 35856 ^ [_1454711, _1454713, _1454715])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1454711, tc_Nat_Onat), _1454715), _1454713))))], (35864 ^ _779308) ^ [_1454972, _1454974] : [-(c_Relation_Orefl__on(_1454972, _1454974, c_Relation_OId__on(_1454972, _1454974)))], (35866 ^ _779308) ^ [_1455001] : [-(c_Relation_Orefl__on(_1455001, c_Orderings_Obot__class_Obot(tc_fun(_1455001, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1455001, _1455001), tc_HOL_Obool))))], (35868 ^ _779308) ^ [_1455038, _1455040, _1455042, _1455044, _1455046] : [c_Relation_Orefl__on(_1455038, _1455040, _1455042), c_Relation_Orefl__on(_1455038, _1455044, _1455046), -(c_Relation_Orefl__on(_1455038, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1455038, tc_HOL_Obool)), _1455040), _1455044), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1455038, _1455038), tc_HOL_Obool)), _1455042), _1455046)))], (35878 ^ _779308) ^ [_1455235, _1455237, _1455239, _1455241, _1455243] : [c_Relation_Orefl__on(_1455235, _1455237, _1455239), c_Relation_Orefl__on(_1455235, _1455241, _1455243), -(c_Relation_Orefl__on(_1455235, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455235, tc_HOL_Obool)), _1455237), _1455241), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1455235, _1455235), tc_HOL_Obool)), _1455239), _1455243)))], (35888 ^ _779308) ^ [_1455432, _1455434, _1455436, _1455438] : [c_Relation_Orefl__on(_1455432, _1455434, _1455436), hBOOL(hAPP(hAPP(c_member(_1455432), _1455438), _1455434)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1455432, _1455432)), hAPP(hAPP(c_Product__Type_OPair(_1455432, _1455432), _1455438), _1455438)), _1455436)))], (35898 ^ _779308) ^ [_1455623, _1455625, _1455627, _1455629, _1455631] : [c_Relation_Orefl__on(_1455623, _1455625, _1455627), hBOOL(hAPP(hAPP(c_member(tc_prod(_1455623, _1455623)), hAPP(hAPP(c_Product__Type_OPair(_1455623, _1455623), _1455629), _1455631)), _1455627)), -(hBOOL(hAPP(hAPP(c_member(_1455623), _1455629), _1455625)))], (35908 ^ _779308) ^ [_1455818, _1455820, _1455822, _1455824, _1455826] : [c_Relation_Orefl__on(_1455818, _1455820, _1455822), hBOOL(hAPP(hAPP(c_member(tc_prod(_1455818, _1455818)), hAPP(hAPP(c_Product__Type_OPair(_1455818, _1455818), _1455824), _1455826)), _1455822)), -(hBOOL(hAPP(hAPP(c_member(_1455818), _1455826), _1455820)))], (35918 ^ _779308) ^ [_1456013, _1456015, _1456017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1456013, _1456013), tc_HOL_Obool)), _1456015), hAPP(hAPP(c_Product__Type_OSigma(_1456013, _1456013), _1456017), hAPP(c_COMBK(tc_fun(_1456013, tc_HOL_Obool), _1456013), _1456017)))), 35924 ^ _779308 : [(35925 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456013), 35923 ^ [_1456013, _1456015, _1456017]), _1456017)))], (35927 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1456013, _1456013)), hAPP(hAPP(c_Product__Type_OPair(_1456013, _1456013), 35923 ^ [_1456013, _1456015, _1456017]), 35923 ^ [_1456013, _1456015, _1456017])), _1456015))]], -(c_Relation_Orefl__on(_1456013, _1456017, _1456015))], (35931 ^ _779308) ^ [_1456360] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1456360), c_Int_OInteg)), -(_1456360 = hAPP(c_Int_ORep__Integ, 35934 ^ [_1456360]))], (35938 ^ _779308) ^ [_1456465, _1456467] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1456465), c_Int_OInteg)), hBOOL(hAPP(_1456467, hAPP(c_Int_ORep__Integ, 35943 ^ [_1456465, _1456467]))), -(hBOOL(hAPP(_1456467, _1456465)))], (35949 ^ _779308) ^ [_1456647, _1456649, _1456651, _1456653, _1456655, _1456657, _1456659, _1456661] : [c_Finite__Set_Ofolding__image__simple(_1456647, _1456649, _1456651, _1456653, _1456655, _1456657), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456649), _1456659)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456649), _1456661)), 35963 ^ _779308 : [(35964 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456649), 35962 ^ [_1456647, _1456649, _1456651, _1456653, _1456655, _1456657, _1456659, _1456661]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1456649, tc_HOL_Obool)), _1456659), _1456661))))], (35966 ^ _779308) ^ [] : [hAPP(_1456655, 35962 ^ [_1456647, _1456649, _1456651, _1456653, _1456655, _1456657, _1456659, _1456661]) = _1456653]], -(hAPP(_1456657, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1456649, tc_HOL_Obool)), _1456659), _1456661)) = hAPP(hAPP(_1456651, hAPP(_1456657, _1456659)), hAPP(_1456657, _1456661)))], (35970 ^ _779308) ^ [_1457148, _1457150] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457148)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_Nat_Onat), c_member(tc_Nat_Onat)), c_Nat_OSuc)), _1457148))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1457150))))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1457148))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1457150))))))], (35976 ^ _779308) ^ [_1457325, _1457327] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1457325)), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1457325))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1457327))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (35982 ^ _779308) ^ [_1457455, _1457457, _1457459] : [hBOOL(hAPP(_1457455, _1457457)), -(hBOOL(hAPP(hAPP(c_member(_1457459), _1457457), hAPP(c_Set_OCollect(_1457459), _1457455))))], (35988 ^ _779308) ^ [_1457562, _1457564, _1457566] : [35989 ^ _779308 : [(35990 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1457562), hAPP(c_Set_OCollect(_1457562), _1457564)))], (35992 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1457562), hAPP(c_Set_OCollect(_1457562), _1457566)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1457562), hAPP(c_Set_OCollect(_1457562), hAPP(hAPP(c_COMBS(_1457562, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1457562), c_fconj), _1457564)), _1457566)))))], (35996 ^ _779308) ^ [_1457773] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1457773)))))], (35998 ^ _779308) ^ [_1457804] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), _1457804)))))], (36000 ^ _779308) ^ [_1457835, _1457837, _1457839, _1457841] : [-(hAPP(c_Set_OCollect(tc_prod(_1457835, _1457837)), hAPP(c_Product__Type_Oprod_Oprod__case(_1457835, _1457837, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1457835, tc_fun(_1457837, tc_HOL_Obool), tc_fun(_1457837, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1457837, tc_HOL_Obool), tc_fun(_1457837, tc_HOL_Obool)), _1457835), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1457837)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1457835), c_fconj), _1457839))), _1457841))) = hAPP(hAPP(c_Product__Type_OSigma(_1457835, _1457837), hAPP(c_Set_OCollect(_1457835), _1457839)), hAPP(hAPP(c_COMBB(tc_fun(_1457837, tc_HOL_Obool), tc_fun(_1457837, tc_HOL_Obool), _1457835), c_Set_OCollect(_1457837)), _1457841)))], (36002 ^ _779308) ^ [_1457960, _1457962, _1457964, _1457966] : [-(hAPP(c_Set_OCollect(tc_prod(_1457960, _1457962)), hAPP(c_Product__Type_Oprod_Oprod__case(_1457960, _1457962, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1457960, tc_fun(_1457962, tc_HOL_Obool), tc_fun(_1457962, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1457962, tc_HOL_Obool), tc_fun(_1457962, tc_HOL_Obool)), _1457960), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1457962)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1457960), c_fconj), _1457964))), _1457966))) = hAPP(hAPP(c_Product__Type_OSigma(_1457960, _1457962), hAPP(c_Set_OCollect(_1457960), _1457964)), hAPP(c_COMBK(tc_fun(_1457962, tc_HOL_Obool), _1457960), hAPP(c_Set_OCollect(_1457962), _1457966))))], (36004 ^ _779308) ^ [_1458081, _1458083] : [-(hAPP(c_Set_OCollect(_1458081), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1458081), c_fNot), _1458083)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1458081, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1458081), _1458083)))], (36006 ^ _779308) ^ [_1458134, _1458136, _1458138] : [-(hAPP(c_Set_OCollect(_1458134), hAPP(hAPP(c_COMBS(_1458134, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1458134), c_fconj), _1458136)), _1458138)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1458134, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1458134), _1458136)), hAPP(c_Set_OCollect(_1458134), _1458138)))], (36008 ^ _779308) ^ [_1458222, _1458224] : [c_Orderings_Obot__class_Obot(tc_fun(_1458222, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1458222), _1458224), 36011 ^ _779308 : [(36012 ^ _779308) ^ [_1458307] : [hBOOL(hAPP(_1458224, _1458307))]]], (36014 ^ _779308) ^ [_1458330, _1458332] : [-(hBOOL(hAPP(_1458332, 36015 ^ [_1458330, _1458332]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1458330, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1458330), _1458332))], (36021 ^ _779308) ^ [_1458402, _1458404] : [hAPP(c_Set_OCollect(_1458402), _1458404) = c_Orderings_Obot__class_Obot(tc_fun(_1458402, tc_HOL_Obool)), 36024 ^ _779308 : [(36025 ^ _779308) ^ [_1458487] : [hBOOL(hAPP(_1458404, _1458487))]]], (36027 ^ _779308) ^ [_1458510, _1458512] : [-(hBOOL(hAPP(_1458512, 36028 ^ [_1458510, _1458512]))), -(hAPP(c_Set_OCollect(_1458510), _1458512) = c_Orderings_Obot__class_Obot(tc_fun(_1458510, tc_HOL_Obool)))], (36034 ^ _779308) ^ [_1458567, _1458569] : [-(hAPP(c_Set_OCollect(_1458567), _1458569) = _1458569)], (36036 ^ _779308) ^ [_1458597, _1458599, _1458601] : [-(hAPP(c_Set_OCollect(_1458597), hAPP(hAPP(c_COMBS(_1458597, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1458597), c_fdisj), _1458599)), _1458601)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1458597, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1458597), _1458599)), hAPP(c_Set_OCollect(_1458597), _1458601)))], (36038 ^ _779308) ^ [_1458670, _1458672, _1458674] : [-(hAPP(hAPP(c_Set_Oinsert(_1458670), _1458672), hAPP(c_Set_OCollect(_1458670), _1458674)) = hAPP(c_Set_OCollect(_1458670), hAPP(hAPP(c_COMBS(_1458670, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1458670), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1458670), c_fNot), hAPP(hAPP(c_COMBC(_1458670, _1458670, tc_HOL_Obool), c_fequal), _1458672)))), _1458674)))], (36040 ^ _779308) ^ [_1458755] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1458755, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1458755), hAPP(c_COMBK(tc_HOL_Obool, _1458755), c_fFalse)))], (36042 ^ _779308) ^ [_1458812, _1458814, _1458816] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1458812), hAPP(c_Set_OCollect(_1458812), hAPP(hAPP(c_COMBS(_1458812, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1458812), c_fdisj), _1458814)), _1458816)))), 36045 ^ _779308 : [(36046 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1458812), hAPP(c_Set_OCollect(_1458812), _1458814))))], (36048 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1458812), hAPP(c_Set_OCollect(_1458812), _1458816))))]]], (36050 ^ _779308) ^ [_1459007, _1459009, _1459011] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1459007), hAPP(c_Set_OCollect(_1459007), hAPP(hAPP(c_COMBS(_1459007, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1459007), c_fdisj), _1459009)), _1459011))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459007), hAPP(c_Set_OCollect(_1459007), _1459009))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1459007), hAPP(c_Set_OCollect(_1459007), _1459011)))], (36060 ^ _779308) ^ [_1459236] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1459236, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1459236), hAPP(c_COMBK(tc_HOL_Obool, _1459236), c_fTrue)))], (36062 ^ _779308) ^ [_1459275, _1459277, _1459279, _1459281] : [-(hAPP(c_Set_Ovimage(_1459275, _1459277, _1459279), hAPP(c_Set_OCollect(_1459277), _1459281)) = hAPP(c_Set_OCollect(_1459275), hAPP(hAPP(c_COMBB(_1459277, tc_HOL_Obool, _1459275), _1459281), _1459279)))], (36064 ^ _779308) ^ [_1459331, _1459333, _1459335] : [hBOOL(hAPP(hAPP(c_member(_1459331), _1459333), hAPP(c_Set_OCollect(_1459331), _1459335))), -(hBOOL(hAPP(_1459335, _1459333)))], (36070 ^ _779308) ^ [_1459438, _1459440, _1459442] : [hBOOL(hAPP(hAPP(c_member(_1459438), _1459440), hAPP(c_Set_OCollect(_1459438), _1459442))), -(hBOOL(hAPP(_1459442, _1459440)))], (36076 ^ _779308) ^ [_1459563, _1459565, _1459567] : [hBOOL(hAPP(hAPP(c_member(_1459563), _1459565), hAPP(c_Set_OCollect(_1459563), _1459567))), -(hBOOL(hAPP(_1459567, _1459565)))], (36082 ^ _779308) ^ [_1459666, _1459668, _1459670] : [hBOOL(hAPP(_1459670, _1459668)), -(hBOOL(hAPP(hAPP(c_member(_1459666), _1459668), hAPP(c_Set_OCollect(_1459666), _1459670))))], (36088 ^ _779308) ^ [_1459775, _1459777] : [-(hAPP(c_Set_OCollect(_1459775), hAPP(hAPP(c_COMBC(_1459775, tc_fun(_1459775, tc_HOL_Obool), tc_HOL_Obool), c_member(_1459775)), _1459777)) = _1459777)], (36090 ^ _779308) ^ [_1459820, _1459822, _1459824] : [-(hAPP(hAPP(c_Set_Oinsert(_1459820), _1459822), _1459824) = hAPP(c_Set_OCollect(_1459820), hAPP(hAPP(c_COMBS(_1459820, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1459820), c_fdisj), hAPP(hAPP(c_COMBC(_1459820, _1459820, tc_HOL_Obool), c_fequal), _1459822))), hAPP(hAPP(c_COMBC(_1459820, tc_fun(_1459820, tc_HOL_Obool), tc_HOL_Obool), c_member(_1459820)), _1459824))))], (36092 ^ _779308) ^ [_1459905, _1459907, _1459909] : [-(hAPP(hAPP(c_Set_Oinsert(_1459905), _1459907), _1459909) = hAPP(c_Set_OCollect(_1459905), hAPP(hAPP(c_COMBS(_1459905, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1459905), c_fdisj), hAPP(hAPP(c_COMBC(_1459905, _1459905, tc_HOL_Obool), c_fequal), _1459907))), hAPP(hAPP(c_COMBC(_1459905, tc_fun(_1459905, tc_HOL_Obool), tc_HOL_Obool), c_member(_1459905)), _1459909))))], (36094 ^ _779308) ^ [_1459990, _1459992, _1459994] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1459990, tc_HOL_Obool)), _1459992), _1459994) = hAPP(c_Set_OCollect(_1459990), hAPP(hAPP(c_COMBS(_1459990, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1459990), c_fdisj), hAPP(hAPP(c_COMBC(_1459990, tc_fun(_1459990, tc_HOL_Obool), tc_HOL_Obool), c_member(_1459990)), _1459992))), hAPP(hAPP(c_COMBC(_1459990, tc_fun(_1459990, tc_HOL_Obool), tc_HOL_Obool), c_member(_1459990)), _1459994))))], (36096 ^ _779308) ^ [_1460104, _1460106, _1460108, _1460110] : [hBOOL(hAPP(hAPP(c_member(_1460104), _1460106), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460104, tc_HOL_Obool)), _1460108), hAPP(c_Set_OCollect(_1460104), _1460110)))), 36099 ^ _779308 : [(36100 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1460104), _1460106), _1460108)))], (36102 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1460110, _1460106)))]]], (36104 ^ _779308) ^ [_1460271, _1460273, _1460275, _1460277] : [-(hBOOL(hAPP(hAPP(c_member(_1460271), _1460273), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460271, tc_HOL_Obool)), _1460275), hAPP(c_Set_OCollect(_1460271), _1460277))))), hBOOL(hAPP(hAPP(c_member(_1460271), _1460273), _1460275)), hBOOL(hAPP(_1460277, _1460273))], (36114 ^ _779308) ^ [_1460474, _1460476, _1460478] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1460474, tc_HOL_Obool)), _1460476), _1460478) = hAPP(c_Set_OCollect(_1460474), hAPP(hAPP(c_COMBS(_1460474, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1460474), c_fconj), hAPP(hAPP(c_COMBC(_1460474, tc_fun(_1460474, tc_HOL_Obool), tc_HOL_Obool), c_member(_1460474)), _1460476))), hAPP(hAPP(c_COMBC(_1460474, tc_fun(_1460474, tc_HOL_Obool), tc_HOL_Obool), c_member(_1460474)), _1460478))))], (36116 ^ _779308) ^ [_1460579, _1460581, _1460583] : [hBOOL(hAPP(_1460579, _1460581)), -(hAPP(c_Set_OCollect(_1460583), hAPP(hAPP(c_COMBS(_1460583, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1460583), c_fconj), hAPP(hAPP(c_COMBC(_1460583, _1460583, tc_HOL_Obool), c_fequal), _1460581))), _1460579)) = hAPP(hAPP(c_Set_Oinsert(_1460583), _1460581), c_Orderings_Obot__class_Obot(tc_fun(_1460583, tc_HOL_Obool))))], (36122 ^ _779308) ^ [_1460752, _1460754, _1460756] : [-(hBOOL(hAPP(_1460752, _1460754))), -(hAPP(c_Set_OCollect(_1460756), hAPP(hAPP(c_COMBS(_1460756, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1460756), c_fconj), hAPP(hAPP(c_COMBC(_1460756, _1460756, tc_HOL_Obool), c_fequal), _1460754))), _1460752)) = c_Orderings_Obot__class_Obot(tc_fun(_1460756, tc_HOL_Obool)))], (36128 ^ _779308) ^ [_1460846, _1460848, _1460850] : [hBOOL(hAPP(_1460846, _1460848)), -(hAPP(c_Set_OCollect(_1460850), hAPP(hAPP(c_COMBS(_1460850, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1460850), c_fconj), hAPP(c_fequal, _1460848))), _1460846)) = hAPP(hAPP(c_Set_Oinsert(_1460850), _1460848), c_Orderings_Obot__class_Obot(tc_fun(_1460850, tc_HOL_Obool))))], (36134 ^ _779308) ^ [_1461005, _1461007, _1461009] : [-(hBOOL(hAPP(_1461005, _1461007))), -(hAPP(c_Set_OCollect(_1461009), hAPP(hAPP(c_COMBS(_1461009, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461009), c_fconj), hAPP(c_fequal, _1461007))), _1461005)) = c_Orderings_Obot__class_Obot(tc_fun(_1461009, tc_HOL_Obool)))], (36140 ^ _779308) ^ [_1461080, _1461082] : [-(hAPP(c_Set_OCollect(_1461080), hAPP(hAPP(c_COMBC(_1461080, _1461080, tc_HOL_Obool), c_fequal), _1461082)) = hAPP(hAPP(c_Set_Oinsert(_1461080), _1461082), c_Orderings_Obot__class_Obot(tc_fun(_1461080, tc_HOL_Obool))))], (36142 ^ _779308) ^ [_1461133, _1461135] : [-(hAPP(c_Set_OCollect(_1461133), hAPP(c_fequal, _1461135)) = hAPP(hAPP(c_Set_Oinsert(_1461133), _1461135), c_Orderings_Obot__class_Obot(tc_fun(_1461133, tc_HOL_Obool))))], (36144 ^ _779308) ^ [_1461179, _1461181, _1461183] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1461179, tc_HOL_Obool)), _1461181), _1461183) = hAPP(c_Set_OCollect(_1461179), hAPP(hAPP(c_COMBS(_1461179, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461179), c_fconj), hAPP(hAPP(c_COMBC(_1461179, tc_fun(_1461179, tc_HOL_Obool), tc_HOL_Obool), c_member(_1461179)), _1461181))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1461179), c_fNot), hAPP(hAPP(c_COMBC(_1461179, tc_fun(_1461179, tc_HOL_Obool), tc_HOL_Obool), c_member(_1461179)), _1461183)))))], (36146 ^ _779308) ^ [_1461282, _1461284] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1461282), hAPP(c_Set_OCollect(_1461282), _1461284))), 36149 ^ _779308 : [(36150 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1461282), hAPP(c_Set_OCollect(_1461282), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1461282), c_fNot), _1461284)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1461282), c_Orderings_Otop__class_Otop(tc_fun(_1461282, tc_HOL_Obool)))))], (36156 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1461282), c_Orderings_Otop__class_Otop(tc_fun(_1461282, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1461282), hAPP(c_Set_OCollect(_1461282), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1461282), c_fNot), _1461284)))))]]], (36162 ^ _779308) ^ [_1461591, _1461593, _1461595] : [-(hAPP(hAPP(c_Set_Oinsert(_1461591), _1461593), _1461595) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461591, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1461591), hAPP(hAPP(c_COMBC(_1461591, _1461591, tc_HOL_Obool), c_fequal), _1461593))), _1461595))], (36164 ^ _779308) ^ [_1461652, _1461654] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1461652, tc_HOL_Obool)), _1461654) = hAPP(c_Set_OCollect(_1461652), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1461652), c_fNot), hAPP(hAPP(c_COMBC(_1461652, tc_fun(_1461652, tc_HOL_Obool), tc_HOL_Obool), c_member(_1461652)), _1461654))))], (36166 ^ _779308) ^ [_1461715, _1461717, _1461719, _1461721] : [-(hAPP(c_Set_Ovimage(_1461715, _1461717, _1461719), _1461721) = hAPP(c_Set_OCollect(_1461715), hAPP(hAPP(c_COMBC(_1461715, tc_fun(_1461717, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1461717, tc_fun(tc_fun(_1461717, tc_HOL_Obool), tc_HOL_Obool), _1461715), c_member(_1461717)), _1461719)), _1461721)))], (36168 ^ _779308) ^ [_1461787, _1461789, _1461791] : [-(hAPP(c_Set_OCollect(_1461787), hAPP(hAPP(c_COMBS(_1461787, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461787), c_fimplies), _1461789)), _1461791)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1461787, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1461787, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1461787), _1461789))), hAPP(c_Set_OCollect(_1461787), _1461791)))], (36170 ^ _779308) ^ [_1461868, _1461870] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), _1461868)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1461870))))))], (36172 ^ _779308) ^ [_1461910, _1461912, _1461914, _1461916, _1461918, _1461920, _1461922] : [class_Groups_Ocomm__monoid__add(_1461910), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461912), _1461914)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1461916), _1461918)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461912, _1461910), hAPP(hAPP(c_COMBS(_1461912, tc_fun(_1461916, tc_HOL_Obool), _1461910), hAPP(hAPP(c_COMBB(tc_fun(_1461916, _1461910), tc_fun(tc_fun(_1461916, tc_HOL_Obool), _1461910), _1461912), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461916, _1461910)), _1461920)), hAPP(hAPP(c_COMBB(tc_fun(_1461916, tc_HOL_Obool), tc_fun(_1461916, tc_HOL_Obool), _1461912), c_Set_OCollect(_1461916)), hAPP(hAPP(c_COMBB(tc_fun(_1461916, tc_HOL_Obool), tc_fun(_1461916, tc_HOL_Obool), _1461912), hAPP(c_COMBS(_1461916, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461916), c_fconj), hAPP(hAPP(c_COMBC(_1461916, tc_fun(_1461916, tc_HOL_Obool), tc_HOL_Obool), c_member(_1461916)), _1461918)))), _1461922)))), _1461914) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461916, _1461910), hAPP(hAPP(c_COMBS(_1461916, tc_fun(_1461912, tc_HOL_Obool), _1461910), hAPP(hAPP(c_COMBB(tc_fun(_1461912, _1461910), tc_fun(tc_fun(_1461912, tc_HOL_Obool), _1461910), _1461916), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1461912, _1461910)), hAPP(c_COMBC(_1461912, _1461916, _1461910), _1461920))), hAPP(hAPP(c_COMBB(tc_fun(_1461912, tc_HOL_Obool), tc_fun(_1461912, tc_HOL_Obool), _1461916), c_Set_OCollect(_1461912)), hAPP(hAPP(c_COMBB(tc_fun(_1461912, tc_HOL_Obool), tc_fun(_1461912, tc_HOL_Obool), _1461916), hAPP(c_COMBS(_1461912, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1461912), c_fconj), hAPP(hAPP(c_COMBC(_1461912, tc_fun(_1461912, tc_HOL_Obool), tc_HOL_Obool), c_member(_1461912)), _1461914)))), hAPP(c_COMBC(_1461912, _1461916, tc_HOL_Obool), _1461922))))), _1461918))], (36186 ^ _779308) ^ [_1462603, _1462605, _1462607, _1462609, _1462611, _1462613] : [-(hAPP(c_Set_Oimage(_1462603, _1462605, hAPP(hAPP(c_COMBS(_1462603, _1462605, _1462605), hAPP(hAPP(c_COMBS(_1462603, _1462605, tc_fun(_1462605, _1462605)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1462605, tc_fun(_1462605, _1462605)), _1462603), c_If(_1462605)), _1462607)), _1462609)), _1462611)), _1462613) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1462605, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1462603, _1462605, _1462609), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462603, tc_HOL_Obool)), _1462613), hAPP(c_Set_OCollect(_1462603), _1462607)))), hAPP(c_Set_Oimage(_1462603, _1462605, _1462611), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462603, tc_HOL_Obool)), _1462613), hAPP(c_Set_OCollect(_1462603), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1462603), c_fNot), _1462607))))))], (36188 ^ _779308) ^ [_1462751, _1462753, _1462755, _1462757] : [_1462751 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1462753, _1462755), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1462757))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1462753), _1462751)))], (36194 ^ _779308) ^ [_1462866, _1462868, _1462870, _1462872, _1462874] : [class_Groups_Ocomm__monoid__add(_1462866), hBOOL(hAPP(c_Finite__Set_Ofinite(_1462868), _1462870)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462868, _1462866), _1462872), hAPP(c_Set_OCollect(_1462868), hAPP(hAPP(c_COMBS(_1462868, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1462868), c_fconj), hAPP(hAPP(c_COMBC(_1462868, tc_fun(_1462868, tc_HOL_Obool), tc_HOL_Obool), c_member(_1462868)), _1462870))), hAPP(hAPP(c_COMBC(_1462868, tc_fun(_1462868, tc_HOL_Obool), tc_HOL_Obool), c_member(_1462868)), _1462874)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1462868, _1462866), hAPP(hAPP(c_COMBC(_1462868, _1462866, _1462866), hAPP(hAPP(c_COMBS(_1462868, _1462866, tc_fun(_1462866, _1462866)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1462866, tc_fun(_1462866, _1462866)), _1462868), c_If(_1462866)), hAPP(hAPP(c_COMBC(_1462868, tc_fun(_1462868, tc_HOL_Obool), tc_HOL_Obool), c_member(_1462868)), _1462874))), _1462872)), c_Groups_Ozero__class_Ozero(_1462866))), _1462870))], (36204 ^ _779308) ^ [_1463275, _1463277, _1463279, _1463281, _1463283, _1463285] : [class_Groups_Ocomm__monoid__add(_1463275), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463277), _1463279)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463277, _1463275), _1463281), _1463279) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463283, _1463275), hAPP(hAPP(c_COMBB(tc_fun(_1463277, tc_HOL_Obool), _1463275, _1463283), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463277, _1463275), _1463281)), hAPP(hAPP(c_COMBB(tc_fun(_1463277, tc_HOL_Obool), tc_fun(_1463277, tc_HOL_Obool), _1463283), c_Set_OCollect(_1463277)), hAPP(hAPP(c_COMBB(tc_fun(_1463277, tc_HOL_Obool), tc_fun(_1463277, tc_HOL_Obool), _1463283), hAPP(c_COMBS(_1463277, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1463277), c_fconj), hAPP(hAPP(c_COMBC(_1463277, tc_fun(_1463277, tc_HOL_Obool), tc_HOL_Obool), c_member(_1463277)), _1463279)))), hAPP(c_COMBC(_1463277, _1463283, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1463283, tc_fun(_1463283, tc_HOL_Obool), _1463277), c_fequal), _1463285)))))), hAPP(c_Set_Oimage(_1463277, _1463283, _1463285), _1463279)))], (36214 ^ _779308) ^ [_1463686, _1463688, _1463690, _1463692] : [-(hAPP(c_Relation_OImage(_1463686, _1463688, _1463690), hAPP(hAPP(c_Set_Oinsert(_1463686), _1463692), c_Orderings_Obot__class_Obot(tc_fun(_1463686, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1463688), hAPP(hAPP(c_COMBC(_1463688, tc_fun(tc_prod(_1463686, _1463688), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1463686, _1463688), tc_fun(tc_fun(tc_prod(_1463686, _1463688), tc_HOL_Obool), tc_HOL_Obool), _1463688), c_member(tc_prod(_1463686, _1463688))), hAPP(c_Product__Type_OPair(_1463686, _1463688), _1463692))), _1463690)))], (36216 ^ _779308) ^ [_1463789, _1463791, _1463793, _1463795, _1463797, _1463799] : [class_Groups_Ocomm__monoid__add(_1463789), hBOOL(hAPP(c_Finite__Set_Ofinite(_1463791), _1463793)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463791, _1463789), hAPP(hAPP(c_COMBS(_1463791, _1463789, _1463789), hAPP(hAPP(c_COMBS(_1463791, _1463789, tc_fun(_1463789, _1463789)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1463789, tc_fun(_1463789, _1463789)), _1463791), c_If(_1463789)), _1463795)), _1463797)), _1463799)), _1463793) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1463789), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463791, _1463789), _1463797), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463791, tc_HOL_Obool)), _1463793), hAPP(c_Set_OCollect(_1463791), _1463795)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1463791, _1463789), _1463799), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1463791, tc_HOL_Obool)), _1463793), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1463791, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1463791), _1463795))))))], (36226 ^ _779308) ^ [_1464168, _1464170] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1464168))), -(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_Nat_Onat), c_member(tc_Nat_Onat)), c_Nat_OSuc)), _1464168))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1464170)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1464168))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1464170))))))], (36232 ^ _779308) ^ [_1464251, _1464253, _1464255, _1464257, _1464259, _1464261] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1464251), _1464253)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464255), _1464257)), 36242 ^ _779308 : [(36243 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1464255), 36241 ^ [_1464251, _1464253, _1464255, _1464257, _1464259, _1464261]), _1464257)))], (36245 ^ _779308) ^ [] : [hAPP(c_Finite__Set_Ocard(_1464251), hAPP(c_Set_OCollect(_1464251), hAPP(hAPP(c_COMBS(_1464251, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1464251), c_fconj), hAPP(hAPP(c_COMBC(_1464251, tc_fun(_1464251, tc_HOL_Obool), tc_HOL_Obool), c_member(_1464251)), _1464253))), hAPP(hAPP(c_COMBC(_1464251, _1464255, tc_HOL_Obool), _1464259), 36241 ^ [_1464251, _1464253, _1464255, _1464257, _1464259, _1464261])))) = _1464261]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1464251, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1464255, tc_HOL_Obool), tc_Nat_Onat, _1464251), c_Finite__Set_Ocard(_1464255)), hAPP(hAPP(c_COMBB(tc_fun(_1464255, tc_HOL_Obool), tc_fun(_1464255, tc_HOL_Obool), _1464251), c_Set_OCollect(_1464255)), hAPP(hAPP(c_COMBB(tc_fun(_1464255, tc_HOL_Obool), tc_fun(_1464255, tc_HOL_Obool), _1464251), hAPP(c_COMBS(_1464255, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1464255), c_fconj), hAPP(hAPP(c_COMBC(_1464255, tc_fun(_1464255, tc_HOL_Obool), tc_HOL_Obool), c_member(_1464255)), _1464257)))), _1464259)))), _1464253) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1464261), hAPP(c_Finite__Set_Ocard(_1464255), _1464257)))], (36249 ^ _779308) ^ [_1464941, _1464943, _1464945] : [class_Orderings_Olinorder(_1464941), hBOOL(hAPP(c_Finite__Set_Ofinite(_1464941), _1464943)), -(_1464943 = c_Orderings_Obot__class_Obot(tc_fun(_1464941, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1464941), _1464945), c_Big__Operators_Olattice_OInf__fin(_1464941, c_Orderings_Oord__class_Omin(_1464941), _1464943)) = c_Big__Operators_Olattice_OInf__fin(_1464941, c_Orderings_Oord__class_Omin(_1464941), hAPP(c_Set_OCollect(_1464941), hAPP(hAPP(c_COMBB(tc_fun(_1464941, tc_HOL_Obool), tc_HOL_Obool, _1464941), c_HOL_OEx(_1464941)), hAPP(hAPP(c_COMBC(_1464941, tc_fun(_1464941, tc_HOL_Obool), tc_fun(_1464941, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464941, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1464941, tc_HOL_Obool), tc_fun(_1464941, tc_HOL_Obool)), _1464941), c_COMBS(_1464941, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464941, tc_HOL_Obool), tc_fun(_1464941, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1464941), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1464941), c_fconj)), hAPP(hAPP(c_COMBC(_1464941, tc_fun(_1464941, _1464941), tc_fun(_1464941, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464941, tc_HOL_Obool), tc_fun(tc_fun(_1464941, _1464941), tc_fun(_1464941, tc_HOL_Obool)), _1464941), c_COMBB(_1464941, tc_HOL_Obool, _1464941)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1464941), _1464945))))), hAPP(hAPP(c_COMBC(_1464941, tc_fun(_1464941, tc_HOL_Obool), tc_HOL_Obool), c_member(_1464941)), _1464943))))))], (36263 ^ _779308) ^ [_1465439, _1465441, _1465443] : [class_Orderings_Olinorder(_1465439), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465439), _1465441)), -(_1465441 = c_Orderings_Obot__class_Obot(tc_fun(_1465439, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1465439), _1465443)), -(_1465443 = c_Orderings_Obot__class_Obot(tc_fun(_1465439, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1465439), c_Big__Operators_Olattice_OInf__fin(_1465439, c_Orderings_Oord__class_Omin(_1465439), _1465441)), c_Big__Operators_Olattice_OInf__fin(_1465439, c_Orderings_Oord__class_Omin(_1465439), _1465443)) = c_Big__Operators_Olattice_OInf__fin(_1465439, c_Orderings_Oord__class_Omin(_1465439), hAPP(c_Set_OCollect(_1465439), hAPP(hAPP(c_COMBB(tc_fun(_1465439, tc_HOL_Obool), tc_HOL_Obool, _1465439), c_HOL_OEx(_1465439)), hAPP(hAPP(c_COMBB(tc_fun(_1465439, tc_fun(_1465439, tc_HOL_Obool)), tc_fun(_1465439, tc_HOL_Obool), _1465439), hAPP(c_COMBB(tc_fun(_1465439, tc_HOL_Obool), tc_HOL_Obool, _1465439), c_HOL_OEx(_1465439))), hAPP(hAPP(c_COMBC(_1465439, tc_fun(_1465439, tc_fun(_1465439, tc_HOL_Obool)), tc_fun(_1465439, tc_fun(_1465439, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1465439, tc_fun(tc_fun(_1465439, tc_HOL_Obool), tc_fun(_1465439, tc_HOL_Obool))), tc_fun(tc_fun(_1465439, tc_fun(_1465439, tc_HOL_Obool)), tc_fun(_1465439, tc_fun(_1465439, tc_HOL_Obool))), _1465439), c_COMBS(_1465439, tc_fun(_1465439, tc_HOL_Obool), tc_fun(_1465439, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1465439, tc_fun(_1465439, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1465439, tc_fun(tc_fun(_1465439, tc_HOL_Obool), tc_fun(_1465439, tc_HOL_Obool))), _1465439), hAPP(c_COMBB(tc_fun(_1465439, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1465439, tc_HOL_Obool), tc_fun(_1465439, tc_HOL_Obool)), _1465439), c_COMBS(_1465439, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1465439, tc_fun(_1465439, tc_HOL_Obool)), tc_fun(_1465439, tc_fun(_1465439, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1465439), hAPP(c_COMBB(tc_fun(_1465439, tc_HOL_Obool), tc_fun(_1465439, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1465439), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1465439), c_fconj))), hAPP(hAPP(c_COMBC(_1465439, tc_fun(_1465439, tc_fun(_1465439, _1465439)), tc_fun(_1465439, tc_fun(_1465439, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1465439, _1465439), tc_fun(_1465439, tc_HOL_Obool)), tc_fun(tc_fun(_1465439, tc_fun(_1465439, _1465439)), tc_fun(_1465439, tc_fun(_1465439, tc_HOL_Obool))), _1465439), c_COMBB(tc_fun(_1465439, _1465439), tc_fun(_1465439, tc_HOL_Obool), _1465439)), hAPP(hAPP(c_COMBB(tc_fun(_1465439, tc_HOL_Obool), tc_fun(tc_fun(_1465439, _1465439), tc_fun(_1465439, tc_HOL_Obool)), _1465439), c_COMBB(_1465439, tc_HOL_Obool, _1465439)), c_fequal))), c_Orderings_Oord__class_Omax(_1465439)))))), hAPP(hAPP(c_COMBC(_1465439, tc_fun(_1465439, tc_HOL_Obool), tc_fun(_1465439, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1465439, tc_HOL_Obool), tc_fun(_1465439, tc_HOL_Obool)), _1465439), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1465439)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1465439), c_fconj), hAPP(hAPP(c_COMBC(_1465439, tc_fun(_1465439, tc_HOL_Obool), tc_HOL_Obool), c_member(_1465439)), _1465441)))), hAPP(hAPP(c_COMBC(_1465439, tc_fun(_1465439, tc_HOL_Obool), tc_HOL_Obool), c_member(_1465439)), _1465443))))))))], (36285 ^ _779308) ^ [_1466556, _1466558] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466556), _1466558)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1466556, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1466556, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1466556, tc_HOL_Obool), tc_fun(_1466556, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1466556, tc_HOL_Obool))), _1466558)))))], (36291 ^ _779308) ^ [_1466713, _1466715] : [-(hAPP(c_Set_OPow(_1466713), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1466713, tc_HOL_Obool)), _1466715)) = hAPP(c_Set_OCollect(tc_fun(_1466713, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1466713, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1466713, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1466713, tc_HOL_Obool), tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1466713, tc_HOL_Obool)), c_COMBS(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1466713, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1466713, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1466713, tc_HOL_Obool), tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_fun(_1466713, tc_HOL_Obool)), tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_fun(_1466713, tc_HOL_Obool)), tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1466713, tc_HOL_Obool)), c_COMBB(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1466713, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1466713, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1466713, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1466713, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1466713, tc_HOL_Obool)), _1466715)), c_Set_OPow(_1466713))))))], (36293 ^ _779308) ^ [_1466993, _1466995] : [-(hAPP(c_Set_OPow(_1466993), _1466995) = hAPP(c_Set_OCollect(tc_fun(_1466993, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1466993, tc_HOL_Obool), tc_fun(_1466993, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1466993, tc_HOL_Obool))), _1466995)))], (36295 ^ _779308) ^ [_1467052, _1467054, _1467056, _1467058] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467052), hAPP(c_Set_OCollect(_1467052), _1467054))), 36298 ^ _779308 : [(36309 ^ _779308) ^ [] : [36311 ^ _779308 : [(36312 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1467054, 36310 ^ [_1467052, _1467054, _1467056, _1467058])))], (36314 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467056), hAPP(c_Set_OCollect(_1467056), hAPP(hAPP(c_COMBC(_1467056, _1467052, tc_HOL_Obool), _1467058), 36310 ^ [_1467052, _1467054, _1467056, _1467058]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1467056), hAPP(c_Set_OCollect(_1467056), hAPP(hAPP(c_COMBB(tc_fun(_1467052, tc_HOL_Obool), tc_HOL_Obool, _1467056), c_HOL_OEx(_1467052)), hAPP(hAPP(c_COMBB(tc_fun(_1467052, tc_HOL_Obool), tc_fun(_1467052, tc_HOL_Obool), _1467056), hAPP(c_COMBS(_1467052, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1467052), c_fconj), _1467054))), _1467058))))))], (36299 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467056), hAPP(c_Set_OCollect(_1467056), hAPP(hAPP(c_COMBB(tc_fun(_1467052, tc_HOL_Obool), tc_HOL_Obool, _1467056), c_HOL_OEx(_1467052)), hAPP(hAPP(c_COMBB(tc_fun(_1467052, tc_HOL_Obool), tc_fun(_1467052, tc_HOL_Obool), _1467056), hAPP(c_COMBS(_1467052, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1467052), c_fconj), _1467054))), _1467058))))), 36302 ^ _779308 : [(36303 ^ _779308) ^ [_1467335] : [hBOOL(hAPP(_1467054, _1467335)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1467056), hAPP(c_Set_OCollect(_1467056), hAPP(hAPP(c_COMBC(_1467056, _1467052, tc_HOL_Obool), _1467058), _1467335)))))]]]]], (36318 ^ _779308) ^ [_1467700, _1467702, _1467704, _1467706] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467700), hAPP(c_Set_OCollect(_1467700), _1467702))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1467704), hAPP(c_Set_OCollect(_1467704), hAPP(hAPP(c_COMBB(tc_fun(_1467700, tc_HOL_Obool), tc_HOL_Obool, _1467704), c_HOL_OEx(_1467700)), hAPP(hAPP(c_COMBC(_1467704, tc_fun(_1467700, tc_HOL_Obool), tc_fun(_1467700, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467700, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1467700, tc_HOL_Obool), tc_fun(_1467700, tc_HOL_Obool)), _1467704), c_COMBS(_1467700, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467700, tc_HOL_Obool), tc_fun(_1467700, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1467704), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1467700), c_fconj)), hAPP(hAPP(c_COMBC(_1467704, tc_fun(_1467700, _1467704), tc_fun(_1467700, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1467704, tc_HOL_Obool), tc_fun(tc_fun(_1467700, _1467704), tc_fun(_1467700, tc_HOL_Obool)), _1467704), c_COMBB(_1467704, tc_HOL_Obool, _1467700)), c_fequal)), _1467706)))), _1467702))))))], (36324 ^ _779308) ^ [_1468061, _1468063] : [-(c_Fun_Oinj__on(tc_fun(_1468061, _1468063), tc_fun(tc_prod(_1468061, _1468063), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1468061, _1468063), tc_HOL_Obool), tc_fun(tc_prod(_1468061, _1468063), tc_HOL_Obool), tc_fun(_1468061, _1468063)), c_Set_OCollect(tc_prod(_1468061, _1468063))), hAPP(hAPP(c_COMBB(tc_fun(_1468061, tc_fun(_1468063, tc_HOL_Obool)), tc_fun(tc_prod(_1468061, _1468063), tc_HOL_Obool), tc_fun(_1468061, _1468063)), c_Product__Type_Oprod_Oprod__case(_1468061, _1468063, tc_HOL_Obool)), hAPP(c_COMBB(_1468063, tc_fun(_1468063, tc_HOL_Obool), _1468061), hAPP(c_COMBC(_1468063, _1468063, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1468061, _1468063), tc_HOL_Obool))))], (36326 ^ _779308) ^ [_1468181] : [-(c_Nat__Transfer_Onat__set(hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), _1468181))))], (36328 ^ _779308) ^ [_1468209] : [-(c_Wellfounded_Ofinite__psubset(_1468209) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1468209, tc_HOL_Obool), tc_fun(_1468209, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1468209, tc_HOL_Obool), tc_fun(_1468209, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1468209, tc_HOL_Obool), tc_fun(tc_fun(_1468209, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1468209, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1468209, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1468209, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1468209, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1468209, tc_HOL_Obool)), c_COMBS(tc_fun(_1468209, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1468209, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1468209, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1468209, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1468209, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1468209, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1468209)))))], (36330 ^ _779308) ^ [_1468369, _1468371, _1468373, _1468375] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1468369, _1468371), _1468373), _1468375) = hAPP(c_Set_OCollect(tc_prod(_1468371, _1468371)), hAPP(c_Product__Type_Oprod_Oprod__case(_1468371, _1468371, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1468371, tc_fun(tc_prod(_1468369, _1468369), tc_HOL_Obool), tc_fun(_1468371, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1468371, tc_fun(tc_fun(tc_prod(_1468369, _1468369), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1468369, _1468369), tc_HOL_Obool), tc_fun(_1468371, tc_HOL_Obool)), _1468371), c_COMBC(_1468371, tc_fun(tc_prod(_1468369, _1468369), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1468371, tc_prod(_1468369, _1468369)), tc_fun(_1468371, tc_fun(tc_fun(tc_prod(_1468369, _1468369), tc_HOL_Obool), tc_HOL_Obool)), _1468371), hAPP(c_COMBB(tc_prod(_1468369, _1468369), tc_fun(tc_fun(tc_prod(_1468369, _1468369), tc_HOL_Obool), tc_HOL_Obool), _1468371), c_member(tc_prod(_1468369, _1468369)))), hAPP(hAPP(c_COMBC(_1468371, tc_fun(_1468371, _1468369), tc_fun(_1468371, tc_prod(_1468369, _1468369))), hAPP(hAPP(c_COMBB(tc_fun(_1468369, tc_prod(_1468369, _1468369)), tc_fun(tc_fun(_1468371, _1468369), tc_fun(_1468371, tc_prod(_1468369, _1468369))), _1468371), c_COMBB(_1468369, tc_prod(_1468369, _1468369), _1468371)), hAPP(hAPP(c_COMBB(_1468369, tc_fun(_1468369, tc_prod(_1468369, _1468369)), _1468371), c_Product__Type_OPair(_1468369, _1468369)), _1468375))), _1468375)))), _1468373))))], (36332 ^ _779308) ^ [_1468610] : [-(hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), _1468610)) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_HOL_Obool, tc_Nat_Onat), _1468610), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (36334 ^ _779308) ^ [_1468651] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1468651) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Int_Oint), _1468651), c_Int_Onat)))))], (36336 ^ _779308) ^ [_1468692, _1468694, _1468696] : [class_Groups_Olinordered__ab__semigroup__add(_1468692), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468692), _1468694)), -(_1468694 = c_Orderings_Obot__class_Obot(tc_fun(_1468692, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1468692), _1468696), c_Big__Operators_Olinorder__class_OMin(_1468692, _1468694)) = c_Big__Operators_Olinorder__class_OMin(_1468692, hAPP(c_Set_OCollect(_1468692), hAPP(hAPP(c_COMBB(tc_fun(_1468692, tc_HOL_Obool), tc_HOL_Obool, _1468692), c_HOL_OEx(_1468692)), hAPP(hAPP(c_COMBC(_1468692, tc_fun(_1468692, tc_HOL_Obool), tc_fun(_1468692, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1468692, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1468692, tc_HOL_Obool), tc_fun(_1468692, tc_HOL_Obool)), _1468692), c_COMBS(_1468692, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1468692, tc_HOL_Obool), tc_fun(_1468692, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1468692), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1468692), c_fconj)), hAPP(hAPP(c_COMBC(_1468692, tc_fun(_1468692, _1468692), tc_fun(_1468692, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1468692, tc_HOL_Obool), tc_fun(tc_fun(_1468692, _1468692), tc_fun(_1468692, tc_HOL_Obool)), _1468692), c_COMBB(_1468692, tc_HOL_Obool, _1468692)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1468692), _1468696))))), hAPP(hAPP(c_COMBC(_1468692, tc_fun(_1468692, tc_HOL_Obool), tc_HOL_Obool), c_member(_1468692)), _1468694))))))], (36350 ^ _779308) ^ [_1469178, _1469180, _1469182] : [class_Groups_Olinordered__ab__semigroup__add(_1469178), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469178), _1469180)), -(_1469180 = c_Orderings_Obot__class_Obot(tc_fun(_1469178, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1469178), _1469182), c_Big__Operators_Olinorder__class_OMax(_1469178, _1469180)) = c_Big__Operators_Olinorder__class_OMax(_1469178, hAPP(c_Set_OCollect(_1469178), hAPP(hAPP(c_COMBB(tc_fun(_1469178, tc_HOL_Obool), tc_HOL_Obool, _1469178), c_HOL_OEx(_1469178)), hAPP(hAPP(c_COMBC(_1469178, tc_fun(_1469178, tc_HOL_Obool), tc_fun(_1469178, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469178, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1469178, tc_HOL_Obool), tc_fun(_1469178, tc_HOL_Obool)), _1469178), c_COMBS(_1469178, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469178, tc_HOL_Obool), tc_fun(_1469178, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1469178), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1469178), c_fconj)), hAPP(hAPP(c_COMBC(_1469178, tc_fun(_1469178, _1469178), tc_fun(_1469178, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469178, tc_HOL_Obool), tc_fun(tc_fun(_1469178, _1469178), tc_fun(_1469178, tc_HOL_Obool)), _1469178), c_COMBB(_1469178, tc_HOL_Obool, _1469178)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1469178), _1469182))))), hAPP(hAPP(c_COMBC(_1469178, tc_fun(_1469178, tc_HOL_Obool), tc_HOL_Obool), c_member(_1469178)), _1469180))))))], (36364 ^ _779308) ^ [_1469664, _1469666, _1469668] : [class_Lattices_Odistrib__lattice(_1469664), hBOOL(hAPP(c_Finite__Set_Ofinite(_1469664), _1469666)), -(_1469666 = c_Orderings_Obot__class_Obot(tc_fun(_1469664, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1469664), _1469668), c_Big__Operators_Olattice__class_OInf__fin(_1469664, _1469666)) = c_Big__Operators_Olattice__class_OInf__fin(_1469664, hAPP(c_Set_OCollect(_1469664), hAPP(hAPP(c_COMBB(tc_fun(_1469664, tc_HOL_Obool), tc_HOL_Obool, _1469664), c_HOL_OEx(_1469664)), hAPP(hAPP(c_COMBC(_1469664, tc_fun(_1469664, tc_HOL_Obool), tc_fun(_1469664, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469664, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1469664, tc_HOL_Obool), tc_fun(_1469664, tc_HOL_Obool)), _1469664), c_COMBS(_1469664, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469664, tc_HOL_Obool), tc_fun(_1469664, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1469664), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1469664), c_fconj)), hAPP(hAPP(c_COMBC(_1469664, tc_fun(_1469664, _1469664), tc_fun(_1469664, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469664, tc_HOL_Obool), tc_fun(tc_fun(_1469664, _1469664), tc_fun(_1469664, tc_HOL_Obool)), _1469664), c_COMBB(_1469664, tc_HOL_Obool, _1469664)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1469664), _1469668))))), hAPP(hAPP(c_COMBC(_1469664, tc_fun(_1469664, tc_HOL_Obool), tc_HOL_Obool), c_member(_1469664)), _1469666))))))], (36378 ^ _779308) ^ [_1470150, _1470152, _1470154] : [class_Lattices_Odistrib__lattice(_1470150), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470150), _1470152)), -(_1470152 = c_Orderings_Obot__class_Obot(tc_fun(_1470150, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470150), _1470154)), -(_1470154 = c_Orderings_Obot__class_Obot(tc_fun(_1470150, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1470150), c_Big__Operators_Olattice__class_OInf__fin(_1470150, _1470152)), c_Big__Operators_Olattice__class_OInf__fin(_1470150, _1470154)) = c_Big__Operators_Olattice__class_OInf__fin(_1470150, hAPP(c_Set_OCollect(_1470150), hAPP(hAPP(c_COMBB(tc_fun(_1470150, tc_HOL_Obool), tc_HOL_Obool, _1470150), c_HOL_OEx(_1470150)), hAPP(hAPP(c_COMBB(tc_fun(_1470150, tc_fun(_1470150, tc_HOL_Obool)), tc_fun(_1470150, tc_HOL_Obool), _1470150), hAPP(c_COMBB(tc_fun(_1470150, tc_HOL_Obool), tc_HOL_Obool, _1470150), c_HOL_OEx(_1470150))), hAPP(hAPP(c_COMBC(_1470150, tc_fun(_1470150, tc_fun(_1470150, tc_HOL_Obool)), tc_fun(_1470150, tc_fun(_1470150, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1470150, tc_fun(tc_fun(_1470150, tc_HOL_Obool), tc_fun(_1470150, tc_HOL_Obool))), tc_fun(tc_fun(_1470150, tc_fun(_1470150, tc_HOL_Obool)), tc_fun(_1470150, tc_fun(_1470150, tc_HOL_Obool))), _1470150), c_COMBS(_1470150, tc_fun(_1470150, tc_HOL_Obool), tc_fun(_1470150, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1470150, tc_fun(_1470150, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1470150, tc_fun(tc_fun(_1470150, tc_HOL_Obool), tc_fun(_1470150, tc_HOL_Obool))), _1470150), hAPP(c_COMBB(tc_fun(_1470150, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1470150, tc_HOL_Obool), tc_fun(_1470150, tc_HOL_Obool)), _1470150), c_COMBS(_1470150, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1470150, tc_fun(_1470150, tc_HOL_Obool)), tc_fun(_1470150, tc_fun(_1470150, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1470150), hAPP(c_COMBB(tc_fun(_1470150, tc_HOL_Obool), tc_fun(_1470150, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1470150), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1470150), c_fconj))), hAPP(hAPP(c_COMBC(_1470150, tc_fun(_1470150, tc_fun(_1470150, _1470150)), tc_fun(_1470150, tc_fun(_1470150, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1470150, _1470150), tc_fun(_1470150, tc_HOL_Obool)), tc_fun(tc_fun(_1470150, tc_fun(_1470150, _1470150)), tc_fun(_1470150, tc_fun(_1470150, tc_HOL_Obool))), _1470150), c_COMBB(tc_fun(_1470150, _1470150), tc_fun(_1470150, tc_HOL_Obool), _1470150)), hAPP(hAPP(c_COMBB(tc_fun(_1470150, tc_HOL_Obool), tc_fun(tc_fun(_1470150, _1470150), tc_fun(_1470150, tc_HOL_Obool)), _1470150), c_COMBB(_1470150, tc_HOL_Obool, _1470150)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1470150)))))), hAPP(hAPP(c_COMBC(_1470150, tc_fun(_1470150, tc_HOL_Obool), tc_fun(_1470150, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1470150, tc_HOL_Obool), tc_fun(_1470150, tc_HOL_Obool)), _1470150), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1470150)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1470150), c_fconj), hAPP(hAPP(c_COMBC(_1470150, tc_fun(_1470150, tc_HOL_Obool), tc_HOL_Obool), c_member(_1470150)), _1470152)))), hAPP(hAPP(c_COMBC(_1470150, tc_fun(_1470150, tc_HOL_Obool), tc_HOL_Obool), c_member(_1470150)), _1470154))))))))], (36400 ^ _779308) ^ [_1471249, _1471251, _1471253] : [class_Lattices_Odistrib__lattice(_1471249), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471249), _1471251)), -(_1471251 = c_Orderings_Obot__class_Obot(tc_fun(_1471249, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471249), _1471253)), -(_1471253 = c_Orderings_Obot__class_Obot(tc_fun(_1471249, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1471249), c_Big__Operators_Olattice__class_OSup__fin(_1471249, _1471251)), c_Big__Operators_Olattice__class_OSup__fin(_1471249, _1471253)) = c_Big__Operators_Olattice__class_OSup__fin(_1471249, hAPP(c_Set_OCollect(_1471249), hAPP(hAPP(c_COMBB(tc_fun(_1471249, tc_HOL_Obool), tc_HOL_Obool, _1471249), c_HOL_OEx(_1471249)), hAPP(hAPP(c_COMBB(tc_fun(_1471249, tc_fun(_1471249, tc_HOL_Obool)), tc_fun(_1471249, tc_HOL_Obool), _1471249), hAPP(c_COMBB(tc_fun(_1471249, tc_HOL_Obool), tc_HOL_Obool, _1471249), c_HOL_OEx(_1471249))), hAPP(hAPP(c_COMBC(_1471249, tc_fun(_1471249, tc_fun(_1471249, tc_HOL_Obool)), tc_fun(_1471249, tc_fun(_1471249, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1471249, tc_fun(tc_fun(_1471249, tc_HOL_Obool), tc_fun(_1471249, tc_HOL_Obool))), tc_fun(tc_fun(_1471249, tc_fun(_1471249, tc_HOL_Obool)), tc_fun(_1471249, tc_fun(_1471249, tc_HOL_Obool))), _1471249), c_COMBS(_1471249, tc_fun(_1471249, tc_HOL_Obool), tc_fun(_1471249, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1471249, tc_fun(_1471249, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1471249, tc_fun(tc_fun(_1471249, tc_HOL_Obool), tc_fun(_1471249, tc_HOL_Obool))), _1471249), hAPP(c_COMBB(tc_fun(_1471249, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1471249, tc_HOL_Obool), tc_fun(_1471249, tc_HOL_Obool)), _1471249), c_COMBS(_1471249, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1471249, tc_fun(_1471249, tc_HOL_Obool)), tc_fun(_1471249, tc_fun(_1471249, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1471249), hAPP(c_COMBB(tc_fun(_1471249, tc_HOL_Obool), tc_fun(_1471249, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1471249), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1471249), c_fconj))), hAPP(hAPP(c_COMBC(_1471249, tc_fun(_1471249, tc_fun(_1471249, _1471249)), tc_fun(_1471249, tc_fun(_1471249, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1471249, _1471249), tc_fun(_1471249, tc_HOL_Obool)), tc_fun(tc_fun(_1471249, tc_fun(_1471249, _1471249)), tc_fun(_1471249, tc_fun(_1471249, tc_HOL_Obool))), _1471249), c_COMBB(tc_fun(_1471249, _1471249), tc_fun(_1471249, tc_HOL_Obool), _1471249)), hAPP(hAPP(c_COMBB(tc_fun(_1471249, tc_HOL_Obool), tc_fun(tc_fun(_1471249, _1471249), tc_fun(_1471249, tc_HOL_Obool)), _1471249), c_COMBB(_1471249, tc_HOL_Obool, _1471249)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1471249)))))), hAPP(hAPP(c_COMBC(_1471249, tc_fun(_1471249, tc_HOL_Obool), tc_fun(_1471249, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1471249, tc_HOL_Obool), tc_fun(_1471249, tc_HOL_Obool)), _1471249), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1471249)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1471249), c_fconj), hAPP(hAPP(c_COMBC(_1471249, tc_fun(_1471249, tc_HOL_Obool), tc_HOL_Obool), c_member(_1471249)), _1471251)))), hAPP(hAPP(c_COMBC(_1471249, tc_fun(_1471249, tc_HOL_Obool), tc_HOL_Obool), c_member(_1471249)), _1471253))))))))], (36422 ^ _779308) ^ [_1472348, _1472350, _1472352] : [class_Lattices_Odistrib__lattice(_1472348), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472348), _1472350)), -(_1472350 = c_Orderings_Obot__class_Obot(tc_fun(_1472348, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1472348), _1472352), c_Big__Operators_Olattice__class_OSup__fin(_1472348, _1472350)) = c_Big__Operators_Olattice__class_OSup__fin(_1472348, hAPP(c_Set_OCollect(_1472348), hAPP(hAPP(c_COMBB(tc_fun(_1472348, tc_HOL_Obool), tc_HOL_Obool, _1472348), c_HOL_OEx(_1472348)), hAPP(hAPP(c_COMBC(_1472348, tc_fun(_1472348, tc_HOL_Obool), tc_fun(_1472348, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472348, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1472348, tc_HOL_Obool), tc_fun(_1472348, tc_HOL_Obool)), _1472348), c_COMBS(_1472348, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472348, tc_HOL_Obool), tc_fun(_1472348, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1472348), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1472348), c_fconj)), hAPP(hAPP(c_COMBC(_1472348, tc_fun(_1472348, _1472348), tc_fun(_1472348, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472348, tc_HOL_Obool), tc_fun(tc_fun(_1472348, _1472348), tc_fun(_1472348, tc_HOL_Obool)), _1472348), c_COMBB(_1472348, tc_HOL_Obool, _1472348)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1472348), _1472352))))), hAPP(hAPP(c_COMBC(_1472348, tc_fun(_1472348, tc_HOL_Obool), tc_HOL_Obool), c_member(_1472348)), _1472350))))))], (36436 ^ _779308) ^ [_1472834, _1472836, _1472838] : [class_Orderings_Olinorder(_1472834), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472834), _1472836)), -(_1472836 = c_Orderings_Obot__class_Obot(tc_fun(_1472834, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1472834), _1472838)), -(_1472838 = c_Orderings_Obot__class_Obot(tc_fun(_1472834, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1472834), c_Big__Operators_Olattice_OSup__fin(_1472834, c_Orderings_Oord__class_Omax(_1472834), _1472836)), c_Big__Operators_Olattice_OSup__fin(_1472834, c_Orderings_Oord__class_Omax(_1472834), _1472838)) = c_Big__Operators_Olattice_OSup__fin(_1472834, c_Orderings_Oord__class_Omax(_1472834), hAPP(c_Set_OCollect(_1472834), hAPP(hAPP(c_COMBB(tc_fun(_1472834, tc_HOL_Obool), tc_HOL_Obool, _1472834), c_HOL_OEx(_1472834)), hAPP(hAPP(c_COMBB(tc_fun(_1472834, tc_fun(_1472834, tc_HOL_Obool)), tc_fun(_1472834, tc_HOL_Obool), _1472834), hAPP(c_COMBB(tc_fun(_1472834, tc_HOL_Obool), tc_HOL_Obool, _1472834), c_HOL_OEx(_1472834))), hAPP(hAPP(c_COMBC(_1472834, tc_fun(_1472834, tc_fun(_1472834, tc_HOL_Obool)), tc_fun(_1472834, tc_fun(_1472834, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1472834, tc_fun(tc_fun(_1472834, tc_HOL_Obool), tc_fun(_1472834, tc_HOL_Obool))), tc_fun(tc_fun(_1472834, tc_fun(_1472834, tc_HOL_Obool)), tc_fun(_1472834, tc_fun(_1472834, tc_HOL_Obool))), _1472834), c_COMBS(_1472834, tc_fun(_1472834, tc_HOL_Obool), tc_fun(_1472834, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1472834, tc_fun(_1472834, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1472834, tc_fun(tc_fun(_1472834, tc_HOL_Obool), tc_fun(_1472834, tc_HOL_Obool))), _1472834), hAPP(c_COMBB(tc_fun(_1472834, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1472834, tc_HOL_Obool), tc_fun(_1472834, tc_HOL_Obool)), _1472834), c_COMBS(_1472834, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1472834, tc_fun(_1472834, tc_HOL_Obool)), tc_fun(_1472834, tc_fun(_1472834, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1472834), hAPP(c_COMBB(tc_fun(_1472834, tc_HOL_Obool), tc_fun(_1472834, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1472834), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1472834), c_fconj))), hAPP(hAPP(c_COMBC(_1472834, tc_fun(_1472834, tc_fun(_1472834, _1472834)), tc_fun(_1472834, tc_fun(_1472834, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1472834, _1472834), tc_fun(_1472834, tc_HOL_Obool)), tc_fun(tc_fun(_1472834, tc_fun(_1472834, _1472834)), tc_fun(_1472834, tc_fun(_1472834, tc_HOL_Obool))), _1472834), c_COMBB(tc_fun(_1472834, _1472834), tc_fun(_1472834, tc_HOL_Obool), _1472834)), hAPP(hAPP(c_COMBB(tc_fun(_1472834, tc_HOL_Obool), tc_fun(tc_fun(_1472834, _1472834), tc_fun(_1472834, tc_HOL_Obool)), _1472834), c_COMBB(_1472834, tc_HOL_Obool, _1472834)), c_fequal))), c_Orderings_Oord__class_Omin(_1472834)))))), hAPP(hAPP(c_COMBC(_1472834, tc_fun(_1472834, tc_HOL_Obool), tc_fun(_1472834, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1472834, tc_HOL_Obool), tc_fun(_1472834, tc_HOL_Obool)), _1472834), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1472834)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1472834), c_fconj), hAPP(hAPP(c_COMBC(_1472834, tc_fun(_1472834, tc_HOL_Obool), tc_HOL_Obool), c_member(_1472834)), _1472836)))), hAPP(hAPP(c_COMBC(_1472834, tc_fun(_1472834, tc_HOL_Obool), tc_HOL_Obool), c_member(_1472834)), _1472838))))))))], (36458 ^ _779308) ^ [_1473951, _1473953, _1473955] : [class_Orderings_Olinorder(_1473951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1473951), _1473953)), -(_1473953 = c_Orderings_Obot__class_Obot(tc_fun(_1473951, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1473951), _1473955), c_Big__Operators_Olattice_OSup__fin(_1473951, c_Orderings_Oord__class_Omax(_1473951), _1473953)) = c_Big__Operators_Olattice_OSup__fin(_1473951, c_Orderings_Oord__class_Omax(_1473951), hAPP(c_Set_OCollect(_1473951), hAPP(hAPP(c_COMBB(tc_fun(_1473951, tc_HOL_Obool), tc_HOL_Obool, _1473951), c_HOL_OEx(_1473951)), hAPP(hAPP(c_COMBC(_1473951, tc_fun(_1473951, tc_HOL_Obool), tc_fun(_1473951, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473951, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1473951, tc_HOL_Obool), tc_fun(_1473951, tc_HOL_Obool)), _1473951), c_COMBS(_1473951, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473951, tc_HOL_Obool), tc_fun(_1473951, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1473951), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1473951), c_fconj)), hAPP(hAPP(c_COMBC(_1473951, tc_fun(_1473951, _1473951), tc_fun(_1473951, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473951, tc_HOL_Obool), tc_fun(tc_fun(_1473951, _1473951), tc_fun(_1473951, tc_HOL_Obool)), _1473951), c_COMBB(_1473951, tc_HOL_Obool, _1473951)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1473951), _1473955))))), hAPP(hAPP(c_COMBC(_1473951, tc_fun(_1473951, tc_HOL_Obool), tc_HOL_Obool), c_member(_1473951)), _1473953))))))], (36472 ^ _779308) ^ [_1474449, _1474451, _1474453, _1474455] : [-(c_Nitpick_Oprod(_1474449, _1474451, _1474453, _1474455) = hAPP(c_Set_OCollect(tc_prod(_1474449, _1474451)), hAPP(c_Product__Type_Oprod_Oprod__case(_1474449, _1474451, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1474449, tc_fun(_1474451, tc_HOL_Obool), tc_fun(_1474451, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1474451, tc_HOL_Obool), tc_fun(_1474451, tc_HOL_Obool)), _1474449), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1474451)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1474449), c_fconj), hAPP(hAPP(c_COMBC(_1474449, tc_fun(_1474449, tc_HOL_Obool), tc_HOL_Obool), c_member(_1474449)), _1474453)))), hAPP(hAPP(c_COMBC(_1474451, tc_fun(_1474451, tc_HOL_Obool), tc_HOL_Obool), c_member(_1474451)), _1474455)))))], (36474 ^ _779308) ^ [_1474577] : [-(c_Int_Oint__ge__less__than(_1474577) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool)), tc_Int_Oint), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1474577)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (36476 ^ _779308) ^ [_1474623] : [-(c_Int_Oint__ge__less__than2(_1474623) = hAPP(c_Set_OCollect(tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_fun(tc_Int_Oint, tc_HOL_Obool), tc_Int_Oint), hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1474623)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (36478 ^ _779308) ^ [_1474684, _1474686] : [c_Predicate_Oreflp(_1474684, _1474686), -(c_Relation_Orefl__on(_1474684, c_Orderings_Otop__class_Otop(tc_fun(_1474684, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1474684, _1474684)), hAPP(c_Product__Type_Oprod_Oprod__case(_1474684, _1474684, tc_HOL_Obool), _1474686))))], (36484 ^ _779308) ^ [_1474799, _1474801] : [c_Relation_Orefl__on(_1474799, c_Orderings_Otop__class_Otop(tc_fun(_1474799, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1474799, _1474799)), hAPP(c_Product__Type_Oprod_Oprod__case(_1474799, _1474799, tc_HOL_Obool), _1474801))), -(c_Predicate_Oreflp(_1474799, _1474801))], (36490 ^ _779308) ^ [_1474920, _1474922, _1474924, _1474926, _1474928, _1474930, _1474932] : [class_Rings_Osemiring__0(_1474920), c_Fun_Oinj__on(tc_prod(_1474922, _1474924), _1474920, hAPP(c_Product__Type_Oprod_Oprod__case(_1474922, _1474924, _1474920), hAPP(hAPP(c_COMBC(_1474922, tc_fun(_1474924, _1474920), tc_fun(_1474924, _1474920)), hAPP(hAPP(c_COMBB(tc_fun(_1474920, _1474920), tc_fun(tc_fun(_1474924, _1474920), tc_fun(_1474924, _1474920)), _1474922), c_COMBB(_1474920, _1474920, _1474924)), hAPP(hAPP(c_COMBB(_1474920, tc_fun(_1474920, _1474920), _1474922), c_Groups_Otimes__class_Otimes(_1474920)), _1474926))), _1474928)), hAPP(hAPP(c_Product__Type_OSigma(_1474922, _1474924), _1474930), hAPP(c_COMBK(tc_fun(_1474924, tc_HOL_Obool), _1474922), _1474932))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1474920), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474922, _1474920), _1474926), _1474930)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474924, _1474920), _1474928), _1474932)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1474920, _1474920), c_Fun_Oid(_1474920)), hAPP(c_Set_OCollect(_1474920), hAPP(hAPP(c_COMBB(tc_fun(_1474922, tc_HOL_Obool), tc_HOL_Obool, _1474920), c_HOL_OEx(_1474922)), hAPP(hAPP(c_COMBB(tc_fun(_1474922, tc_fun(_1474924, tc_HOL_Obool)), tc_fun(_1474922, tc_HOL_Obool), _1474920), hAPP(c_COMBB(tc_fun(_1474924, tc_HOL_Obool), tc_HOL_Obool, _1474922), c_HOL_OEx(_1474924))), hAPP(hAPP(c_COMBC(_1474920, tc_fun(_1474922, tc_fun(_1474924, tc_HOL_Obool)), tc_fun(_1474922, tc_fun(_1474924, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1474922, tc_fun(tc_fun(_1474924, tc_HOL_Obool), tc_fun(_1474924, tc_HOL_Obool))), tc_fun(tc_fun(_1474922, tc_fun(_1474924, tc_HOL_Obool)), tc_fun(_1474922, tc_fun(_1474924, tc_HOL_Obool))), _1474920), c_COMBS(_1474922, tc_fun(_1474924, tc_HOL_Obool), tc_fun(_1474924, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1474922, tc_fun(_1474924, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1474922, tc_fun(tc_fun(_1474924, tc_HOL_Obool), tc_fun(_1474924, tc_HOL_Obool))), _1474920), hAPP(c_COMBB(tc_fun(_1474924, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1474924, tc_HOL_Obool), tc_fun(_1474924, tc_HOL_Obool)), _1474922), c_COMBS(_1474924, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1474922, tc_fun(_1474924, tc_HOL_Obool)), tc_fun(_1474922, tc_fun(_1474924, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1474920), hAPP(c_COMBB(tc_fun(_1474924, tc_HOL_Obool), tc_fun(_1474924, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1474922), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1474924), c_fconj))), hAPP(hAPP(c_COMBC(_1474920, tc_fun(_1474922, tc_fun(_1474924, _1474920)), tc_fun(_1474922, tc_fun(_1474924, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1474924, _1474920), tc_fun(_1474924, tc_HOL_Obool)), tc_fun(tc_fun(_1474922, tc_fun(_1474924, _1474920)), tc_fun(_1474922, tc_fun(_1474924, tc_HOL_Obool))), _1474920), c_COMBB(tc_fun(_1474924, _1474920), tc_fun(_1474924, tc_HOL_Obool), _1474922)), hAPP(hAPP(c_COMBB(tc_fun(_1474920, tc_HOL_Obool), tc_fun(tc_fun(_1474924, _1474920), tc_fun(_1474924, tc_HOL_Obool)), _1474920), c_COMBB(_1474920, tc_HOL_Obool, _1474924)), c_fequal))), hAPP(hAPP(c_COMBC(_1474922, tc_fun(_1474924, _1474920), tc_fun(_1474924, _1474920)), hAPP(hAPP(c_COMBB(tc_fun(_1474920, _1474920), tc_fun(tc_fun(_1474924, _1474920), tc_fun(_1474924, _1474920)), _1474922), c_COMBB(_1474920, _1474920, _1474924)), hAPP(hAPP(c_COMBB(_1474920, tc_fun(_1474920, _1474920), _1474922), c_Groups_Otimes__class_Otimes(_1474920)), _1474926))), _1474928)))))), hAPP(hAPP(c_COMBC(_1474922, tc_fun(_1474924, tc_HOL_Obool), tc_fun(_1474924, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1474924, tc_HOL_Obool), tc_fun(_1474924, tc_HOL_Obool)), _1474922), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1474924)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1474922), c_fconj), hAPP(hAPP(c_COMBC(_1474922, tc_fun(_1474922, tc_HOL_Obool), tc_HOL_Obool), c_member(_1474922)), _1474930)))), hAPP(hAPP(c_COMBC(_1474924, tc_fun(_1474924, tc_HOL_Obool), tc_HOL_Obool), c_member(_1474924)), _1474932))))))))], (36500 ^ _779308) ^ [_1476197, _1476199, _1476201, _1476203, _1476205, _1476207] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1476197), _1476199)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476201), _1476203)), 36510 ^ _779308 : [(36511 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476201), 36509 ^ [_1476197, _1476199, _1476201, _1476203, _1476205, _1476207]), _1476203)))], (36513 ^ _779308) ^ [] : [hAPP(c_Finite__Set_Ocard(_1476197), hAPP(c_Set_OCollect(_1476197), hAPP(hAPP(c_COMBS(_1476197, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1476197), c_fconj), hAPP(hAPP(c_COMBC(_1476197, tc_fun(_1476197, tc_HOL_Obool), tc_HOL_Obool), c_member(_1476197)), _1476199))), hAPP(hAPP(c_COMBC(_1476197, _1476201, tc_HOL_Obool), _1476205), 36509 ^ [_1476197, _1476199, _1476201, _1476203, _1476205, _1476207])))) = hAPP(_1476207, 36509 ^ [_1476197, _1476199, _1476201, _1476203, _1476205, _1476207])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476197, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1476201, tc_HOL_Obool), tc_Nat_Onat, _1476197), c_Finite__Set_Ocard(_1476201)), hAPP(hAPP(c_COMBB(tc_fun(_1476201, tc_HOL_Obool), tc_fun(_1476201, tc_HOL_Obool), _1476197), c_Set_OCollect(_1476201)), hAPP(hAPP(c_COMBB(tc_fun(_1476201, tc_HOL_Obool), tc_fun(_1476201, tc_HOL_Obool), _1476197), hAPP(c_COMBS(_1476201, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1476201), c_fconj), hAPP(hAPP(c_COMBC(_1476201, tc_fun(_1476201, tc_HOL_Obool), tc_HOL_Obool), c_member(_1476201)), _1476203)))), _1476205)))), _1476199) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1476201, tc_Nat_Onat), _1476207), _1476203))], (36517 ^ _779308) ^ [_1476907, _1476909] : [-(c_Fun_Oinj__on(_1476907, _1476907, c_Fun_Oid(_1476907), _1476909))], (36519 ^ _779308) ^ [_1476936, _1476938] : [-(hAPP(c_Set_Ovimage(_1476936, _1476936, c_Fun_Oid(_1476936)), _1476938) = _1476938)], (36521 ^ _779308) ^ [_1476970, _1476972] : [-(c_Product__Type_Oapfst(_1476970, _1476970, _1476972, c_Fun_Oid(_1476970)) = c_Fun_Oid(tc_prod(_1476970, _1476972)))], (36523 ^ _779308) ^ [_1477007, _1477009] : [-(hAPP(c_Fun_Oid(_1477007), _1477009) = _1477009)], (36525 ^ _779308) ^ [_1477037, _1477039] : [-(hAPP(c_Fun_Oid(_1477037), _1477039) = _1477039)], (36527 ^ _779308) ^ [_1477067, _1477069, _1477071] : [c_Predicate_Oreflp(_1477067, _1477069), -(hBOOL(hAPP(hAPP(_1477069, _1477071), _1477071)))], (36533 ^ _779308) ^ [_1477156, _1477158] : [-(c_Product__Type_Oapsnd(_1477156, _1477156, _1477158, c_Fun_Oid(_1477156)) = c_Fun_Oid(tc_prod(_1477158, _1477156)))], (36535 ^ _779308) ^ [_1477193, _1477195] : [-(c_Product__Type_Omap__pair(_1477193, _1477193, _1477195, _1477195, c_Fun_Oid(_1477193), c_Fun_Oid(_1477195)) = c_Fun_Oid(tc_prod(_1477193, _1477195)))], (36537 ^ _779308) ^ [_1477234, _1477236] : [-(c_Product__Type_Omap__pair(_1477234, _1477234, _1477236, _1477236, c_COMBI(_1477234), c_COMBI(_1477236)) = c_Fun_Oid(tc_prod(_1477234, _1477236)))], (36539 ^ _779308) ^ [_1477275, _1477277] : [-(hAPP(c_Set_Oimage(_1477275, _1477275, c_Fun_Oid(_1477275)), _1477277) = _1477277)], (36541 ^ _779308) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (36543 ^ _779308) ^ [_1477327] : [-(hAPP(c_Set_Oimage(_1477327, _1477327, c_Fun_Oid(_1477327)), c_Orderings_Otop__class_Otop(tc_fun(_1477327, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1477327, tc_HOL_Obool)))], (36545 ^ _779308) ^ [_1477369, _1477371, _1477373, _1477375] : [-(c_Product__Type_Oapfst(_1477369, _1477371, _1477373, _1477375) = c_Product__Type_Omap__pair(_1477369, _1477371, _1477373, _1477373, _1477375, c_Fun_Oid(_1477373)))], (36547 ^ _779308) ^ [_1477412, _1477414, _1477416, _1477418] : [-(c_Product__Type_Oapsnd(_1477412, _1477414, _1477416, _1477418) = c_Product__Type_Omap__pair(_1477416, _1477416, _1477412, _1477414, c_Fun_Oid(_1477416), _1477418))], (36549 ^ _779308) ^ [_1477455, _1477457] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1477455, _1477457, tc_prod(_1477455, _1477457)), c_Product__Type_OPair(_1477455, _1477457)) = c_Fun_Oid(tc_prod(_1477455, _1477457)))], (36551 ^ _779308) ^ [_1477498, _1477500, _1477502, _1477504] : [class_Groups_Ocomm__monoid__add(_1477498), c_Fun_Oinj__on(_1477500, _1477498, _1477502, _1477504), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477500, _1477498), _1477502), _1477504) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1477498, _1477498), c_Fun_Oid(_1477498)), hAPP(c_Set_Oimage(_1477500, _1477498, _1477502), _1477504)))], (36561 ^ _779308) ^ [_1477691, _1477693, _1477695, _1477697] : [class_Groups_Ocomm__monoid__mult(_1477691), c_Fun_Oinj__on(_1477693, _1477691, _1477695, _1477697), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1477693, _1477691), _1477695), _1477697) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1477691, _1477691), c_Fun_Oid(_1477691)), hAPP(c_Set_Oimage(_1477693, _1477691, _1477695), _1477697)))], (36571 ^ _779308) ^ [_1477899, _1477901] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1477899), _1477901)), -(_1477901 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1477899, 36575 ^ [_1477899, _1477901]), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), 36574 ^ [_1477899, _1477901]))))], (36579 ^ _779308) ^ [_1478030, _1478032] : [36580 ^ _779308 : [(36581 ^ _779308) ^ [_1478094, _1478096] : [_1478032 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1478030, _1478094), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1478096)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1478030), _1478032)))], (36585 ^ _779308) ^ [_1478166, _1478168, _1478170, _1478172, _1478174] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1478166, _1478168, _1478170), _1478172), _1478174) = hAPP(c_Set_OCollect(tc_prod(_1478166, _1478170)), hAPP(c_Product__Type_Oprod_Oprod__case(_1478166, _1478170, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1478170, tc_fun(_1478168, tc_HOL_Obool)), tc_fun(_1478170, tc_HOL_Obool), _1478166), hAPP(c_COMBB(tc_fun(_1478168, tc_HOL_Obool), tc_HOL_Obool, _1478170), c_HOL_OEx(_1478168))), hAPP(hAPP(c_COMBC(_1478166, tc_fun(_1478170, tc_fun(_1478168, tc_HOL_Obool)), tc_fun(_1478170, tc_fun(_1478168, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1478168, tc_HOL_Obool), tc_fun(_1478168, tc_HOL_Obool)), tc_fun(tc_fun(_1478170, tc_fun(_1478168, tc_HOL_Obool)), tc_fun(_1478170, tc_fun(_1478168, tc_HOL_Obool))), _1478166), c_COMBB(tc_fun(_1478168, tc_HOL_Obool), tc_fun(_1478168, tc_HOL_Obool), _1478170)), hAPP(hAPP(c_COMBB(tc_fun(_1478168, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1478168, tc_HOL_Obool), tc_fun(_1478168, tc_HOL_Obool)), _1478166), c_COMBS(_1478168, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478168, tc_HOL_Obool), tc_fun(_1478168, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1478166), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1478168), c_fconj)), hAPP(hAPP(c_COMBC(_1478166, tc_fun(tc_prod(_1478166, _1478168), tc_HOL_Obool), tc_fun(_1478168, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478168, tc_fun(tc_fun(tc_prod(_1478166, _1478168), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1478166, _1478168), tc_HOL_Obool), tc_fun(_1478168, tc_HOL_Obool)), _1478166), c_COMBC(_1478168, tc_fun(tc_prod(_1478166, _1478168), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478168, tc_prod(_1478166, _1478168)), tc_fun(_1478168, tc_fun(tc_fun(tc_prod(_1478166, _1478168), tc_HOL_Obool), tc_HOL_Obool)), _1478166), hAPP(c_COMBB(tc_prod(_1478166, _1478168), tc_fun(tc_fun(tc_prod(_1478166, _1478168), tc_HOL_Obool), tc_HOL_Obool), _1478168), c_member(tc_prod(_1478166, _1478168)))), c_Product__Type_OPair(_1478166, _1478168)))), _1478172))))), hAPP(hAPP(c_COMBC(_1478170, tc_fun(tc_prod(_1478168, _1478170), tc_HOL_Obool), tc_fun(_1478168, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478168, tc_fun(tc_fun(tc_prod(_1478168, _1478170), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1478168, _1478170), tc_HOL_Obool), tc_fun(_1478168, tc_HOL_Obool)), _1478170), c_COMBC(_1478168, tc_fun(tc_prod(_1478168, _1478170), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478168, tc_prod(_1478168, _1478170)), tc_fun(_1478168, tc_fun(tc_fun(tc_prod(_1478168, _1478170), tc_HOL_Obool), tc_HOL_Obool)), _1478170), hAPP(c_COMBB(tc_prod(_1478168, _1478170), tc_fun(tc_fun(tc_prod(_1478168, _1478170), tc_HOL_Obool), tc_HOL_Obool), _1478168), c_member(tc_prod(_1478168, _1478170)))), hAPP(c_COMBC(_1478168, _1478170, tc_prod(_1478168, _1478170)), c_Product__Type_OPair(_1478168, _1478170))))), _1478174))))))], (36587 ^ _779308) ^ [_1478614, _1478616, _1478618] : [-(hAPP(c_Relation_ORange(_1478614, _1478616), hAPP(c_Set_OCollect(tc_prod(_1478614, _1478616)), hAPP(c_Product__Type_Oprod_Oprod__case(_1478614, _1478616, tc_HOL_Obool), _1478618))) = hAPP(c_Set_OCollect(_1478616), hAPP(hAPP(c_COMBB(tc_fun(_1478614, tc_HOL_Obool), tc_HOL_Obool, _1478616), c_HOL_OEx(_1478614)), hAPP(c_COMBC(_1478614, _1478616, tc_HOL_Obool), _1478618))))], (36589 ^ _779308) ^ [_1478689, _1478691, _1478693, _1478695, _1478697, _1478699, _1478701, _1478703] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1478689, _1478691)), hAPP(hAPP(c_Product__Type_OPair(_1478689, _1478691), _1478693), _1478695)), _1478697)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1478691, _1478699)), hAPP(hAPP(c_Product__Type_OPair(_1478691, _1478699), _1478695), _1478701)), _1478703)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1478689, _1478699)), hAPP(hAPP(c_Product__Type_OPair(_1478689, _1478699), _1478693), _1478701)), hAPP(hAPP(c_Relation_Orel__comp(_1478689, _1478691, _1478699), _1478697), _1478703))))], (36599 ^ _779308) ^ [_1478976, _1478978, _1478980, _1478982, _1478984] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1478976, _1478978)), hAPP(hAPP(c_Product__Type_OPair(_1478976, _1478978), _1478980), _1478982)), _1478984)), -(hBOOL(hAPP(hAPP(c_member(_1478978), _1478982), hAPP(c_Relation_ORange(_1478976, _1478978), _1478984))))], (36605 ^ _779308) ^ [_1479123, _1479125, _1479127, _1479129, _1479131, _1479133, _1479135] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1479123, _1479125, _1479127), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479129, tc_fun(tc_prod(_1479123, _1479125), tc_HOL_Obool)), _1479131), _1479133)), _1479135) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479129, tc_fun(tc_prod(_1479123, _1479127), tc_HOL_Obool)), _1479131), hAPP(hAPP(c_COMBC(_1479129, tc_fun(tc_prod(_1479125, _1479127), tc_HOL_Obool), tc_fun(tc_prod(_1479123, _1479127), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1479123, _1479125), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1479125, _1479127), tc_HOL_Obool), tc_fun(tc_prod(_1479123, _1479127), tc_HOL_Obool)), _1479129), c_Relation_Orel__comp(_1479123, _1479125, _1479127)), _1479133)), _1479135)))], (36607 ^ _779308) ^ [_1479255, _1479257, _1479259, _1479261, _1479263, _1479265, _1479267] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1479255, _1479257, _1479259), _1479261), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479263, tc_fun(tc_prod(_1479257, _1479259), tc_HOL_Obool)), _1479265), _1479267)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479263, tc_fun(tc_prod(_1479255, _1479259), tc_HOL_Obool)), _1479265), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1479257, _1479259), tc_HOL_Obool), tc_fun(tc_prod(_1479255, _1479259), tc_HOL_Obool), _1479263), hAPP(c_Relation_Orel__comp(_1479255, _1479257, _1479259), _1479261)), _1479267)))], (36609 ^ _779308) ^ [_1479359, _1479361, _1479363, _1479365, _1479367, _1479369, _1479371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1479359, _1479361), tc_HOL_Obool)), _1479363), _1479365)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1479361, _1479367), tc_HOL_Obool)), _1479369), _1479371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1479359, _1479367), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1479359, _1479361, _1479367), _1479363), _1479369)), hAPP(hAPP(c_Relation_Orel__comp(_1479359, _1479361, _1479367), _1479365), _1479371))))], (36619 ^ _779308) ^ [_1479626, _1479628, _1479630, _1479632] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1479626, _1479628, _1479630), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1479626, _1479628), tc_HOL_Obool))), _1479632) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1479626, _1479630), tc_HOL_Obool)))], (36621 ^ _779308) ^ [_1479681, _1479683, _1479685, _1479687] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1479681, _1479683, _1479685), _1479687), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1479683, _1479685), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1479681, _1479685), tc_HOL_Obool)))], (36623 ^ _779308) ^ [_1479736, _1479738, _1479740, _1479742, _1479744, _1479746] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1479736, _1479738, _1479740), _1479742), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1479738, _1479740), tc_HOL_Obool)), _1479744), _1479746)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1479736, _1479740), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1479736, _1479738, _1479740), _1479742), _1479744)), hAPP(hAPP(c_Relation_Orel__comp(_1479736, _1479738, _1479740), _1479742), _1479746)))], (36625 ^ _779308) ^ [_1479827, _1479829, _1479831, _1479833, _1479835, _1479837] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1479827, _1479829, _1479831), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1479827, _1479829), tc_HOL_Obool)), _1479833), _1479835)), _1479837) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1479827, _1479831), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1479827, _1479829, _1479831), _1479833), _1479837)), hAPP(hAPP(c_Relation_Orel__comp(_1479827, _1479829, _1479831), _1479835), _1479837)))], (36627 ^ _779308) ^ [_1479918, _1479920, _1479922, _1479924, _1479926, _1479928, _1479930] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1479918, _1479920, _1479922), hAPP(hAPP(c_Relation_Orel__comp(_1479918, _1479924, _1479920), _1479926), _1479928)), _1479930) = hAPP(hAPP(c_Relation_Orel__comp(_1479918, _1479924, _1479922), _1479926), hAPP(hAPP(c_Relation_Orel__comp(_1479924, _1479920, _1479922), _1479928), _1479930)))], (36629 ^ _779308) ^ [_1479993, _1479995] : [-(hAPP(c_Relation_ORange(_1479993, _1479993), c_Relation_OId__on(_1479993, _1479995)) = _1479995)], (36631 ^ _779308) ^ [_1480027, _1480029, _1480031, _1480033] : [hAPP(hAPP(c_Relation_Orel__comp(_1480027, _1480027, _1480027), _1480029), _1480031) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480027, _1480027), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1480027, _1480027, _1480027), _1480029), _1480033) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480027, _1480027), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1480027, _1480027, _1480027), _1480029), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1480027, _1480027), tc_HOL_Obool)), _1480031), _1480033)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480027, _1480027), tc_HOL_Obool)))], (36641 ^ _779308) ^ [_1480300, _1480302, _1480304, _1480306] : [hAPP(hAPP(c_Relation_Orel__comp(_1480300, _1480300, _1480300), _1480302), _1480304) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480300, _1480300), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1480300, _1480300, _1480300), _1480306), _1480304) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480300, _1480300), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1480300, _1480300, _1480300), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1480300, _1480300), tc_HOL_Obool)), _1480302), _1480306)), _1480304) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480300, _1480300), tc_HOL_Obool)))], (36651 ^ _779308) ^ [_1480573, _1480575] : [-(hAPP(c_Relation_ORange(_1480573, _1480575), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480573, _1480575), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1480575, tc_HOL_Obool)))], (36653 ^ _779308) ^ [_1480635, _1480637, _1480639] : [hAPP(c_Relation_ORange(_1480635, _1480637), _1480639) = c_Orderings_Obot__class_Obot(tc_fun(_1480637, tc_HOL_Obool)), -(_1480639 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480635, _1480637), tc_HOL_Obool)))], (36659 ^ _779308) ^ [_1480748, _1480750, _1480752] : [_1480752 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1480748, _1480750), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1480748, _1480750), _1480752) = c_Orderings_Obot__class_Obot(tc_fun(_1480750, tc_HOL_Obool)))], (36665 ^ _779308) ^ [_1480867, _1480869, _1480871, _1480873, _1480875, _1480877, _1480879, _1480881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1480867, _1480869), tc_HOL_Obool)), _1480871), hAPP(hAPP(c_Product__Type_OSigma(_1480867, _1480869), _1480873), hAPP(c_COMBK(tc_fun(_1480869, tc_HOL_Obool), _1480867), _1480875)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1480869, _1480877), tc_HOL_Obool)), _1480879), hAPP(hAPP(c_Product__Type_OSigma(_1480869, _1480877), _1480875), hAPP(c_COMBK(tc_fun(_1480877, tc_HOL_Obool), _1480869), _1480881)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1480867, _1480877), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1480867, _1480869, _1480877), _1480871), _1480879)), hAPP(hAPP(c_Product__Type_OSigma(_1480867, _1480877), _1480873), hAPP(c_COMBK(tc_fun(_1480877, tc_HOL_Obool), _1480867), _1480881)))))], (36675 ^ _779308) ^ [_1481226, _1481228, _1481230, _1481232] : [-(hAPP(c_Relation_ORange(_1481226, _1481228), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1481226, _1481228), tc_HOL_Obool)), _1481230), _1481232)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481228, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1481226, _1481228), _1481230)), hAPP(c_Relation_ORange(_1481226, _1481228), _1481232)))], (36677 ^ _779308) ^ [_1481298, _1481300, _1481302] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1481298, _1481300)), _1481302)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1481300), hAPP(c_Relation_ORange(_1481298, _1481300), _1481302))))], (36683 ^ _779308) ^ [_1481411, _1481413, _1481415] : [-(hAPP(c_Set_Oimage(tc_prod(_1481411, _1481413), _1481413, c_Product__Type_Osnd(_1481411, _1481413)), _1481415) = hAPP(c_Relation_ORange(_1481411, _1481413), _1481415))], (36685 ^ _779308) ^ [_1481478, _1481480, _1481482, _1481484] : [hBOOL(hAPP(hAPP(c_member(_1481478), _1481480), hAPP(c_Relation_ORange(_1481482, _1481478), _1481484))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1481482, _1481478)), hAPP(hAPP(c_Product__Type_OPair(_1481482, _1481478), 36688 ^ [_1481478, _1481480, _1481482, _1481484]), _1481480)), _1481484)))], (36692 ^ _779308) ^ [_1481635, _1481637, _1481639, _1481641] : [36693 ^ _779308 : [(36694 ^ _779308) ^ [_1481710] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1481639, _1481635)), hAPP(hAPP(c_Product__Type_OPair(_1481639, _1481635), _1481710), _1481637)), _1481641))]], -(hBOOL(hAPP(hAPP(c_member(_1481635), _1481637), hAPP(c_Relation_ORange(_1481639, _1481635), _1481641))))], (36698 ^ _779308) ^ [_1481795, _1481797, _1481799, _1481801, _1481803] : [-(hAPP(c_Relation_ORange(_1481795, _1481797), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1481795, _1481797)), hAPP(hAPP(c_Product__Type_OPair(_1481795, _1481797), _1481799), _1481801)), _1481803)) = hAPP(hAPP(c_Set_Oinsert(_1481797), _1481801), hAPP(c_Relation_ORange(_1481795, _1481797), _1481803)))], (36700 ^ _779308) ^ [_1481866, _1481868, _1481870, _1481872] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1481866, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1481868, _1481866), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1481868, _1481866), tc_HOL_Obool)), _1481870), _1481872))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481866, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1481868, _1481866), _1481870)), hAPP(c_Relation_ORange(_1481868, _1481866), _1481872)))))], (36702 ^ _779308) ^ [_1481948, _1481950, _1481952, _1481954] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1481948, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1481948, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1481950, _1481948), _1481952)), hAPP(c_Relation_ORange(_1481950, _1481948), _1481954))), hAPP(c_Relation_ORange(_1481950, _1481948), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1481950, _1481948), tc_HOL_Obool)), _1481952), _1481954)))))], (36704 ^ _779308) ^ [_1482030, _1482032, _1482034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1482030, _1482030), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1482030, _1482030, _1482030), _1482032), _1482034)), _1482032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1482030, tc_HOL_Obool), tc_fun(_1482030, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1482030, tc_HOL_Obool), tc_fun(_1482030, tc_HOL_Obool), tc_fun(_1482030, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1482030, _1482032)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1482030, tc_HOL_Obool), tc_fun(_1482030, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1482030, _1482034)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1482030, tc_HOL_Obool), tc_fun(_1482030, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1482030, tc_HOL_Obool), tc_fun(_1482030, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1482030, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1482030, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1482030, tc_HOL_Obool), tc_fun(_1482030, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1482030, _1482032))))], (36710 ^ _779308) ^ [_1482401, _1482403, _1482405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1482401, _1482401), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1482401, _1482401, _1482401), _1482403), _1482405)), _1482403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1482401, tc_HOL_Obool), tc_fun(_1482401, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1482401, tc_HOL_Obool), tc_fun(_1482401, tc_HOL_Obool), tc_fun(_1482401, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1482401, _1482403)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1482401, tc_HOL_Obool), tc_fun(_1482401, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1482401, _1482405)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1482401, tc_HOL_Obool), tc_fun(_1482401, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1482401, tc_HOL_Obool), tc_fun(_1482401, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1482401, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1482401, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1482401, tc_HOL_Obool), tc_fun(_1482401, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1482401, _1482403))))], (36716 ^ _779308) ^ [_1482793, _1482795, _1482797, _1482799] : [hBOOL(hAPP(c_Predicate_ORangeP(_1482793, _1482795, hAPP(hAPP(c_COMBC(_1482793, tc_fun(tc_prod(_1482793, _1482795), tc_HOL_Obool), tc_fun(_1482795, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1482795, tc_fun(tc_fun(tc_prod(_1482793, _1482795), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1482793, _1482795), tc_HOL_Obool), tc_fun(_1482795, tc_HOL_Obool)), _1482793), c_COMBC(_1482795, tc_fun(tc_prod(_1482793, _1482795), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1482795, tc_prod(_1482793, _1482795)), tc_fun(_1482795, tc_fun(tc_fun(tc_prod(_1482793, _1482795), tc_HOL_Obool), tc_HOL_Obool)), _1482793), hAPP(c_COMBB(tc_prod(_1482793, _1482795), tc_fun(tc_fun(tc_prod(_1482793, _1482795), tc_HOL_Obool), tc_HOL_Obool), _1482795), c_member(tc_prod(_1482793, _1482795)))), c_Product__Type_OPair(_1482793, _1482795)))), _1482797)), _1482799)), -(hBOOL(hAPP(hAPP(c_member(_1482795), _1482799), hAPP(c_Relation_ORange(_1482793, _1482795), _1482797))))], (36722 ^ _779308) ^ [_1483144, _1483146, _1483148, _1483150] : [hBOOL(hAPP(hAPP(c_member(_1483146), _1483150), hAPP(c_Relation_ORange(_1483144, _1483146), _1483148))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1483144, _1483146, hAPP(hAPP(c_COMBC(_1483144, tc_fun(tc_prod(_1483144, _1483146), tc_HOL_Obool), tc_fun(_1483146, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483146, tc_fun(tc_fun(tc_prod(_1483144, _1483146), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1483144, _1483146), tc_HOL_Obool), tc_fun(_1483146, tc_HOL_Obool)), _1483144), c_COMBC(_1483146, tc_fun(tc_prod(_1483144, _1483146), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483146, tc_prod(_1483144, _1483146)), tc_fun(_1483146, tc_fun(tc_fun(tc_prod(_1483144, _1483146), tc_HOL_Obool), tc_HOL_Obool)), _1483144), hAPP(c_COMBB(tc_prod(_1483144, _1483146), tc_fun(tc_fun(tc_prod(_1483144, _1483146), tc_HOL_Obool), tc_HOL_Obool), _1483146), c_member(tc_prod(_1483144, _1483146)))), c_Product__Type_OPair(_1483144, _1483146)))), _1483148)), _1483150)))], (36728 ^ _779308) ^ [_1483501, _1483503, _1483505, _1483507] : [hBOOL(hAPP(hAPP(c_member(_1483501), _1483503), hAPP(c_Relation_ORange(_1483505, _1483501), _1483507))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1483505, _1483501)), hAPP(hAPP(c_Product__Type_OPair(_1483505, _1483501), 36731 ^ [_1483501, _1483503, _1483505, _1483507]), _1483503)), _1483507)))], (36735 ^ _779308) ^ [_1483696, _1483698, _1483700, _1483702, _1483704, _1483706, _1483708] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1483696, _1483698, _1483700, hAPP(hAPP(c_COMBC(_1483696, tc_fun(tc_prod(_1483696, _1483698), tc_HOL_Obool), tc_fun(_1483698, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483698, tc_fun(tc_fun(tc_prod(_1483696, _1483698), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1483696, _1483698), tc_HOL_Obool), tc_fun(_1483698, tc_HOL_Obool)), _1483696), c_COMBC(_1483698, tc_fun(tc_prod(_1483696, _1483698), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483698, tc_prod(_1483696, _1483698)), tc_fun(_1483698, tc_fun(tc_fun(tc_prod(_1483696, _1483698), tc_HOL_Obool), tc_HOL_Obool)), _1483696), hAPP(c_COMBB(tc_prod(_1483696, _1483698), tc_fun(tc_fun(tc_prod(_1483696, _1483698), tc_HOL_Obool), tc_HOL_Obool), _1483698), c_member(tc_prod(_1483696, _1483698)))), c_Product__Type_OPair(_1483696, _1483698)))), _1483702), hAPP(hAPP(c_COMBC(_1483698, tc_fun(tc_prod(_1483698, _1483700), tc_HOL_Obool), tc_fun(_1483700, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483700, tc_fun(tc_fun(tc_prod(_1483698, _1483700), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1483698, _1483700), tc_HOL_Obool), tc_fun(_1483700, tc_HOL_Obool)), _1483698), c_COMBC(_1483700, tc_fun(tc_prod(_1483698, _1483700), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483700, tc_prod(_1483698, _1483700)), tc_fun(_1483700, tc_fun(tc_fun(tc_prod(_1483698, _1483700), tc_HOL_Obool), tc_HOL_Obool)), _1483698), hAPP(c_COMBB(tc_prod(_1483698, _1483700), tc_fun(tc_fun(tc_prod(_1483698, _1483700), tc_HOL_Obool), tc_HOL_Obool), _1483700), c_member(tc_prod(_1483698, _1483700)))), c_Product__Type_OPair(_1483698, _1483700)))), _1483704)), _1483706), _1483708)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1483696, _1483700)), hAPP(hAPP(c_Product__Type_OPair(_1483696, _1483700), _1483706), _1483708)), hAPP(hAPP(c_Relation_Orel__comp(_1483696, _1483698, _1483700), _1483702), _1483704))))], (36741 ^ _779308) ^ [_1484331, _1484333, _1484335, _1484337, _1484339, _1484341, _1484343] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1484331, _1484335)), hAPP(hAPP(c_Product__Type_OPair(_1484331, _1484335), _1484341), _1484343)), hAPP(hAPP(c_Relation_Orel__comp(_1484331, _1484333, _1484335), _1484337), _1484339))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1484331, _1484333, _1484335, hAPP(hAPP(c_COMBC(_1484331, tc_fun(tc_prod(_1484331, _1484333), tc_HOL_Obool), tc_fun(_1484333, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484333, tc_fun(tc_fun(tc_prod(_1484331, _1484333), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484331, _1484333), tc_HOL_Obool), tc_fun(_1484333, tc_HOL_Obool)), _1484331), c_COMBC(_1484333, tc_fun(tc_prod(_1484331, _1484333), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484333, tc_prod(_1484331, _1484333)), tc_fun(_1484333, tc_fun(tc_fun(tc_prod(_1484331, _1484333), tc_HOL_Obool), tc_HOL_Obool)), _1484331), hAPP(c_COMBB(tc_prod(_1484331, _1484333), tc_fun(tc_fun(tc_prod(_1484331, _1484333), tc_HOL_Obool), tc_HOL_Obool), _1484333), c_member(tc_prod(_1484331, _1484333)))), c_Product__Type_OPair(_1484331, _1484333)))), _1484337), hAPP(hAPP(c_COMBC(_1484333, tc_fun(tc_prod(_1484333, _1484335), tc_HOL_Obool), tc_fun(_1484335, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484335, tc_fun(tc_fun(tc_prod(_1484333, _1484335), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484333, _1484335), tc_HOL_Obool), tc_fun(_1484335, tc_HOL_Obool)), _1484333), c_COMBC(_1484335, tc_fun(tc_prod(_1484333, _1484335), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484335, tc_prod(_1484333, _1484335)), tc_fun(_1484335, tc_fun(tc_fun(tc_prod(_1484333, _1484335), tc_HOL_Obool), tc_HOL_Obool)), _1484333), hAPP(c_COMBB(tc_prod(_1484333, _1484335), tc_fun(tc_fun(tc_prod(_1484333, _1484335), tc_HOL_Obool), tc_HOL_Obool), _1484335), c_member(tc_prod(_1484333, _1484335)))), c_Product__Type_OPair(_1484333, _1484335)))), _1484339)), _1484341), _1484343)))], (36747 ^ _779308) ^ [_1484972, _1484974, _1484976, _1484978, _1484980, _1484982, _1484984, _1484986] : [hBOOL(hAPP(hAPP(_1484972, _1484974), _1484976)), hBOOL(hAPP(hAPP(_1484978, _1484976), _1484980)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1484982, _1484984, _1484986, _1484972, _1484978), _1484974), _1484980)))], (36757 ^ _779308) ^ [_1485167, _1485169, _1485171, _1485173, _1485175] : [hBOOL(hAPP(hAPP(_1485167, _1485169), _1485171)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1485173, _1485175, _1485167), _1485171)))], (36763 ^ _779308) ^ [_1485302, _1485304, _1485306, _1485308, _1485310, _1485312, _1485314] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1485302, _1485304, _1485306, _1485308, _1485310), _1485312), _1485314)), 36767 ^ _779308 : [(36768 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1485308, _1485312), 36766 ^ [_1485302, _1485304, _1485306, _1485308, _1485310, _1485312, _1485314])))], (36770 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1485310, 36766 ^ [_1485302, _1485304, _1485306, _1485308, _1485310, _1485312, _1485314]), _1485314)))]]], (36772 ^ _779308) ^ [_1485492, _1485494, _1485496, _1485498, _1485500, _1485502, _1485504] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1485492, _1485494, _1485496, _1485498, _1485500), _1485502), _1485504))), 36773 ^ _779308 : [(36774 ^ _779308) ^ [_1485563] : [hBOOL(hAPP(hAPP(_1485498, _1485502), _1485563)), hBOOL(hAPP(hAPP(_1485500, _1485563), _1485504))]]], (36782 ^ _779308) ^ [_1485733, _1485735, _1485737, _1485739] : [hBOOL(hAPP(c_Predicate_ORangeP(_1485733, _1485735, _1485737), _1485739)), -(hBOOL(hAPP(hAPP(_1485737, 36785 ^ [_1485733, _1485735, _1485737, _1485739]), _1485739)))], (36789 ^ _779308) ^ [_1485848, _1485850, _1485852, _1485854] : [36790 ^ _779308 : [(36791 ^ _779308) ^ [_1485902] : [hBOOL(hAPP(hAPP(_1485852, _1485902), _1485854))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1485848, _1485850, _1485852), _1485854)))], (36795 ^ _779308) ^ [_1485966, _1485968, _1485970] : [c_Wellfounded_Owf(_1485966, _1485968), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1485966, _1485966), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1485966, _1485966, _1485966), _1485968), _1485970)), _1485968)), -(c_FunDef_Oreduction__pair(_1485966, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1485966, _1485966), tc_HOL_Obool), tc_fun(tc_prod(_1485966, _1485966), tc_HOL_Obool)), _1485968), _1485970)))], (36805 ^ _779308) ^ [_1486187, _1486189, _1486191] : [-(hAPP(c_Relation_ODomain(_1486187, _1486189), hAPP(c_Set_OCollect(tc_prod(_1486187, _1486189)), hAPP(c_Product__Type_Oprod_Oprod__case(_1486187, _1486189, tc_HOL_Obool), _1486191))) = hAPP(c_Set_OCollect(_1486187), hAPP(hAPP(c_COMBB(tc_fun(_1486189, tc_HOL_Obool), tc_HOL_Obool, _1486187), c_HOL_OEx(_1486189)), _1486191)))], (36807 ^ _779308) ^ [_1486254, _1486256, _1486258, _1486260] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1486254), _1486256))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1486258), hAPP(c_Set_Oimage(_1486254, _1486258, _1486260), _1486256))), 36815 ^ _779308 : [(36816 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486254), 36814 ^ [_1486254, _1486256, _1486258, _1486260]), _1486256)))], (36818 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1486254), hAPP(c_Set_OCollect(_1486254), hAPP(hAPP(c_COMBS(_1486254, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1486254), c_fconj), hAPP(hAPP(c_COMBC(_1486254, tc_fun(_1486254, tc_HOL_Obool), tc_HOL_Obool), c_member(_1486254)), _1486256))), hAPP(hAPP(c_COMBC(_1486254, _1486258, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1486258, tc_fun(_1486258, tc_HOL_Obool), _1486254), c_fequal), _1486260)), hAPP(_1486260, 36814 ^ [_1486254, _1486256, _1486258, _1486260]))))))]]], (36820 ^ _779308) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (36822 ^ _779308) ^ [_1486737] : [-(c_Wellfounded_Owf(_1486737, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1486737, _1486737), tc_HOL_Obool))))], (36824 ^ _779308) ^ [_1486768, _1486770, _1486772, _1486774] : [c_Wellfounded_Owf(_1486768, _1486770), -(c_Wellfounded_Owf(_1486772, hAPP(hAPP(c_Relation_Oinv__image(_1486768, _1486772), _1486770), _1486774)))], (36830 ^ _779308) ^ [_1486867, _1486869, _1486871, _1486873] : [c_Wellfounded_Owf(_1486867, _1486869), c_Wellfounded_Owf(_1486871, _1486873), -(c_Wellfounded_Owf(tc_prod(_1486867, _1486871), c_Wellfounded_Olex__prod(_1486867, _1486871, _1486869, _1486873)))], (36840 ^ _779308) ^ [_1487020, _1487022] : [-(c_Wellfounded_Owf(_1487020, hAPP(c_Wellfounded_Omeasure(_1487020), _1487022)))], (36842 ^ _779308) ^ [_1487050, _1487052, _1487054, _1487056, _1487058] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1487050, _1487052)), hAPP(hAPP(c_Product__Type_OPair(_1487050, _1487052), _1487054), _1487056)), _1487058)), -(hBOOL(hAPP(hAPP(c_member(_1487050), _1487054), hAPP(c_Relation_ODomain(_1487050, _1487052), _1487058))))], (36848 ^ _779308) ^ [_1487212, _1487214] : [c_Wellfounded_Owf(_1487212, _1487214), -(c_Wellfounded_Owf(_1487212, hAPP(hAPP(c_Relation_Orel__comp(_1487212, _1487212, _1487212), _1487214), _1487214)))], (36854 ^ _779308) ^ [_1487305, _1487307] : [c_Wellfounded_Owf(_1487305, hAPP(hAPP(c_Relation_Orel__comp(_1487305, _1487305, _1487305), _1487307), _1487307)), -(c_Wellfounded_Owf(_1487305, _1487307))], (36860 ^ _779308) ^ [_1487404, _1487406] : [c_Wellfounded_Owf(_1487404, _1487406), -(c_Wellfounded_Owf(tc_fun(_1487404, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1487404, _1487406)))], (36866 ^ _779308) ^ [_1487493, _1487495, _1487497] : [c_Wellfounded_Owf(_1487493, _1487495), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1487493, _1487493), tc_HOL_Obool)), _1487497), _1487495)), -(c_Wellfounded_Owf(_1487493, _1487497))], (36876 ^ _779308) ^ [_1487652] : [-(c_Wellfounded_Owf(tc_fun(_1487652, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1487652)))], (36878 ^ _779308) ^ [_1487680, _1487682, _1487684] : [c_Wellfounded_Owf(_1487680, _1487682), -(c_Wellfounded_Owf(_1487680, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1487680, _1487680), tc_HOL_Obool)), _1487682), _1487684)))], (36884 ^ _779308) ^ [_1487787, _1487789, _1487791] : [c_Wellfounded_Owf(_1487787, _1487789), -(c_Wellfounded_Owf(_1487787, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1487787, _1487787), tc_HOL_Obool)), _1487791), _1487789)))], (36890 ^ _779308) ^ [_1487894, _1487896] : [c_Wellfounded_Owf(_1487894, _1487896), -(c_Wellfounded_Owf(tc_fun(_1487894, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1487894, _1487896)))], (36896 ^ _779308) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (36898 ^ _779308) ^ [_1488001, _1488003] : [-(hAPP(c_Relation_ODomain(_1488001, _1488001), c_Relation_OId__on(_1488001, _1488003)) = _1488003)], (36900 ^ _779308) ^ [_1488035, _1488037, _1488039] : [c_Wellfounded_Owf(_1488035, _1488037), -(c_Wellfounded_Owf(_1488035, c_Wellfounded_Omlex__prod(_1488035, _1488039, _1488037)))], (36906 ^ _779308) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)))))], (36908 ^ _779308) ^ [_1488140, _1488142, _1488144] : [c_Wellfounded_Owf(_1488140, _1488142), hBOOL(hAPP(hAPP(c_member(tc_prod(_1488140, _1488140)), hAPP(hAPP(c_Product__Type_OPair(_1488140, _1488140), _1488144), _1488144)), _1488142))], (36914 ^ _779308) ^ [_1488258, _1488260, _1488262, _1488264] : [c_Wellfounded_Owf(_1488258, _1488260), hBOOL(hAPP(hAPP(c_member(tc_prod(_1488258, _1488258)), hAPP(hAPP(c_Product__Type_OPair(_1488258, _1488258), _1488262), _1488264)), _1488260)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1488258, _1488258)), hAPP(hAPP(c_Product__Type_OPair(_1488258, _1488258), _1488264), _1488262)), _1488260))], (36924 ^ _779308) ^ [_1488472, _1488474, _1488476, _1488478] : [c_Wellfounded_Owf(_1488472, _1488474), hBOOL(hAPP(hAPP(c_member(tc_prod(_1488472, _1488472)), hAPP(hAPP(c_Product__Type_OPair(_1488472, _1488472), _1488476), _1488478)), _1488474)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1488472, _1488472)), hAPP(hAPP(c_Product__Type_OPair(_1488472, _1488472), _1488478), _1488476)), _1488474))], (36934 ^ _779308) ^ [_1488686, _1488688, _1488690] : [c_Wellfounded_Owf(_1488686, _1488688), hBOOL(hAPP(hAPP(c_member(tc_prod(_1488686, _1488686)), hAPP(hAPP(c_Product__Type_OPair(_1488686, _1488686), _1488690), _1488690)), _1488688))], (36940 ^ _779308) ^ [_1488804] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1488804)))], (36942 ^ _779308) ^ [_1488829] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1488829)))], (36944 ^ _779308) ^ [_1488854, _1488856, _1488858] : [c_Wellfounded_Owf(_1488854, _1488856), c_Wellfounded_Owf(_1488854, _1488858), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488854, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1488854, _1488854), _1488856)), hAPP(c_Relation_ORange(_1488854, _1488854), _1488858)) = c_Orderings_Obot__class_Obot(tc_fun(_1488854, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1488854, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1488854, _1488854), tc_HOL_Obool)), _1488856), _1488858)))], (36958 ^ _779308) ^ [_1489140, _1489142] : [c_Wellfounded_Owf(_1489140, _1489142), 36961 ^ _779308 : [(36962 ^ _779308) ^ [_1489209] : [-(hBOOL(hAPP(hAPP(c_member(_1489140), _1489209), c_Wellfounded_Oacc(_1489140, _1489142))))]]], (36964 ^ _779308) ^ [_1489242, _1489244] : [hBOOL(hAPP(hAPP(c_member(_1489242), 36965 ^ [_1489242, _1489244]), c_Wellfounded_Oacc(_1489242, _1489244))), -(c_Wellfounded_Owf(_1489242, _1489244))], (36971 ^ _779308) ^ [_1489375, _1489377, _1489379] : [c_Wellfounded_Owf(_1489375, _1489377), -(hBOOL(hAPP(hAPP(c_member(_1489375), _1489379), c_Wellfounded_Oacc(_1489375, _1489377))))], (36977 ^ _779308) ^ [_1489474, _1489476] : [hAPP(hAPP(c_Relation_Orel__comp(_1489474, _1489474, _1489474), _1489476), _1489476) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489474, _1489474), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1489474, _1489476))], (36983 ^ _779308) ^ [_1489605, _1489607, _1489609] : [c_Wellfounded_Owf(_1489605, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1489605, _1489605), tc_HOL_Obool)), _1489607), _1489609)), -(c_Wellfounded_Owf(_1489605, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1489605, _1489605), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1489605, _1489605), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1489605, _1489605, _1489605), _1489607), _1489607)), hAPP(hAPP(c_Relation_Orel__comp(_1489605, _1489605, _1489605), _1489609), _1489607))), _1489609)))], (36989 ^ _779308) ^ [_1489804, _1489806, _1489808] : [c_Wellfounded_Owf(_1489804, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1489804, _1489804), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1489804, _1489804), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1489804, _1489804, _1489804), _1489806), _1489806)), hAPP(hAPP(c_Relation_Orel__comp(_1489804, _1489804, _1489804), _1489808), _1489806))), _1489808)), -(c_Wellfounded_Owf(_1489804, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1489804, _1489804), tc_HOL_Obool)), _1489806), _1489808)))], (36995 ^ _779308) ^ [_1490009, _1490011] : [-(hAPP(c_Relation_ODomain(_1490009, _1490011), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490009, _1490011), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1490009, tc_HOL_Obool)))], (36997 ^ _779308) ^ [_1490071, _1490073, _1490075] : [hAPP(c_Relation_ODomain(_1490071, _1490073), _1490075) = c_Orderings_Obot__class_Obot(tc_fun(_1490071, tc_HOL_Obool)), -(_1490075 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490071, _1490073), tc_HOL_Obool)))], (37003 ^ _779308) ^ [_1490184, _1490186, _1490188] : [_1490188 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490184, _1490186), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1490184, _1490186), _1490188) = c_Orderings_Obot__class_Obot(tc_fun(_1490184, tc_HOL_Obool)))], (37009 ^ _779308) ^ [_1490303, _1490305, _1490307, _1490309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1490303, _1490305), tc_HOL_Obool)), _1490307), _1490309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1490303, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1490303, _1490305), _1490307)), hAPP(c_Relation_ODomain(_1490303, _1490305), _1490309))))], (37015 ^ _779308) ^ [_1490454, _1490456, _1490458, _1490460] : [-(hAPP(c_Relation_ODomain(_1490454, _1490456), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1490454, _1490456), tc_HOL_Obool)), _1490458), _1490460)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1490454, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1490454, _1490456), _1490458)), hAPP(c_Relation_ODomain(_1490454, _1490456), _1490460)))], (37017 ^ _779308) ^ [_1490526, _1490528, _1490530] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1490526, _1490528)), _1490530)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1490526), hAPP(c_Relation_ODomain(_1490526, _1490528), _1490530))))], (37023 ^ _779308) ^ [_1490639, _1490641, _1490643] : [-(hAPP(c_Set_Oimage(tc_prod(_1490639, _1490641), _1490639, c_Product__Type_Ofst(_1490639, _1490641)), _1490643) = hAPP(c_Relation_ODomain(_1490639, _1490641), _1490643))], (37025 ^ _779308) ^ [_1490700, _1490702] : [c_Wellfounded_Owf(_1490700, _1490702), 37029 ^ _779308 : [(37030 ^ _779308) ^ [_1490836] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1490700, _1490700)), hAPP(hAPP(c_Product__Type_OPair(_1490700, _1490700), hAPP(_1490836, hAPP(c_Nat_OSuc, 37028 ^ [_1490700, _1490702, _1490836]))), hAPP(_1490836, 37028 ^ [_1490700, _1490702, _1490836]))), _1490702))]]], (37032 ^ _779308) ^ [_1490903, _1490905] : [37034 ^ _779308 : [(37035 ^ _779308) ^ [_1490928] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1490903, _1490903)), hAPP(hAPP(c_Product__Type_OPair(_1490903, _1490903), hAPP(37033 ^ [_1490903, _1490905], hAPP(c_Nat_OSuc, _1490928))), hAPP(37033 ^ [_1490903, _1490905], _1490928))), _1490905)))]], -(c_Wellfounded_Owf(_1490903, _1490905))], (37039 ^ _779308) ^ [_1491004, _1491006, _1491008] : [c_Wellfounded_Owf(_1491004, _1491006), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1491004, tc_HOL_Obool)), _1491008), hAPP(c_Relation_OImage(_1491004, _1491004, _1491006), _1491008))), -(_1491008 = c_Orderings_Obot__class_Obot(tc_fun(_1491004, tc_HOL_Obool)))], (37049 ^ _779308) ^ [_1491181, _1491183, _1491185] : [c_Wellfounded_Owf(_1491181, _1491183), c_Wellfounded_Owf(_1491181, _1491185), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1491181, _1491181), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1491181, _1491181, _1491181), _1491183), _1491185)), _1491183)), -(c_Wellfounded_Owf(_1491181, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1491181, _1491181), tc_HOL_Obool)), _1491183), _1491185)))], (37063 ^ _779308) ^ [_1491463, _1491465, _1491467, _1491469] : [hBOOL(hAPP(hAPP(c_member(_1491463), _1491465), hAPP(c_Relation_ODomain(_1491463, _1491467), _1491469))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1491463, _1491467)), hAPP(hAPP(c_Product__Type_OPair(_1491463, _1491467), _1491465), 37066 ^ [_1491463, _1491465, _1491467, _1491469])), _1491469)))], (37070 ^ _779308) ^ [_1491620, _1491622, _1491624, _1491626] : [37071 ^ _779308 : [(37072 ^ _779308) ^ [_1491695] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1491620, _1491624)), hAPP(hAPP(c_Product__Type_OPair(_1491620, _1491624), _1491622), _1491695)), _1491626))]], -(hBOOL(hAPP(hAPP(c_member(_1491620), _1491622), hAPP(c_Relation_ODomain(_1491620, _1491624), _1491626))))], (37076 ^ _779308) ^ [_1491780] : [class_Orderings_Owellorder(_1491780), -(c_Wellfounded_Owf(_1491780, hAPP(c_Set_OCollect(tc_prod(_1491780, _1491780)), hAPP(c_Product__Type_Oprod_Oprod__case(_1491780, _1491780, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1491780)))))], (37082 ^ _779308) ^ [_1491887, _1491889, _1491891, _1491893, _1491895] : [-(hAPP(c_Relation_ODomain(_1491887, _1491889), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1491887, _1491889)), hAPP(hAPP(c_Product__Type_OPair(_1491887, _1491889), _1491891), _1491893)), _1491895)) = hAPP(hAPP(c_Set_Oinsert(_1491887), _1491891), hAPP(c_Relation_ODomain(_1491887, _1491889), _1491895)))], (37084 ^ _779308) ^ [_1491973, _1491975] : [c_FunDef_Oreduction__pair(_1491973, _1491975), 37087 ^ _779308 : [(37088 ^ _779308) ^ [] : [-(c_Wellfounded_Owf(_1491973, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1491973, _1491973), tc_HOL_Obool), tc_fun(tc_prod(_1491973, _1491973), tc_HOL_Obool)), _1491975)))], (37090 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1491973, _1491973), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1491973, _1491973, _1491973), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1491973, _1491973), tc_HOL_Obool), tc_fun(tc_prod(_1491973, _1491973), tc_HOL_Obool)), _1491975)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1491973, _1491973), tc_HOL_Obool), tc_fun(tc_prod(_1491973, _1491973), tc_HOL_Obool)), _1491975))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1491973, _1491973), tc_HOL_Obool), tc_fun(tc_prod(_1491973, _1491973), tc_HOL_Obool)), _1491975))))]]], (37092 ^ _779308) ^ [_1492262, _1492264] : [-(c_FunDef_Oreduction__pair(_1492262, _1492264)), c_Wellfounded_Owf(_1492262, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1492262, _1492262), tc_HOL_Obool), tc_fun(tc_prod(_1492262, _1492262), tc_HOL_Obool)), _1492264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1492262, _1492262), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1492262, _1492262, _1492262), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1492262, _1492262), tc_HOL_Obool), tc_fun(tc_prod(_1492262, _1492262), tc_HOL_Obool)), _1492264)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1492262, _1492262), tc_HOL_Obool), tc_fun(tc_prod(_1492262, _1492262), tc_HOL_Obool)), _1492264))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1492262, _1492262), tc_HOL_Obool), tc_fun(tc_prod(_1492262, _1492262), tc_HOL_Obool)), _1492264)))], (37102 ^ _779308) ^ [_1492583, _1492585, _1492587, _1492589] : [c_FunDef_Oreduction__pair(_1492583, _1492585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1492583, _1492583), tc_HOL_Obool)), _1492587), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1492583, _1492583), tc_HOL_Obool), tc_fun(tc_prod(_1492583, _1492583), tc_HOL_Obool)), _1492585))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1492583, _1492583), tc_HOL_Obool)), _1492589), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1492583, _1492583), tc_HOL_Obool), tc_fun(tc_prod(_1492583, _1492583), tc_HOL_Obool)), _1492585))), c_Wellfounded_Owf(_1492583, _1492589), -(c_Wellfounded_Owf(_1492583, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1492583, _1492583), tc_HOL_Obool)), _1492587), _1492589)))], (37120 ^ _779308) ^ [_1492984, _1492986, _1492988, _1492990] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492984, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1492984, _1492986), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1492984, _1492986), tc_HOL_Obool)), _1492988), _1492990))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1492984, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1492984, _1492986), _1492988)), hAPP(c_Relation_ODomain(_1492984, _1492986), _1492990)))))], (37122 ^ _779308) ^ [_1493066, _1493068, _1493070, _1493072] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1493066, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1493066, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1493066, _1493068), _1493070)), hAPP(c_Relation_ODomain(_1493066, _1493068), _1493072))), hAPP(c_Relation_ODomain(_1493066, _1493068), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1493066, _1493068), tc_HOL_Obool)), _1493070), _1493072)))))], (37124 ^ _779308) ^ [_1493148, _1493150] : [-(hAPP(c_Relation_OField(_1493148), _1493150) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1493148, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1493148, _1493148), _1493150)), hAPP(c_Relation_ORange(_1493148, _1493148), _1493150)))], (37126 ^ _779308) ^ [_1493201, _1493203, _1493205, _1493207] : [c_Wellfounded_Owf(_1493201, _1493203), c_Fun_Oinj__on(_1493201, _1493205, _1493207, c_Orderings_Otop__class_Otop(tc_fun(_1493201, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1493205, hAPP(c_Set_Oimage(tc_prod(_1493201, _1493201), tc_prod(_1493205, _1493205), c_Product__Type_Omap__pair(_1493201, _1493205, _1493201, _1493205, _1493207, _1493207)), _1493203)))], (37136 ^ _779308) ^ [_1493413, _1493415, _1493417, _1493419] : [hBOOL(hAPP(c_Predicate_ODomainP(_1493413, _1493415, hAPP(hAPP(c_COMBC(_1493413, tc_fun(tc_prod(_1493413, _1493415), tc_HOL_Obool), tc_fun(_1493415, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493415, tc_fun(tc_fun(tc_prod(_1493413, _1493415), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1493413, _1493415), tc_HOL_Obool), tc_fun(_1493415, tc_HOL_Obool)), _1493413), c_COMBC(_1493415, tc_fun(tc_prod(_1493413, _1493415), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493415, tc_prod(_1493413, _1493415)), tc_fun(_1493415, tc_fun(tc_fun(tc_prod(_1493413, _1493415), tc_HOL_Obool), tc_HOL_Obool)), _1493413), hAPP(c_COMBB(tc_prod(_1493413, _1493415), tc_fun(tc_fun(tc_prod(_1493413, _1493415), tc_HOL_Obool), tc_HOL_Obool), _1493415), c_member(tc_prod(_1493413, _1493415)))), c_Product__Type_OPair(_1493413, _1493415)))), _1493417)), _1493419)), -(hBOOL(hAPP(hAPP(c_member(_1493413), _1493419), hAPP(c_Relation_ODomain(_1493413, _1493415), _1493417))))], (37142 ^ _779308) ^ [_1493764, _1493766, _1493768, _1493770] : [hBOOL(hAPP(hAPP(c_member(_1493764), _1493770), hAPP(c_Relation_ODomain(_1493764, _1493766), _1493768))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1493764, _1493766, hAPP(hAPP(c_COMBC(_1493764, tc_fun(tc_prod(_1493764, _1493766), tc_HOL_Obool), tc_fun(_1493766, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493766, tc_fun(tc_fun(tc_prod(_1493764, _1493766), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1493764, _1493766), tc_HOL_Obool), tc_fun(_1493766, tc_HOL_Obool)), _1493764), c_COMBC(_1493766, tc_fun(tc_prod(_1493764, _1493766), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493766, tc_prod(_1493764, _1493766)), tc_fun(_1493766, tc_fun(tc_fun(tc_prod(_1493764, _1493766), tc_HOL_Obool), tc_HOL_Obool)), _1493764), hAPP(c_COMBB(tc_prod(_1493764, _1493766), tc_fun(tc_fun(tc_prod(_1493764, _1493766), tc_HOL_Obool), tc_HOL_Obool), _1493766), c_member(tc_prod(_1493764, _1493766)))), c_Product__Type_OPair(_1493764, _1493766)))), _1493768)), _1493770)))], (37148 ^ _779308) ^ [_1494121, _1494123] : [c_Wellfounded_Owf(_1494121, _1494123), -(c_Wellfounded_Owf(tc_List_Olist(_1494121), c_List_Olenlex(_1494121, _1494123)))], (37154 ^ _779308) ^ [_1494208, _1494210, _1494212, _1494214] : [hBOOL(hAPP(hAPP(c_member(_1494208), _1494210), hAPP(c_Relation_ODomain(_1494208, _1494212), _1494214))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494208, _1494212)), hAPP(hAPP(c_Product__Type_OPair(_1494208, _1494212), _1494210), 37157 ^ [_1494208, _1494210, _1494212, _1494214])), _1494214)))], (37161 ^ _779308) ^ [_1494373, _1494375, _1494377, _1494379, _1494381] : [hBOOL(hAPP(hAPP(_1494373, _1494375), _1494377)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1494379, _1494381, _1494373), _1494375)))], (37167 ^ _779308) ^ [_1494499, _1494501, _1494503, _1494505] : [hBOOL(hAPP(c_Predicate_ODomainP(_1494499, _1494501, _1494503), _1494505)), -(hBOOL(hAPP(hAPP(_1494503, _1494505), 37170 ^ [_1494499, _1494501, _1494503, _1494505])))], (37174 ^ _779308) ^ [_1494614, _1494616, _1494618, _1494620] : [37175 ^ _779308 : [(37176 ^ _779308) ^ [_1494668] : [hBOOL(hAPP(hAPP(_1494618, _1494620), _1494668))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1494614, _1494616, _1494618), _1494620)))], (37180 ^ _779308) ^ [] : [-(c_Wellfounded_Opred__nat = hAPP(c_Set_OCollect(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_fequal)), c_Nat_OSuc))))], (37182 ^ _779308) ^ [_1494750, _1494752] : [c_Wellfounded_Owf(_1494750, _1494752), -(c_Wellfounded_Owf(tc_List_Olist(_1494750), c_List_Olex(_1494750, _1494752)))], (37188 ^ _779308) ^ [_1494837, _1494839, _1494841] : [c_Wellfounded_Owf(_1494837, _1494839), -(c_Wellfounded_Owf(tc_List_Olist(_1494837), hAPP(c_List_Olexn(_1494837, _1494839), _1494841)))], (37194 ^ _779308) ^ [_1494932, _1494934] : [-(c_List_Olex(_1494932, _1494934) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1494932), tc_List_Olist(_1494932)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1494932, _1494934)))], (37196 ^ _779308) ^ [_1494982, _1494984] : [-(hAPP(c_List_Olexn(_1494982, _1494984), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1494982), tc_List_Olist(_1494982)), tc_HOL_Obool)))], (37198 ^ _779308) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (37200 ^ _779308) ^ [_1495043, _1495045, _1495047, _1495049] : [37202 ^ _779308 : [(37203 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1495043, 37201 ^ [_1495043, _1495045, _1495047, _1495049])))], (37205 ^ _779308) ^ [] : [c_Wellfounded_Owf(_1495045, hAPP(_1495047, 37201 ^ [_1495043, _1495045, _1495047, _1495049]))]], -(c_Wellfounded_Owf(tc_prod(_1495049, _1495045), c_Recdef_Osame__fst(_1495049, _1495045, _1495043, _1495047)))], (37209 ^ _779308) ^ [_1495228, _1495230, _1495232, _1495234] : [37211 ^ _779308 : [(37212 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1495228, 37210 ^ [_1495228, _1495230, _1495232, _1495234])))], (37214 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1495230, hAPP(_1495232, 37210 ^ [_1495228, _1495230, _1495232, _1495234]))), hAPP(_1495230, 37210 ^ [_1495228, _1495230, _1495232, _1495234])))]], -(c_Wellfounded_Owf(_1495234, hAPP(c_Set_OCollect(tc_prod(_1495234, _1495234)), hAPP(c_Product__Type_Oprod_Oprod__case(_1495234, _1495234, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1495234, tc_HOL_Obool), tc_fun(_1495234, tc_HOL_Obool), _1495234), hAPP(c_COMBS(_1495234, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1495234), c_fconj), _1495228))), hAPP(hAPP(c_COMBC(_1495234, tc_fun(_1495234, _1495234), tc_fun(_1495234, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495234, tc_HOL_Obool), tc_fun(tc_fun(_1495234, _1495234), tc_fun(_1495234, tc_HOL_Obool)), _1495234), c_COMBB(_1495234, tc_HOL_Obool, _1495234)), c_fequal)), _1495232))))))], (37218 ^ _779308) ^ [_1495636, _1495638] : [c_Wellfounded_OwfP(_1495636, _1495638), -(c_Wellfounded_Owf(_1495636, hAPP(c_Set_OCollect(tc_prod(_1495636, _1495636)), hAPP(c_Product__Type_Oprod_Oprod__case(_1495636, _1495636, tc_HOL_Obool), _1495638))))], (37224 ^ _779308) ^ [_1495739, _1495741] : [c_Wellfounded_Owf(_1495739, hAPP(c_Set_OCollect(tc_prod(_1495739, _1495739)), hAPP(c_Product__Type_Oprod_Oprod__case(_1495739, _1495739, tc_HOL_Obool), _1495741))), -(c_Wellfounded_OwfP(_1495739, _1495741))], (37230 ^ _779308) ^ [_1495848] : [-(c_Wellfounded_OwfP(_1495848, hAPP(c_COMBK(tc_fun(_1495848, tc_HOL_Obool), _1495848), hAPP(c_COMBK(tc_HOL_Obool, _1495848), c_fFalse))))], (37232 ^ _779308) ^ [_1495886, _1495888, _1495890] : [c_Wellfounded_OwfP(_1495886, _1495888), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1495886, _1495888), _1495890)))], (37238 ^ _779308) ^ [_1495990, _1495992] : [c_Wellfounded_OwfP(_1495990, _1495992), 37241 ^ _779308 : [(37242 ^ _779308) ^ [_1496054] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1495990, _1495992), _1496054)))]]], (37244 ^ _779308) ^ [_1496082, _1496084] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1496082, _1496084), 37245 ^ [_1496082, _1496084])), -(c_Wellfounded_OwfP(_1496082, _1496084))], (37251 ^ _779308) ^ [_1496200, _1496202, _1496204] : [c_Wellfounded_OwfP(_1496200, _1496202), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496200, tc_fun(_1496200, tc_HOL_Obool))), _1496204), _1496202)), -(c_Wellfounded_OwfP(_1496200, _1496204))], (37261 ^ _779308) ^ [_1496359, _1496361] : [c_Wellfounded_Owf(_1496359, _1496361), -(c_Wellfounded_OwfP(_1496359, c_FunDef_Oin__rel(_1496359, _1496359, _1496361)))], (37267 ^ _779308) ^ [_1496459, _1496461] : [c_Wellfounded_OwfP(_1496459, hAPP(hAPP(c_COMBC(_1496459, tc_fun(tc_prod(_1496459, _1496459), tc_HOL_Obool), tc_fun(_1496459, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1496459, tc_fun(tc_fun(tc_prod(_1496459, _1496459), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1496459, _1496459), tc_HOL_Obool), tc_fun(_1496459, tc_HOL_Obool)), _1496459), c_COMBC(_1496459, tc_fun(tc_prod(_1496459, _1496459), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1496459, tc_prod(_1496459, _1496459)), tc_fun(_1496459, tc_fun(tc_fun(tc_prod(_1496459, _1496459), tc_HOL_Obool), tc_HOL_Obool)), _1496459), hAPP(c_COMBB(tc_prod(_1496459, _1496459), tc_fun(tc_fun(tc_prod(_1496459, _1496459), tc_HOL_Obool), tc_HOL_Obool), _1496459), c_member(tc_prod(_1496459, _1496459)))), c_Product__Type_OPair(_1496459, _1496459)))), _1496461)), -(c_Wellfounded_Owf(_1496459, _1496461))], (37273 ^ _779308) ^ [_1496768, _1496770] : [c_Wellfounded_Owf(_1496768, _1496770), -(c_Wellfounded_OwfP(_1496768, hAPP(hAPP(c_COMBC(_1496768, tc_fun(tc_prod(_1496768, _1496768), tc_HOL_Obool), tc_fun(_1496768, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1496768, tc_fun(tc_fun(tc_prod(_1496768, _1496768), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1496768, _1496768), tc_HOL_Obool), tc_fun(_1496768, tc_HOL_Obool)), _1496768), c_COMBC(_1496768, tc_fun(tc_prod(_1496768, _1496768), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1496768, tc_prod(_1496768, _1496768)), tc_fun(_1496768, tc_fun(tc_fun(tc_prod(_1496768, _1496768), tc_HOL_Obool), tc_HOL_Obool)), _1496768), hAPP(c_COMBB(tc_prod(_1496768, _1496768), tc_fun(tc_fun(tc_prod(_1496768, _1496768), tc_HOL_Obool), tc_HOL_Obool), _1496768), c_member(tc_prod(_1496768, _1496768)))), c_Product__Type_OPair(_1496768, _1496768)))), _1496770)))], (37279 ^ _779308) ^ [_1497083, _1497085] : [c_Wellfounded_OwfP(_1497083, _1497085), -(c_Wellfounded_Oacyclic(_1497083, hAPP(c_Set_OCollect(tc_prod(_1497083, _1497083)), hAPP(c_Product__Type_Oprod_Oprod__case(_1497083, _1497083, tc_HOL_Obool), _1497085))))], (37301 ^ _779308) ^ [_1497827, _1497829, _1497831] : [-(c_Relation_Orefl__on(_1497827, _1497829, _1497831)), 37305 ^ _779308 : [(37306 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1497827, _1497827)), 37304 ^ [_1497827, _1497829, _1497831]), _1497831)))], (37308 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1497827, _1497827, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1497827, tc_fun(_1497827, tc_HOL_Obool), tc_fun(_1497827, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1497827, tc_HOL_Obool), tc_fun(_1497827, tc_HOL_Obool)), _1497827), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1497827)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497827), c_fconj), hAPP(hAPP(c_COMBC(_1497827, tc_fun(_1497827, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497827)), _1497829)))), hAPP(hAPP(c_COMBC(_1497827, tc_fun(_1497827, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497827)), _1497829))), 37304 ^ [_1497827, _1497829, _1497831]))]], 37310 ^ _779308 : [(37311 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1497827), 37309 ^ [_1497827, _1497829, _1497831]), _1497829)))], (37313 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1497827, _1497827)), hAPP(hAPP(c_Product__Type_OPair(_1497827, _1497827), 37309 ^ [_1497827, _1497829, _1497831]), 37309 ^ [_1497827, _1497829, _1497831])), _1497831))]]], (37285 ^ _779308) ^ [_1497208, _1497210, _1497212] : [c_Relation_Orefl__on(_1497208, _1497210, _1497212), 37288 ^ _779308 : [(37289 ^ _779308) ^ [_1497419] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1497208, _1497208)), _1497419), _1497212)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1497208, _1497208, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1497208, tc_fun(_1497208, tc_HOL_Obool), tc_fun(_1497208, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1497208, tc_HOL_Obool), tc_fun(_1497208, tc_HOL_Obool)), _1497208), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1497208)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497208), c_fconj), hAPP(hAPP(c_COMBC(_1497208, tc_fun(_1497208, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497208)), _1497210)))), hAPP(hAPP(c_COMBC(_1497208, tc_fun(_1497208, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497208)), _1497210))), _1497419)))], (37295 ^ _779308) ^ [_1497692] : [hBOOL(hAPP(hAPP(c_member(_1497208), _1497692), _1497210)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1497208, _1497208)), hAPP(hAPP(c_Product__Type_OPair(_1497208, _1497208), _1497692), _1497692)), _1497212)))]]], (37317 ^ _779308) ^ [_1498468, _1498470] : [37319 ^ _779308 : [(37320 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 37318 ^ [_1498468, _1498470]), c_Int_OInteg)))], (37322 ^ _779308) ^ [] : [hBOOL(hAPP(_1498468, hAPP(c_Int_OAbs__Integ, 37318 ^ [_1498468, _1498470])))]], -(hBOOL(hAPP(_1498468, _1498470)))], (37326 ^ _779308) ^ [_1498637, _1498639, _1498641] : [hBOOL(hAPP(hAPP(c_member(_1498639), _1498637), c_Orderings_Obot__class_Obot(tc_fun(_1498639, tc_HOL_Obool)))), -(hBOOL(hAPP(_1498641, _1498637)))], (37332 ^ _779308) ^ [_1498744, _1498746] : [c_Wellfounded_Owf(_1498744, _1498746), -(c_Wellfounded_Oacyclic(_1498744, _1498746))], (37338 ^ _779308) ^ [_1498821, _1498823, _1498825] : [c_Wellfounded_Oacyclic(_1498821, _1498823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1498821, _1498821), tc_HOL_Obool)), _1498825), _1498823)), -(c_Wellfounded_Oacyclic(_1498821, _1498825))], (37358 ^ _779308) ^ [_1499181, _1499183, _1499185] : [37360 ^ _779308 : [(37361 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1499181), 37359 ^ [_1499181, _1499183, _1499185]), _1499185)))], (37363 ^ _779308) ^ [] : [hBOOL(hAPP(_1499183, 37359 ^ [_1499181, _1499183, _1499185]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1499181, _1499183), _1499185)))], (37348 ^ _779308) ^ [_1498998, _1499000, _1499002] : [hBOOL(hAPP(c_Predicate_OPowp(_1498998, _1499000), _1499002)), 37351 ^ _779308 : [(37352 ^ _779308) ^ [_1499082] : [hBOOL(hAPP(hAPP(c_member(_1498998), _1499082), _1499002)), -(hBOOL(hAPP(_1499000, _1499082)))]]], (37377 ^ _779308) ^ [_1499758, _1499760, _1499762, _1499764] : [37379 ^ _779308 : [(37380 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1499758, _1499758)), 37378 ^ [_1499758, _1499760, _1499762, _1499764]), _1499762)))], (37382 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1499758, _1499758, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1499758, tc_fun(_1499758, _1499760), tc_fun(_1499758, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499760, tc_HOL_Obool), tc_fun(tc_fun(_1499758, _1499760), tc_fun(_1499758, tc_HOL_Obool)), _1499758), c_COMBB(_1499760, tc_HOL_Obool, _1499758)), hAPP(hAPP(c_COMBB(_1499760, tc_fun(_1499760, tc_HOL_Obool), _1499758), c_fequal), _1499764))), _1499764)), 37378 ^ [_1499758, _1499760, _1499762, _1499764]))]], -(c_Equiv__Relations_Ocongruent(_1499758, _1499760, _1499762, _1499764))], (37367 ^ _779308) ^ [_1499382, _1499384, _1499386, _1499388] : [c_Equiv__Relations_Ocongruent(_1499382, _1499384, _1499386, _1499388), 37370 ^ _779308 : [(37371 ^ _779308) ^ [_1499527] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1499382, _1499382)), _1499527), _1499386)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1499382, _1499382, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1499382, tc_fun(_1499382, _1499384), tc_fun(_1499382, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499384, tc_HOL_Obool), tc_fun(tc_fun(_1499382, _1499384), tc_fun(_1499382, tc_HOL_Obool)), _1499382), c_COMBB(_1499384, tc_HOL_Obool, _1499382)), hAPP(hAPP(c_COMBB(_1499384, tc_fun(_1499384, tc_HOL_Obool), _1499382), c_fequal), _1499388))), _1499388)), _1499527)))]]], (37386 ^ _779308) ^ [_1500133, _1500135] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1500133, _1500133)), _1500135)), c_Wellfounded_Oacyclic(_1500133, _1500135), -(c_Wellfounded_Owf(_1500133, _1500135))], (37396 ^ _779308) ^ [_1500276, _1500278] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1500276, _1500276)), _1500278)), 37399 ^ _779308 : [(37400 ^ _779308) ^ [] : [c_Wellfounded_Owf(_1500276, _1500278), -(c_Wellfounded_Oacyclic(_1500276, _1500278))], (37406 ^ _779308) ^ [] : [c_Wellfounded_Oacyclic(_1500276, _1500278), -(c_Wellfounded_Owf(_1500276, _1500278))]]], (37412 ^ _779308) ^ [_1500512, _1500514] : [c_Nitpick_Owf_H(_1500512, _1500514), 37415 ^ _779308 : [(37416 ^ _779308) ^ [] : [-(c_Wellfounded_Oacyclic(_1500512, _1500514))], (37418 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1500512, _1500512)), _1500514))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (37424 ^ _779308) ^ [_1500632, _1500634] : [-(c_Nitpick_Owf_H(_1500632, _1500634)), c_Wellfounded_Oacyclic(_1500632, _1500634), 37429 ^ _779308 : [(37430 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1500632, _1500632)), _1500634))], (37432 ^ _779308) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (37437 ^ _779308) ^ [_1500807] : [-(_1500807 = hAPP(c_Int_OAbs__Integ, 37435 ^ [_1500807]))], (37439 ^ _779308) ^ [_1500835] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 37435 ^ [_1500835]), c_Int_OInteg)))], (37441 ^ _779308) ^ [_1500870, _1500872, _1500874, _1500876] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1500870), _1500872)), 37447 ^ _779308 : [(37448 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1500870), 37446 ^ [_1500870, _1500872, _1500874, _1500876]), _1500872)))], (37450 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1500874), hAPP(_1500876, 37446 ^ [_1500870, _1500872, _1500874, _1500876])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1500874), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500870, tc_fun(_1500874, tc_HOL_Obool)), _1500872), _1500876))))], (37454 ^ _779308) ^ [_1501157, _1501159, _1501161] : [c_Wellfounded_OwfP(_1501157, hAPP(_1501159, 37455 ^ [_1501157, _1501159, _1501161])), 37462 ^ _779308 : [(37463 ^ _779308) ^ [] : [hAPP(_1501159, 37460 ^ [_1501157, _1501159, _1501161]) = hAPP(_1501159, 37461 ^ [_1501157, _1501159, _1501161])], (37465 ^ _779308) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501157, tc_HOL_Obool)), c_Predicate_ODomainP(_1501157, _1501157, hAPP(_1501159, 37460 ^ [_1501157, _1501159, _1501161]))), c_Predicate_ORangeP(_1501157, _1501157, hAPP(_1501159, 37461 ^ [_1501157, _1501159, _1501161]))) = c_Orderings_Obot__class_Obot(tc_fun(_1501157, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1501157, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501161, tc_fun(_1501157, tc_fun(_1501157, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1501161, tc_HOL_Obool))), _1501159)))], (37469 ^ _779308) ^ [_1501597, _1501599, _1501601, _1501603, _1501605, _1501607] : [hBOOL(hAPP(hAPP(c_member(_1501597), _1501599), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1501601, _1501603, tc_fun(_1501597, tc_HOL_Obool)), _1501605), _1501607))), 37474 ^ _779308 : [(37475 ^ _779308) ^ [] : [-(_1501607 = hAPP(hAPP(c_Product__Type_OPair(_1501601, _1501603), 37472 ^ [_1501597, _1501599, _1501601, _1501603, _1501605, _1501607]), 37473 ^ [_1501597, _1501599, _1501601, _1501603, _1501605, _1501607]))], (37477 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501597), _1501599), hAPP(hAPP(_1501605, 37472 ^ [_1501597, _1501599, _1501601, _1501603, _1501605, _1501607]), 37473 ^ [_1501597, _1501599, _1501601, _1501603, _1501605, _1501607]))))]]], (37479 ^ _779308) ^ [_1501866, _1501868, _1501870, _1501872, _1501874, _1501876] : [37482 ^ _779308 : [(37483 ^ _779308) ^ [] : [-(_1501866 = hAPP(hAPP(c_Product__Type_OPair(_1501868, _1501870), 37480 ^ [_1501866, _1501868, _1501870, _1501872, _1501874, _1501876]), 37481 ^ [_1501866, _1501868, _1501870, _1501872, _1501874, _1501876]))], (37485 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1501872), _1501874), hAPP(hAPP(_1501876, 37480 ^ [_1501866, _1501868, _1501870, _1501872, _1501874, _1501876]), 37481 ^ [_1501866, _1501868, _1501870, _1501872, _1501874, _1501876])))]], -(hBOOL(hAPP(hAPP(c_member(_1501872), _1501874), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1501868, _1501870, tc_fun(_1501872, tc_HOL_Obool)), _1501876), _1501866))))], (37489 ^ _779308) ^ [_1502191, _1502193, _1502195, _1502197, _1502199, _1502201] : [-(hAPP(c_Set_Ovimage(_1502191, tc_prod(_1502193, _1502195), _1502197), hAPP(hAPP(c_Product__Type_OSigma(_1502193, _1502195), _1502199), hAPP(c_COMBK(tc_fun(_1502195, tc_HOL_Obool), _1502193), _1502201))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1502191, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1502191, _1502193, hAPP(c_Fun_Ocomp(tc_prod(_1502193, _1502195), _1502193, _1502191, c_Product__Type_Ofst(_1502193, _1502195)), _1502197)), _1502199)), hAPP(c_Set_Ovimage(_1502191, _1502195, hAPP(c_Fun_Ocomp(tc_prod(_1502193, _1502195), _1502195, _1502191, c_Product__Type_Osnd(_1502193, _1502195)), _1502197)), _1502201)))], (37491 ^ _779308) ^ [_1502305, _1502307, _1502309, _1502311] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1502305, tc_Nat_Onat), _1502307), _1502309) = hAPP(c_Nat_OSuc, _1502311), 37495 ^ _779308 : [(37496 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502305), 37494 ^ [_1502305, _1502307, _1502309, _1502311]), _1502309)))], (37498 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1502307, 37494 ^ [_1502305, _1502307, _1502309, _1502311]))))]]], (37500 ^ _779308) ^ [_1502487, _1502489, _1502491] : [-(c_Hilbert__Choice_OEps(tc_prod(_1502487, _1502489), hAPP(c_Product__Type_Oprod_Oprod__case(_1502487, _1502489, tc_HOL_Obool), _1502491)) = c_Hilbert__Choice_OEps(tc_prod(_1502487, _1502489), hAPP(hAPP(c_COMBS(tc_prod(_1502487, _1502489), _1502489, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1502487, tc_fun(_1502489, tc_HOL_Obool), tc_prod(_1502487, _1502489)), _1502491), c_Product__Type_Ofst(_1502487, _1502489))), c_Product__Type_Osnd(_1502487, _1502489))))], (37502 ^ _779308) ^ [_1502568, _1502570, _1502572] : [-(hAPP(c_Fun_Ocomp(_1502568, _1502568, _1502570, c_Fun_Oid(_1502568)), _1502572) = _1502572)], (37504 ^ _779308) ^ [_1502605, _1502607, _1502609] : [-(hAPP(c_Fun_Ocomp(_1502605, _1502607, _1502605, _1502609), c_Fun_Oid(_1502605)) = _1502609)], (37506 ^ _779308) ^ [_1502642, _1502644, _1502646, _1502648, _1502650, _1502652, _1502654] : [hAPP(c_Fun_Ocomp(_1502642, _1502644, _1502646, _1502648), _1502650) = hAPP(c_Fun_Ocomp(_1502644, _1502644, _1502646, c_Fun_Oid(_1502644)), _1502652), -(hAPP(_1502648, hAPP(_1502650, _1502654)) = hAPP(_1502652, _1502654))], (37512 ^ _779308) ^ [_1502783, _1502785, _1502787] : [37513 ^ _779308 : [(37514 ^ _779308) ^ [_1502837] : [hBOOL(hAPP(_1502783, _1502837))]], _1502785 = c_Hilbert__Choice_OEps(_1502787, _1502783), -(hBOOL(hAPP(_1502783, _1502785)))], (37522 ^ _779308) ^ [_1502943, _1502945, _1502947, _1502949, _1502951, _1502953] : [-(hAPP(c_Set_Ovimage(_1502943, _1502945, hAPP(c_Fun_Ocomp(_1502947, _1502945, _1502943, _1502949), _1502951)), _1502953) = hAPP(c_Set_Ovimage(_1502943, _1502947, _1502951), hAPP(c_Set_Ovimage(_1502947, _1502945, _1502949), _1502953)))], (37524 ^ _779308) ^ [_1503005, _1503007, _1503009, _1503011, _1503013, _1503015, _1503017] : [-(hAPP(c_Product__Type_Oapfst(_1503005, _1503007, _1503009, _1503011), hAPP(c_Product__Type_Oapfst(_1503013, _1503005, _1503009, _1503015), _1503017)) = hAPP(c_Product__Type_Oapfst(_1503013, _1503007, _1503009, hAPP(c_Fun_Ocomp(_1503005, _1503007, _1503013, _1503011), _1503015)), _1503017))], (37526 ^ _779308) ^ [_1503072, _1503074, _1503076, _1503078] : [c_Finite__Set_Ofun__left__comm__idem(_1503072, _1503074, _1503076), -(hAPP(c_Fun_Ocomp(_1503074, _1503074, _1503074, hAPP(_1503076, _1503078)), hAPP(_1503076, _1503078)) = hAPP(_1503076, _1503078))], (37532 ^ _779308) ^ [_1503189, _1503191, _1503193, _1503195, _1503197, _1503199] : [-(hAPP(hAPP(c_Fun_Ocomp(_1503189, _1503191, _1503193, _1503195), _1503197), _1503199) = hAPP(_1503195, hAPP(_1503197, _1503199)))], (37534 ^ _779308) ^ [_1503239, _1503241] : [37535 ^ _779308 : [(37536 ^ _779308) ^ [_1503285] : [hBOOL(hAPP(_1503239, _1503285))]], -(hBOOL(hAPP(_1503239, c_Hilbert__Choice_OEps(_1503241, _1503239))))], (37540 ^ _779308) ^ [_1503358, _1503360] : [hBOOL(hAPP(_1503358, c_Hilbert__Choice_OEps(_1503360, _1503358))), -(hBOOL(hAPP(_1503358, 37543 ^ [_1503358, _1503360])))], (37547 ^ _779308) ^ [_1503457, _1503459] : [37548 ^ _779308 : [(37549 ^ _779308) ^ [_1503503] : [hBOOL(hAPP(_1503457, _1503503))]], -(hBOOL(hAPP(_1503457, c_Hilbert__Choice_OEps(_1503459, _1503457))))], (37553 ^ _779308) ^ [_1503563, _1503565] : [-(c_Hilbert__Choice_OEps(_1503563, hAPP(hAPP(c_COMBC(_1503563, _1503563, tc_HOL_Obool), c_fequal), _1503565)) = _1503565)], (37555 ^ _779308) ^ [_1503601, _1503603] : [-(c_Hilbert__Choice_OEps(_1503601, hAPP(c_fequal, _1503603)) = _1503603)], (37557 ^ _779308) ^ [_1503632, _1503634, _1503636, _1503638, _1503640, _1503642, _1503644] : [-(hAPP(c_Fun_Ocomp(_1503632, _1503634, _1503636, _1503638), hAPP(c_Fun_Ocomp(_1503640, _1503632, _1503636, _1503642), _1503644)) = hAPP(c_Fun_Ocomp(_1503640, _1503634, _1503636, hAPP(c_Fun_Ocomp(_1503632, _1503634, _1503640, _1503638), _1503642)), _1503644))], (37559 ^ _779308) ^ [_1503699, _1503701, _1503703, _1503705, _1503707, _1503709] : [-(hAPP(hAPP(c_Fun_Ocomp(_1503699, _1503701, _1503703, _1503705), _1503707), _1503709) = hAPP(_1503705, hAPP(_1503707, _1503709)))], (37561 ^ _779308) ^ [_1503749, _1503751, _1503753, _1503755, _1503757, _1503759, _1503761, _1503763, _1503765] : [hAPP(c_Fun_Ocomp(_1503749, _1503751, _1503753, _1503755), _1503757) = hAPP(c_Fun_Ocomp(_1503759, _1503751, _1503753, _1503761), _1503763), -(hAPP(_1503755, hAPP(_1503757, _1503765)) = hAPP(_1503761, hAPP(_1503763, _1503765)))], (37567 ^ _779308) ^ [_1503896, _1503898, _1503900, _1503902, _1503904, _1503906, _1503908, _1503910] : [hAPP(c_Fun_Ocomp(_1503896, _1503898, _1503900, _1503902), _1503904) = hAPP(c_Fun_Ocomp(_1503906, _1503898, _1503900, _1503908), _1503910), 37570 ^ _779308 : [(37571 ^ _779308) ^ [_1504011] : [-(hAPP(_1503902, hAPP(_1503904, _1504011)) = hAPP(_1503908, hAPP(_1503910, _1504011)))]]], (37573 ^ _779308) ^ [_1504050, _1504052] : [37574 ^ _779308 : [(37575 ^ _779308) ^ [_1504096] : [hBOOL(hAPP(_1504050, _1504096))]], -(hBOOL(hAPP(_1504050, c_Hilbert__Choice_OEps(_1504052, _1504050))))], (37579 ^ _779308) ^ [_1504154, _1504156, _1504158] : [hBOOL(hAPP(_1504154, _1504156)), -(hBOOL(hAPP(_1504154, c_Hilbert__Choice_OEps(_1504158, _1504154))))], (37585 ^ _779308) ^ [_1504247, _1504249, _1504251, _1504253, _1504255, _1504257, _1504259, _1504261, _1504263, _1504265, _1504267] : [hAPP(_1504247, hAPP(_1504249, _1504251)) = hAPP(_1504253, hAPP(_1504255, _1504257)), -(hAPP(hAPP(c_Fun_Ocomp(_1504259, _1504261, _1504263, _1504247), _1504249), _1504251) = hAPP(hAPP(c_Fun_Ocomp(_1504265, _1504261, _1504267, _1504253), _1504255), _1504257))], (37591 ^ _779308) ^ [_1504410, _1504412, _1504414, _1504416, _1504418, _1504420, _1504422] : [-(hAPP(c_Fun_Ocomp(_1504410, _1504412, _1504414, _1504416), c_Fun_Ofun__upd(_1504414, _1504410, _1504418, _1504420, _1504422)) = c_Fun_Ofun__upd(_1504414, _1504412, hAPP(c_Fun_Ocomp(_1504410, _1504412, _1504414, _1504416), _1504418), _1504420, hAPP(_1504416, _1504422)))], (37593 ^ _779308) ^ [_1504476, _1504478, _1504480, _1504482, _1504484, _1504486, _1504488] : [-(hAPP(c_Product__Type_Oapsnd(_1504476, _1504478, _1504480, _1504482), hAPP(c_Product__Type_Oapsnd(_1504484, _1504476, _1504480, _1504486), _1504488)) = hAPP(c_Product__Type_Oapsnd(_1504484, _1504478, _1504480, hAPP(c_Fun_Ocomp(_1504476, _1504478, _1504484, _1504482), _1504486)), _1504488))], (37595 ^ _779308) ^ [_1504543, _1504545, _1504547, _1504549, _1504551, _1504553, _1504555] : [hAPP(c_Fun_Ocomp(_1504543, _1504545, _1504547, _1504549), _1504551) = _1504553, -(hAPP(_1504549, hAPP(_1504551, _1504555)) = hAPP(_1504553, _1504555))], (37601 ^ _779308) ^ [_1504664, _1504666, _1504668, _1504670, _1504672, _1504674] : [-(hAPP(hAPP(c_Fun_Ocomp(_1504664, _1504666, _1504668, hAPP(c_COMBK(_1504666, _1504664), _1504670)), _1504672), _1504674) = _1504670)], (37603 ^ _779308) ^ [_1504714, _1504716, _1504718, _1504720, _1504722, _1504724, _1504726, _1504728, _1504730, _1504732, _1504734] : [-(hAPP(c_Product__Type_Omap__pair(_1504714, _1504716, _1504718, _1504720, _1504722, _1504724), hAPP(c_Product__Type_Omap__pair(_1504726, _1504714, _1504728, _1504718, _1504730, _1504732), _1504734)) = hAPP(c_Product__Type_Omap__pair(_1504726, _1504716, _1504728, _1504720, hAPP(c_Fun_Ocomp(_1504714, _1504716, _1504726, _1504722), _1504730), hAPP(c_Fun_Ocomp(_1504718, _1504720, _1504728, _1504724), _1504732)), _1504734))], (37605 ^ _779308) ^ [_1504803, _1504805, _1504807, _1504809, _1504811, _1504813, _1504815, _1504817, _1504819, _1504821] : [-(c_Product__Type_Omap__pair(_1504803, _1504805, _1504807, _1504809, hAPP(c_Fun_Ocomp(_1504811, _1504805, _1504803, _1504813), _1504815), hAPP(c_Fun_Ocomp(_1504817, _1504809, _1504807, _1504819), _1504821)) = hAPP(c_Fun_Ocomp(tc_prod(_1504811, _1504817), tc_prod(_1504805, _1504809), tc_prod(_1504803, _1504807), c_Product__Type_Omap__pair(_1504811, _1504805, _1504817, _1504809, _1504813, _1504819)), c_Product__Type_Omap__pair(_1504803, _1504811, _1504807, _1504817, _1504815, _1504821)))], (37607 ^ _779308) ^ [_1504898, _1504900, _1504902, _1504904, _1504906, _1504908, _1504910, _1504912, _1504914, _1504916] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1504898, _1504900), tc_prod(_1504902, _1504904), tc_prod(_1504906, _1504908), c_Product__Type_Omap__pair(_1504898, _1504902, _1504900, _1504904, _1504910, _1504912)), c_Product__Type_Omap__pair(_1504906, _1504898, _1504908, _1504900, _1504914, _1504916)) = c_Product__Type_Omap__pair(_1504906, _1504902, _1504908, _1504904, hAPP(c_Fun_Ocomp(_1504898, _1504902, _1504906, _1504910), _1504914), hAPP(c_Fun_Ocomp(_1504900, _1504904, _1504908, _1504912), _1504916)))], (37609 ^ _779308) ^ [_1504993, _1504995, _1504997, _1504999, _1505001, _1505003] : [-(hAPP(c_Set_Oimage(_1504993, _1504995, hAPP(c_Fun_Ocomp(_1504997, _1504995, _1504993, _1504999), _1505001)), _1505003) = hAPP(c_Set_Oimage(_1504997, _1504995, _1504999), hAPP(c_Set_Oimage(_1504993, _1504997, _1505001), _1505003)))], (37611 ^ _779308) ^ [_1505055, _1505057, _1505059, _1505061, _1505063, _1505065] : [c_Fun_Oinj__on(_1505055, _1505057, hAPP(c_Fun_Ocomp(_1505059, _1505057, _1505055, _1505061), _1505063), _1505065), -(c_Fun_Oinj__on(_1505055, _1505059, _1505063, _1505065))], (37617 ^ _779308) ^ [_1505164, _1505166, _1505168, _1505170, _1505172, _1505174] : [c_Fun_Oinj__on(_1505164, _1505166, hAPP(c_Fun_Ocomp(_1505168, _1505166, _1505164, _1505170), _1505172), _1505174), -(c_Fun_Oinj__on(_1505168, _1505166, _1505170, hAPP(c_Set_Oimage(_1505164, _1505168, _1505172), _1505174)))], (37623 ^ _779308) ^ [_1505287, _1505289, _1505291, _1505293, _1505295, _1505297] : [c_Fun_Oinj__on(_1505287, _1505289, _1505291, _1505293), c_Fun_Oinj__on(_1505289, _1505295, _1505297, hAPP(c_Set_Oimage(_1505287, _1505289, _1505291), _1505293)), -(c_Fun_Oinj__on(_1505287, _1505295, hAPP(c_Fun_Ocomp(_1505289, _1505295, _1505287, _1505297), _1505291), _1505293))], (37633 ^ _779308) ^ [_1505474, _1505476, _1505478, _1505480, _1505482, _1505484] : [c_Fun_Oinj__on(_1505474, _1505476, _1505478, _1505480), 37636 ^ _779308 : [(37637 ^ _779308) ^ [] : [c_Fun_Oinj__on(_1505476, _1505482, _1505484, hAPP(c_Set_Oimage(_1505474, _1505476, _1505478), _1505480)), -(c_Fun_Oinj__on(_1505474, _1505482, hAPP(c_Fun_Ocomp(_1505476, _1505482, _1505474, _1505484), _1505478), _1505480))], (37643 ^ _779308) ^ [] : [c_Fun_Oinj__on(_1505474, _1505482, hAPP(c_Fun_Ocomp(_1505476, _1505482, _1505474, _1505484), _1505478), _1505480), -(c_Fun_Oinj__on(_1505476, _1505482, _1505484, hAPP(c_Set_Oimage(_1505474, _1505476, _1505478), _1505480)))]]], (37649 ^ _779308) ^ [_1505766, _1505768, _1505770, _1505772, _1505774] : [c_Fun_Oinj__on(_1505766, _1505768, _1505770, c_Orderings_Otop__class_Otop(tc_fun(_1505766, tc_HOL_Obool))), c_Fun_Oinj__on(_1505772, _1505766, _1505774, c_Orderings_Otop__class_Otop(tc_fun(_1505772, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1505772, _1505768, hAPP(c_Fun_Ocomp(_1505766, _1505768, _1505772, _1505770), _1505774), c_Orderings_Otop__class_Otop(tc_fun(_1505772, tc_HOL_Obool))))], (37659 ^ _779308) ^ [_1505965, _1505967, _1505969, _1505971, _1505973] : [hAPP(c_Set_Oimage(_1505965, _1505967, _1505969), c_Orderings_Otop__class_Otop(tc_fun(_1505965, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1505967, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1505967, _1505971, _1505973), c_Orderings_Otop__class_Otop(tc_fun(_1505967, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1505971, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1505965, _1505971, hAPP(c_Fun_Ocomp(_1505967, _1505971, _1505965, _1505973), _1505969)), c_Orderings_Otop__class_Otop(tc_fun(_1505965, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1505971, tc_HOL_Obool)))], (37669 ^ _779308) ^ [_1506224, _1506226, _1506228, _1506230, _1506232, _1506234] : [class_Groups_Ocomm__monoid__add(_1506224), c_Fun_Oinj__on(_1506226, _1506228, _1506230, _1506232), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1506228, _1506224), _1506234), hAPP(c_Set_Oimage(_1506226, _1506228, _1506230), _1506232)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1506226, _1506224), hAPP(c_Fun_Ocomp(_1506228, _1506224, _1506226, _1506234), _1506230)), _1506232))], (37679 ^ _779308) ^ [_1506437, _1506439, _1506441, _1506443, _1506445, _1506447] : [class_Groups_Ocomm__monoid__mult(_1506437), c_Fun_Oinj__on(_1506439, _1506441, _1506443, _1506445), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1506441, _1506437), _1506447), hAPP(c_Set_Oimage(_1506439, _1506441, _1506443), _1506445)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1506439, _1506437), hAPP(c_Fun_Ocomp(_1506441, _1506437, _1506439, _1506447), _1506443)), _1506445))], (37689 ^ _779308) ^ [_1506650, _1506652, _1506654, _1506656, _1506658, _1506660, _1506662, _1506664] : [class_Groups_Ocomm__monoid__mult(_1506650), c_Fun_Oinj__on(_1506652, _1506654, _1506656, _1506658), _1506660 = hAPP(c_Set_Oimage(_1506652, _1506654, _1506656), _1506658), _1506662 = hAPP(c_Fun_Ocomp(_1506654, _1506650, _1506652, _1506664), _1506656), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1506654, _1506650), _1506664), _1506660) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1506652, _1506650), _1506662), _1506658))], (37707 ^ _779308) ^ [_1506999, _1507001, _1507003, _1507005] : [-(c_Hilbert__Choice_OEps(tc_prod(_1506999, _1507001), hAPP(c_Product__Type_Oprod_Oprod__case(_1506999, _1507001, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1506999, tc_fun(_1507001, tc_HOL_Obool), tc_fun(_1507001, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1507001, tc_HOL_Obool), tc_fun(_1507001, tc_HOL_Obool)), _1506999), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1507001)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506999), c_fconj), hAPP(c_fequal, _1507003)))), hAPP(c_fequal, _1507005)))) = hAPP(hAPP(c_Product__Type_OPair(_1506999, _1507001), _1507003), _1507005))], (37709 ^ _779308) ^ [_1507105, _1507107, _1507109] : [-(c_Hilbert__Choice_OEps(tc_prod(_1507105, _1507107), _1507109) = c_Hilbert__Choice_OEps(tc_prod(_1507105, _1507107), hAPP(c_Product__Type_Oprod_Oprod__case(_1507105, _1507107, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1507107, tc_prod(_1507105, _1507107)), tc_fun(_1507107, tc_HOL_Obool), _1507105), hAPP(c_COMBB(tc_prod(_1507105, _1507107), tc_HOL_Obool, _1507107), _1507109)), c_Product__Type_OPair(_1507105, _1507107)))))], (37711 ^ _779308) ^ [_1507183, _1507185, _1507187, _1507189, _1507191] : [class_Groups_Ocomm__monoid__add(_1507183), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507185), _1507187)), c_Fun_Oinj__on(_1507185, _1507185, _1507189, _1507187), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1507185, _1507183), _1507191), hAPP(c_Set_Oimage(_1507185, _1507185, _1507189), _1507187)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1507185, _1507183), hAPP(c_Fun_Ocomp(_1507185, _1507183, _1507185, _1507191), _1507189)), _1507187))], (37725 ^ _779308) ^ [_1507458, _1507460, _1507462, _1507464, _1507466] : [class_Groups_Ocomm__monoid__mult(_1507458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507460), _1507462)), c_Fun_Oinj__on(_1507460, _1507460, _1507464, _1507462), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1507460, _1507458), _1507466), hAPP(c_Set_Oimage(_1507460, _1507460, _1507464), _1507462)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1507460, _1507458), hAPP(c_Fun_Ocomp(_1507460, _1507458, _1507460, _1507466), _1507464)), _1507462))], (37739 ^ _779308) ^ [_1507733, _1507735, _1507737, _1507739, _1507741, _1507743, _1507745] : [c_Fun_Oinj__on(_1507733, _1507735, _1507737, hAPP(c_Set_Oimage(_1507739, _1507733, _1507741), _1507743)), c_Fun_Oinj__on(_1507739, _1507733, _1507741, _1507743), hBOOL(hAPP(hAPP(c_member(_1507735), _1507745), hAPP(c_Set_Oimage(_1507733, _1507735, _1507737), hAPP(c_Set_Oimage(_1507739, _1507733, _1507741), _1507743)))), -(hAPP(c_Fun_Othe__inv__into(_1507739, _1507735, _1507743, hAPP(c_Fun_Ocomp(_1507733, _1507735, _1507739, _1507737), _1507741)), _1507745) = hAPP(hAPP(c_Fun_Ocomp(_1507733, _1507739, _1507735, c_Fun_Othe__inv__into(_1507739, _1507733, _1507743, _1507741)), c_Fun_Othe__inv__into(_1507733, _1507735, hAPP(c_Set_Oimage(_1507739, _1507733, _1507741), _1507743), _1507737)), _1507745))], (37753 ^ _779308) ^ [_1508096, _1508098, _1508100, _1508102, _1508104, _1508106, _1508108] : [class_Groups_Oab__semigroup__mult(_1508096), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508098), _1508100)), c_Fun_Oinj__on(_1508098, _1508102, _1508104, _1508100), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1508096, _1508102, c_Groups_Otimes__class_Otimes(_1508096)), _1508106), _1508108), hAPP(c_Set_Oimage(_1508098, _1508102, _1508104), _1508100)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1508096, _1508098, c_Groups_Otimes__class_Otimes(_1508096)), hAPP(c_Fun_Ocomp(_1508102, _1508096, _1508098, _1508106), _1508104)), _1508108), _1508100))], (37767 ^ _779308) ^ [_1508407, _1508409, _1508411, _1508413, _1508415, _1508417] : [c_Finite__Set_Ofolding(_1508407, _1508409, _1508411, _1508413), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508407), _1508415)), hBOOL(hAPP(hAPP(c_member(_1508407), _1508417), _1508415)), -(hAPP(_1508413, _1508415) = hAPP(c_Fun_Ocomp(_1508409, _1508409, _1508409, hAPP(_1508413, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1508407, tc_HOL_Obool)), _1508415), hAPP(hAPP(c_Set_Oinsert(_1508407), _1508417), c_Orderings_Obot__class_Obot(tc_fun(_1508407, tc_HOL_Obool)))))), hAPP(_1508411, _1508417)))], (37781 ^ _779308) ^ [_1508720, _1508722, _1508724, _1508726, _1508728, _1508730, _1508732, _1508734] : [c_Finite__Set_Ofolding__image(_1508720, _1508722, _1508724, _1508726, _1508728), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508722), _1508730)), c_Fun_Oinj__on(_1508722, _1508722, _1508732, _1508730), -(hAPP(hAPP(_1508728, _1508734), hAPP(c_Set_Oimage(_1508722, _1508722, _1508732), _1508730)) = hAPP(hAPP(_1508728, hAPP(c_Fun_Ocomp(_1508722, _1508720, _1508722, _1508734), _1508732)), _1508730))], (37795 ^ _779308) ^ [_1509009, _1509011, _1509013, _1509015, _1509017, _1509019] : [c_Finite__Set_Ofolding(_1509009, _1509011, _1509013, _1509015), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509009), _1509017)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509009), _1509019)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1509009, tc_HOL_Obool)), _1509017), _1509019) = c_Orderings_Obot__class_Obot(tc_fun(_1509009, tc_HOL_Obool)), -(hAPP(_1509015, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1509009, tc_HOL_Obool)), _1509017), _1509019)) = hAPP(c_Fun_Ocomp(_1509011, _1509011, _1509011, hAPP(_1509015, _1509017)), hAPP(_1509015, _1509019)))], (37813 ^ _779308) ^ [_1509382, _1509384, _1509386, _1509388, _1509390, _1509392, _1509394, _1509396, _1509398, _1509400, _1509402] : [c_Finite__Set_Ofolding(_1509382, _1509384, _1509386, _1509388), -(hAPP(c_Fun_Ocomp(_1509390, _1509392, _1509394, _1509396), hAPP(c_Fun_Ocomp(_1509398, _1509390, _1509394, _1509400), _1509402)) = hAPP(c_Fun_Ocomp(_1509398, _1509392, _1509394, hAPP(c_Fun_Ocomp(_1509390, _1509392, _1509398, _1509396), _1509400)), _1509402))], (37819 ^ _779308) ^ [_1509545, _1509547, _1509549, _1509551, _1509553, _1509555] : [c_Finite__Set_Ofolding(_1509545, _1509547, _1509549, _1509551), -(hAPP(c_Fun_Ocomp(_1509547, _1509547, _1509547, hAPP(_1509549, _1509553)), hAPP(_1509549, _1509555)) = hAPP(c_Fun_Ocomp(_1509547, _1509547, _1509547, hAPP(_1509549, _1509555)), hAPP(_1509549, _1509553)))], (37825 ^ _779308) ^ [_1509690, _1509692, _1509694, _1509696, _1509698, _1509700, _1509702, _1509704] : [c_Finite__Set_Ofolding(_1509690, _1509692, _1509694, _1509696), -(hAPP(c_Fun_Ocomp(_1509692, _1509692, _1509698, hAPP(_1509694, _1509700)), hAPP(c_Fun_Ocomp(_1509692, _1509692, _1509698, hAPP(_1509694, _1509702)), _1509704)) = hAPP(c_Fun_Ocomp(_1509692, _1509692, _1509698, hAPP(_1509694, _1509702)), hAPP(c_Fun_Ocomp(_1509692, _1509692, _1509698, hAPP(_1509694, _1509700)), _1509704)))], (37831 ^ _779308) ^ [_1509871, _1509873, _1509875, _1509877, _1509879, _1509881] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1509871, tc_fun(_1509873, tc_HOL_Obool)), _1509875), hAPP(c_Fun_Ocomp(_1509877, tc_fun(_1509873, tc_HOL_Obool), _1509871, _1509879), _1509881)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1509877, tc_fun(_1509873, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1509871, _1509877, _1509881), _1509875)), _1509879))], (37833 ^ _779308) ^ [_1509946, _1509948, _1509950, _1509952, _1509954, _1509956] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1509946, _1509948), _1509946, tc_prod(_1509950, _1509952), c_Product__Type_Ofst(_1509946, _1509948)), c_Product__Type_Omap__pair(_1509950, _1509946, _1509952, _1509948, _1509954, _1509956)) = hAPP(c_Fun_Ocomp(_1509950, _1509946, tc_prod(_1509950, _1509952), _1509954), c_Product__Type_Ofst(_1509950, _1509952)))], (37835 ^ _779308) ^ [_1510017, _1510019, _1510021, _1510023, _1510025, _1510027] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1510017, _1510019), _1510019, tc_prod(_1510021, _1510023), c_Product__Type_Osnd(_1510017, _1510019)), c_Product__Type_Omap__pair(_1510021, _1510017, _1510023, _1510019, _1510025, _1510027)) = hAPP(c_Fun_Ocomp(_1510023, _1510019, tc_prod(_1510021, _1510023), _1510027), c_Product__Type_Osnd(_1510021, _1510023)))], (37837 ^ _779308) ^ [_1510088, _1510090, _1510092, _1510094, _1510096, _1510098, _1510100, _1510102] : [c_Finite__Set_Ofolding__image(_1510088, _1510090, _1510092, _1510094, _1510096), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510090), _1510098)), -(hAPP(hAPP(_1510096, hAPP(hAPP(c_COMBS(_1510090, _1510088, _1510088), hAPP(hAPP(c_COMBB(_1510088, tc_fun(_1510088, _1510088), _1510090), _1510092), _1510100)), _1510102)), _1510098) = hAPP(hAPP(_1510092, hAPP(hAPP(_1510096, _1510100), _1510098)), hAPP(hAPP(_1510096, _1510102), _1510098)))], (37847 ^ _779308) ^ [_1510349, _1510351, _1510353, _1510355, _1510357, _1510359, _1510361] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1510349, _1510351, _1510353), hAPP(c_Fun_Ocomp(_1510355, tc_fun(_1510351, _1510353), _1510349, _1510357), _1510359)), _1510361) = hAPP(hAPP(_1510357, hAPP(_1510359, hAPP(c_Product__Type_Ofst(_1510349, _1510351), _1510361))), hAPP(c_Product__Type_Osnd(_1510349, _1510351), _1510361)))], (37849 ^ _779308) ^ [_1510426, _1510428, _1510430, _1510432, _1510434, _1510436] : [c_Finite__Set_Ofolding(_1510426, _1510428, _1510430, _1510432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510426), _1510434)), -(hAPP(c_Fun_Ocomp(_1510428, _1510428, _1510428, hAPP(_1510430, _1510436)), hAPP(_1510432, _1510434)) = hAPP(c_Fun_Ocomp(_1510428, _1510428, _1510428, hAPP(_1510432, _1510434)), hAPP(_1510430, _1510436)))], (37859 ^ _779308) ^ [_1510639, _1510641, _1510643, _1510645, _1510647, _1510649, _1510651, _1510653] : [c_Finite__Set_Ofolding(_1510639, _1510641, _1510643, _1510645), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510639), _1510647)), -(hAPP(c_Fun_Ocomp(_1510641, _1510641, _1510649, hAPP(_1510643, _1510651)), hAPP(c_Fun_Ocomp(_1510641, _1510641, _1510649, hAPP(_1510645, _1510647)), _1510653)) = hAPP(c_Fun_Ocomp(_1510641, _1510641, _1510649, hAPP(_1510645, _1510647)), hAPP(c_Fun_Ocomp(_1510641, _1510641, _1510649, hAPP(_1510643, _1510651)), _1510653)))], (37869 ^ _779308) ^ [_1510892, _1510894, _1510896, _1510898, _1510900, _1510902] : [c_Finite__Set_Ofolding(_1510892, _1510894, _1510896, _1510898), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510892), _1510900)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510892), _1510902)), -(hAPP(c_Fun_Ocomp(_1510894, _1510894, _1510894, hAPP(_1510898, _1510902)), hAPP(_1510898, _1510900)) = hAPP(c_Fun_Ocomp(_1510894, _1510894, _1510894, hAPP(_1510898, _1510900)), hAPP(_1510898, _1510902)))], (37883 ^ _779308) ^ [_1511173, _1511175, _1511177, _1511179, _1511181, _1511183, _1511185, _1511187] : [c_Finite__Set_Ofolding(_1511173, _1511175, _1511177, _1511179), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511173), _1511181)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511173), _1511183)), -(hAPP(c_Fun_Ocomp(_1511175, _1511175, _1511185, hAPP(_1511179, _1511183)), hAPP(c_Fun_Ocomp(_1511175, _1511175, _1511185, hAPP(_1511179, _1511181)), _1511187)) = hAPP(c_Fun_Ocomp(_1511175, _1511175, _1511185, hAPP(_1511179, _1511181)), hAPP(c_Fun_Ocomp(_1511175, _1511175, _1511185, hAPP(_1511179, _1511183)), _1511187)))], (37897 ^ _779308) ^ [_1511498, _1511500, _1511502, _1511504] : [c_Finite__Set_Ofolding(_1511498, _1511500, _1511502, _1511504), -(hAPP(_1511504, c_Orderings_Obot__class_Obot(tc_fun(_1511498, tc_HOL_Obool))) = c_Fun_Oid(_1511500))], (37903 ^ _779308) ^ [_1511603, _1511605, _1511607, _1511609, _1511611, _1511613, _1511615] : [c_Finite__Set_Ofolding__image(_1511603, _1511605, _1511607, _1511609, _1511611), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511605), _1511613)), -(hAPP(hAPP(_1511611, _1511615), _1511613) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1511603, _1511605, _1511607), _1511615), _1511609), _1511613))], (37913 ^ _779308) ^ [_1511804, _1511806, _1511808, _1511810, _1511812, _1511814] : [c_Finite__Set_Ofolding(_1511804, _1511806, _1511808, _1511810), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511804), _1511812)), -(hBOOL(hAPP(hAPP(c_member(_1511804), _1511814), _1511812))), -(hAPP(_1511810, hAPP(hAPP(c_Set_Oinsert(_1511804), _1511814), _1511812)) = hAPP(c_Fun_Ocomp(_1511806, _1511806, _1511806, hAPP(_1511810, _1511812)), hAPP(_1511808, _1511814)))], (37927 ^ _779308) ^ [_1512040, _1512042, _1512044, _1512046, _1512048, _1512050] : [c_Finite__Set_Ofolding(_1512040, _1512042, _1512044, _1512046), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512040), _1512048)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512040), _1512050)), -(hAPP(c_Fun_Ocomp(_1512042, _1512042, _1512042, hAPP(_1512046, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1512040, tc_HOL_Obool)), _1512048), _1512050))), hAPP(_1512046, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1512040, tc_HOL_Obool)), _1512048), _1512050))) = hAPP(c_Fun_Ocomp(_1512042, _1512042, _1512042, hAPP(_1512046, _1512048)), hAPP(_1512046, _1512050)))], (37941 ^ _779308) ^ [_1512365, _1512367, _1512369, _1512371, _1512373, _1512375] : [c_Finite__Set_Ofolding(_1512365, _1512367, _1512369, _1512371), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512365), _1512373)), -(hAPP(_1512371, hAPP(hAPP(c_Set_Oinsert(_1512365), _1512375), _1512373)) = hAPP(c_Fun_Ocomp(_1512367, _1512367, _1512367, hAPP(_1512371, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1512365, tc_HOL_Obool)), _1512373), hAPP(hAPP(c_Set_Oinsert(_1512365), _1512375), c_Orderings_Obot__class_Obot(tc_fun(_1512365, tc_HOL_Obool)))))), hAPP(_1512369, _1512375)))], (37951 ^ _779308) ^ [_1512620, _1512622, _1512624, _1512626, _1512628, _1512630] : [class_Groups_Ocomm__monoid__add(_1512620), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512622), _1512624)), 37961 ^ _779308 : [(37962 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512622), 37960 ^ [_1512620, _1512622, _1512624, _1512626, _1512628, _1512630]), _1512624)))], (37965 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512622), 37963 ^ [_1512620, _1512622, _1512624, _1512626, _1512628, _1512630]), _1512624)))], (37967 ^ _779308) ^ [] : [37960 ^ [_1512620, _1512622, _1512624, _1512626, _1512628, _1512630] = 37963 ^ [_1512620, _1512622, _1512624, _1512626, _1512628, _1512630]], (37969 ^ _779308) ^ [] : [-(hAPP(_1512626, 37960 ^ [_1512620, _1512622, _1512624, _1512626, _1512628, _1512630]) = hAPP(_1512626, 37963 ^ [_1512620, _1512622, _1512624, _1512626, _1512628, _1512630]))], (37971 ^ _779308) ^ [] : [hAPP(_1512628, hAPP(_1512626, 37960 ^ [_1512620, _1512622, _1512624, _1512626, _1512628, _1512630])) = c_Groups_Ozero__class_Ozero(_1512620)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512630, _1512620), _1512628), hAPP(c_Set_Oimage(_1512622, _1512630, _1512626), _1512624)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512622, _1512620), hAPP(c_Fun_Ocomp(_1512630, _1512620, _1512622, _1512628), _1512626)), _1512624))], (37975 ^ _779308) ^ [_1513357, _1513359, _1513361, _1513363, _1513365, _1513367] : [c_Finite__Set_Ofolding__idem(_1513357, _1513359, _1513361, _1513363), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513357), _1513365)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513357), _1513367)), -(hAPP(_1513363, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1513357, tc_HOL_Obool)), _1513365), _1513367)) = hAPP(c_Fun_Ocomp(_1513359, _1513359, _1513359, hAPP(_1513363, _1513365)), hAPP(_1513363, _1513367)))], (37989 ^ _779308) ^ [_1513638, _1513640, _1513642, _1513644, _1513646, _1513648] : [c_Finite__Set_Ofolding__idem(_1513638, _1513640, _1513642, _1513644), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513638), _1513646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1513638, tc_HOL_Obool)), _1513648), _1513646)), -(hAPP(c_Fun_Ocomp(_1513640, _1513640, _1513640, hAPP(_1513644, _1513646)), hAPP(_1513644, _1513648)) = hAPP(_1513644, _1513646))], (38003 ^ _779308) ^ [_1513909, _1513911, _1513913, _1513915, _1513917] : [c_Finite__Set_Ofolding__idem(_1513909, _1513911, _1513913, _1513915), -(hAPP(c_Fun_Ocomp(_1513911, _1513911, _1513911, hAPP(_1513913, _1513917)), hAPP(_1513913, _1513917)) = hAPP(_1513913, _1513917))], (38009 ^ _779308) ^ [_1514030, _1514032, _1514034, _1514036, _1514038, _1514040, _1514042] : [c_Finite__Set_Ofolding__idem(_1514030, _1514032, _1514034, _1514036), -(hAPP(c_Fun_Ocomp(_1514032, _1514032, _1514038, hAPP(_1514034, _1514040)), hAPP(c_Fun_Ocomp(_1514032, _1514032, _1514038, hAPP(_1514034, _1514040)), _1514042)) = hAPP(c_Fun_Ocomp(_1514032, _1514032, _1514038, hAPP(_1514034, _1514040)), _1514042))], (38015 ^ _779308) ^ [_1514187, _1514189, _1514191, _1514193, _1514195, _1514197] : [c_Finite__Set_Ofolding__idem(_1514187, _1514189, _1514191, _1514193), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514187), _1514195)), hBOOL(hAPP(hAPP(c_member(_1514187), _1514197), _1514195)), -(hAPP(c_Fun_Ocomp(_1514189, _1514189, _1514189, hAPP(_1514193, _1514195)), hAPP(_1514191, _1514197)) = hAPP(_1514193, _1514195))], (38029 ^ _779308) ^ [_1514452, _1514454, _1514456, _1514458, _1514460, _1514462] : [c_Finite__Set_Ofolding__idem(_1514452, _1514454, _1514456, _1514458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514452), _1514460)), -(hAPP(_1514458, hAPP(hAPP(c_Set_Oinsert(_1514452), _1514462), _1514460)) = hAPP(c_Fun_Ocomp(_1514454, _1514454, _1514454, hAPP(_1514458, _1514460)), hAPP(_1514456, _1514462)))], (38039 ^ _779308) ^ [_1514659, _1514661, _1514663, _1514665, _1514667, _1514669, _1514671, _1514673] : [class_Groups_Ocomm__monoid__mult(_1514659), c_Fun_Oinj__on(_1514661, _1514663, _1514665, _1514667), _1514669 = hAPP(c_Set_Oimage(_1514661, _1514663, _1514665), _1514667), 38053 ^ _779308 : [(38054 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514661), 38052 ^ [_1514659, _1514661, _1514663, _1514665, _1514667, _1514669, _1514671, _1514673]), _1514667)))], (38056 ^ _779308) ^ [] : [hAPP(_1514671, 38052 ^ [_1514659, _1514661, _1514663, _1514665, _1514667, _1514669, _1514671, _1514673]) = hAPP(hAPP(c_Fun_Ocomp(_1514663, _1514659, _1514661, _1514673), _1514665), 38052 ^ [_1514659, _1514661, _1514663, _1514665, _1514667, _1514669, _1514671, _1514673])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514663, _1514659), _1514673), _1514669) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1514661, _1514659), _1514671), _1514667))], (38060 ^ _779308) ^ [_1515167, _1515169, _1515171] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1515167, _1515169) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1515171, _1515169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1515171), _1515167)), -(_1515167 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1515171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1515169), 38067 ^ [_1515167, _1515169, _1515171])))], (38071 ^ _779308) ^ [_1515364, _1515366] : [38073 ^ _779308 : [(38074 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515364, tc_HOL_Obool)), 38072 ^ [_1515364, _1515366]), hAPP(c_Relation_OImage(_1515364, _1515364, _1515366), 38072 ^ [_1515364, _1515366]))))], (38076 ^ _779308) ^ [] : [38072 ^ [_1515364, _1515366] = c_Orderings_Obot__class_Obot(tc_fun(_1515364, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1515364, _1515366))], (38080 ^ _779308) ^ [_1515561, _1515563, _1515565, _1515567, _1515569, _1515571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515561, tc_HOL_Obool)), _1515563), _1515565)), 38086 ^ _779308 : [(38087 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515561), 38085 ^ [_1515561, _1515563, _1515565, _1515567, _1515569, _1515571]), _1515563)))], (38089 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515567, tc_HOL_Obool)), hAPP(_1515569, 38085 ^ [_1515561, _1515563, _1515565, _1515567, _1515569, _1515571])), hAPP(_1515571, 38085 ^ [_1515561, _1515563, _1515565, _1515567, _1515569, _1515571])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1515561, _1515567), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1515561, _1515567), _1515563), _1515569)), hAPP(hAPP(c_Product__Type_OSigma(_1515561, _1515567), _1515565), _1515571))))], (38093 ^ _779308) ^ [_1515951, _1515953, _1515955] : [-(hBOOL(hAPP(hAPP(c_member(_1515951), _1515953), c_Wellfounded_Oacc(_1515951, _1515955)))), 38097 ^ _779308 : [(38098 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515951, _1515951)), hAPP(hAPP(c_Product__Type_OPair(_1515951, _1515951), 38096 ^ [_1515951, _1515953, _1515955]), _1515953)), _1515955)))], (38100 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1515951), 38096 ^ [_1515951, _1515953, _1515955]), c_Wellfounded_Oacc(_1515951, _1515955)))]]], (38102 ^ _779308) ^ [_1516178, _1516180, _1516182] : [38104 ^ _779308 : [(38105 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516178, _1516178)), hAPP(hAPP(c_Product__Type_OPair(_1516178, _1516178), 38103 ^ [_1516178, _1516180, _1516182]), _1516180)), _1516182)))], (38107 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1516178), 38103 ^ [_1516178, _1516180, _1516182]), c_Wellfounded_Oacc(_1516178, _1516182)))]], -(hBOOL(hAPP(hAPP(c_member(_1516178), _1516180), c_Wellfounded_Oacc(_1516178, _1516182))))], (38111 ^ _779308) ^ [_1516437, _1516439, _1516441, _1516443] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1516437, tc_HOL_Obool), tc_fun(_1516437, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1516437, tc_HOL_Obool), tc_fun(_1516437, tc_HOL_Obool)), _1516439), _1516441)), c_Wellfounded_Omax__ext(_1516437, _1516443))), 38114 ^ _779308 : [(38115 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1516437), _1516439)))], (38117 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1516437), _1516441)))], (38119 ^ _779308) ^ [] : [_1516441 = c_Orderings_Obot__class_Obot(tc_fun(_1516437, tc_HOL_Obool))], (38121 ^ _779308) ^ [_1516731] : [hBOOL(hAPP(hAPP(c_member(_1516437), _1516731), _1516439)), 38125 ^ _779308 : [(38126 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1516437), 38124 ^ [_1516437, _1516439, _1516441, _1516443, _1516731]), _1516441)))], (38128 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516437, _1516437)), hAPP(hAPP(c_Product__Type_OPair(_1516437, _1516437), _1516731), 38124 ^ [_1516437, _1516439, _1516441, _1516443, _1516731])), _1516443)))]]]]], (38130 ^ _779308) ^ [_1516943, _1516945, _1516947, _1516949] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1516943, tc_HOL_Obool), tc_fun(_1516943, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1516943, tc_HOL_Obool), tc_fun(_1516943, tc_HOL_Obool)), _1516945), _1516947)), c_Wellfounded_Omax__ext(_1516943, _1516949)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516943), _1516945)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1516943), _1516947)), -(_1516947 = c_Orderings_Obot__class_Obot(tc_fun(_1516943, tc_HOL_Obool))), 38144 ^ _779308 : [(38145 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1516943), 38143 ^ [_1516943, _1516945, _1516947, _1516949]), _1516945)))], (38147 ^ _779308) ^ [_1517348] : [hBOOL(hAPP(hAPP(c_member(_1516943), _1517348), _1516947)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1516943, _1516943)), hAPP(hAPP(c_Product__Type_OPair(_1516943, _1516943), 38143 ^ [_1516943, _1516945, _1516947, _1516949]), _1517348)), _1516949))]]], (38155 ^ _779308) ^ [_1517576, _1517578, _1517580] : [38157 ^ _779308 : [(38158 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 38156 ^ [_1517576, _1517578, _1517580]), _1517576)))], (38160 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1517578, 38156 ^ [_1517576, _1517578, _1517580])))], (38162 ^ _779308) ^ [] : [hBOOL(hAPP(_1517578, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 38156 ^ [_1517576, _1517578, _1517580]), _1517576)))]], hBOOL(hAPP(_1517578, _1517580)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1517580), _1517576)), -(hBOOL(hAPP(_1517578, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38174 ^ _779308) ^ [_1517938, _1517940, _1517942, _1517944, _1517946, _1517948] : [class_Groups_Oab__semigroup__mult(_1517938), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517940), _1517942)), 38184 ^ _779308 : [(38185 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1517940), 38183 ^ [_1517938, _1517940, _1517942, _1517944, _1517946, _1517948]), _1517942)))], (38187 ^ _779308) ^ [] : [hAPP(_1517944, 38183 ^ [_1517938, _1517940, _1517942, _1517944, _1517946, _1517948]) = hAPP(_1517946, 38183 ^ [_1517938, _1517940, _1517942, _1517944, _1517946, _1517948])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1517938, _1517940, c_Groups_Otimes__class_Otimes(_1517938)), _1517944), _1517948), _1517942) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1517938, _1517940, c_Groups_Otimes__class_Otimes(_1517938)), _1517946), _1517948), _1517942))], (38191 ^ _779308) ^ [_1518343, _1518345, _1518347] : [class_Orderings_Olinorder(_1518343), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518343), _1518345)), 38201 ^ _779308 : [(38202 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1518343), 38200 ^ [_1518343, _1518345, _1518347]), _1518345)))], (38204 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1518343), 38200 ^ [_1518343, _1518345, _1518347]), _1518347))]], hBOOL(hAPP(hAPP(c_member(_1518343), _1518347), _1518345)), -(c_Big__Operators_Olinorder__class_OMax(_1518343, _1518345) = _1518347)], (38212 ^ _779308) ^ [_1518715, _1518717, _1518719] : [class_Orderings_Olinorder(_1518715), hBOOL(hAPP(c_Finite__Set_Ofinite(_1518715), _1518717)), 38222 ^ _779308 : [(38223 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1518715), 38221 ^ [_1518715, _1518717, _1518719]), _1518717)))], (38225 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1518715), _1518719), 38221 ^ [_1518715, _1518717, _1518719]))]], hBOOL(hAPP(hAPP(c_member(_1518715), _1518719), _1518717)), -(c_Big__Operators_Olinorder__class_OMin(_1518715, _1518717) = _1518719)], (38233 ^ _779308) ^ [_1519087, _1519089, _1519091] : [c_Wellfounded_Owf(_1519087, _1519089), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519087, _1519087)), hAPP(hAPP(c_Product__Type_OPair(_1519087, _1519087), hAPP(_1519091, hAPP(c_Nat_OSuc, 38236 ^ [_1519087, _1519089, _1519091]))), hAPP(_1519091, 38236 ^ [_1519087, _1519089, _1519091]))), _1519089))], (38240 ^ _779308) ^ [_1519288, _1519290, _1519292, _1519294, _1519296, _1519298, _1519300, _1519302] : [class_Groups_Ocomm__monoid__add(_1519288), c_Fun_Oinj__on(_1519290, _1519292, _1519294, _1519296), _1519298 = hAPP(c_Set_Oimage(_1519290, _1519292, _1519294), _1519296), 38254 ^ _779308 : [(38255 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519290), 38253 ^ [_1519288, _1519290, _1519292, _1519294, _1519296, _1519298, _1519300, _1519302]), _1519296)))], (38257 ^ _779308) ^ [] : [hAPP(_1519300, 38253 ^ [_1519288, _1519290, _1519292, _1519294, _1519296, _1519298, _1519300, _1519302]) = hAPP(_1519302, hAPP(_1519294, 38253 ^ [_1519288, _1519290, _1519292, _1519294, _1519296, _1519298, _1519300, _1519302]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1519292, _1519288), _1519302), _1519298) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1519290, _1519288), _1519300), _1519296))], (38261 ^ _779308) ^ [_1519780, _1519782, _1519784, _1519786, _1519788, _1519790, _1519792] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1519780, _1519782, _1519784, _1519786), _1519788), _1519790), _1519792) = hAPP(hAPP(_1519790, hAPP(c_Product__Type_Ofst(_1519782, _1519784), hAPP(_1519788, _1519792))), hAPP(c_Product__Type_Osnd(_1519782, _1519784), hAPP(_1519788, _1519792))))], (38263 ^ _779308) ^ [_1519853, _1519855, _1519857, _1519859, _1519861, _1519863, _1519865, _1519867] : [class_Groups_Ocomm__monoid__add(_1519853), class_Orderings_Oord(_1519855), _1519857 = _1519859, _1519861 = _1519863, 38281 ^ _779308 : [(38282 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1519855), _1519859), 38280 ^ [_1519853, _1519855, _1519857, _1519859, _1519861, _1519863, _1519865, _1519867])))], (38284 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1519855), 38280 ^ [_1519853, _1519855, _1519857, _1519859, _1519861, _1519863, _1519865, _1519867]), _1519863)))], (38286 ^ _779308) ^ [] : [hAPP(_1519865, 38280 ^ [_1519853, _1519855, _1519857, _1519859, _1519861, _1519863, _1519865, _1519867]) = hAPP(_1519867, 38280 ^ [_1519853, _1519855, _1519857, _1519859, _1519861, _1519863, _1519865, _1519867])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1519855, _1519853), _1519865), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1519855, _1519857), _1519861)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1519855, _1519853), _1519867), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1519855, _1519859), _1519863)))], (38290 ^ _779308) ^ [_1520482, _1520484, _1520486, _1520488, _1520490] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1520482, _1520484, _1520482, _1520486), hAPP(c_Product__Type_OPair(_1520484, _1520482), _1520488)), _1520490) = hAPP(_1520490, _1520488))], (38292 ^ _779308) ^ [_1520533, _1520535, _1520537, _1520539] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1520533, _1520535, _1520537, tc_prod(_1520535, _1520537)), _1520539), c_Product__Type_OPair(_1520535, _1520537)) = _1520539)], (38294 ^ _779308) ^ [_1520579, _1520581, _1520583, _1520585, _1520587, _1520589, _1520591, _1520593, _1520595] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1520579, _1520581, _1520583, _1520585), hAPP(hAPP(c_Product__Type_Oscomp(_1520579, _1520587, _1520589, tc_prod(_1520581, _1520583)), _1520591), _1520593)), _1520595) = hAPP(hAPP(c_Product__Type_Oscomp(_1520579, _1520587, _1520589, _1520585), _1520591), hAPP(hAPP(c_COMBC(_1520587, tc_fun(_1520581, tc_fun(_1520583, _1520585)), tc_fun(_1520589, _1520585)), hAPP(hAPP(c_COMBB(tc_fun(_1520589, tc_prod(_1520581, _1520583)), tc_fun(tc_fun(_1520581, tc_fun(_1520583, _1520585)), tc_fun(_1520589, _1520585)), _1520587), c_Product__Type_Oscomp(_1520589, _1520581, _1520583, _1520585)), _1520593)), _1520595)))], (38296 ^ _779308) ^ [_1520706, _1520708, _1520710, _1520712, _1520714, _1520716, _1520718] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1520706, _1520708, _1520710, _1520712), _1520714), _1520716), _1520718) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1520708, _1520710, _1520712), _1520716), hAPP(_1520714, _1520718)))], (38298 ^ _779308) ^ [_1520768, _1520770, _1520772, _1520774, _1520776, _1520778, _1520780] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1520768, _1520770, _1520772, _1520774), _1520776), _1520778), _1520780) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1520770, _1520772, _1520774), _1520778), hAPP(_1520776, _1520780)))], (38300 ^ _779308) ^ [_1520848, _1520850, _1520852, _1520854, _1520856] : [_1520848 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1520850, _1520852, _1520848, _1520854), _1520856) = hAPP(c_Product__Type_OPair(_1520850, _1520852), _1520856))], (38306 ^ _779308) ^ [_1520953, _1520955, _1520957, _1520959, _1520961] : [-(_1520953 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1520955, _1520957, _1520953, _1520959), _1520961) = hAPP(hAPP(c_Product__Type_Oscomp(_1520957, _1520955, _1520957, tc_prod(_1520955, _1520957)), hAPP(_1520959, _1520961)), c_Random_Oiterate(_1520955, _1520957, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1520953), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1520959)))], (38312 ^ _779308) ^ [_1521048, _1521050] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1521048), _1521050)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521048), _1521050)))], (38318 ^ _779308) ^ [_1521153, _1521155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521153), _1521155)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1521153), _1521155)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (38324 ^ _779308) ^ [_1521264, _1521266, _1521268, _1521270] : [38326 ^ _779308 : [(38327 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1521264), 38325 ^ [_1521264, _1521266, _1521268, _1521270])))], (38329 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 38325 ^ [_1521264, _1521266, _1521268, _1521270]), _1521266)))], (38331 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(_1521268, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 38325 ^ [_1521264, _1521266, _1521268, _1521270]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1521268, 38325 ^ [_1521264, _1521266, _1521268, _1521270])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521264), _1521266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1521268, _1521264)), _1521270)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1521270), hAPP(_1521268, _1521266))), 38345 ^ _779308 : [(38346 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1521264), 38344 ^ [_1521264, _1521266, _1521268, _1521270])))], (38348 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 38344 ^ [_1521264, _1521266, _1521268, _1521270]), _1521266)))], (38350 ^ _779308) ^ [] : [-(hAPP(_1521268, 38344 ^ [_1521264, _1521266, _1521268, _1521270]) = _1521270)]]], (38352 ^ _779308) ^ [_1521890, _1521892] : [c_Wellfounded_Owf(_1521890, _1521892), -(c_Wellfounded_Owf(_1521890, c_Transitive__Closure_Otrancl(_1521890, _1521892)))], (38358 ^ _779308) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (38360 ^ _779308) ^ [_1522006, _1522008] : [c_Wellfounded_Oacyclic(_1522006, _1522008), 38363 ^ _779308 : [(38364 ^ _779308) ^ [_1522091] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1522006, _1522006)), hAPP(hAPP(c_Product__Type_OPair(_1522006, _1522006), _1522091), _1522091)), c_Transitive__Closure_Otrancl(_1522006, _1522008)))]]], (38366 ^ _779308) ^ [_1522134, _1522136] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1522134, _1522134)), hAPP(hAPP(c_Product__Type_OPair(_1522134, _1522134), 38367 ^ [_1522134, _1522136]), 38367 ^ [_1522134, _1522136])), c_Transitive__Closure_Otrancl(_1522134, _1522136)))), -(c_Wellfounded_Oacyclic(_1522134, _1522136))], (38373 ^ _779308) ^ [_1522208, _1522210, _1522212, _1522214] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1522208, _1522208)), hAPP(hAPP(c_Product__Type_OPair(_1522208, _1522208), _1522210), _1522212)), _1522214)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1522208, _1522208)), hAPP(hAPP(c_Product__Type_OPair(_1522208, _1522208), _1522210), _1522212)), c_Transitive__Closure_Otrancl(_1522208, _1522214))))], (38379 ^ _779308) ^ [_1522371, _1522373] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522371, _1522371), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1522371, _1522373)), hAPP(hAPP(c_Product__Type_OSigma(_1522371, _1522371), hAPP(c_Relation_OField(_1522371), _1522373)), hAPP(c_COMBK(tc_fun(_1522371, tc_HOL_Obool), _1522371), hAPP(c_Relation_OField(_1522371), _1522373))))))], (38381 ^ _779308) ^ [_1522440, _1522442, _1522444] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522440, _1522440), tc_HOL_Obool)), _1522442), _1522444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522440, _1522440), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1522440, _1522440, _1522440), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1522440, _1522440), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1522440, _1522442)), _1522444)), _1522442)), _1522444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522440, _1522440), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1522440, _1522442)), _1522444)))], (38391 ^ _779308) ^ [_1522711, _1522713, _1522715] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1522711, _1522711)), _1522713), _1522715)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1522711, _1522711)), _1522713), c_Transitive__Closure_Otrancl(_1522711, _1522715))))], (38397 ^ _779308) ^ [_1522836] : [-(c_Transitive__Closure_Otrancl(_1522836, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1522836, _1522836), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1522836, _1522836), tc_HOL_Obool)))], (38399 ^ _779308) ^ [_1522878, _1522880] : [-(hAPP(c_Relation_ODomain(_1522878, _1522878), c_Transitive__Closure_Otrancl(_1522878, _1522880)) = hAPP(c_Relation_ODomain(_1522878, _1522878), _1522880))], (38401 ^ _779308) ^ [_1522918, _1522920] : [-(hAPP(c_Relation_ORange(_1522918, _1522918), c_Transitive__Closure_Otrancl(_1522918, _1522920)) = hAPP(c_Relation_ORange(_1522918, _1522918), _1522920))], (38403 ^ _779308) ^ [_1522973, _1522975] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1522973, _1522973)), c_Transitive__Closure_Otrancl(_1522973, _1522975))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1522973, _1522973)), _1522975)))], (38409 ^ _779308) ^ [_1523080, _1523082] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1523080, _1523080)), _1523082)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1523080, _1523080)), c_Transitive__Closure_Otrancl(_1523080, _1523082))))], (38415 ^ _779308) ^ [_1523193, _1523195, _1523197, _1523199, _1523201] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523193, _1523193)), hAPP(hAPP(c_Product__Type_OPair(_1523193, _1523193), _1523195), _1523197)), _1523199)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1523193, _1523193)), hAPP(hAPP(c_Product__Type_OPair(_1523193, _1523193), _1523197), _1523201)), _1523199)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523193, _1523193)), hAPP(hAPP(c_Product__Type_OPair(_1523193, _1523193), _1523195), _1523201)), c_Transitive__Closure_Otrancl(_1523193, _1523199))))], (38425 ^ _779308) ^ [_1523454, _1523456, _1523458, _1523460, _1523462] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523454, _1523454)), hAPP(hAPP(c_Product__Type_OPair(_1523454, _1523454), _1523456), _1523458)), _1523460)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1523454, _1523454)), hAPP(hAPP(c_Product__Type_OPair(_1523454, _1523454), _1523458), _1523462)), c_Transitive__Closure_Otrancl(_1523454, _1523460))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523454, _1523454)), hAPP(hAPP(c_Product__Type_OPair(_1523454, _1523454), _1523456), _1523462)), c_Transitive__Closure_Otrancl(_1523454, _1523460))))], (38435 ^ _779308) ^ [_1523721, _1523723, _1523725, _1523727, _1523729] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523721, _1523721)), hAPP(hAPP(c_Product__Type_OPair(_1523721, _1523721), _1523723), _1523725)), c_Transitive__Closure_Otrancl(_1523721, _1523727))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1523721, _1523721)), hAPP(hAPP(c_Product__Type_OPair(_1523721, _1523721), _1523725), _1523729)), _1523727)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523721, _1523721)), hAPP(hAPP(c_Product__Type_OPair(_1523721, _1523721), _1523723), _1523729)), c_Transitive__Closure_Otrancl(_1523721, _1523727))))], (38445 ^ _779308) ^ [_1523988, _1523990, _1523992, _1523994, _1523996] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523988, _1523988)), hAPP(hAPP(c_Product__Type_OPair(_1523988, _1523988), _1523990), _1523992)), c_Transitive__Closure_Otrancl(_1523988, _1523994))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1523988, _1523988)), hAPP(hAPP(c_Product__Type_OPair(_1523988, _1523988), _1523992), _1523996)), c_Transitive__Closure_Otrancl(_1523988, _1523994))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523988, _1523988)), hAPP(hAPP(c_Product__Type_OPair(_1523988, _1523988), _1523990), _1523996)), c_Transitive__Closure_Otrancl(_1523988, _1523994))))], (38455 ^ _779308) ^ [_1524261, _1524263, _1524265, _1524267] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524261, _1524261)), _1524263), c_Transitive__Closure_Otrancl(_1524261, _1524265))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524261, _1524261), tc_HOL_Obool)), _1524265), _1524267)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524261, _1524261)), _1524263), c_Transitive__Closure_Otrancl(_1524261, _1524267))))], (38465 ^ _779308) ^ [_1524476, _1524478] : [-(c_Transitive__Closure_Otrancl(_1524476, _1524478) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1524476, _1524476), tc_HOL_Obool)), _1524478), hAPP(hAPP(c_Relation_Orel__comp(_1524476, _1524476, _1524476), c_Transitive__Closure_Otrancl(_1524476, _1524478)), _1524478)))], (38467 ^ _779308) ^ [_1524531, _1524533, _1524535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524531, _1524531), tc_HOL_Obool)), _1524533), hAPP(hAPP(c_Product__Type_OSigma(_1524531, _1524531), _1524535), hAPP(c_COMBK(tc_fun(_1524531, tc_HOL_Obool), _1524531), _1524535)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524531, _1524531), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1524531, _1524533)), hAPP(hAPP(c_Product__Type_OSigma(_1524531, _1524531), _1524535), hAPP(c_COMBK(tc_fun(_1524531, tc_HOL_Obool), _1524531), _1524535)))))], (38473 ^ _779308) ^ [_1524749, _1524751] : [38474 ^ _779308 : [(38475 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1524749), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (38477 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1524751), _1524749))]], -(c_Random_Olog(_1524749, _1524751) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (38481 ^ _779308) ^ [_1524884, _1524886] : [-(c_Random_Olog(_1524884, _1524886) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), c_Random_Olog(_1524884, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1524886), _1524884)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1524884), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1524886), _1524884)))], (38491 ^ _779308) ^ [_1524966, _1524968, _1524970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1524966), _1524968)), -(c_Random_Ominus__shift(_1524970, _1524966, _1524968) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1524970), _1524966)), _1524968))], (38497 ^ _779308) ^ [_1525081, _1525083, _1525085] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1525081), _1525083))), -(c_Random_Ominus__shift(_1525085, _1525081, _1525083) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1525081), _1525083))], (38503 ^ _779308) ^ [_1525145, _1525147] : [_1525145 = _1525147, -(c_Random_Oinc__shift(_1525145, _1525147) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (38509 ^ _779308) ^ [_1525222, _1525224] : [-(_1525222 = _1525224), -(c_Random_Oinc__shift(_1525222, _1525224) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1525224), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (38515 ^ _779308) ^ [_1525269, _1525271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1525269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Orange(_1525269), _1525271))), _1525269)))], (38521 ^ _779308) ^ [_1525376, _1525378, _1525380, _1525382] : [-(c_Transitive__Closure_Otrancl(_1525376, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1525376, _1525376)), hAPP(hAPP(c_Product__Type_OPair(_1525376, _1525376), _1525378), _1525380)), _1525382)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1525376, _1525376), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1525376, _1525382)), hAPP(c_Set_OCollect(tc_prod(_1525376, _1525376)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525376, _1525376, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1525376, tc_fun(_1525376, tc_HOL_Obool), tc_fun(_1525376, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1525376, tc_HOL_Obool), tc_fun(_1525376, tc_HOL_Obool)), _1525376), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1525376)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525376), c_fconj), hAPP(hAPP(c_COMBC(_1525376, tc_fun(tc_prod(_1525376, _1525376), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1525376, _1525376), tc_fun(tc_fun(tc_prod(_1525376, _1525376), tc_HOL_Obool), tc_HOL_Obool), _1525376), c_member(tc_prod(_1525376, _1525376))), hAPP(hAPP(c_COMBC(_1525376, _1525376, tc_prod(_1525376, _1525376)), c_Product__Type_OPair(_1525376, _1525376)), _1525378))), c_Transitive__Closure_Ortrancl(_1525376, _1525382))))), hAPP(hAPP(c_COMBC(_1525376, tc_fun(tc_prod(_1525376, _1525376), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1525376, _1525376), tc_fun(tc_fun(tc_prod(_1525376, _1525376), tc_HOL_Obool), tc_HOL_Obool), _1525376), c_member(tc_prod(_1525376, _1525376))), hAPP(c_Product__Type_OPair(_1525376, _1525376), _1525380))), c_Transitive__Closure_Ortrancl(_1525376, _1525382)))))))], (38523 ^ _779308) ^ [_1525644, _1525646, _1525648, _1525650] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525644, tc_fun(_1525644, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1525644, tc_fun(tc_prod(_1525644, _1525644), tc_HOL_Obool), tc_fun(_1525644, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525644, tc_fun(tc_fun(tc_prod(_1525644, _1525644), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525644, _1525644), tc_HOL_Obool), tc_fun(_1525644, tc_HOL_Obool)), _1525644), c_COMBC(_1525644, tc_fun(tc_prod(_1525644, _1525644), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525644, tc_prod(_1525644, _1525644)), tc_fun(_1525644, tc_fun(tc_fun(tc_prod(_1525644, _1525644), tc_HOL_Obool), tc_HOL_Obool)), _1525644), hAPP(c_COMBB(tc_prod(_1525644, _1525644), tc_fun(tc_fun(tc_prod(_1525644, _1525644), tc_HOL_Obool), tc_HOL_Obool), _1525644), c_member(tc_prod(_1525644, _1525644)))), c_Product__Type_OPair(_1525644, _1525644)))), _1525646)), c_fequal), _1525648), _1525650)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1525644, _1525644)), hAPP(hAPP(c_Product__Type_OPair(_1525644, _1525644), _1525648), _1525650)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1525644, _1525644), tc_HOL_Obool)), _1525646), c_Relation_OId(_1525644)))))], (38529 ^ _779308) ^ [_1526065, _1526067, _1526069, _1526071] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526065, _1526065)), hAPP(hAPP(c_Product__Type_OPair(_1526065, _1526065), _1526069), _1526071)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1526065, _1526065), tc_HOL_Obool)), _1526067), c_Relation_OId(_1526065)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1526065, tc_fun(_1526065, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1526065, tc_fun(tc_prod(_1526065, _1526065), tc_HOL_Obool), tc_fun(_1526065, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526065, tc_fun(tc_fun(tc_prod(_1526065, _1526065), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526065, _1526065), tc_HOL_Obool), tc_fun(_1526065, tc_HOL_Obool)), _1526065), c_COMBC(_1526065, tc_fun(tc_prod(_1526065, _1526065), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526065, tc_prod(_1526065, _1526065)), tc_fun(_1526065, tc_fun(tc_fun(tc_prod(_1526065, _1526065), tc_HOL_Obool), tc_HOL_Obool)), _1526065), hAPP(c_COMBB(tc_prod(_1526065, _1526065), tc_fun(tc_fun(tc_prod(_1526065, _1526065), tc_HOL_Obool), tc_HOL_Obool), _1526065), c_member(tc_prod(_1526065, _1526065)))), c_Product__Type_OPair(_1526065, _1526065)))), _1526067)), c_fequal), _1526069), _1526071)))], (38535 ^ _779308) ^ [_1526492, _1526494, _1526496] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526492, _1526492)), _1526494), _1526496)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526492, _1526492)), _1526494), c_Transitive__Closure_Ortrancl(_1526492, _1526496))))], (38541 ^ _779308) ^ [_1526617, _1526619, _1526621] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526617, _1526617)), hAPP(hAPP(c_Product__Type_OPair(_1526617, _1526617), _1526619), _1526619)), c_Transitive__Closure_Ortrancl(_1526617, _1526621))))], (38543 ^ _779308) ^ [_1526666, _1526668] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526666, _1526666)), hAPP(hAPP(c_Product__Type_OPair(_1526666, _1526666), _1526668), _1526668)), c_Relation_OId(_1526666))))], (38545 ^ _779308) ^ [_1526712, _1526714, _1526716, _1526718] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526712, _1526712)), hAPP(hAPP(c_Product__Type_OPair(_1526712, _1526712), _1526714), _1526716)), c_Transitive__Closure_Otrancl(_1526712, _1526718))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526712, _1526712)), hAPP(hAPP(c_Product__Type_OPair(_1526712, _1526712), _1526714), _1526716)), c_Transitive__Closure_Ortrancl(_1526712, _1526718))))], (38551 ^ _779308) ^ [_1526881, _1526883, _1526885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526881, _1526881), tc_HOL_Obool)), c_Relation_OId(_1526881)), _1526883)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526881, _1526881), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1526881, _1526881, _1526881), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1526881, _1526881), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1526881, _1526885)), _1526883)), _1526885)), _1526883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526881, _1526881), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1526881, _1526885)), _1526883)))], (38561 ^ _779308) ^ [_1527156, _1527158, _1527160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1527156, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1527156, _1527156, _1527158), _1527160)), _1527160)), -(hAPP(c_Relation_OImage(_1527156, _1527156, c_Transitive__Closure_Ortrancl(_1527156, _1527158)), _1527160) = _1527160)], (38567 ^ _779308) ^ [_1527289, _1527291, _1527293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527289, _1527289), tc_HOL_Obool)), _1527291), _1527293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527289, _1527289), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1527289, _1527291)), c_Transitive__Closure_Ortrancl(_1527289, _1527293))))], (38573 ^ _779308) ^ [_1527432, _1527434, _1527436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527432, _1527432), tc_HOL_Obool)), _1527434), _1527436)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527432, _1527432), tc_HOL_Obool)), _1527436), c_Transitive__Closure_Ortrancl(_1527432, _1527434))), -(c_Transitive__Closure_Ortrancl(_1527432, _1527436) = c_Transitive__Closure_Ortrancl(_1527432, _1527434))], (38583 ^ _779308) ^ [_1527635, _1527637, _1527639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527635, _1527635), tc_HOL_Obool)), _1527637), c_Transitive__Closure_Ortrancl(_1527635, _1527639))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527635, _1527635), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1527635, _1527637)), c_Transitive__Closure_Ortrancl(_1527635, _1527639))))], (38589 ^ _779308) ^ [_1527784, _1527786, _1527788] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527784, _1527786, _1527786), _1527788), c_Relation_OId(_1527786)) = _1527788)], (38591 ^ _779308) ^ [_1527823, _1527825, _1527827] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1527823, _1527823, _1527825), c_Relation_OId(_1527823)), _1527827) = _1527827)], (38593 ^ _779308) ^ [_1527862, _1527864] : [-(hAPP(c_Relation_OImage(_1527862, _1527862, c_Relation_OId(_1527862)), _1527864) = _1527864)], (38595 ^ _779308) ^ [_1527896, _1527898, _1527900, _1527902, _1527904] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1527896, _1527896)), hAPP(hAPP(c_Product__Type_OPair(_1527896, _1527896), _1527898), _1527900)), c_Transitive__Closure_Ortrancl(_1527896, _1527902))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1527896, _1527896)), hAPP(hAPP(c_Product__Type_OPair(_1527896, _1527896), _1527900), _1527904)), c_Transitive__Closure_Ortrancl(_1527896, _1527902))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1527896, _1527896)), hAPP(hAPP(c_Product__Type_OPair(_1527896, _1527896), _1527898), _1527904)), c_Transitive__Closure_Ortrancl(_1527896, _1527902))))], (38605 ^ _779308) ^ [_1528169, _1528171, _1528173, _1528175, _1528177] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528169, _1528169)), hAPP(hAPP(c_Product__Type_OPair(_1528169, _1528169), _1528171), _1528173)), c_Transitive__Closure_Ortrancl(_1528169, _1528175))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528169, _1528169)), hAPP(hAPP(c_Product__Type_OPair(_1528169, _1528169), _1528173), _1528177)), _1528175)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1528169, _1528169)), hAPP(hAPP(c_Product__Type_OPair(_1528169, _1528169), _1528171), _1528177)), c_Transitive__Closure_Ortrancl(_1528169, _1528175))))], (38615 ^ _779308) ^ [_1528436, _1528438, _1528440, _1528442, _1528444] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1528436, _1528436)), hAPP(hAPP(c_Product__Type_OPair(_1528436, _1528436), _1528438), _1528440)), _1528442)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528436, _1528436)), hAPP(hAPP(c_Product__Type_OPair(_1528436, _1528436), _1528440), _1528444)), c_Transitive__Closure_Ortrancl(_1528436, _1528442))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1528436, _1528436)), hAPP(hAPP(c_Product__Type_OPair(_1528436, _1528436), _1528438), _1528444)), c_Transitive__Closure_Ortrancl(_1528436, _1528442))))], (38625 ^ _779308) ^ [_1528703, _1528705] : [-(c_Transitive__Closure_Ortrancl(_1528703, c_Transitive__Closure_Ortrancl(_1528703, _1528705)) = c_Transitive__Closure_Ortrancl(_1528703, _1528705))], (38627 ^ _779308) ^ [_1528737, _1528739] : [-(c_Transitive__Closure_Ortrancl(_1528737, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1528737, _1528737), tc_HOL_Obool)), _1528739), c_Relation_OId(_1528737))) = c_Transitive__Closure_Ortrancl(_1528737, _1528739))], (38629 ^ _779308) ^ [_1528784, _1528786] : [-(c_Transitive__Closure_Ortrancl(_1528784, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528784, _1528784), tc_HOL_Obool)), _1528786), c_Relation_OId(_1528784))) = c_Transitive__Closure_Ortrancl(_1528784, _1528786))], (38631 ^ _779308) ^ [_1528831, _1528833, _1528835] : [-(c_Transitive__Closure_Ortrancl(_1528831, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528831, _1528831), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1528831, _1528833)), c_Transitive__Closure_Ortrancl(_1528831, _1528835))) = c_Transitive__Closure_Ortrancl(_1528831, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528831, _1528831), tc_HOL_Obool)), _1528833), _1528835)))], (38633 ^ _779308) ^ [_1528898, _1528900] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528898, _1528898), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1528898, _1528900)), c_Relation_OId(_1528898)) = c_Transitive__Closure_Ortrancl(_1528898, _1528900))], (38635 ^ _779308) ^ [_1528945, _1528947] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1528945, _1528945, _1528945), c_Transitive__Closure_Ortrancl(_1528945, _1528947)), c_Transitive__Closure_Ortrancl(_1528945, _1528947)) = c_Transitive__Closure_Ortrancl(_1528945, _1528947))], (38637 ^ _779308) ^ [_1528989, _1528991] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1528989, _1528989, _1528989), _1528991), c_Transitive__Closure_Ortrancl(_1528989, _1528991)) = hAPP(hAPP(c_Relation_Orel__comp(_1528989, _1528989, _1528989), c_Transitive__Closure_Ortrancl(_1528989, _1528991)), _1528991))], (38639 ^ _779308) ^ [_1529040, _1529042] : [-(c_Transitive__Closure_Ortrancl(_1529040, _1529042) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529040, _1529040), tc_HOL_Obool)), c_Relation_OId(_1529040)), hAPP(hAPP(c_Relation_Orel__comp(_1529040, _1529040, _1529040), c_Transitive__Closure_Ortrancl(_1529040, _1529042)), _1529042)))], (38641 ^ _779308) ^ [_1529097] : [-(c_Transitive__Closure_Ortrancl(_1529097, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529097, _1529097), tc_HOL_Obool))) = c_Relation_OId(_1529097))], (38643 ^ _779308) ^ [_1529133, _1529135] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529133, _1529133), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1529133, _1529135)), c_Relation_OId(_1529133)) = c_Transitive__Closure_Ortrancl(_1529133, _1529135))], (38645 ^ _779308) ^ [_1529180, _1529182] : [-(c_Transitive__Closure_Otrancl(_1529180, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529180, _1529180), tc_HOL_Obool)), _1529182), c_Relation_OId(_1529180))) = c_Transitive__Closure_Ortrancl(_1529180, _1529182))], (38647 ^ _779308) ^ [_1529227, _1529229] : [-(c_Transitive__Closure_Otrancl(_1529227, c_Transitive__Closure_Ortrancl(_1529227, _1529229)) = c_Transitive__Closure_Ortrancl(_1529227, _1529229))], (38649 ^ _779308) ^ [_1529261, _1529263] : [-(c_Transitive__Closure_Ortrancl(_1529261, c_Transitive__Closure_Otrancl(_1529261, _1529263)) = c_Transitive__Closure_Ortrancl(_1529261, _1529263))], (38651 ^ _779308) ^ [_1529295, _1529297, _1529299, _1529301] : [38652 ^ _779308 : [(38653 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1529295, _1529295)), _1529297), c_Transitive__Closure_Ortrancl(_1529295, _1529299)))], (38655 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1529295, _1529295)), _1529297), c_Transitive__Closure_Ortrancl(_1529295, _1529301)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1529295, _1529295)), _1529297), c_Transitive__Closure_Ortrancl(_1529295, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529295, _1529295), tc_HOL_Obool)), _1529299), _1529301)))))], (38659 ^ _779308) ^ [_1529520, _1529522] : [-(hAPP(c_Relation_ODomain(_1529520, _1529520), c_Transitive__Closure_Ortrancl(_1529520, _1529522)) = c_Orderings_Otop__class_Otop(tc_fun(_1529520, tc_HOL_Obool)))], (38661 ^ _779308) ^ [_1529559, _1529561] : [-(hAPP(c_Relation_ORange(_1529559, _1529559), c_Transitive__Closure_Ortrancl(_1529559, _1529561)) = c_Orderings_Otop__class_Otop(tc_fun(_1529559, tc_HOL_Obool)))], (38663 ^ _779308) ^ [_1529598, _1529600] : [-(c_Relation_Orefl__on(_1529598, c_Orderings_Otop__class_Otop(tc_fun(_1529598, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1529598, _1529600)))], (38665 ^ _779308) ^ [_1529632, _1529634] : [-(c_Transitive__Closure_Otrancl(_1529632, _1529634) = hAPP(hAPP(c_Relation_Orel__comp(_1529632, _1529632, _1529632), c_Transitive__Closure_Ortrancl(_1529632, _1529634)), _1529634))], (38667 ^ _779308) ^ [_1529673, _1529675] : [-(c_Transitive__Closure_Otrancl(_1529673, _1529675) = hAPP(hAPP(c_Relation_Orel__comp(_1529673, _1529673, _1529673), _1529675), c_Transitive__Closure_Ortrancl(_1529673, _1529675)))], (38669 ^ _779308) ^ [_1529714, _1529716, _1529718] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529714, _1529714), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529714, _1529714), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1529714, _1529716)), c_Transitive__Closure_Ortrancl(_1529714, _1529718))), c_Transitive__Closure_Ortrancl(_1529714, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529714, _1529714), tc_HOL_Obool)), _1529716), _1529718)))))], (38671 ^ _779308) ^ [_1529809, _1529811, _1529813] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1529809, _1529809)), hAPP(hAPP(c_Product__Type_OPair(_1529809, _1529809), _1529811), _1529813)), c_Relation_OId(_1529809))), -(_1529811 = _1529813)], (38677 ^ _779308) ^ [_1529926, _1529928, _1529930] : [_1529928 = _1529930, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1529926, _1529926)), hAPP(hAPP(c_Product__Type_OPair(_1529926, _1529926), _1529928), _1529930)), c_Relation_OId(_1529926))))], (38683 ^ _779308) ^ [_1530049, _1530051, _1530053, _1530055, _1530057] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530049, _1530049)), hAPP(hAPP(c_Product__Type_OPair(_1530049, _1530049), _1530051), _1530053)), c_Transitive__Closure_Ortrancl(_1530049, _1530055))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1530049, _1530049)), hAPP(hAPP(c_Product__Type_OPair(_1530049, _1530049), _1530053), _1530057)), c_Transitive__Closure_Otrancl(_1530049, _1530055))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530049, _1530049)), hAPP(hAPP(c_Product__Type_OPair(_1530049, _1530049), _1530051), _1530057)), c_Transitive__Closure_Otrancl(_1530049, _1530055))))], (38693 ^ _779308) ^ [_1530322, _1530324, _1530326, _1530328, _1530330] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530322, _1530322)), hAPP(hAPP(c_Product__Type_OPair(_1530322, _1530322), _1530324), _1530326)), c_Transitive__Closure_Otrancl(_1530322, _1530328))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1530322, _1530322)), hAPP(hAPP(c_Product__Type_OPair(_1530322, _1530322), _1530326), _1530330)), c_Transitive__Closure_Ortrancl(_1530322, _1530328))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530322, _1530322)), hAPP(hAPP(c_Product__Type_OPair(_1530322, _1530322), _1530324), _1530330)), c_Transitive__Closure_Otrancl(_1530322, _1530328))))], (38703 ^ _779308) ^ [_1530595, _1530597, _1530599, _1530601, _1530603] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530595, _1530595)), hAPP(hAPP(c_Product__Type_OPair(_1530595, _1530595), _1530597), _1530599)), c_Transitive__Closure_Ortrancl(_1530595, _1530601))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1530595, _1530595)), hAPP(hAPP(c_Product__Type_OPair(_1530595, _1530595), _1530599), _1530603)), _1530601)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530595, _1530595)), hAPP(hAPP(c_Product__Type_OPair(_1530595, _1530595), _1530597), _1530603)), c_Transitive__Closure_Otrancl(_1530595, _1530601))))], (38713 ^ _779308) ^ [_1530862, _1530864, _1530866, _1530868] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530862, _1530862)), hAPP(hAPP(c_Product__Type_OPair(_1530862, _1530862), _1530864), _1530866)), c_Transitive__Closure_Ortrancl(_1530862, _1530868))), -(_1530864 = _1530866), 38720 ^ _779308 : [(38721 ^ _779308) ^ [] : [_1530864 = _1530866], (38723 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530862, _1530862)), hAPP(hAPP(c_Product__Type_OPair(_1530862, _1530862), _1530864), _1530866)), c_Transitive__Closure_Otrancl(_1530862, _1530868))))]]], (38725 ^ _779308) ^ [_1531124, _1531126, _1531128, _1531130, _1531132] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531124, _1531124)), hAPP(hAPP(c_Product__Type_OPair(_1531124, _1531124), _1531126), _1531128)), _1531130)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1531124, _1531124)), hAPP(hAPP(c_Product__Type_OPair(_1531124, _1531124), _1531128), _1531132)), c_Transitive__Closure_Ortrancl(_1531124, _1531130))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531124, _1531124)), hAPP(hAPP(c_Product__Type_OPair(_1531124, _1531124), _1531126), _1531132)), c_Transitive__Closure_Otrancl(_1531124, _1531130))))], (38735 ^ _779308) ^ [_1531412, _1531414, _1531416, _1531418] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531412, _1531412)), hAPP(hAPP(c_Product__Type_OPair(_1531412, _1531412), _1531414), _1531416)), c_Transitive__Closure_Ortrancl(_1531412, _1531418))), -(_1531414 = _1531416), 38742 ^ _779308 : [(38743 ^ _779308) ^ [] : [_1531414 = _1531416], (38745 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531412, _1531412)), hAPP(hAPP(c_Product__Type_OPair(_1531412, _1531412), _1531414), _1531416)), c_Transitive__Closure_Otrancl(_1531412, _1531418))))]]], (38747 ^ _779308) ^ [_1531670, _1531672, _1531674, _1531676] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531670, _1531670)), hAPP(hAPP(c_Product__Type_OPair(_1531670, _1531670), _1531672), _1531674)), c_Transitive__Closure_Ortrancl(_1531670, _1531676)))), 38748 ^ _779308 : [(38749 ^ _779308) ^ [] : [_1531672 = _1531674], (38751 ^ _779308) ^ [] : [-(_1531672 = _1531674), hBOOL(hAPP(hAPP(c_member(tc_prod(_1531670, _1531670)), hAPP(hAPP(c_Product__Type_OPair(_1531670, _1531670), _1531672), _1531674)), c_Transitive__Closure_Otrancl(_1531670, _1531676)))]]], (38759 ^ _779308) ^ [_1531936] : [-(hAPP(c_Relation_ODomain(_1531936, _1531936), c_Relation_OId(_1531936)) = c_Orderings_Otop__class_Otop(tc_fun(_1531936, tc_HOL_Obool)))], (38761 ^ _779308) ^ [_1531972] : [-(hAPP(c_Relation_ORange(_1531972, _1531972), c_Relation_OId(_1531972)) = c_Orderings_Otop__class_Otop(tc_fun(_1531972, tc_HOL_Obool)))], (38763 ^ _779308) ^ [_1532008] : [-(c_Relation_Orefl__on(_1532008, c_Orderings_Otop__class_Otop(tc_fun(_1532008, tc_HOL_Obool)), c_Relation_OId(_1532008)))], (38765 ^ _779308) ^ [] : [-(c_FunDef_Opair__leq = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_prod(tc_Nat_Onat, tc_Nat_Onat)), tc_HOL_Obool)), c_FunDef_Opair__less), c_Relation_OId(tc_prod(tc_Nat_Onat, tc_Nat_Onat))))], (38767 ^ _779308) ^ [_1532056, _1532058, _1532060, _1532062] : [-(hBOOL(hAPP(hAPP(c_member(_1532056), _1532058), hAPP(c_Relation_ODomain(_1532056, _1532056), _1532060)))), 38770 ^ _779308 : [(38771 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532056, _1532056)), hAPP(hAPP(c_Product__Type_OPair(_1532056, _1532056), _1532058), _1532062)), c_Transitive__Closure_Ortrancl(_1532056, _1532060))), -(_1532058 = _1532062)], (38777 ^ _779308) ^ [] : [_1532058 = _1532062, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532056, _1532056)), hAPP(hAPP(c_Product__Type_OPair(_1532056, _1532056), _1532058), _1532062)), c_Transitive__Closure_Ortrancl(_1532056, _1532060))))]]], (38783 ^ _779308) ^ [_1532352, _1532354, _1532356, _1532358] : [hBOOL(hAPP(hAPP(c_member(_1532352), _1532354), c_Wellfounded_Oacc(_1532352, _1532356))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1532352, _1532352)), hAPP(hAPP(c_Product__Type_OPair(_1532352, _1532352), _1532358), _1532354)), c_Transitive__Closure_Ortrancl(_1532352, _1532356))), -(hBOOL(hAPP(hAPP(c_member(_1532352), _1532358), c_Wellfounded_Oacc(_1532352, _1532356))))], (38793 ^ _779308) ^ [_1532573, _1532575, _1532577, _1532579] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532573, _1532573)), hAPP(hAPP(c_Product__Type_OPair(_1532573, _1532573), _1532575), _1532577)), c_Transitive__Closure_Ortrancl(_1532573, _1532579))), hBOOL(hAPP(hAPP(c_member(_1532573), _1532577), c_Wellfounded_Oacc(_1532573, _1532579))), -(hBOOL(hAPP(hAPP(c_member(_1532573), _1532575), c_Wellfounded_Oacc(_1532573, _1532579))))], (38803 ^ _779308) ^ [_1532815, _1532817, _1532819, _1532821] : [c_Wellfounded_Owf(_1532815, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1532815, _1532815)), hAPP(hAPP(c_Product__Type_OPair(_1532815, _1532815), _1532817), _1532819)), _1532821)), 38806 ^ _779308 : [(38807 ^ _779308) ^ [] : [-(c_Wellfounded_Owf(_1532815, _1532821))], (38809 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532815, _1532815)), hAPP(hAPP(c_Product__Type_OPair(_1532815, _1532815), _1532819), _1532817)), c_Transitive__Closure_Ortrancl(_1532815, _1532821)))]]], (38811 ^ _779308) ^ [_1533010, _1533012, _1533014, _1533016] : [-(c_Wellfounded_Owf(_1533010, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1533010, _1533010)), hAPP(hAPP(c_Product__Type_OPair(_1533010, _1533010), _1533012), _1533014)), _1533016))), c_Wellfounded_Owf(_1533010, _1533016), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1533010, _1533010)), hAPP(hAPP(c_Product__Type_OPair(_1533010, _1533010), _1533014), _1533012)), c_Transitive__Closure_Ortrancl(_1533010, _1533016))))], (38821 ^ _779308) ^ [_1533257, _1533259, _1533261, _1533263] : [c_Wellfounded_Oacyclic(_1533257, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1533257, _1533257)), hAPP(hAPP(c_Product__Type_OPair(_1533257, _1533257), _1533259), _1533261)), _1533263)), 38824 ^ _779308 : [(38825 ^ _779308) ^ [] : [-(c_Wellfounded_Oacyclic(_1533257, _1533263))], (38827 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1533257, _1533257)), hAPP(hAPP(c_Product__Type_OPair(_1533257, _1533257), _1533261), _1533259)), c_Transitive__Closure_Ortrancl(_1533257, _1533263)))]]], (38829 ^ _779308) ^ [_1533452, _1533454, _1533456, _1533458] : [-(c_Wellfounded_Oacyclic(_1533452, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1533452, _1533452)), hAPP(hAPP(c_Product__Type_OPair(_1533452, _1533452), _1533454), _1533456)), _1533458))), c_Wellfounded_Oacyclic(_1533452, _1533458), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1533452, _1533452)), hAPP(hAPP(c_Product__Type_OPair(_1533452, _1533452), _1533456), _1533454)), c_Transitive__Closure_Ortrancl(_1533452, _1533458))))], (38839 ^ _779308) ^ [_1533678, _1533680] : [-(c_Relation_Orefl__on(_1533678, c_Orderings_Otop__class_Otop(tc_fun(_1533678, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1533678, _1533678), tc_HOL_Obool)), _1533680), c_Relation_OId(_1533678))))], (38841 ^ _779308) ^ [_1533725] : [-(c_Relation_OId(_1533725) = hAPP(c_Set_OCollect(tc_prod(_1533725, _1533725)), hAPP(hAPP(c_COMBB(tc_fun(_1533725, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1533725, _1533725)), c_HOL_OEx(_1533725)), hAPP(hAPP(c_COMBC(tc_prod(_1533725, _1533725), tc_fun(_1533725, tc_prod(_1533725, _1533725)), tc_fun(_1533725, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1533725, _1533725), tc_HOL_Obool), tc_fun(tc_fun(_1533725, tc_prod(_1533725, _1533725)), tc_fun(_1533725, tc_HOL_Obool)), tc_prod(_1533725, _1533725)), c_COMBB(tc_prod(_1533725, _1533725), tc_HOL_Obool, _1533725)), c_fequal)), hAPP(hAPP(c_COMBS(_1533725, _1533725, tc_prod(_1533725, _1533725)), c_Product__Type_OPair(_1533725, _1533725)), c_COMBI(_1533725))))))], (38843 ^ _779308) ^ [_1533854, _1533856] : [-(c_Relation_Oirrefl(_1533854, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1533854, _1533854), tc_HOL_Obool)), _1533856), c_Relation_OId(_1533854))))], (38845 ^ _779308) ^ [_1533910, _1533912] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1533910), _1533912)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1533910), _1533912)))], (38851 ^ _779308) ^ [_1534015, _1534017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1534015), _1534017)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1534015), _1534017)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (38857 ^ _779308) ^ [_1534126, _1534128, _1534130, _1534132, _1534134] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1534126, _1534126)), hAPP(hAPP(c_Product__Type_OPair(_1534126, _1534126), _1534128), _1534130)), c_Transitive__Closure_Ortrancl(_1534126, _1534132))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534126, _1534126), tc_HOL_Obool)), _1534132), hAPP(hAPP(c_Product__Type_OSigma(_1534126, _1534126), _1534134), hAPP(c_COMBK(tc_fun(_1534126, tc_HOL_Obool), _1534126), _1534134)))), -(_1534128 = _1534130), -(hBOOL(hAPP(hAPP(c_member(_1534126), _1534128), _1534134)))], (38871 ^ _779308) ^ [_1534400, _1534402, _1534404] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1534400, _1534400), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1534400, _1534400), _1534402)), c_Transitive__Closure_Ortrancl(_1534400, _1534402)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1534400, _1534400), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1534400, _1534400)), hAPP(hAPP(c_Product__Type_OPair(_1534400, _1534400), _1534404), _1534404)), c_Transitive__Closure_Otrancl(_1534400, _1534402)))], (38877 ^ _779308) ^ [_1534586, _1534588, _1534590, _1534592, _1534594] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1534586, _1534586)), hAPP(hAPP(c_Product__Type_OPair(_1534586, _1534586), hAPP(_1534588, hAPP(c_Nat_OSuc, 38878 ^ [_1534586, _1534588, _1534590, _1534592, _1534594]))), hAPP(_1534588, 38878 ^ [_1534586, _1534588, _1534590, _1534592, _1534594]))), c_Transitive__Closure_Ortrancl(_1534586, _1534590))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534586, _1534586)), hAPP(hAPP(c_Product__Type_OPair(_1534586, _1534586), hAPP(_1534588, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1534592), _1534594))), hAPP(_1534588, _1534592))), c_Transitive__Closure_Ortrancl(_1534586, _1534590))))], (38884 ^ _779308) ^ [_1534897, _1534899, _1534901] : [c_Relation_Ototal__on(_1534897, _1534899, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1534897, _1534897), tc_HOL_Obool)), _1534901), c_Relation_OId(_1534897))), -(c_Relation_Ototal__on(_1534897, _1534899, _1534901))], (38890 ^ _779308) ^ [_1535008, _1535010, _1535012] : [c_Relation_Ototal__on(_1535008, _1535010, _1535012), -(c_Relation_Ototal__on(_1535008, _1535010, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1535008, _1535008), tc_HOL_Obool)), _1535012), c_Relation_OId(_1535008))))], (38896 ^ _779308) ^ [_1535125] : [-(hAPP(c_Relation_Oconverse(_1535125, _1535125), c_Relation_OId(_1535125)) = c_Relation_OId(_1535125))], (38898 ^ _779308) ^ [_1535158, _1535160] : [-(c_Transitive__Closure_Ortrancl(_1535158, hAPP(c_Relation_Oconverse(_1535158, _1535158), _1535160)) = hAPP(c_Relation_Oconverse(_1535158, _1535158), c_Transitive__Closure_Ortrancl(_1535158, _1535160)))], (38900 ^ _779308) ^ [_1535201, _1535203] : [-(c_Transitive__Closure_Otrancl(_1535201, hAPP(c_Relation_Oconverse(_1535201, _1535201), _1535203)) = hAPP(c_Relation_Oconverse(_1535201, _1535201), c_Transitive__Closure_Otrancl(_1535201, _1535203)))], (38902 ^ _779308) ^ [_1535259, _1535261] : [c_Wellfounded_Oacyclic(_1535259, hAPP(c_Relation_Oconverse(_1535259, _1535259), _1535261)), -(c_Wellfounded_Oacyclic(_1535259, _1535261))], (38908 ^ _779308) ^ [_1535344, _1535346] : [c_Wellfounded_Oacyclic(_1535344, _1535346), -(c_Wellfounded_Oacyclic(_1535344, hAPP(c_Relation_Oconverse(_1535344, _1535344), _1535346)))], (38914 ^ _779308) ^ [_1535453, _1535455, _1535457] : [c_Relation_Orefl__on(_1535453, _1535455, hAPP(c_Relation_Oconverse(_1535453, _1535453), _1535457)), -(c_Relation_Orefl__on(_1535453, _1535455, _1535457))], (38920 ^ _779308) ^ [_1535544, _1535546, _1535548] : [c_Relation_Orefl__on(_1535544, _1535546, _1535548), -(c_Relation_Orefl__on(_1535544, _1535546, hAPP(c_Relation_Oconverse(_1535544, _1535544), _1535548)))], (38926 ^ _779308) ^ [_1535659, _1535661, _1535663] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1535659, _1535661)), hAPP(c_Relation_Oconverse(_1535661, _1535659), _1535663))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1535661, _1535659)), _1535663)))], (38932 ^ _779308) ^ [_1535774, _1535776, _1535778] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1535776, _1535774)), _1535778)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1535774, _1535776)), hAPP(c_Relation_Oconverse(_1535776, _1535774), _1535778))))], (38938 ^ _779308) ^ [_1535895, _1535897] : [-(hAPP(c_Relation_Oconverse(_1535895, _1535895), c_Relation_OId__on(_1535895, _1535897)) = c_Relation_OId__on(_1535895, _1535897))], (38940 ^ _779308) ^ [_1535932, _1535934] : [-(hAPP(c_Relation_OField(_1535932), hAPP(c_Relation_Oconverse(_1535932, _1535932), _1535934)) = hAPP(c_Relation_OField(_1535932), _1535934))], (38942 ^ _779308) ^ [_1535973, _1535975, _1535977] : [-(hAPP(c_Relation_Oconverse(_1535973, _1535975), hAPP(c_Relation_Oconverse(_1535975, _1535973), _1535977)) = _1535977)], (38944 ^ _779308) ^ [_1536030, _1536032, _1536034] : [c_Relation_Ototal__on(_1536030, _1536032, hAPP(c_Relation_Oconverse(_1536030, _1536030), _1536034)), -(c_Relation_Ototal__on(_1536030, _1536032, _1536034))], (38950 ^ _779308) ^ [_1536121, _1536123, _1536125] : [c_Relation_Ototal__on(_1536121, _1536123, _1536125), -(c_Relation_Ototal__on(_1536121, _1536123, hAPP(c_Relation_Oconverse(_1536121, _1536121), _1536125)))], (38956 ^ _779308) ^ [_1536218, _1536220, _1536222, _1536224] : [-(hAPP(c_Relation_Oconverse(_1536218, _1536218), hAPP(hAPP(c_Relation_Oinv__image(_1536220, _1536218), _1536222), _1536224)) = hAPP(hAPP(c_Relation_Oinv__image(_1536220, _1536218), hAPP(c_Relation_Oconverse(_1536220, _1536220), _1536222)), _1536224))], (38958 ^ _779308) ^ [_1536277, _1536279, _1536281, _1536283] : [-(hAPP(c_Relation_Oconverse(_1536277, _1536279), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1536277, _1536279), tc_HOL_Obool)), _1536281), _1536283)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1536279, _1536277), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1536277, _1536279), _1536281)), hAPP(c_Relation_Oconverse(_1536277, _1536279), _1536283)))], (38960 ^ _779308) ^ [_1536352, _1536354, _1536356, _1536358] : [-(hAPP(c_Relation_Oconverse(_1536352, _1536354), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1536352, _1536354), tc_HOL_Obool)), _1536356), _1536358)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1536354, _1536352), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1536352, _1536354), _1536356)), hAPP(c_Relation_Oconverse(_1536352, _1536354), _1536358)))], (38962 ^ _779308) ^ [_1536427, _1536429, _1536431, _1536433, _1536435] : [-(hAPP(c_Relation_Oconverse(_1536427, _1536429), hAPP(hAPP(c_Relation_Orel__comp(_1536427, _1536431, _1536429), _1536433), _1536435)) = hAPP(hAPP(c_Relation_Orel__comp(_1536429, _1536431, _1536427), hAPP(c_Relation_Oconverse(_1536431, _1536429), _1536435)), hAPP(c_Relation_Oconverse(_1536427, _1536431), _1536433)))], (38964 ^ _779308) ^ [_1536496, _1536498, _1536500, _1536502, _1536504] : [-(hAPP(c_Relation_Oconverse(_1536496, _1536498), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536500, tc_fun(tc_prod(_1536496, _1536498), tc_HOL_Obool)), _1536502), _1536504)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536500, tc_fun(tc_prod(_1536498, _1536496), tc_HOL_Obool)), _1536502), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1536496, _1536498), tc_HOL_Obool), tc_fun(tc_prod(_1536498, _1536496), tc_HOL_Obool), _1536500), c_Relation_Oconverse(_1536496, _1536498)), _1536504)))], (38966 ^ _779308) ^ [_1536612, _1536614, _1536616, _1536618, _1536620] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1536612, _1536614)), hAPP(hAPP(c_Product__Type_OPair(_1536612, _1536614), _1536616), _1536618)), hAPP(c_Relation_Oconverse(_1536614, _1536612), _1536620))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1536614, _1536612)), hAPP(hAPP(c_Product__Type_OPair(_1536614, _1536612), _1536618), _1536616)), _1536620)))], (38972 ^ _779308) ^ [_1536779, _1536781, _1536783, _1536785, _1536787] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1536781, _1536779)), hAPP(hAPP(c_Product__Type_OPair(_1536781, _1536779), _1536785), _1536783)), _1536787)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1536779, _1536781)), hAPP(hAPP(c_Product__Type_OPair(_1536779, _1536781), _1536783), _1536785)), hAPP(c_Relation_Oconverse(_1536781, _1536779), _1536787))))], (38978 ^ _779308) ^ [_1536952, _1536954, _1536956, _1536958, _1536960] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1536952, _1536954)), hAPP(hAPP(c_Product__Type_OPair(_1536952, _1536954), _1536956), _1536958)), _1536960)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1536954, _1536952)), hAPP(hAPP(c_Product__Type_OPair(_1536954, _1536952), _1536958), _1536956)), hAPP(c_Relation_Oconverse(_1536952, _1536954), _1536960))))], (38984 ^ _779308) ^ [_1537123, _1537125, _1537127, _1537129, _1537131] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537123, _1537125)), hAPP(hAPP(c_Product__Type_OPair(_1537123, _1537125), _1537127), _1537129)), hAPP(c_Relation_Oconverse(_1537125, _1537123), _1537131))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1537125, _1537123)), hAPP(hAPP(c_Product__Type_OPair(_1537125, _1537123), _1537129), _1537127)), _1537131)))], (38990 ^ _779308) ^ [_1537294, _1537296] : [c_Wellfounded_Owf(_1537294, hAPP(c_Relation_Oconverse(_1537294, _1537294), _1537296)), -(c_Wellfounded_Owf(_1537294, hAPP(c_Relation_Oconverse(_1537294, _1537294), c_Transitive__Closure_Otrancl(_1537294, _1537296))))], (38996 ^ _779308) ^ [_1537401, _1537403, _1537405] : [c_Equiv__Relations_Oequiv(_1537401, _1537403, _1537405), -(hAPP(hAPP(c_Relation_Orel__comp(_1537401, _1537401, _1537401), hAPP(c_Relation_Oconverse(_1537401, _1537401), _1537405)), _1537405) = _1537405)], (39002 ^ _779308) ^ [_1537514, _1537516, _1537518] : [-(hAPP(c_Relation_ORange(_1537514, _1537516), _1537518) = hAPP(c_Relation_ODomain(_1537516, _1537514), hAPP(c_Relation_Oconverse(_1537514, _1537516), _1537518)))], (39004 ^ _779308) ^ [_1537559, _1537561, _1537563] : [-(hAPP(c_Relation_ODomain(_1537559, _1537561), hAPP(c_Relation_Oconverse(_1537561, _1537559), _1537563)) = hAPP(c_Relation_ORange(_1537561, _1537559), _1537563))], (39006 ^ _779308) ^ [_1537604, _1537606, _1537608] : [-(hAPP(c_Relation_ORange(_1537604, _1537606), hAPP(c_Relation_Oconverse(_1537606, _1537604), _1537608)) = hAPP(c_Relation_ODomain(_1537606, _1537604), _1537608))], (39008 ^ _779308) ^ [_1537649, _1537651] : [-(c_Relation_Ototal__on(_1537649, c_Orderings_Obot__class_Obot(tc_fun(_1537649, tc_HOL_Obool)), _1537651))], (39010 ^ _779308) ^ [_1537680, _1537682, _1537684, _1537686] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537680, _1537680)), hAPP(hAPP(c_Product__Type_OPair(_1537680, _1537680), _1537682), _1537684)), c_Transitive__Closure_Ortrancl(_1537680, _1537686))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1537680, _1537680)), hAPP(hAPP(c_Product__Type_OPair(_1537680, _1537680), _1537684), _1537682)), c_Transitive__Closure_Ortrancl(_1537680, hAPP(c_Relation_Oconverse(_1537680, _1537680), _1537686)))))], (39016 ^ _779308) ^ [_1537861, _1537863, _1537865, _1537867] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1537861, _1537861)), hAPP(hAPP(c_Product__Type_OPair(_1537861, _1537861), _1537863), _1537865)), c_Transitive__Closure_Ortrancl(_1537861, hAPP(c_Relation_Oconverse(_1537861, _1537861), _1537867)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1537861, _1537861)), hAPP(hAPP(c_Product__Type_OPair(_1537861, _1537861), _1537865), _1537863)), c_Transitive__Closure_Ortrancl(_1537861, _1537867))))], (39022 ^ _779308) ^ [_1538042, _1538044, _1538046, _1538048] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1538042, _1538042)), hAPP(hAPP(c_Product__Type_OPair(_1538042, _1538042), _1538044), _1538046)), c_Transitive__Closure_Otrancl(_1538042, hAPP(c_Relation_Oconverse(_1538042, _1538042), _1538048)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1538042, _1538042)), hAPP(hAPP(c_Product__Type_OPair(_1538042, _1538042), _1538044), _1538046)), hAPP(c_Relation_Oconverse(_1538042, _1538042), c_Transitive__Closure_Otrancl(_1538042, _1538048)))))], (39028 ^ _779308) ^ [_1538235, _1538237, _1538239, _1538241] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1538235, _1538235)), hAPP(hAPP(c_Product__Type_OPair(_1538235, _1538235), _1538237), _1538239)), hAPP(c_Relation_Oconverse(_1538235, _1538235), c_Transitive__Closure_Otrancl(_1538235, _1538241)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1538235, _1538235)), hAPP(hAPP(c_Product__Type_OPair(_1538235, _1538235), _1538237), _1538239)), c_Transitive__Closure_Otrancl(_1538235, hAPP(c_Relation_Oconverse(_1538235, _1538235), _1538241)))))], (39034 ^ _779308) ^ [_1538452, _1538454, _1538456, _1538458, _1538460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1538452, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1538454, _1538452, _1538456), _1538458)), _1538460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1538454, tc_HOL_Obool)), _1538458), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1538454, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1538452, _1538454, hAPP(c_Relation_Oconverse(_1538454, _1538452), _1538456)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1538452, tc_HOL_Obool)), _1538460))))))], (39040 ^ _779308) ^ [_1538643, _1538645, _1538647, _1538649, _1538651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1538645, tc_HOL_Obool)), _1538649), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1538645, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1538643, _1538645, hAPP(c_Relation_Oconverse(_1538645, _1538643), _1538647)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1538643, tc_HOL_Obool)), _1538651))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1538643, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1538645, _1538643, _1538647), _1538649)), _1538651)))], (39046 ^ _779308) ^ [_1538840, _1538842, _1538844] : [c_Relation_Orefl__on(_1538840, _1538842, _1538844), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1538840, _1538840), tc_HOL_Obool)), _1538844), hAPP(hAPP(c_Relation_Orel__comp(_1538840, _1538840, _1538840), hAPP(c_Relation_Oconverse(_1538840, _1538840), _1538844)), _1538844))))], (39052 ^ _779308) ^ [_1538979, _1538981, _1538983] : [hAPP(hAPP(c_Relation_Orel__comp(_1538979, _1538979, _1538979), hAPP(c_Relation_Oconverse(_1538979, _1538979), _1538981)), _1538981) = _1538981, hAPP(c_Relation_ODomain(_1538979, _1538979), _1538981) = _1538983, -(c_Equiv__Relations_Oequiv(_1538979, _1538983, _1538981))], (39062 ^ _779308) ^ [_1539158, _1539160] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539158, _1539158)), _1539160)), c_Wellfounded_Oacyclic(_1539158, _1539160), -(c_Wellfounded_Owf(_1539158, hAPP(c_Relation_Oconverse(_1539158, _1539158), _1539160)))], (39094 ^ _779308) ^ [_1539820, _1539822, _1539824] : [39096 ^ _779308 : [(39097 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539820), 39095 ^ [_1539820, _1539822, _1539824]), _1539822)))], (39100 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539820), 39098 ^ [_1539820, _1539822, _1539824]), _1539822)))], (39102 ^ _779308) ^ [] : [39095 ^ [_1539820, _1539822, _1539824] = 39098 ^ [_1539820, _1539822, _1539824]], (39104 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539820, _1539820)), hAPP(hAPP(c_Product__Type_OPair(_1539820, _1539820), 39095 ^ [_1539820, _1539822, _1539824]), 39098 ^ [_1539820, _1539822, _1539824])), _1539824))], (39106 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539820, _1539820)), hAPP(hAPP(c_Product__Type_OPair(_1539820, _1539820), 39098 ^ [_1539820, _1539822, _1539824]), 39095 ^ [_1539820, _1539822, _1539824])), _1539824))]], -(c_Relation_Ototal__on(_1539820, _1539822, _1539824))], (39072 ^ _779308) ^ [_1539331, _1539333, _1539335] : [c_Relation_Ototal__on(_1539331, _1539333, _1539335), 39075 ^ _779308 : [(39076 ^ _779308) ^ [_1539475] : [hBOOL(hAPP(hAPP(c_member(_1539331), _1539475), _1539333)), 39079 ^ _779308 : [(39080 ^ _779308) ^ [_1539615] : [hBOOL(hAPP(hAPP(c_member(_1539331), _1539615), _1539333)), -(_1539475 = _1539615), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539331, _1539331)), hAPP(hAPP(c_Product__Type_OPair(_1539331, _1539331), _1539475), _1539615)), _1539335))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539331, _1539331)), hAPP(hAPP(c_Product__Type_OPair(_1539331, _1539331), _1539615), _1539475)), _1539335)))]]]]], (39110 ^ _779308) ^ [_1540402, _1540404, _1540406] : [-(hAPP(c_Relation_Oconverse(_1540402, _1540404), _1540406) = hAPP(c_Set_OCollect(tc_prod(_1540404, _1540402)), hAPP(c_Product__Type_Oprod_Oprod__case(_1540404, _1540402, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1540404, tc_fun(tc_prod(_1540402, _1540404), tc_HOL_Obool), tc_fun(_1540402, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540402, tc_fun(tc_fun(tc_prod(_1540402, _1540404), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1540402, _1540404), tc_HOL_Obool), tc_fun(_1540402, tc_HOL_Obool)), _1540404), c_COMBC(_1540402, tc_fun(tc_prod(_1540402, _1540404), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1540402, tc_prod(_1540402, _1540404)), tc_fun(_1540402, tc_fun(tc_fun(tc_prod(_1540402, _1540404), tc_HOL_Obool), tc_HOL_Obool)), _1540404), hAPP(c_COMBB(tc_prod(_1540402, _1540404), tc_fun(tc_fun(tc_prod(_1540402, _1540404), tc_HOL_Obool), tc_HOL_Obool), _1540402), c_member(tc_prod(_1540402, _1540404)))), hAPP(c_COMBC(_1540402, _1540404, tc_prod(_1540402, _1540404)), c_Product__Type_OPair(_1540402, _1540404))))), _1540406))))], (39112 ^ _779308) ^ [_1540578, _1540580, _1540582] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540578, _1540578)), _1540580), c_Transitive__Closure_Ortrancl(_1540578, _1540582))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540578, _1540578)), _1540580), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1540578, _1540578), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_prod(_1540578, _1540578), tc_HOL_Obool), tc_fun(tc_prod(_1540578, _1540578), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1540578, _1540578), tc_HOL_Obool)), _1540582)))))], (39118 ^ _779308) ^ [_1540785, _1540787] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540785, _1540785)), hAPP(hAPP(c_Product__Type_OPair(_1540785, _1540785), 39119 ^ [_1540785, _1540787]), 39119 ^ [_1540785, _1540787])), c_Transitive__Closure_Otrancl(_1540785, _1540787)))), -(c_Wellfounded_Oacyclic(_1540785, _1540787))], (39125 ^ _779308) ^ [_1540857, _1540859, _1540861, _1540863, _1540865] : [c_Relation_Osingle__valued(_1540857, _1540859, hAPP(c_Relation_Oconverse(_1540859, _1540857), _1540861)), -(hAPP(c_Relation_OImage(_1540859, _1540857, _1540861), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1540859, tc_HOL_Obool)), _1540863), _1540865)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1540857, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1540859, _1540857, _1540861), _1540863)), hAPP(c_Relation_OImage(_1540859, _1540857, _1540861), _1540865)))], (39131 ^ _779308) ^ [_1541040, _1541042, _1541044, _1541046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541040, _1541042), tc_HOL_Obool)), _1541044), _1541046)), c_Relation_Osingle__valued(_1541040, _1541042, _1541046), -(c_Relation_Osingle__valued(_1541040, _1541042, _1541044))], (39141 ^ _779308) ^ [_1541207, _1541209, _1541211, _1541213] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1541207, _1541209), tc_fun(_1541207, _1541209)), _1541211), c_Fun_Ocomp(_1541209, _1541209, _1541207, _1541213)) = c_Fun_Ocomp(_1541209, _1541209, _1541207, hAPP(hAPP(c_Nat_Ocompow(_1541209, _1541209), _1541211), _1541213)))], (39143 ^ _779308) ^ [_1541270, _1541272, _1541274] : [c_Wellfounded_Owf(_1541270, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1541270, _1541270), tc_HOL_Obool), _1541272), _1541274)), -(c_Wellfounded_Owf(_1541270, _1541274))], (39149 ^ _779308) ^ [_1541373, _1541375, _1541377, _1541379] : [-(hAPP(hAPP(c_Nat_Ocompow(_1541373, _1541373), _1541375), hAPP(hAPP(c_Nat_Ocompow(_1541373, _1541373), _1541377), _1541379)) = hAPP(hAPP(c_Nat_Ocompow(_1541373, _1541373), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1541377), _1541375)), _1541379))], (39151 ^ _779308) ^ [_1541435, _1541437, _1541439, _1541441] : [-(hAPP(_1541435, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1541437, _1541437), _1541439), _1541435), _1541441)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1541437, _1541437), _1541439), _1541435), hAPP(_1541435, _1541441)))], (39153 ^ _779308) ^ [_1541494, _1541496] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1541494, _1541494), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1541496) = _1541496)], (39155 ^ _779308) ^ [_1541531, _1541533, _1541535] : [c_Relation_Osingle__valued(_1541531, _1541531, _1541533), -(c_Relation_Osingle__valued(_1541531, _1541531, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1541531, _1541531), tc_HOL_Obool), _1541535), _1541533)))], (39161 ^ _779308) ^ [_1541638, _1541640, _1541642] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1541638, _1541638, _1541638), _1541640), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1541638, _1541638), tc_HOL_Obool), _1541642), _1541640)) = hAPP(hAPP(c_Relation_Orel__comp(_1541638, _1541638, _1541638), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1541638, _1541638), tc_HOL_Obool), _1541642), _1541640)), _1541640))], (39163 ^ _779308) ^ [_1541709, _1541711, _1541713, _1541715, _1541717] : [c_Relation_Osingle__valued(_1541709, _1541711, _1541713), c_Relation_Osingle__valued(_1541711, _1541715, _1541717), -(c_Relation_Osingle__valued(_1541709, _1541715, hAPP(hAPP(c_Relation_Orel__comp(_1541709, _1541711, _1541715), _1541713), _1541717)))], (39173 ^ _779308) ^ [_1541876] : [-(c_Relation_Osingle__valued(_1541876, _1541876, c_Relation_OId(_1541876)))], (39175 ^ _779308) ^ [_1541902, _1541904, _1541906, _1541908] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1541902, _1541902)), _1541904), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1541902, _1541902), tc_HOL_Obool), _1541906), _1541908))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1541902, _1541902)), _1541904), c_Transitive__Closure_Ortrancl(_1541902, _1541908))))], (39181 ^ _779308) ^ [_1542071, _1542073, _1542075] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542071, _1542071)), _1542073), c_Transitive__Closure_Ortrancl(_1542071, _1542075))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542071, _1542071)), _1542073), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542071, _1542071), tc_HOL_Obool), 39184 ^ [_1542071, _1542073, _1542075]), _1542075))))], (39188 ^ _779308) ^ [_1542230, _1542232, _1542234] : [39189 ^ _779308 : [(39190 ^ _779308) ^ [_1542306] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542230, _1542230)), _1542232), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542230, _1542230), tc_HOL_Obool), _1542306), _1542234)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542230, _1542230)), _1542232), c_Transitive__Closure_Ortrancl(_1542230, _1542234))))], (39194 ^ _779308) ^ [_1542394, _1542396] : [-(c_Relation_Osingle__valued(_1542394, _1542394, c_Relation_OId__on(_1542394, _1542396)))], (39196 ^ _779308) ^ [_1542423, _1542425, _1542427] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542423, _1542423), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1542425)), _1542427) = hAPP(hAPP(c_Relation_Orel__comp(_1542423, _1542423, _1542423), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542423, _1542423), tc_HOL_Obool), _1542425), _1542427)), _1542427))], (39198 ^ _779308) ^ [_1542487, _1542489, _1542491, _1542493] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542487, _1542487), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1542489), _1542491)), _1542493) = hAPP(hAPP(c_Relation_Orel__comp(_1542487, _1542487, _1542487), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542487, _1542487), tc_HOL_Obool), _1542489), _1542493)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542487, _1542487), tc_HOL_Obool), _1542491), _1542493)))], (39200 ^ _779308) ^ [_1542568, _1542570] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542568, _1542568), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1542570) = c_Relation_OId(_1542568))], (39202 ^ _779308) ^ [_1542607, _1542609, _1542611] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542607, _1542607)), hAPP(hAPP(c_Product__Type_OPair(_1542607, _1542607), _1542609), _1542609)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542607, _1542607), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1542611))))], (39204 ^ _779308) ^ [_1542665, _1542667, _1542669, _1542671] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542665, _1542665)), hAPP(hAPP(c_Product__Type_OPair(_1542665, _1542665), _1542667), _1542669)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542665, _1542665), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1542671))), -(_1542667 = _1542669)], (39210 ^ _779308) ^ [_1542808, _1542810, _1542812, _1542814, _1542816, _1542818] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542808, _1542808)), hAPP(hAPP(c_Product__Type_OPair(_1542808, _1542808), _1542810), _1542812)), _1542814)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1542808, _1542808)), hAPP(hAPP(c_Product__Type_OPair(_1542808, _1542808), _1542812), _1542816)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542808, _1542808), tc_HOL_Obool), _1542818), _1542814))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542808, _1542808)), hAPP(hAPP(c_Product__Type_OPair(_1542808, _1542808), _1542810), _1542816)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1542808, _1542808), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1542818)), _1542814))))], (39220 ^ _779308) ^ [_1543121, _1543123, _1543125, _1543127, _1543129, _1543131] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1543121, _1543121)), hAPP(hAPP(c_Product__Type_OPair(_1543121, _1543121), _1543123), _1543125)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1543121, _1543121), tc_HOL_Obool), _1543127), _1543129))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1543121, _1543121)), hAPP(hAPP(c_Product__Type_OPair(_1543121, _1543121), _1543125), _1543131)), _1543129)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1543121, _1543121)), hAPP(hAPP(c_Product__Type_OPair(_1543121, _1543121), _1543123), _1543131)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1543121, _1543121), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1543127)), _1543129))))], (39230 ^ _779308) ^ [_1543434, _1543436, _1543438] : [-(hAPP(hAPP(c_Nat_Ocompow(_1543434, _1543434), hAPP(c_Nat_OSuc, _1543436)), _1543438) = hAPP(c_Fun_Ocomp(_1543434, _1543434, _1543434, _1543438), hAPP(hAPP(c_Nat_Ocompow(_1543434, _1543434), _1543436), _1543438)))], (39232 ^ _779308) ^ [_1543490, _1543492, _1543494, _1543496] : [-(hAPP(hAPP(c_Nat_Ocompow(_1543490, _1543490), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1543492), _1543494)), _1543496) = hAPP(c_Fun_Ocomp(_1543490, _1543490, _1543490, hAPP(hAPP(c_Nat_Ocompow(_1543490, _1543490), _1543492), _1543496)), hAPP(hAPP(c_Nat_Ocompow(_1543490, _1543490), _1543494), _1543496)))], (39234 ^ _779308) ^ [_1543560, _1543562, _1543564, _1543566, _1543568, _1543570] : [c_Relation_Osingle__valued(_1543560, _1543562, _1543564), hBOOL(hAPP(hAPP(c_member(tc_prod(_1543560, _1543562)), hAPP(hAPP(c_Product__Type_OPair(_1543560, _1543562), _1543566), _1543568)), _1543564)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1543560, _1543562)), hAPP(hAPP(c_Product__Type_OPair(_1543560, _1543562), _1543566), _1543570)), _1543564)), -(_1543568 = _1543570)], (39262 ^ _779308) ^ [_1544235, _1544237, _1544239] : [39265 ^ _779308 : [(39266 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544235, _1544237)), hAPP(hAPP(c_Product__Type_OPair(_1544235, _1544237), 39263 ^ [_1544235, _1544237, _1544239]), 39264 ^ [_1544235, _1544237, _1544239])), _1544239)))], (39269 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544235, _1544237)), hAPP(hAPP(c_Product__Type_OPair(_1544235, _1544237), 39263 ^ [_1544235, _1544237, _1544239]), 39267 ^ [_1544235, _1544237, _1544239])), _1544239)))], (39271 ^ _779308) ^ [] : [39264 ^ [_1544235, _1544237, _1544239] = 39267 ^ [_1544235, _1544237, _1544239]]], -(c_Relation_Osingle__valued(_1544235, _1544237, _1544239))], (39248 ^ _779308) ^ [_1543861, _1543863, _1543865] : [c_Relation_Osingle__valued(_1543861, _1543863, _1543865), 39251 ^ _779308 : [(39252 ^ _779308) ^ [_1543982, _1543984] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1543861, _1543863)), hAPP(hAPP(c_Product__Type_OPair(_1543861, _1543863), _1543984), _1543982)), _1543865)), 39255 ^ _779308 : [(39256 ^ _779308) ^ [_1544108] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1543861, _1543863)), hAPP(hAPP(c_Product__Type_OPair(_1543861, _1543863), _1543984), _1544108)), _1543865)), -(_1543982 = _1544108)]]]]], (39275 ^ _779308) ^ [_1544605, _1544607] : [-(hAPP(hAPP(c_Nat_Ocompow(_1544605, _1544605), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1544607) = c_Fun_Oid(_1544605))], (39277 ^ _779308) ^ [_1544659, _1544661, _1544663] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544659, _1544659)), _1544661), c_Transitive__Closure_Otrancl(_1544659, _1544663))), 39281 ^ _779308 : [(39282 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 39280 ^ [_1544659, _1544661, _1544663])))], (39284 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544659, _1544659)), _1544661), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1544659, _1544659), tc_HOL_Obool), 39280 ^ [_1544659, _1544661, _1544663]), _1544663))))]]], (39286 ^ _779308) ^ [_1544857, _1544859, _1544861] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544857, _1544857)), _1544859), c_Transitive__Closure_Otrancl(_1544857, _1544861)))), 39287 ^ _779308 : [(39288 ^ _779308) ^ [_1544936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1544936)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1544857, _1544857)), _1544859), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1544857, _1544857), tc_HOL_Obool), _1544936), _1544861)))]]], (39296 ^ _779308) ^ [_1545107, _1545109] : [-(c_Transitive__Closure_Ortrancl(_1545107, _1545109) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1545107, _1545107), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_prod(_1545107, _1545107), tc_HOL_Obool), tc_fun(tc_prod(_1545107, _1545107), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1545107, _1545107), tc_HOL_Obool)), _1545109)))], (39298 ^ _779308) ^ [_1545178, _1545180, _1545182, _1545184, _1545186] : [c_Relation_Osingle__valued(_1545178, _1545178, _1545180), hBOOL(hAPP(hAPP(c_member(tc_prod(_1545178, _1545178)), hAPP(hAPP(c_Product__Type_OPair(_1545178, _1545178), _1545182), _1545184)), c_Transitive__Closure_Ortrancl(_1545178, _1545180))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1545178, _1545178)), hAPP(hAPP(c_Product__Type_OPair(_1545178, _1545178), _1545182), _1545186)), c_Transitive__Closure_Ortrancl(_1545178, _1545180))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545178, _1545178)), hAPP(hAPP(c_Product__Type_OPair(_1545178, _1545178), _1545184), _1545186)), c_Transitive__Closure_Ortrancl(_1545178, _1545180)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545178, _1545178)), hAPP(hAPP(c_Product__Type_OPair(_1545178, _1545178), _1545186), _1545184)), c_Transitive__Closure_Ortrancl(_1545178, _1545180))))], (39316 ^ _779308) ^ [_1545568] : [-(c_Nat_Ofunpow(_1545568) = c_Nat_Ocompow(_1545568, _1545568))], (39318 ^ _779308) ^ [_1545596, _1545598, _1545600, _1545602, _1545604] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545596, _1545596)), hAPP(hAPP(c_Product__Type_OPair(_1545596, _1545596), _1545598), _1545600)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1545596, _1545596), tc_HOL_Obool), _1545602), _1545604))), 39323 ^ _779308 : [(39324 ^ _779308) ^ [] : [-(_1545602 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39326 ^ _779308) ^ [] : [-(_1545598 = _1545600)]], 39329 ^ _779308 : [(39330 ^ _779308) ^ [] : [-(_1545602 = hAPP(c_Nat_OSuc, 39328 ^ [_1545596, _1545598, _1545600, _1545602, _1545604]))], (39332 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545596, _1545596)), hAPP(hAPP(c_Product__Type_OPair(_1545596, _1545596), _1545598), 39327 ^ [_1545596, _1545598, _1545600, _1545602, _1545604])), _1545604)))], (39334 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545596, _1545596)), hAPP(hAPP(c_Product__Type_OPair(_1545596, _1545596), 39327 ^ [_1545596, _1545598, _1545600, _1545602, _1545604]), _1545600)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1545596, _1545596), tc_HOL_Obool), 39328 ^ [_1545596, _1545598, _1545600, _1545602, _1545604]), _1545604))))]]], (39336 ^ _779308) ^ [_1546038, _1546040, _1546042, _1546044, _1546046] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546038, _1546038)), hAPP(hAPP(c_Product__Type_OPair(_1546038, _1546038), _1546040), _1546042)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1546038, _1546038), tc_HOL_Obool), _1546044), _1546046))), 39341 ^ _779308 : [(39342 ^ _779308) ^ [] : [-(_1546044 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39344 ^ _779308) ^ [] : [-(_1546040 = _1546042)]], 39347 ^ _779308 : [(39348 ^ _779308) ^ [] : [-(_1546044 = hAPP(c_Nat_OSuc, 39346 ^ [_1546038, _1546040, _1546042, _1546044, _1546046]))], (39350 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546038, _1546038)), hAPP(hAPP(c_Product__Type_OPair(_1546038, _1546038), _1546040), 39345 ^ [_1546038, _1546040, _1546042, _1546044, _1546046])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1546038, _1546038), tc_HOL_Obool), 39346 ^ [_1546038, _1546040, _1546042, _1546044, _1546046]), _1546046))))], (39352 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546038, _1546038)), hAPP(hAPP(c_Product__Type_OPair(_1546038, _1546038), 39345 ^ [_1546038, _1546040, _1546042, _1546044, _1546046]), _1546042)), _1546046)))]]], (39354 ^ _779308) ^ [_1546480, _1546482, _1546484, _1546486, _1546488] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546480, _1546480)), hAPP(hAPP(c_Product__Type_OPair(_1546480, _1546480), _1546482), _1546484)), c_Transitive__Closure_Ortrancl(_1546480, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1546480, _1546480), tc_HOL_Obool)), _1546486), _1546488)))), 39360 ^ _779308 : [(39361 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546480, _1546480)), hAPP(hAPP(c_Product__Type_OPair(_1546480, _1546480), _1546482), 39359 ^ [_1546480, _1546482, _1546484, _1546486, _1546488])), c_Transitive__Closure_Ortrancl(_1546480, _1546486))))], (39364 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546480, _1546480)), hAPP(hAPP(c_Product__Type_OPair(_1546480, _1546480), 39359 ^ [_1546480, _1546482, _1546484, _1546486, _1546488]), 39362 ^ [_1546480, _1546482, _1546484, _1546486, _1546488])), _1546488)))], (39366 ^ _779308) ^ [] : [39359 ^ [_1546480, _1546482, _1546484, _1546486, _1546488] = 39362 ^ [_1546480, _1546482, _1546484, _1546486, _1546488]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546480, _1546480)), hAPP(hAPP(c_Product__Type_OPair(_1546480, _1546480), _1546482), _1546484)), c_Transitive__Closure_Ortrancl(_1546480, _1546486))))], (39370 ^ _779308) ^ [_1547039, _1547041, _1547043, _1547045, _1547047] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547039, _1547039)), hAPP(hAPP(c_Product__Type_OPair(_1547039, _1547039), _1547041), _1547043)), c_Transitive__Closure_Ortrancl(_1547039, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1547039, _1547039), tc_HOL_Obool)), _1547045), _1547047)))), 39376 ^ _779308 : [(39377 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547039, _1547039)), hAPP(hAPP(c_Product__Type_OPair(_1547039, _1547039), 39375 ^ [_1547039, _1547041, _1547043, _1547045, _1547047]), _1547043)), c_Transitive__Closure_Ortrancl(_1547039, _1547045))))], (39380 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547039, _1547039)), hAPP(hAPP(c_Product__Type_OPair(_1547039, _1547039), 39378 ^ [_1547039, _1547041, _1547043, _1547045, _1547047]), 39375 ^ [_1547039, _1547041, _1547043, _1547045, _1547047])), _1547047)))], (39382 ^ _779308) ^ [] : [39378 ^ [_1547039, _1547041, _1547043, _1547045, _1547047] = 39375 ^ [_1547039, _1547041, _1547043, _1547045, _1547047]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547039, _1547039)), hAPP(hAPP(c_Product__Type_OPair(_1547039, _1547039), _1547041), _1547043)), c_Transitive__Closure_Ortrancl(_1547039, _1547045))))], (39386 ^ _779308) ^ [_1547598, _1547600, _1547602, _1547604, _1547606] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547598, _1547598)), hAPP(hAPP(c_Product__Type_OPair(_1547598, _1547598), _1547600), _1547602)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1547598, _1547598), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1547604)), _1547606))), 39390 ^ _779308 : [(39391 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547598, _1547598)), hAPP(hAPP(c_Product__Type_OPair(_1547598, _1547598), _1547600), 39389 ^ [_1547598, _1547600, _1547602, _1547604, _1547606])), _1547606)))], (39393 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547598, _1547598)), hAPP(hAPP(c_Product__Type_OPair(_1547598, _1547598), 39389 ^ [_1547598, _1547600, _1547602, _1547604, _1547606]), _1547602)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1547598, _1547598), tc_HOL_Obool), _1547604), _1547606))))]]], (39395 ^ _779308) ^ [_1547906, _1547908, _1547910, _1547912, _1547914] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547906, _1547906)), hAPP(hAPP(c_Product__Type_OPair(_1547906, _1547906), _1547908), _1547910)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1547906, _1547906), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1547912)), _1547914))), 39399 ^ _779308 : [(39400 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547906, _1547906)), hAPP(hAPP(c_Product__Type_OPair(_1547906, _1547906), _1547908), 39398 ^ [_1547906, _1547908, _1547910, _1547912, _1547914])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1547906, _1547906), tc_HOL_Obool), _1547912), _1547914))))], (39402 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547906, _1547906)), hAPP(hAPP(c_Product__Type_OPair(_1547906, _1547906), 39398 ^ [_1547906, _1547908, _1547910, _1547912, _1547914]), _1547910)), _1547914)))]]], (39404 ^ _779308) ^ [_1548218, _1548220, _1548222, _1548224, _1548226] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548218, _1548218)), hAPP(hAPP(c_Product__Type_OPair(_1548218, _1548218), _1548220), _1548222)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1548218, _1548218), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1548224)), _1548226))), 39408 ^ _779308 : [(39409 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548218, _1548218)), hAPP(hAPP(c_Product__Type_OPair(_1548218, _1548218), _1548220), 39407 ^ [_1548218, _1548220, _1548222, _1548224, _1548226])), _1548226)))], (39411 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548218, _1548218)), hAPP(hAPP(c_Product__Type_OPair(_1548218, _1548218), 39407 ^ [_1548218, _1548220, _1548222, _1548224, _1548226]), _1548222)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1548218, _1548218), tc_HOL_Obool), _1548224), _1548226))))]]], (39413 ^ _779308) ^ [_1548530, _1548532, _1548534, _1548536] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548530, _1548530)), hAPP(hAPP(c_Product__Type_OPair(_1548530, _1548530), _1548532), _1548534)), c_Transitive__Closure_Otrancl(_1548530, _1548536))), 39417 ^ _779308 : [(39418 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548530, _1548530)), hAPP(hAPP(c_Product__Type_OPair(_1548530, _1548530), _1548532), 39416 ^ [_1548530, _1548532, _1548534, _1548536])), _1548536)))], (39420 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548530, _1548530)), hAPP(hAPP(c_Product__Type_OPair(_1548530, _1548530), 39416 ^ [_1548530, _1548532, _1548534, _1548536]), _1548534)), c_Transitive__Closure_Ortrancl(_1548530, _1548536))))]]], (39422 ^ _779308) ^ [_1548790, _1548792, _1548794, _1548796] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548790, _1548790)), hAPP(hAPP(c_Product__Type_OPair(_1548790, _1548790), _1548792), _1548794)), c_Transitive__Closure_Otrancl(_1548790, _1548796))), 39426 ^ _779308 : [(39427 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548790, _1548790)), hAPP(hAPP(c_Product__Type_OPair(_1548790, _1548790), _1548792), 39425 ^ [_1548790, _1548792, _1548794, _1548796])), c_Transitive__Closure_Ortrancl(_1548790, _1548796))))], (39429 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548790, _1548790)), hAPP(hAPP(c_Product__Type_OPair(_1548790, _1548790), 39425 ^ [_1548790, _1548792, _1548794, _1548796]), _1548794)), _1548796)))]]], (39431 ^ _779308) ^ [_1549050, _1549052] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1549050, _1549050)), _1549052), c_Relation_OId(_1549050))), -(_1549052 = hAPP(hAPP(c_Product__Type_OPair(_1549050, _1549050), 39434 ^ [_1549050, _1549052]), 39434 ^ [_1549050, _1549052]))], (39438 ^ _779308) ^ [_1549192, _1549194, _1549196] : [class_Orderings_Olinorder(_1549192), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549192), _1549194)), -(hBOOL(hAPP(hAPP(c_member(_1549192), _1549196), _1549194))), -(c_Big__Operators_Olattice_OSup__fin(_1549192, c_Orderings_Oord__class_Omax(_1549192), hAPP(hAPP(c_Set_Oinsert(_1549192), _1549196), _1549194)) = hAPP(hAPP(c_Finite__Set_Ofold(_1549192, _1549192, c_Orderings_Oord__class_Omax(_1549192)), _1549196), _1549194))], (39452 ^ _779308) ^ [_1549412, _1549414, _1549416, _1549418] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1549412, _1549414, _1549416), _1549418), c_Orderings_Obot__class_Obot(tc_fun(_1549412, tc_HOL_Obool))) = _1549418)], (39454 ^ _779308) ^ [_1549456, _1549458, _1549460, _1549462] : [-(hAPP(c_Finite__Set_Ofold__image(_1549456, _1549458, _1549460), _1549462) = c_Finite__Set_Ofold(_1549458, _1549456, hAPP(hAPP(c_COMBB(_1549456, tc_fun(_1549456, _1549456), _1549458), _1549460), _1549462)))], (39456 ^ _779308) ^ [_1549509, _1549511, _1549513, _1549515, _1549517, _1549519] : [c_Finite__Set_Ofolding(_1549509, _1549511, _1549513, _1549515), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549509), _1549517)), -(hAPP(hAPP(_1549515, _1549517), _1549519) = hAPP(hAPP(c_Finite__Set_Ofold(_1549509, _1549511, _1549513), _1549519), _1549517))], (39466 ^ _779308) ^ [_1549698, _1549700, _1549702, _1549704, _1549706] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1549698, _1549700, _1549702), _1549704), _1549706) = c_HOL_OThe(_1549700, c_Finite__Set_Ofold__graph(_1549698, _1549700, _1549702, _1549704, _1549706)))], (39468 ^ _779308) ^ [_1549748, _1549750, _1549752] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1549748), _1549750)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1549748, tc_HOL_Obool)), _1549750), _1549752) = hAPP(hAPP(c_Finite__Set_Ofold(_1549748, tc_fun(_1549748, tc_HOL_Obool), c_Set_Oinsert(_1549748)), _1549752), _1549750))], (39474 ^ _779308) ^ [_1549887, _1549889, _1549891, _1549893] : [class_Lattices_Osemilattice__sup(_1549887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549887), _1549889)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1549887, _1549887, c_Lattices_Osemilattice__sup__class_Osup(_1549887)), _1549891), hAPP(hAPP(c_Set_Oinsert(_1549887), _1549893), _1549889)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1549887), _1549893), hAPP(hAPP(c_Finite__Set_Ofold(_1549887, _1549887, c_Lattices_Osemilattice__sup__class_Osup(_1549887)), _1549891), _1549889)))], (39484 ^ _779308) ^ [_1550110, _1550112, _1550114, _1550116] : [class_Lattices_Osemilattice__inf(_1550110), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550110), _1550112)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1550110, _1550110, c_Lattices_Osemilattice__inf__class_Oinf(_1550110)), _1550114), hAPP(hAPP(c_Set_Oinsert(_1550110), _1550116), _1550112)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1550110), _1550116), hAPP(hAPP(c_Finite__Set_Ofold(_1550110, _1550110, c_Lattices_Osemilattice__inf__class_Oinf(_1550110)), _1550114), _1550112)))], (39494 ^ _779308) ^ [_1550333, _1550335, _1550337, _1550339] : [class_Orderings_Olinorder(_1550333), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550333), _1550335)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1550333, _1550333, c_Orderings_Oord__class_Omin(_1550333)), _1550337), hAPP(hAPP(c_Set_Oinsert(_1550333), _1550339), _1550335)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1550333), _1550339), hAPP(hAPP(c_Finite__Set_Ofold(_1550333, _1550333, c_Orderings_Oord__class_Omin(_1550333)), _1550337), _1550335)))], (39504 ^ _779308) ^ [_1550556, _1550558, _1550560, _1550562] : [class_Orderings_Olinorder(_1550556), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550556), _1550558)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1550556, _1550556, c_Orderings_Oord__class_Omax(_1550556)), _1550560), hAPP(hAPP(c_Set_Oinsert(_1550556), _1550562), _1550558)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1550556), _1550562), hAPP(hAPP(c_Finite__Set_Ofold(_1550556, _1550556, c_Orderings_Oord__class_Omax(_1550556)), _1550560), _1550558)))], (39514 ^ _779308) ^ [_1550779, _1550781, _1550783, _1550785, _1550787, _1550789] : [c_Finite__Set_Ofun__left__comm__idem(_1550779, _1550781, _1550783), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550779), _1550785)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1550779, _1550781, _1550783), _1550787), hAPP(hAPP(c_Set_Oinsert(_1550779), _1550789), _1550785)) = hAPP(hAPP(c_Finite__Set_Ofold(_1550779, _1550781, _1550783), hAPP(hAPP(_1550783, _1550789), _1550787)), _1550785))], (39524 ^ _779308) ^ [_1551002, _1551004, _1551006, _1551008, _1551010, _1551012] : [c_Finite__Set_Ofun__left__comm__idem(_1551002, _1551004, _1551006), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551002), _1551008)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1551002, _1551004, _1551006), _1551010), hAPP(hAPP(c_Set_Oinsert(_1551002), _1551012), _1551008)) = hAPP(hAPP(_1551006, _1551012), hAPP(hAPP(c_Finite__Set_Ofold(_1551002, _1551004, _1551006), _1551010), _1551008)))], (39534 ^ _779308) ^ [_1551225, _1551227, _1551229, _1551231, _1551233] : [class_Complete__Lattice_Ocomplete__lattice(_1551225), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551227), _1551229)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1551225), _1551231), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1551227, _1551225), _1551229), _1551233)) = hAPP(hAPP(c_Finite__Set_Ofold(_1551227, _1551225, hAPP(hAPP(c_COMBB(_1551225, tc_fun(_1551225, _1551225), _1551227), c_Lattices_Osemilattice__sup__class_Osup(_1551225)), _1551233)), _1551231), _1551229))], (39544 ^ _779308) ^ [_1551456, _1551458, _1551460, _1551462, _1551464] : [c_Finite__Set_Ofolding__one__idem(_1551456, _1551458, _1551460), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551456), _1551462)), -(hAPP(_1551460, hAPP(hAPP(c_Set_Oinsert(_1551456), _1551464), _1551462)) = hAPP(hAPP(c_Finite__Set_Ofold(_1551456, _1551456, _1551458), _1551464), _1551462))], (39554 ^ _779308) ^ [_1551649, _1551651, _1551653, _1551655] : [class_Lattices_Osemilattice__sup(_1551649), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551649), _1551651)), hBOOL(hAPP(hAPP(c_member(_1551649), _1551653), _1551651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1551649), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1551649), _1551653), _1551655)), hAPP(hAPP(c_Finite__Set_Ofold(_1551649, _1551649, c_Lattices_Osemilattice__sup__class_Osup(_1551649)), _1551655), _1551651))))], (39568 ^ _779308) ^ [_1551916, _1551918, _1551920, _1551922] : [class_Lattices_Osemilattice__inf(_1551916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551916), _1551918)), hBOOL(hAPP(hAPP(c_member(_1551916), _1551920), _1551918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1551916), hAPP(hAPP(c_Finite__Set_Ofold(_1551916, _1551916, c_Lattices_Osemilattice__inf__class_Oinf(_1551916)), _1551922), _1551918)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1551916), _1551920), _1551922))))], (39582 ^ _779308) ^ [_1552183, _1552185, _1552187, _1552189] : [class_Orderings_Olinorder(_1552183), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552183), _1552185)), hBOOL(hAPP(hAPP(c_member(_1552183), _1552187), _1552185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552183), hAPP(hAPP(c_Finite__Set_Ofold(_1552183, _1552183, c_Orderings_Oord__class_Omin(_1552183)), _1552189), _1552185)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1552183), _1552187), _1552189))))], (39596 ^ _779308) ^ [_1552450, _1552452, _1552454, _1552456] : [class_Orderings_Olinorder(_1552450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552450), _1552452)), hBOOL(hAPP(hAPP(c_member(_1552450), _1552454), _1552452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1552450), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1552450), _1552454), _1552456)), hAPP(hAPP(c_Finite__Set_Ofold(_1552450, _1552450, c_Orderings_Oord__class_Omax(_1552450)), _1552456), _1552452))))], (39610 ^ _779308) ^ [_1552717, _1552719, _1552721] : [class_Lattices_Oab__semigroup__idem__mult(_1552717), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552717), _1552719)), -(hAPP(c_Finite__Set_Ofold1(_1552717, c_Groups_Otimes__class_Otimes(_1552717)), hAPP(hAPP(c_Set_Oinsert(_1552717), _1552721), _1552719)) = hAPP(hAPP(c_Finite__Set_Ofold(_1552717, _1552717, c_Groups_Otimes__class_Otimes(_1552717)), _1552721), _1552719))], (39620 ^ _779308) ^ [_1552912, _1552914, _1552916] : [class_Lattices_Olattice(_1552912), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552912), _1552914)), -(c_Big__Operators_Olattice__class_OSup__fin(_1552912, hAPP(hAPP(c_Set_Oinsert(_1552912), _1552916), _1552914)) = hAPP(hAPP(c_Finite__Set_Ofold(_1552912, _1552912, c_Lattices_Osemilattice__sup__class_Osup(_1552912)), _1552916), _1552914))], (39630 ^ _779308) ^ [_1553097, _1553099, _1553101] : [class_Lattices_Olattice(_1553097), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553097), _1553099)), -(c_Big__Operators_Olattice__class_OInf__fin(_1553097, hAPP(hAPP(c_Set_Oinsert(_1553097), _1553101), _1553099)) = hAPP(hAPP(c_Finite__Set_Ofold(_1553097, _1553097, c_Lattices_Osemilattice__inf__class_Oinf(_1553097)), _1553101), _1553099))], (39640 ^ _779308) ^ [_1553282, _1553284, _1553286] : [class_Orderings_Olinorder(_1553282), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553282), _1553284)), -(c_Big__Operators_Olinorder__class_OMin(_1553282, hAPP(hAPP(c_Set_Oinsert(_1553282), _1553286), _1553284)) = hAPP(hAPP(c_Finite__Set_Ofold(_1553282, _1553282, c_Orderings_Oord__class_Omin(_1553282)), _1553286), _1553284))], (39650 ^ _779308) ^ [_1553467, _1553469, _1553471] : [class_Orderings_Olinorder(_1553467), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553467), _1553469)), -(c_Big__Operators_Olinorder__class_OMax(_1553467, hAPP(hAPP(c_Set_Oinsert(_1553467), _1553471), _1553469)) = hAPP(hAPP(c_Finite__Set_Ofold(_1553467, _1553467, c_Orderings_Oord__class_Omax(_1553467)), _1553471), _1553469))], (39660 ^ _779308) ^ [_1553652, _1553654, _1553656] : [class_Orderings_Olinorder(_1553652), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553652), _1553654)), -(c_Big__Operators_Olattice_OInf__fin(_1553652, c_Orderings_Oord__class_Omin(_1553652), hAPP(hAPP(c_Set_Oinsert(_1553652), _1553656), _1553654)) = hAPP(hAPP(c_Finite__Set_Ofold(_1553652, _1553652, c_Orderings_Oord__class_Omin(_1553652)), _1553656), _1553654))], (39670 ^ _779308) ^ [_1553843, _1553845, _1553847] : [class_Orderings_Olinorder(_1553843), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553843), _1553845)), -(c_Big__Operators_Olattice_OSup__fin(_1553843, c_Orderings_Oord__class_Omax(_1553843), hAPP(hAPP(c_Set_Oinsert(_1553843), _1553847), _1553845)) = hAPP(hAPP(c_Finite__Set_Ofold(_1553843, _1553843, c_Orderings_Oord__class_Omax(_1553843)), _1553847), _1553845))], (39680 ^ _779308) ^ [_1554034, _1554036, _1554038] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1554034), _1554036)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1554034, tc_HOL_Obool)), _1554038), _1554036) = hAPP(hAPP(c_Finite__Set_Ofold(_1554034, tc_fun(_1554034, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1554034, tc_HOL_Obool), tc_fun(tc_fun(_1554034, tc_HOL_Obool), tc_fun(_1554034, tc_HOL_Obool)), _1554034), hAPP(c_COMBC(tc_fun(_1554034, tc_HOL_Obool), tc_fun(_1554034, tc_HOL_Obool), tc_fun(_1554034, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1554034, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1554034, tc_fun(_1554034, tc_HOL_Obool), tc_fun(_1554034, tc_HOL_Obool)), c_Set_Oinsert(_1554034)), c_Orderings_Obot__class_Obot(tc_fun(_1554034, tc_HOL_Obool))))), _1554038), _1554036))], (39686 ^ _779308) ^ [_1554301, _1554303, _1554305, _1554307, _1554309] : [c_Finite__Set_Ofolding__one(_1554301, _1554303, _1554305), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554301), _1554307)), -(hBOOL(hAPP(hAPP(c_member(_1554301), _1554309), _1554307))), -(hAPP(_1554305, hAPP(hAPP(c_Set_Oinsert(_1554301), _1554309), _1554307)) = hAPP(hAPP(c_Finite__Set_Ofold(_1554301, _1554301, _1554303), _1554309), _1554307))], (39700 ^ _779308) ^ [_1554523, _1554525, _1554527, _1554529] : [class_Complete__Lattice_Ocomplete__lattice(_1554523), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554525), _1554527)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1554525, _1554523), _1554527), _1554529) = hAPP(hAPP(c_Finite__Set_Ofold(_1554525, _1554523, hAPP(hAPP(c_COMBB(_1554523, tc_fun(_1554523, _1554523), _1554525), c_Lattices_Osemilattice__sup__class_Osup(_1554523)), _1554529)), c_Orderings_Obot__class_Obot(_1554523)), _1554527))], (39710 ^ _779308) ^ [_1554738, _1554740, _1554742] : [class_Groups_Oab__semigroup__mult(_1554738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554738), _1554740)), -(hBOOL(hAPP(hAPP(c_member(_1554738), _1554742), _1554740))), -(hAPP(c_Finite__Set_Ofold1(_1554738, c_Groups_Otimes__class_Otimes(_1554738)), hAPP(hAPP(c_Set_Oinsert(_1554738), _1554742), _1554740)) = hAPP(hAPP(c_Finite__Set_Ofold(_1554738, _1554738, c_Groups_Otimes__class_Otimes(_1554738)), _1554742), _1554740))], (39724 ^ _779308) ^ [_1554962, _1554964, _1554966] : [class_Lattices_Olattice(_1554962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554962), _1554964)), -(hBOOL(hAPP(hAPP(c_member(_1554962), _1554966), _1554964))), -(c_Big__Operators_Olattice__class_OSup__fin(_1554962, hAPP(hAPP(c_Set_Oinsert(_1554962), _1554966), _1554964)) = hAPP(hAPP(c_Finite__Set_Ofold(_1554962, _1554962, c_Lattices_Osemilattice__sup__class_Osup(_1554962)), _1554966), _1554964))], (39738 ^ _779308) ^ [_1555176, _1555178, _1555180] : [class_Lattices_Olattice(_1555176), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555176), _1555178)), -(hBOOL(hAPP(hAPP(c_member(_1555176), _1555180), _1555178))), -(c_Big__Operators_Olattice__class_OInf__fin(_1555176, hAPP(hAPP(c_Set_Oinsert(_1555176), _1555180), _1555178)) = hAPP(hAPP(c_Finite__Set_Ofold(_1555176, _1555176, c_Lattices_Osemilattice__inf__class_Oinf(_1555176)), _1555180), _1555178))], (39752 ^ _779308) ^ [_1555390, _1555392, _1555394] : [class_Orderings_Olinorder(_1555390), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555390), _1555392)), -(hBOOL(hAPP(hAPP(c_member(_1555390), _1555394), _1555392))), -(c_Big__Operators_Olinorder__class_OMin(_1555390, hAPP(hAPP(c_Set_Oinsert(_1555390), _1555394), _1555392)) = hAPP(hAPP(c_Finite__Set_Ofold(_1555390, _1555390, c_Orderings_Oord__class_Omin(_1555390)), _1555394), _1555392))], (39766 ^ _779308) ^ [_1555604, _1555606, _1555608] : [class_Orderings_Olinorder(_1555604), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555604), _1555606)), -(hBOOL(hAPP(hAPP(c_member(_1555604), _1555608), _1555606))), -(c_Big__Operators_Olinorder__class_OMax(_1555604, hAPP(hAPP(c_Set_Oinsert(_1555604), _1555608), _1555606)) = hAPP(hAPP(c_Finite__Set_Ofold(_1555604, _1555604, c_Orderings_Oord__class_Omax(_1555604)), _1555608), _1555606))], (39780 ^ _779308) ^ [_1555818, _1555820, _1555822] : [class_Orderings_Olinorder(_1555818), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555818), _1555820)), -(hBOOL(hAPP(hAPP(c_member(_1555818), _1555822), _1555820))), -(c_Big__Operators_Olattice_OInf__fin(_1555818, c_Orderings_Oord__class_Omin(_1555818), hAPP(hAPP(c_Set_Oinsert(_1555818), _1555822), _1555820)) = hAPP(hAPP(c_Finite__Set_Ofold(_1555818, _1555818, c_Orderings_Oord__class_Omin(_1555818)), _1555822), _1555820))], (39794 ^ _779308) ^ [_1556038, _1556040, _1556042, _1556044, _1556046, _1556048] : [c_Finite__Set_Ofun__left__comm(_1556038, _1556040, _1556042), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556038), _1556044)), hBOOL(hAPP(hAPP(c_member(_1556038), _1556046), _1556044)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1556038, _1556040, _1556042), _1556048), _1556044) = hAPP(hAPP(_1556042, _1556046), hAPP(hAPP(c_Finite__Set_Ofold(_1556038, _1556040, _1556042), _1556048), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1556038, tc_HOL_Obool)), _1556044), hAPP(hAPP(c_Set_Oinsert(_1556038), _1556046), c_Orderings_Obot__class_Obot(tc_fun(_1556038, tc_HOL_Obool)))))))], (39808 ^ _779308) ^ [_1556367, _1556369, _1556371, _1556373, _1556375, _1556377] : [c_Finite__Set_Ofun__left__comm(_1556367, _1556369, _1556371), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556367), _1556373)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1556367, _1556369, _1556371), _1556375), hAPP(hAPP(c_Set_Oinsert(_1556367), _1556377), _1556373)) = hAPP(hAPP(_1556371, _1556377), hAPP(hAPP(c_Finite__Set_Ofold(_1556367, _1556369, _1556371), _1556375), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1556367, tc_HOL_Obool)), _1556373), hAPP(hAPP(c_Set_Oinsert(_1556367), _1556377), c_Orderings_Obot__class_Obot(tc_fun(_1556367, tc_HOL_Obool)))))))], (39818 ^ _779308) ^ [_1556638, _1556640, _1556642, _1556644] : [class_Complete__Lattice_Ocomplete__lattice(_1556638), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556640), _1556642)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1556640, _1556638), _1556642), _1556644) = hAPP(hAPP(c_Finite__Set_Ofold(_1556640, _1556638, hAPP(hAPP(c_COMBB(_1556638, tc_fun(_1556638, _1556638), _1556640), c_Lattices_Osemilattice__inf__class_Oinf(_1556638)), _1556644)), c_Orderings_Otop__class_Otop(_1556638)), _1556642))], (39828 ^ _779308) ^ [_1556853, _1556855, _1556857, _1556859, _1556861, _1556863] : [hBOOL(hAPP(hAPP(c_member(_1556853), _1556855), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1556857, tc_fun(_1556853, tc_HOL_Obool)), _1556859), _1556861))), hBOOL(hAPP(hAPP(c_member(_1556857), _1556863), _1556859)), -(hBOOL(hAPP(hAPP(c_member(_1556853), _1556855), hAPP(_1556861, _1556863))))], (39838 ^ _779308) ^ [_1557070, _1557072, _1557074, _1557076, _1557078, _1557080] : [hBOOL(hAPP(hAPP(c_member(_1557070), _1557072), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1557074, tc_fun(_1557070, tc_HOL_Obool)), _1557076), _1557078))), -(hBOOL(hAPP(hAPP(c_member(_1557070), _1557072), hAPP(_1557078, _1557080)))), hBOOL(hAPP(hAPP(c_member(_1557074), _1557080), _1557076))], (39848 ^ _779308) ^ [_1557291, _1557293, _1557295, _1557297, _1557299, _1557301] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1557291, tc_fun(_1557293, tc_HOL_Obool)), _1557295), _1557297), _1557299)), hBOOL(hAPP(hAPP(c_member(_1557291), _1557301), _1557295)), -(hBOOL(hAPP(hAPP(_1557297, _1557301), _1557299)))], (39858 ^ _779308) ^ [_1557488, _1557490, _1557492, _1557494, _1557496, _1557498] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1557488, tc_fun(_1557490, tc_HOL_Obool)), _1557492), _1557494), _1557496)), -(hBOOL(hAPP(hAPP(_1557494, _1557498), _1557496))), hBOOL(hAPP(hAPP(c_member(_1557488), _1557498), _1557492))], (39868 ^ _779308) ^ [_1557689, _1557691, _1557693, _1557695, _1557697, _1557699, _1557701, _1557703] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1557689, tc_fun(_1557691, tc_fun(_1557693, tc_HOL_Obool))), _1557695), _1557697), _1557699), _1557701)), hBOOL(hAPP(hAPP(c_member(_1557689), _1557703), _1557695)), -(hBOOL(hAPP(hAPP(hAPP(_1557697, _1557703), _1557699), _1557701)))], (39878 ^ _779308) ^ [_1557912, _1557914, _1557916, _1557918, _1557920, _1557922, _1557924, _1557926] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1557912, tc_fun(_1557914, tc_fun(_1557916, tc_HOL_Obool))), _1557918), _1557920), _1557922), _1557924)), -(hBOOL(hAPP(hAPP(hAPP(_1557920, _1557926), _1557922), _1557924))), hBOOL(hAPP(hAPP(c_member(_1557912), _1557926), _1557918))], (39888 ^ _779308) ^ [_1558139, _1558141, _1558143, _1558145] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1558143), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558139, tc_fun(_1558143, tc_HOL_Obool)), _1558141), _1558145)))), 39889 ^ _779308 : [(39890 ^ _779308) ^ [_1558213] : [hBOOL(hAPP(hAPP(c_member(_1558139), _1558213), _1558141)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558143), hAPP(_1558145, _1558213)))]]], (39898 ^ _779308) ^ [_1558367, _1558369, _1558371] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558367, tc_fun(_1558369, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1558367, tc_HOL_Obool))), _1558371) = c_Orderings_Otop__class_Otop(tc_fun(_1558369, tc_HOL_Obool)))], (39900 ^ _779308) ^ [_1558431, _1558433, _1558435, _1558437] : [_1558431 = c_Orderings_Obot__class_Obot(tc_fun(_1558433, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558433, tc_fun(_1558435, tc_HOL_Obool)), _1558431), hAPP(c_COMBK(tc_fun(_1558435, tc_HOL_Obool), _1558433), _1558437)) = c_Orderings_Otop__class_Otop(tc_fun(_1558435, tc_HOL_Obool)))], (39906 ^ _779308) ^ [_1558568, _1558570, _1558572, _1558574] : [-(_1558568 = c_Orderings_Obot__class_Obot(tc_fun(_1558570, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558570, tc_fun(_1558572, tc_HOL_Obool)), _1558568), hAPP(c_COMBK(tc_fun(_1558572, tc_HOL_Obool), _1558570), _1558574)) = _1558574)], (39912 ^ _779308) ^ [_1558636, _1558638, _1558640, _1558642, _1558644, _1558646] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558636, tc_fun(_1558638, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1558640, tc_fun(_1558636, tc_HOL_Obool)), _1558642), _1558644)), _1558646) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558640, tc_fun(_1558638, tc_HOL_Obool)), _1558642), hAPP(hAPP(c_COMBC(_1558640, tc_fun(_1558636, tc_fun(_1558638, tc_HOL_Obool)), tc_fun(_1558638, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558636, tc_HOL_Obool), tc_fun(tc_fun(_1558636, tc_fun(_1558638, tc_HOL_Obool)), tc_fun(_1558638, tc_HOL_Obool)), _1558640), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558636, tc_fun(_1558638, tc_HOL_Obool))), _1558644)), _1558646)))], (39914 ^ _779308) ^ [_1558755, _1558757, _1558759, _1558761, _1558763, _1558765] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558755, tc_fun(_1558757, tc_HOL_Obool)), _1558759), hAPP(hAPP(c_COMBC(_1558755, tc_fun(_1558761, tc_fun(_1558757, tc_HOL_Obool)), tc_fun(_1558757, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558761, tc_HOL_Obool), tc_fun(tc_fun(_1558761, tc_fun(_1558757, tc_HOL_Obool)), tc_fun(_1558757, tc_HOL_Obool)), _1558755), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558761, tc_fun(_1558757, tc_HOL_Obool))), _1558763)), _1558765)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558761, tc_fun(_1558757, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1558755, tc_fun(_1558761, tc_HOL_Obool)), _1558759), _1558763)), _1558765))], (39916 ^ _779308) ^ [_1558874, _1558876, _1558878, _1558880, _1558882] : [class_Complete__Lattice_Ocomplete__lattice(_1558874), 39919 ^ _779308 : [(39930 ^ _779308) ^ [] : [39932 ^ _779308 : [(39933 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558878), 39931 ^ [_1558874, _1558876, _1558878, _1558880, _1558882]), _1558880)))], (39935 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1558874), _1558876), hAPP(_1558882, 39931 ^ [_1558874, _1558876, _1558878, _1558880, _1558882])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1558874), _1558876), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558878, _1558874), _1558880), _1558882))))], (39920 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1558874), _1558876), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1558878, _1558874), _1558880), _1558882))), 39923 ^ _779308 : [(39924 ^ _779308) ^ [_1559055] : [hBOOL(hAPP(hAPP(c_member(_1558878), _1559055), _1558880)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1558874), _1558876), hAPP(_1558882, _1559055))))]]]]], (39939 ^ _779308) ^ [_1559368, _1559370, _1559372, _1559374, _1559376] : [class_Complete__Lattice_Ocomplete__lattice(_1559368), class_Orderings_Olinorder(_1559368), 39946 ^ _779308 : [(39947 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1559368), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1559370, _1559368), _1559372), _1559374)), _1559376)), 39951 ^ _779308 : [(39952 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559370), 39950 ^ [_1559368, _1559370, _1559372, _1559374, _1559376]), _1559372)))], (39954 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1559368), hAPP(_1559374, 39950 ^ [_1559368, _1559370, _1559372, _1559374, _1559376])), _1559376)))]]], (39956 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1559368), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1559370, _1559368), _1559372), _1559374)), _1559376))), 39957 ^ _779308 : [(39958 ^ _779308) ^ [_1559716] : [hBOOL(hAPP(hAPP(c_member(_1559370), _1559716), _1559372)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1559368), hAPP(_1559374, _1559716)), _1559376))]]]]], (39966 ^ _779308) ^ [_1559886, _1559888, _1559890, _1559892, _1559894, _1559896] : [hBOOL(hAPP(hAPP(c_member(_1559886), _1559888), _1559890)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1559886, tc_fun(_1559892, tc_HOL_Obool)), _1559890), hAPP(hAPP(c_COMBB(tc_fun(_1559892, tc_HOL_Obool), tc_fun(_1559892, tc_HOL_Obool), _1559886), hAPP(c_Set_Oinsert(_1559892), _1559894)), _1559896)) = hAPP(hAPP(c_Set_Oinsert(_1559892), _1559894), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1559886, tc_fun(_1559892, tc_HOL_Obool)), _1559890), _1559896)))], (39972 ^ _779308) ^ [_1560091] : [class_Groups_Oab__semigroup__mult(_1560091), -(c_Finite__Set_Ofun__left__comm(_1560091, _1560091, c_Groups_Otimes__class_Otimes(_1560091)))], (39988 ^ _779308) ^ [_1560437, _1560439, _1560441, _1560443, _1560445] : [39990 ^ _779308 : [(39991 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560441), 39989 ^ [_1560437, _1560439, _1560441, _1560443, _1560445]), _1560443)))], (39993 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1560437), _1560439), hAPP(_1560445, 39989 ^ [_1560437, _1560439, _1560441, _1560443, _1560445])))]], -(hBOOL(hAPP(hAPP(c_member(_1560437), _1560439), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1560441, tc_fun(_1560437, tc_HOL_Obool)), _1560443), _1560445))))], (39978 ^ _779308) ^ [_1560194, _1560196, _1560198, _1560200, _1560202] : [hBOOL(hAPP(hAPP(c_member(_1560194), _1560196), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1560198, tc_fun(_1560194, tc_HOL_Obool)), _1560200), _1560202))), 39981 ^ _779308 : [(39982 ^ _779308) ^ [_1560318] : [hBOOL(hAPP(hAPP(c_member(_1560198), _1560318), _1560200)), -(hBOOL(hAPP(hAPP(c_member(_1560194), _1560196), hAPP(_1560202, _1560318))))]]], (39997 ^ _779308) ^ [_1560712, _1560714, _1560716, _1560718, _1560720, _1560722] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1560712, tc_fun(_1560714, tc_fun(_1560716, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1560712, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1560714, _1560716), tc_HOL_Obool), tc_fun(_1560714, tc_fun(_1560716, tc_HOL_Obool)), _1560712), hAPP(c_COMBC(_1560714, tc_fun(tc_prod(_1560714, _1560716), tc_HOL_Obool), tc_fun(_1560716, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560716, tc_fun(tc_fun(tc_prod(_1560714, _1560716), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1560714, _1560716), tc_HOL_Obool), tc_fun(_1560716, tc_HOL_Obool)), _1560714), c_COMBC(_1560716, tc_fun(tc_prod(_1560714, _1560716), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560716, tc_prod(_1560714, _1560716)), tc_fun(_1560716, tc_fun(tc_fun(tc_prod(_1560714, _1560716), tc_HOL_Obool), tc_HOL_Obool)), _1560714), hAPP(c_COMBB(tc_prod(_1560714, _1560716), tc_fun(tc_fun(tc_prod(_1560714, _1560716), tc_HOL_Obool), tc_HOL_Obool), _1560716), c_member(tc_prod(_1560714, _1560716)))), c_Product__Type_OPair(_1560714, _1560716))))), _1560718)), _1560720), _1560722)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1560714, _1560716)), hAPP(hAPP(c_Product__Type_OPair(_1560714, _1560716), _1560720), _1560722)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1560712, tc_fun(tc_prod(_1560714, _1560716), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1560712, tc_HOL_Obool))), _1560718))))], (40003 ^ _779308) ^ [_1561195, _1561197, _1561199, _1561201, _1561203, _1561205] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561197, _1561199)), hAPP(hAPP(c_Product__Type_OPair(_1561197, _1561199), _1561203), _1561205)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1561195, tc_fun(tc_prod(_1561197, _1561199), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1561195, tc_HOL_Obool))), _1561201))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1561195, tc_fun(_1561197, tc_fun(_1561199, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1561195, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1561197, _1561199), tc_HOL_Obool), tc_fun(_1561197, tc_fun(_1561199, tc_HOL_Obool)), _1561195), hAPP(c_COMBC(_1561197, tc_fun(tc_prod(_1561197, _1561199), tc_HOL_Obool), tc_fun(_1561199, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1561199, tc_fun(tc_fun(tc_prod(_1561197, _1561199), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1561197, _1561199), tc_HOL_Obool), tc_fun(_1561199, tc_HOL_Obool)), _1561197), c_COMBC(_1561199, tc_fun(tc_prod(_1561197, _1561199), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1561199, tc_prod(_1561197, _1561199)), tc_fun(_1561199, tc_fun(tc_fun(tc_prod(_1561197, _1561199), tc_HOL_Obool), tc_HOL_Obool)), _1561197), hAPP(c_COMBB(tc_prod(_1561197, _1561199), tc_fun(tc_fun(tc_prod(_1561197, _1561199), tc_HOL_Obool), tc_HOL_Obool), _1561199), c_member(tc_prod(_1561197, _1561199)))), c_Product__Type_OPair(_1561197, _1561199))))), _1561201)), _1561203), _1561205)))], (40019 ^ _779308) ^ [_1561934, _1561936, _1561938, _1561940] : [40021 ^ _779308 : [(40022 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561934), 40020 ^ [_1561934, _1561936, _1561938, _1561940]), _1561938)))], (40024 ^ _779308) ^ [] : [hAPP(_1561940, 40020 ^ [_1561934, _1561936, _1561938, _1561940]) = c_Orderings_Otop__class_Otop(tc_fun(_1561936, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1561934, tc_fun(_1561936, tc_HOL_Obool)), _1561938), _1561940) = c_Orderings_Otop__class_Otop(tc_fun(_1561936, tc_HOL_Obool)))], (40009 ^ _779308) ^ [_1561705, _1561707, _1561709, _1561711] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1561705, tc_fun(_1561707, tc_HOL_Obool)), _1561709), _1561711) = c_Orderings_Otop__class_Otop(tc_fun(_1561707, tc_HOL_Obool)), 40012 ^ _779308 : [(40013 ^ _779308) ^ [_1561821] : [hBOOL(hAPP(hAPP(c_member(_1561705), _1561821), _1561709)), -(hAPP(_1561711, _1561821) = c_Orderings_Otop__class_Otop(tc_fun(_1561707, tc_HOL_Obool)))]]], (40038 ^ _779308) ^ [_1562414, _1562416, _1562418, _1562420] : [40040 ^ _779308 : [(40041 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562416), 40039 ^ [_1562414, _1562416, _1562418, _1562420]), _1562418)))], (40043 ^ _779308) ^ [] : [hAPP(_1562420, 40039 ^ [_1562414, _1562416, _1562418, _1562420]) = c_Orderings_Otop__class_Otop(tc_fun(_1562414, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1562414, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1562416, tc_fun(_1562414, tc_HOL_Obool)), _1562418), _1562420))], (40028 ^ _779308) ^ [_1562185, _1562187, _1562189, _1562191] : [c_Orderings_Otop__class_Otop(tc_fun(_1562185, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1562187, tc_fun(_1562185, tc_HOL_Obool)), _1562189), _1562191), 40031 ^ _779308 : [(40032 ^ _779308) ^ [_1562301] : [hBOOL(hAPP(hAPP(c_member(_1562187), _1562301), _1562189)), -(hAPP(_1562191, _1562301) = c_Orderings_Otop__class_Otop(tc_fun(_1562185, tc_HOL_Obool)))]]], (40047 ^ _779308) ^ [_1562644, _1562646, _1562648, _1562650, _1562652] : [c_Finite__Set_Ofun__left__comm(_1562644, _1562646, _1562648), -(c_Finite__Set_Ofun__left__comm(_1562650, _1562646, hAPP(hAPP(c_COMBB(_1562644, tc_fun(_1562646, _1562646), _1562650), _1562648), _1562652)))], (40053 ^ _779308) ^ [_1562757, _1562759, _1562761, _1562763, _1562765, _1562767] : [c_Finite__Set_Ofun__left__comm(_1562757, _1562759, _1562761), -(hAPP(hAPP(_1562761, _1562763), hAPP(hAPP(_1562761, _1562765), _1562767)) = hAPP(hAPP(_1562761, _1562765), hAPP(hAPP(_1562761, _1562763), _1562767)))], (40059 ^ _779308) ^ [_1562892, _1562894, _1562896, _1562898, _1562900] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1562892, tc_fun(_1562894, tc_HOL_Obool)), _1562896), hAPP(hAPP(c_COMBS(_1562892, tc_fun(_1562894, tc_HOL_Obool), tc_fun(_1562894, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1562894, tc_HOL_Obool), tc_fun(tc_fun(_1562894, tc_HOL_Obool), tc_fun(_1562894, tc_HOL_Obool)), _1562892), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1562894, tc_HOL_Obool))), _1562898)), _1562900)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1562894, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1562892, tc_fun(_1562894, tc_HOL_Obool)), _1562896), _1562898)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1562892, tc_fun(_1562894, tc_HOL_Obool)), _1562896), _1562900)))], (40061 ^ _779308) ^ [_1563013, _1563015, _1563017, _1563019, _1563021, _1563023] : [class_Complete__Lattice_Ocomplete__lattice(_1563013), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563015, tc_fun(_1563017, _1563013)), _1563019), _1563021), _1563023) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563015, _1563013), _1563019), hAPP(hAPP(c_COMBC(_1563015, _1563017, _1563013), _1563021), _1563023)))], (40067 ^ _779308) ^ [_1563164, _1563166, _1563168, _1563170, _1563172, _1563174] : [class_Complete__Lattice_Ocomplete__lattice(_1563164), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563166, _1563164), _1563168), hAPP(hAPP(c_COMBB(tc_fun(_1563170, _1563164), _1563164, _1563166), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563170, _1563164), _1563172)), _1563174)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563170, _1563164), _1563172), hAPP(hAPP(c_COMBB(tc_fun(_1563166, _1563164), _1563164, _1563170), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563166, _1563164), _1563168)), hAPP(c_COMBC(_1563166, _1563170, _1563164), _1563174))))], (40073 ^ _779308) ^ [_1563373, _1563375, _1563377, _1563379] : [-(hAPP(c_Set_OPow(_1563373), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563375, tc_fun(_1563373, tc_HOL_Obool)), _1563377), _1563379)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563375, tc_fun(tc_fun(_1563373, tc_HOL_Obool), tc_HOL_Obool)), _1563377), hAPP(hAPP(c_COMBB(tc_fun(_1563373, tc_HOL_Obool), tc_fun(tc_fun(_1563373, tc_HOL_Obool), tc_HOL_Obool), _1563375), c_Set_OPow(_1563373)), _1563379)))], (40075 ^ _779308) ^ [_1563455, _1563457, _1563459, _1563461, _1563463, _1563465] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563455, tc_fun(_1563457, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1563459, _1563455, _1563461), _1563463)), _1563465) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563459, tc_fun(_1563457, tc_HOL_Obool)), _1563463), hAPP(hAPP(c_COMBB(_1563455, tc_fun(_1563457, tc_HOL_Obool), _1563459), _1563465), _1563461)))], (40077 ^ _779308) ^ [_1563532, _1563534, _1563536, _1563538, _1563540, _1563542] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563532, tc_fun(_1563534, tc_HOL_Obool)), _1563536), hAPP(hAPP(c_COMBB(_1563538, tc_fun(_1563534, tc_HOL_Obool), _1563532), _1563540), _1563542)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563538, tc_fun(_1563534, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1563532, _1563538, _1563542), _1563536)), _1563540))], (40079 ^ _779308) ^ [_1563609, _1563611, _1563613, _1563615, _1563617] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563609, tc_fun(_1563611, tc_HOL_Obool)), _1563613), hAPP(hAPP(c_COMBB(tc_fun(_1563611, tc_HOL_Obool), tc_fun(_1563611, tc_HOL_Obool), _1563609), hAPP(c_Set_Oinsert(_1563611), _1563615)), _1563617)) = hAPP(hAPP(c_Set_Oinsert(_1563611), _1563615), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563609, tc_fun(_1563611, tc_HOL_Obool)), _1563613), _1563617)))], (40081 ^ _779308) ^ [_1563693, _1563695, _1563697, _1563699, _1563701] : [-(hAPP(hAPP(c_Set_Oinsert(_1563693), _1563695), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563697, tc_fun(_1563693, tc_HOL_Obool)), _1563699), _1563701)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563697, tc_fun(_1563693, tc_HOL_Obool)), _1563699), hAPP(hAPP(c_COMBB(tc_fun(_1563693, tc_HOL_Obool), tc_fun(_1563693, tc_HOL_Obool), _1563697), hAPP(c_Set_Oinsert(_1563693), _1563695)), _1563701)))], (40083 ^ _779308) ^ [_1563777] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563777, tc_HOL_Obool) = c_Set_OBall(_1563777))], (40085 ^ _779308) ^ [_1563805, _1563807, _1563809, _1563811, _1563813, _1563815] : [-(hAPP(c_Set_Ovimage(_1563805, _1563807, _1563809), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563811, tc_fun(_1563807, tc_HOL_Obool)), _1563813), _1563815)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1563811, tc_fun(_1563805, tc_HOL_Obool)), _1563813), hAPP(hAPP(c_COMBB(tc_fun(_1563807, tc_HOL_Obool), tc_fun(_1563805, tc_HOL_Obool), _1563811), c_Set_Ovimage(_1563805, _1563807, _1563809)), _1563815)))], (40087 ^ _779308) ^ [_1563889, _1563891, _1563893, _1563895, _1563897] : [c_Finite__Set_Ofun__left__comm(_1563889, _1563891, _1563893), -(hAPP(c_Fun_Ocomp(_1563891, _1563891, _1563891, hAPP(_1563893, _1563895)), hAPP(_1563893, _1563897)) = hAPP(c_Fun_Ocomp(_1563891, _1563891, _1563891, hAPP(_1563893, _1563897)), hAPP(_1563893, _1563895)))], (40103 ^ _779308) ^ [_1564312, _1564314, _1564316, _1564318, _1564320] : [40105 ^ _779308 : [(40106 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1564316), 40104 ^ [_1564312, _1564314, _1564316, _1564318, _1564320]), _1564318)))], (40108 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564312, tc_HOL_Obool)), _1564314), hAPP(_1564320, 40104 ^ [_1564312, _1564314, _1564316, _1564318, _1564320])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564312, tc_HOL_Obool)), _1564314), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564316, tc_fun(_1564312, tc_HOL_Obool)), _1564318), _1564320))))], (40093 ^ _779308) ^ [_1564054, _1564056, _1564058, _1564060, _1564062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564054, tc_HOL_Obool)), _1564056), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564058, tc_fun(_1564054, tc_HOL_Obool)), _1564060), _1564062))), 40096 ^ _779308 : [(40097 ^ _779308) ^ [_1564187] : [hBOOL(hAPP(hAPP(c_member(_1564058), _1564187), _1564060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564054, tc_HOL_Obool)), _1564056), hAPP(_1564062, _1564187))))]]], (40112 ^ _779308) ^ [_1564575, _1564577, _1564579, _1564581, _1564583, _1564585, _1564587] : [c_Finite__Set_Ofun__left__comm(_1564575, _1564577, _1564579), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1564575, _1564577, _1564579, _1564581, _1564583), _1564585)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1564575, _1564577, _1564579, _1564581, _1564583), _1564587)), -(_1564587 = _1564585)], (40126 ^ _779308) ^ [_1564820, _1564822, _1564824, _1564826, _1564828, _1564830, _1564832] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1564820, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564822, tc_fun(_1564820, tc_HOL_Obool)), _1564824), _1564826)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564828, tc_fun(_1564820, tc_HOL_Obool)), _1564830), _1564832)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564822, tc_fun(_1564820, tc_HOL_Obool)), _1564824), hAPP(hAPP(c_COMBB(tc_fun(_1564828, tc_fun(_1564820, tc_HOL_Obool)), tc_fun(_1564820, tc_HOL_Obool), _1564822), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1564828, tc_fun(_1564820, tc_HOL_Obool)), _1564830)), hAPP(hAPP(c_COMBC(_1564822, tc_fun(_1564828, tc_fun(_1564820, tc_HOL_Obool)), tc_fun(_1564828, tc_fun(_1564820, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1564820, tc_HOL_Obool), tc_fun(_1564820, tc_HOL_Obool)), tc_fun(tc_fun(_1564828, tc_fun(_1564820, tc_HOL_Obool)), tc_fun(_1564828, tc_fun(_1564820, tc_HOL_Obool))), _1564822), c_COMBB(tc_fun(_1564820, tc_HOL_Obool), tc_fun(_1564820, tc_HOL_Obool), _1564828)), hAPP(hAPP(c_COMBB(tc_fun(_1564820, tc_HOL_Obool), tc_fun(tc_fun(_1564820, tc_HOL_Obool), tc_fun(_1564820, tc_HOL_Obool)), _1564822), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1564820, tc_HOL_Obool))), _1564826))), _1564832))))], (40128 ^ _779308) ^ [_1565023, _1565025, _1565027, _1565029, _1565031] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565023, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565025, tc_fun(_1565023, tc_HOL_Obool)), _1565027), _1565029)), _1565031) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565025, tc_fun(_1565023, tc_HOL_Obool)), _1565027), hAPP(hAPP(c_COMBC(_1565025, tc_fun(_1565023, tc_HOL_Obool), tc_fun(_1565023, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565023, tc_HOL_Obool), tc_fun(tc_fun(_1565023, tc_HOL_Obool), tc_fun(_1565023, tc_HOL_Obool)), _1565025), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565023, tc_HOL_Obool))), _1565029)), _1565031)))], (40130 ^ _779308) ^ [_1565132, _1565134, _1565136, _1565138, _1565140] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565132, tc_HOL_Obool)), _1565134), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565136, tc_fun(_1565132, tc_HOL_Obool)), _1565138), _1565140)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565136, tc_fun(_1565132, tc_HOL_Obool)), _1565138), hAPP(hAPP(c_COMBB(tc_fun(_1565132, tc_HOL_Obool), tc_fun(_1565132, tc_HOL_Obool), _1565136), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565132, tc_HOL_Obool)), _1565134)), _1565140)))], (40132 ^ _779308) ^ [_1565222, _1565224, _1565226, _1565228, _1565230] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565222, tc_HOL_Obool)), _1565224), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565226, tc_fun(_1565222, tc_HOL_Obool)), _1565228), _1565230)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565226, tc_fun(_1565222, tc_HOL_Obool)), _1565228), hAPP(hAPP(c_COMBB(tc_fun(_1565222, tc_HOL_Obool), tc_fun(_1565222, tc_HOL_Obool), _1565226), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565222, tc_HOL_Obool)), _1565224)), _1565230)))], (40134 ^ _779308) ^ [_1565312, _1565314, _1565316, _1565318, _1565320] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565312, tc_fun(_1565314, tc_HOL_Obool)), _1565316), hAPP(hAPP(c_COMBC(_1565312, tc_fun(_1565314, tc_HOL_Obool), tc_fun(_1565314, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1565314, tc_HOL_Obool), tc_fun(tc_fun(_1565314, tc_HOL_Obool), tc_fun(_1565314, tc_HOL_Obool)), _1565312), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565314, tc_HOL_Obool))), _1565318)), _1565320)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565314, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565312, tc_fun(_1565314, tc_HOL_Obool)), _1565316), _1565318)), _1565320))], (40136 ^ _779308) ^ [_1565421, _1565423, _1565425, _1565427, _1565429] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565421, tc_fun(_1565423, tc_HOL_Obool)), _1565425), hAPP(hAPP(c_COMBB(tc_fun(_1565423, tc_HOL_Obool), tc_fun(_1565423, tc_HOL_Obool), _1565421), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565423, tc_HOL_Obool)), _1565427)), _1565429)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1565423, tc_HOL_Obool)), _1565427), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565421, tc_fun(_1565423, tc_HOL_Obool)), _1565425), _1565429)))], (40138 ^ _779308) ^ [_1565511, _1565513, _1565515, _1565517, _1565519] : [-(hAPP(c_Relation_Oconverse(_1565511, _1565513), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565515, tc_fun(tc_prod(_1565511, _1565513), tc_HOL_Obool)), _1565517), _1565519)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565515, tc_fun(tc_prod(_1565513, _1565511), tc_HOL_Obool)), _1565517), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1565511, _1565513), tc_HOL_Obool), tc_fun(tc_prod(_1565513, _1565511), tc_HOL_Obool), _1565515), c_Relation_Oconverse(_1565511, _1565513)), _1565519)))], (40140 ^ _779308) ^ [_1565603, _1565605, _1565607, _1565609] : [class_Complete__Lattice_Ocomplete__lattice(_1565603), -(_1565605 = c_Orderings_Obot__class_Obot(tc_fun(_1565607, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565607, _1565603), _1565605), hAPP(c_COMBK(_1565603, _1565607), _1565609)) = _1565609)], (40150 ^ _779308) ^ [_1565737, _1565739, _1565741, _1565743, _1565745] : [hBOOL(hAPP(hAPP(c_member(_1565737), _1565739), _1565741)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1565743, tc_HOL_Obool)), hAPP(_1565745, _1565739)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565737, tc_fun(_1565743, tc_HOL_Obool)), _1565741), _1565745)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565737, tc_fun(_1565743, tc_HOL_Obool)), _1565741), _1565745))], (40156 ^ _779308) ^ [_1565931, _1565933, _1565935, _1565937] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565931, tc_fun(_1565933, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1565931, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1565933, tc_HOL_Obool), tc_fun(_1565933, tc_HOL_Obool), _1565931), hAPP(c_COMBC(_1565933, tc_fun(_1565933, tc_HOL_Obool), tc_HOL_Obool), c_member(_1565933))), _1565935)), _1565937)), -(hBOOL(hAPP(hAPP(c_member(_1565933), _1565937), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1565931, tc_fun(_1565933, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1565931, tc_HOL_Obool))), _1565935))))], (40162 ^ _779308) ^ [_1566150, _1566152, _1566154, _1566156] : [hBOOL(hAPP(hAPP(c_member(_1566152), _1566156), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566150, tc_fun(_1566152, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1566150, tc_HOL_Obool))), _1566154))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566150, tc_fun(_1566152, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1566150, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1566152, tc_HOL_Obool), tc_fun(_1566152, tc_HOL_Obool), _1566150), hAPP(c_COMBC(_1566152, tc_fun(_1566152, tc_HOL_Obool), tc_HOL_Obool), c_member(_1566152))), _1566154)), _1566156)))], (40168 ^ _779308) ^ [_1566375, _1566377, _1566379, _1566381, _1566383] : [hBOOL(hAPP(hAPP(c_member(_1566375), _1566377), _1566379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1566381, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566375, tc_fun(_1566381, tc_HOL_Obool)), _1566379), _1566383)), hAPP(_1566383, _1566377))))], (40174 ^ _779308) ^ [_1566540, _1566542, _1566544, _1566546, _1566548] : [_1566540 = c_Orderings_Obot__class_Obot(tc_fun(_1566542, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566544, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566542, tc_fun(_1566544, tc_HOL_Obool)), _1566540), _1566546)), _1566548) = _1566548)], (40180 ^ _779308) ^ [_1566673, _1566675, _1566677, _1566679, _1566681] : [-(_1566673 = c_Orderings_Obot__class_Obot(tc_fun(_1566675, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566677, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566675, tc_fun(_1566677, tc_HOL_Obool)), _1566673), _1566679)), _1566681) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566675, tc_fun(_1566677, tc_HOL_Obool)), _1566673), hAPP(hAPP(c_COMBC(_1566675, tc_fun(_1566677, tc_HOL_Obool), tc_fun(_1566677, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566677, tc_HOL_Obool), tc_fun(tc_fun(_1566677, tc_HOL_Obool), tc_fun(_1566677, tc_HOL_Obool)), _1566675), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566677, tc_HOL_Obool))), _1566679)), _1566681)))], (40186 ^ _779308) ^ [_1566818, _1566820, _1566822, _1566824, _1566826] : [_1566818 = c_Orderings_Obot__class_Obot(tc_fun(_1566820, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566822, tc_HOL_Obool)), _1566824), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566820, tc_fun(_1566822, tc_HOL_Obool)), _1566818), _1566826)) = _1566824)], (40192 ^ _779308) ^ [_1566951, _1566953, _1566955, _1566957, _1566959] : [-(_1566951 = c_Orderings_Obot__class_Obot(tc_fun(_1566953, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566955, tc_HOL_Obool)), _1566957), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566953, tc_fun(_1566955, tc_HOL_Obool)), _1566951), _1566959)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1566953, tc_fun(_1566955, tc_HOL_Obool)), _1566951), hAPP(hAPP(c_COMBB(tc_fun(_1566955, tc_HOL_Obool), tc_fun(_1566955, tc_HOL_Obool), _1566953), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1566955, tc_HOL_Obool)), _1566957)), _1566959)))], (40198 ^ _779308) ^ [_1567059, _1567061, _1567063, _1567065, _1567067] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567059, tc_fun(_1567061, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1567059), _1567063), _1567065)), _1567067) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567061, tc_HOL_Obool)), hAPP(_1567067, _1567063)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567059, tc_fun(_1567061, tc_HOL_Obool)), _1567065), _1567067)))], (40200 ^ _779308) ^ [_1567136, _1567138, _1567140, _1567142] : [-(hAPP(c_Set_OCollect(_1567136), hAPP(hAPP(c_COMBB(tc_fun(_1567138, tc_HOL_Obool), tc_HOL_Obool, _1567136), c_HOL_OAll(_1567138)), hAPP(hAPP(c_COMBB(tc_fun(_1567138, tc_HOL_Obool), tc_fun(_1567138, tc_HOL_Obool), _1567136), hAPP(c_COMBS(_1567138, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1567138), c_fimplies), hAPP(hAPP(c_COMBC(_1567138, tc_fun(_1567138, tc_HOL_Obool), tc_HOL_Obool), c_member(_1567138)), _1567140)))), _1567142))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567138, tc_fun(_1567136, tc_HOL_Obool)), _1567140), hAPP(hAPP(c_COMBB(tc_fun(_1567136, tc_HOL_Obool), tc_fun(_1567136, tc_HOL_Obool), _1567138), c_Set_OCollect(_1567136)), hAPP(c_COMBC(_1567136, _1567138, tc_HOL_Obool), _1567142))))], (40202 ^ _779308) ^ [_1567270, _1567272, _1567274, _1567276, _1567278] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567270, tc_fun(_1567272, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1567270, tc_HOL_Obool)), _1567274), _1567276)), _1567278) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567272, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567270, tc_fun(_1567272, tc_HOL_Obool)), _1567274), _1567278)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567270, tc_fun(_1567272, tc_HOL_Obool)), _1567276), _1567278)))], (40204 ^ _779308) ^ [_1567359, _1567361, _1567363, _1567365, _1567367] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1567359, tc_fun(_1567361, tc_HOL_Obool)), _1567363), hAPP(hAPP(c_COMBB(tc_fun(_1567361, tc_HOL_Obool), tc_fun(_1567361, tc_HOL_Obool), _1567359), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1567361, tc_HOL_Obool)), _1567365)), _1567367)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1567361, tc_HOL_Obool)), _1567365), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567359, tc_fun(_1567361, tc_HOL_Obool)), _1567363), _1567367)))], (40206 ^ _779308) ^ [_1567449, _1567451, _1567453, _1567455, _1567457] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1567449, tc_HOL_Obool)), _1567451), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567453, tc_fun(_1567449, tc_HOL_Obool)), _1567455), _1567457)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1567453, tc_fun(_1567449, tc_HOL_Obool)), _1567455), hAPP(hAPP(c_COMBB(tc_fun(_1567449, tc_HOL_Obool), tc_fun(_1567449, tc_HOL_Obool), _1567453), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1567449, tc_HOL_Obool)), _1567451)), _1567457)))], (40208 ^ _779308) ^ [_1567539, _1567541, _1567543, _1567545, _1567547, _1567549] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1567539, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1567541, _1567539, _1567543), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567545, tc_fun(_1567541, tc_HOL_Obool)), _1567547), _1567549))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567545, tc_fun(_1567539, tc_HOL_Obool)), _1567547), hAPP(hAPP(c_COMBB(tc_fun(_1567541, tc_HOL_Obool), tc_fun(_1567539, tc_HOL_Obool), _1567545), c_Relation_OImage(_1567541, _1567539, _1567543)), _1567549)))))], (40210 ^ _779308) ^ [_1567633, _1567635, _1567637, _1567639] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1567633, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567635, tc_fun(_1567633, tc_HOL_Obool)), _1567637), _1567639)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1567635, tc_fun(_1567633, tc_HOL_Obool)), _1567637), hAPP(hAPP(c_COMBB(tc_fun(_1567633, tc_HOL_Obool), tc_fun(_1567633, tc_HOL_Obool), _1567635), c_Groups_Ouminus__class_Ouminus(tc_fun(_1567633, tc_HOL_Obool))), _1567639)))], (40212 ^ _779308) ^ [_1567715, _1567717, _1567719, _1567721] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1567715, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1567717, tc_fun(_1567715, tc_HOL_Obool)), _1567719), _1567721)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567717, tc_fun(_1567715, tc_HOL_Obool)), _1567719), hAPP(hAPP(c_COMBB(tc_fun(_1567715, tc_HOL_Obool), tc_fun(_1567715, tc_HOL_Obool), _1567717), c_Groups_Ouminus__class_Ouminus(tc_fun(_1567715, tc_HOL_Obool))), _1567721)))], (40214 ^ _779308) ^ [_1567797, _1567799, _1567801, _1567803, _1567805] : [class_Complete__Lattice_Ocomplete__lattice(_1567797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1567799, tc_HOL_Obool)), _1567801), _1567803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1567797), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567799, _1567797), _1567803), _1567805)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1567799, _1567797), _1567801), _1567805))))], (40224 ^ _779308) ^ [_1568006, _1568008, _1568010, _1568012] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568006, tc_fun(_1568008, tc_HOL_Obool)), _1568010), _1568012) = hAPP(c_Set_OCollect(_1568008), hAPP(hAPP(c_COMBB(tc_fun(_1568006, tc_HOL_Obool), tc_HOL_Obool, _1568008), c_HOL_OAll(_1568006)), hAPP(hAPP(c_COMBB(tc_fun(_1568006, tc_HOL_Obool), tc_fun(_1568006, tc_HOL_Obool), _1568008), hAPP(c_COMBS(_1568006, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1568006), c_fimplies), hAPP(hAPP(c_COMBC(_1568006, tc_fun(_1568006, tc_HOL_Obool), tc_HOL_Obool), c_member(_1568006)), _1568010)))), hAPP(hAPP(c_COMBC(_1568008, tc_fun(_1568006, tc_fun(_1568008, tc_HOL_Obool)), tc_fun(_1568006, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1568008, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1568006, tc_fun(_1568008, tc_HOL_Obool)), tc_fun(_1568006, tc_HOL_Obool)), _1568008), c_COMBB(tc_fun(_1568008, tc_HOL_Obool), tc_HOL_Obool, _1568006)), c_member(_1568008))), _1568012)))))], (40226 ^ _779308) ^ [_1568189, _1568191, _1568193, _1568195, _1568197] : [_1568189 = c_Orderings_Obot__class_Obot(tc_fun(_1568191, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568191, tc_fun(_1568193, tc_HOL_Obool)), _1568189), hAPP(hAPP(c_COMBC(_1568191, tc_fun(_1568193, tc_HOL_Obool), tc_fun(_1568193, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568193, tc_HOL_Obool), tc_fun(tc_fun(_1568193, tc_HOL_Obool), tc_fun(_1568193, tc_HOL_Obool)), _1568191), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568193, tc_HOL_Obool))), _1568195)), _1568197)) = c_Orderings_Otop__class_Otop(tc_fun(_1568193, tc_HOL_Obool)))], (40232 ^ _779308) ^ [_1568396, _1568398, _1568400, _1568402, _1568404] : [-(_1568396 = c_Orderings_Obot__class_Obot(tc_fun(_1568398, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568398, tc_fun(_1568400, tc_HOL_Obool)), _1568396), hAPP(hAPP(c_COMBC(_1568398, tc_fun(_1568400, tc_HOL_Obool), tc_fun(_1568400, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568400, tc_HOL_Obool), tc_fun(tc_fun(_1568400, tc_HOL_Obool), tc_fun(_1568400, tc_HOL_Obool)), _1568398), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568400, tc_HOL_Obool))), _1568402)), _1568404)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568400, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568398, tc_fun(_1568400, tc_HOL_Obool)), _1568396), _1568402)), _1568404))], (40238 ^ _779308) ^ [_1568541, _1568543, _1568545, _1568547, _1568549] : [_1568541 = c_Orderings_Obot__class_Obot(tc_fun(_1568543, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568543, tc_fun(_1568545, tc_HOL_Obool)), _1568541), hAPP(hAPP(c_COMBB(tc_fun(_1568545, tc_HOL_Obool), tc_fun(_1568545, tc_HOL_Obool), _1568543), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568545, tc_HOL_Obool)), _1568547)), _1568549)) = c_Orderings_Otop__class_Otop(tc_fun(_1568545, tc_HOL_Obool)))], (40244 ^ _779308) ^ [_1568710, _1568712, _1568714, _1568716, _1568718] : [-(_1568710 = c_Orderings_Obot__class_Obot(tc_fun(_1568712, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568712, tc_fun(_1568714, tc_HOL_Obool)), _1568710), hAPP(hAPP(c_COMBB(tc_fun(_1568714, tc_HOL_Obool), tc_fun(_1568714, tc_HOL_Obool), _1568712), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568714, tc_HOL_Obool)), _1568716)), _1568718)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1568714, tc_HOL_Obool)), _1568716), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568712, tc_fun(_1568714, tc_HOL_Obool)), _1568710), _1568718)))], (40250 ^ _779308) ^ [_1568836, _1568838, _1568840, _1568842, _1568844] : [_1568836 = c_Orderings_Obot__class_Obot(tc_fun(_1568838, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1568838, tc_fun(_1568840, tc_HOL_Obool)), _1568836), hAPP(hAPP(c_COMBC(_1568838, tc_fun(_1568840, tc_HOL_Obool), tc_fun(_1568840, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568840, tc_HOL_Obool), tc_fun(tc_fun(_1568840, tc_HOL_Obool), tc_fun(_1568840, tc_HOL_Obool)), _1568838), c_Groups_Ominus__class_Ominus(tc_fun(_1568840, tc_HOL_Obool))), _1568842)), _1568844)) = c_Orderings_Otop__class_Otop(tc_fun(_1568840, tc_HOL_Obool)))], (40256 ^ _779308) ^ [_1569043, _1569045, _1569047, _1569049, _1569051] : [-(_1569043 = c_Orderings_Obot__class_Obot(tc_fun(_1569045, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569045, tc_fun(_1569047, tc_HOL_Obool)), _1569043), hAPP(hAPP(c_COMBC(_1569045, tc_fun(_1569047, tc_HOL_Obool), tc_fun(_1569047, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569047, tc_HOL_Obool), tc_fun(tc_fun(_1569047, tc_HOL_Obool), tc_fun(_1569047, tc_HOL_Obool)), _1569045), c_Groups_Ominus__class_Ominus(tc_fun(_1569047, tc_HOL_Obool))), _1569049)), _1569051)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569047, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569045, tc_fun(_1569047, tc_HOL_Obool)), _1569043), _1569049)), _1569051))], (40262 ^ _779308) ^ [_1569188, _1569190, _1569192, _1569194, _1569196] : [_1569188 = c_Orderings_Obot__class_Obot(tc_fun(_1569190, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569192, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569190, tc_fun(_1569192, tc_HOL_Obool)), _1569188), _1569194)), _1569196) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569192, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1569192, tc_HOL_Obool))), _1569196))], (40268 ^ _779308) ^ [_1569353, _1569355, _1569357, _1569359, _1569361] : [-(_1569353 = c_Orderings_Obot__class_Obot(tc_fun(_1569355, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569357, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569355, tc_fun(_1569357, tc_HOL_Obool)), _1569353), _1569359)), _1569361) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569355, tc_fun(_1569357, tc_HOL_Obool)), _1569353), hAPP(hAPP(c_COMBC(_1569355, tc_fun(_1569357, tc_HOL_Obool), tc_fun(_1569357, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1569357, tc_HOL_Obool), tc_fun(tc_fun(_1569357, tc_HOL_Obool), tc_fun(_1569357, tc_HOL_Obool)), _1569355), c_Groups_Ominus__class_Ominus(tc_fun(_1569357, tc_HOL_Obool))), _1569359)), _1569361)))], (40274 ^ _779308) ^ [_1569498, _1569500, _1569502, _1569504, _1569506] : [_1569498 = c_Orderings_Obot__class_Obot(tc_fun(_1569500, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569502, tc_HOL_Obool)), _1569504), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1569500, tc_fun(_1569502, tc_HOL_Obool)), _1569498), _1569506)) = _1569504)], (40280 ^ _779308) ^ [_1569631, _1569633, _1569635, _1569637, _1569639] : [-(_1569631 = c_Orderings_Obot__class_Obot(tc_fun(_1569633, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569635, tc_HOL_Obool)), _1569637), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1569633, tc_fun(_1569635, tc_HOL_Obool)), _1569631), _1569639)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569633, tc_fun(_1569635, tc_HOL_Obool)), _1569631), hAPP(hAPP(c_COMBB(tc_fun(_1569635, tc_HOL_Obool), tc_fun(_1569635, tc_HOL_Obool), _1569633), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1569635, tc_HOL_Obool)), _1569637)), _1569639)))], (40286 ^ _779308) ^ [_1569739, _1569741, _1569743, _1569745, _1569747, _1569749] : [c_Finite__Set_Ofun__left__comm(_1569739, _1569741, _1569743), hBOOL(hAPP(c_Finite__Set_Ofinite(_1569739), _1569745)), -(hAPP(hAPP(_1569743, _1569747), hAPP(hAPP(c_Finite__Set_Ofold(_1569739, _1569741, _1569743), _1569749), _1569745)) = hAPP(hAPP(c_Finite__Set_Ofold(_1569739, _1569741, _1569743), hAPP(hAPP(_1569743, _1569747), _1569749)), _1569745))], (40296 ^ _779308) ^ [_1569958, _1569960, _1569962, _1569964, _1569966] : [class_Complete__Lattice_Ocomplete__lattice(_1569958), hBOOL(hAPP(hAPP(c_member(_1569960), _1569962), _1569964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1569958), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1569960, _1569958), _1569964), _1569966)), hAPP(_1569966, _1569962))))], (40306 ^ _779308) ^ [_1570149, _1570151, _1570153, _1570155, _1570157, _1570159] : [c_Finite__Set_Ofun__left__comm(_1570149, _1570151, _1570153), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1570149, _1570151, _1570153, _1570155, _1570157), _1570159)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1570149, _1570151, _1570153), _1570155), _1570157) = _1570159)], (40316 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (40318 ^ _779308) ^ [_1570368, _1570370, _1570372, _1570374, _1570376] : [_1570368 = c_Orderings_Obot__class_Obot(tc_fun(_1570370, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1570370, tc_fun(_1570372, tc_HOL_Obool)), _1570368), hAPP(hAPP(c_COMBB(tc_fun(_1570372, tc_HOL_Obool), tc_fun(_1570372, tc_HOL_Obool), _1570370), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1570372, tc_HOL_Obool)), _1570374)), _1570376)) = c_Orderings_Otop__class_Otop(tc_fun(_1570372, tc_HOL_Obool)))], (40324 ^ _779308) ^ [_1570537, _1570539, _1570541, _1570543, _1570545] : [-(_1570537 = c_Orderings_Obot__class_Obot(tc_fun(_1570539, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1570539, tc_fun(_1570541, tc_HOL_Obool)), _1570537), hAPP(hAPP(c_COMBB(tc_fun(_1570541, tc_HOL_Obool), tc_fun(_1570541, tc_HOL_Obool), _1570539), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1570541, tc_HOL_Obool)), _1570543)), _1570545)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1570541, tc_HOL_Obool)), _1570543), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1570539, tc_fun(_1570541, tc_HOL_Obool)), _1570537), _1570545)))], (40330 ^ _779308) ^ [_1570645, _1570647, _1570649, _1570651, _1570653, _1570655] : [c_Relation_Osingle__valued(_1570645, _1570647, hAPP(c_Relation_Oconverse(_1570647, _1570645), _1570649)), -(_1570651 = c_Orderings_Obot__class_Obot(tc_fun(_1570653, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1570647, _1570645, _1570649), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1570653, tc_fun(_1570647, tc_HOL_Obool)), _1570651), _1570655)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1570653, tc_fun(_1570645, tc_HOL_Obool)), _1570651), hAPP(hAPP(c_COMBB(tc_fun(_1570647, tc_HOL_Obool), tc_fun(_1570645, tc_HOL_Obool), _1570653), c_Relation_OImage(_1570647, _1570645, _1570649)), _1570655)))], (40340 ^ _779308) ^ [_1570871, _1570873, _1570875, _1570877, _1570879] : [class_Complete__Lattice_Ocomplete__lattice(_1570871), hBOOL(hAPP(c_Finite__Set_Ofinite(_1570873), _1570875)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1570871), _1570877), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1570873, _1570871), _1570875), _1570879)) = hAPP(hAPP(c_Finite__Set_Ofold(_1570873, _1570871, hAPP(hAPP(c_COMBB(_1570871, tc_fun(_1570871, _1570871), _1570873), c_Lattices_Osemilattice__inf__class_Oinf(_1570871)), _1570879)), _1570877), _1570875))], (40350 ^ _779308) ^ [_1571102, _1571104, _1571106, _1571108, _1571110] : [c_Finite__Set_Ofun__left__comm(_1571102, _1571104, _1571106), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571102), _1571108)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1571102, _1571104, _1571106, _1571110, _1571108), hAPP(hAPP(c_Finite__Set_Ofold(_1571102, _1571104, _1571106), _1571110), _1571108))))], (40360 ^ _779308) ^ [_1571289, _1571291, _1571293, _1571295, _1571297, _1571299] : [c_Finite__Set_Ofun__left__comm(_1571289, _1571291, _1571293), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571289), _1571295)), -(hBOOL(hAPP(hAPP(c_member(_1571289), _1571297), _1571295))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1571289, _1571291, _1571293), _1571299), hAPP(hAPP(c_Set_Oinsert(_1571289), _1571297), _1571295)) = hAPP(hAPP(c_Finite__Set_Ofold(_1571289, _1571291, _1571293), hAPP(hAPP(_1571293, _1571297), _1571299)), _1571295))], (40374 ^ _779308) ^ [_1571541, _1571543, _1571545, _1571547, _1571549, _1571551] : [c_Finite__Set_Ofun__left__comm(_1571541, _1571543, _1571545), hBOOL(hAPP(c_Finite__Set_Ofinite(_1571541), _1571547)), -(hBOOL(hAPP(hAPP(c_member(_1571541), _1571549), _1571547))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1571541, _1571543, _1571545), _1571551), hAPP(hAPP(c_Set_Oinsert(_1571541), _1571549), _1571547)) = hAPP(hAPP(_1571545, _1571549), hAPP(hAPP(c_Finite__Set_Ofold(_1571541, _1571543, _1571545), _1571551), _1571547)))], (40388 ^ _779308) ^ [_1571793, _1571795, _1571797, _1571799, _1571801, _1571803, _1571805] : [c_Finite__Set_Ofun__left__comm(_1571793, _1571795, _1571797), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1571793, _1571795, _1571797, _1571799, _1571801), _1571803)), hBOOL(hAPP(hAPP(c_member(_1571793), _1571805), _1571801)), 40400 ^ _779308 : [(40401 ^ _779308) ^ [] : [-(_1571803 = hAPP(hAPP(_1571797, _1571805), 40399 ^ [_1571793, _1571795, _1571797, _1571799, _1571801, _1571803, _1571805]))], (40403 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1571793, _1571795, _1571797, _1571799, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1571793, tc_HOL_Obool)), _1571801), hAPP(hAPP(c_Set_Oinsert(_1571793), _1571805), c_Orderings_Obot__class_Obot(tc_fun(_1571793, tc_HOL_Obool))))), 40399 ^ [_1571793, _1571795, _1571797, _1571799, _1571801, _1571803, _1571805])))]]], (40405 ^ _779308) ^ [_1572177, _1572179] : [class_Complete__Lattice_Ocomplete__lattice(_1572177), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572177), _1572179)), -(c_Complete__Lattice_OInf__class_OInf(_1572177, _1572179) = hAPP(hAPP(c_Finite__Set_Ofold(_1572177, _1572177, c_Lattices_Osemilattice__inf__class_Oinf(_1572177)), c_Orderings_Otop__class_Otop(_1572177)), _1572179))], (40415 ^ _779308) ^ [_1572346, _1572348] : [class_Complete__Lattice_Ocomplete__lattice(_1572346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572346), _1572348)), -(c_Complete__Lattice_OSup__class_OSup(_1572346, _1572348) = hAPP(hAPP(c_Finite__Set_Ofold(_1572346, _1572346, c_Lattices_Osemilattice__sup__class_Osup(_1572346)), c_Orderings_Obot__class_Obot(_1572346)), _1572348))], (40425 ^ _779308) ^ [_1572515, _1572517] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1572515), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1572515, tc_HOL_Obool), _1572517)))), 40426 ^ _779308 : [(40427 ^ _779308) ^ [_1572579] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1572515, tc_HOL_Obool)), _1572579), _1572517)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1572515), _1572579))]]], (40435 ^ _779308) ^ [_1572723, _1572725, _1572727, _1572729] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1572723, tc_HOL_Obool)), _1572725), _1572727)), hBOOL(hAPP(hAPP(c_member(_1572723), _1572729), _1572725)), -(hBOOL(hAPP(hAPP(c_member(_1572723), _1572729), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1572723, tc_HOL_Obool), _1572727))))], (40445 ^ _779308) ^ [_1572920, _1572922, _1572924, _1572926] : [hBOOL(hAPP(hAPP(c_member(_1572920), _1572922), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1572920, tc_HOL_Obool), _1572924))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1572920, tc_HOL_Obool)), _1572926), _1572924)), -(hBOOL(hAPP(hAPP(c_member(_1572920), _1572922), _1572926)))], (40455 ^ _779308) ^ [_1573117, _1573119, _1573121, _1573123] : [hBOOL(hAPP(hAPP(c_member(_1573117), _1573119), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1573117, tc_HOL_Obool), _1573121))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1573117, tc_HOL_Obool)), _1573123), _1573121)), -(hBOOL(hAPP(hAPP(c_member(_1573117), _1573119), _1573123)))], (40475 ^ _779308) ^ [_1573591, _1573593, _1573595, _1573597, _1573599, _1573601, _1573603] : [40477 ^ _779308 : [(40478 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1573591), 40476 ^ [_1573591, _1573593, _1573595, _1573597, _1573599, _1573601, _1573603]), _1573597)))], (40480 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1573599, 40476 ^ [_1573591, _1573593, _1573595, _1573597, _1573599, _1573601, _1573603]), _1573601), _1573603))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1573591, tc_fun(_1573593, tc_fun(_1573595, tc_HOL_Obool))), _1573597), _1573599), _1573601), _1573603)))], (40465 ^ _779308) ^ [_1573344, _1573346, _1573348, _1573350, _1573352, _1573354, _1573356] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1573344, tc_fun(_1573346, tc_fun(_1573348, tc_HOL_Obool))), _1573350), _1573352), _1573354), _1573356)), 40468 ^ _779308 : [(40469 ^ _779308) ^ [_1573472] : [hBOOL(hAPP(hAPP(c_member(_1573344), _1573472), _1573350)), -(hBOOL(hAPP(hAPP(hAPP(_1573352, _1573472), _1573354), _1573356)))]]], (40494 ^ _779308) ^ [_1574093, _1574095, _1574097, _1574099, _1574101] : [40496 ^ _779308 : [(40497 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1574093), 40495 ^ [_1574093, _1574095, _1574097, _1574099, _1574101]), _1574097)))], (40499 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1574099, 40495 ^ [_1574093, _1574095, _1574097, _1574099, _1574101]), _1574101))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574093, tc_fun(_1574095, tc_HOL_Obool)), _1574097), _1574099), _1574101)))], (40484 ^ _779308) ^ [_1573875, _1573877, _1573879, _1573881, _1573883] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1573875, tc_fun(_1573877, tc_HOL_Obool)), _1573879), _1573881), _1573883)), 40487 ^ _779308 : [(40488 ^ _779308) ^ [_1573984] : [hBOOL(hAPP(hAPP(c_member(_1573875), _1573984), _1573879)), -(hBOOL(hAPP(hAPP(_1573881, _1573984), _1573883)))]]], (40503 ^ _779308) ^ [_1574316, _1574318, _1574320, _1574322] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574316, tc_fun(_1574318, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1574316, tc_HOL_Obool), _1574320)), _1574322) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1574316, tc_HOL_Obool), tc_fun(_1574318, tc_HOL_Obool)), _1574320), hAPP(hAPP(c_COMBC(tc_fun(_1574316, tc_HOL_Obool), tc_fun(_1574316, tc_fun(_1574318, tc_HOL_Obool)), tc_fun(_1574318, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574316, tc_fun(_1574318, tc_HOL_Obool))), _1574322)))], (40505 ^ _779308) ^ [_1574406, _1574408, _1574410, _1574412] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1574406, tc_HOL_Obool), tc_fun(_1574408, tc_HOL_Obool)), _1574410), hAPP(hAPP(c_COMBC(tc_fun(_1574406, tc_HOL_Obool), tc_fun(_1574406, tc_fun(_1574408, tc_HOL_Obool)), tc_fun(_1574408, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574406, tc_fun(_1574408, tc_HOL_Obool))), _1574412)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574406, tc_fun(_1574408, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1574406, tc_HOL_Obool), _1574410)), _1574412))], (40507 ^ _779308) ^ [_1574496, _1574498, _1574500, _1574502] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1574496, tc_HOL_Obool), hAPP(c_Set_Oimage(_1574498, tc_fun(_1574496, tc_HOL_Obool), _1574500), _1574502)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574498, tc_fun(_1574496, tc_HOL_Obool)), _1574502), _1574500))], (40509 ^ _779308) ^ [_1574553, _1574555, _1574557, _1574559] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1574553, tc_fun(_1574555, tc_HOL_Obool)), _1574557), _1574559) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1574555, tc_HOL_Obool), hAPP(c_Set_Oimage(_1574553, tc_fun(_1574555, tc_HOL_Obool), _1574559), _1574557)))], (40511 ^ _779308) ^ [_1574610, _1574612, _1574614] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574610, tc_HOL_Obool)), _1574612), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1574610, tc_HOL_Obool), _1574614)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1574610, tc_HOL_Obool), tc_fun(_1574610, tc_HOL_Obool)), _1574614), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1574610, tc_HOL_Obool)), _1574612)))], (40523 ^ _779308) ^ [_1574963, _1574965, _1574967] : [40525 ^ _779308 : [(40526 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1574963, tc_HOL_Obool)), 40524 ^ [_1574963, _1574965, _1574967]), _1574965)))], (40528 ^ _779308) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1574963, tc_HOL_Obool)), 40524 ^ [_1574963, _1574965, _1574967]), _1574967) = c_Orderings_Obot__class_Obot(tc_fun(_1574963, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1574963, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1574963, tc_HOL_Obool), _1574965)), _1574967) = c_Orderings_Obot__class_Obot(tc_fun(_1574963, tc_HOL_Obool)))], (40513 ^ _779308) ^ [_1574695, _1574697, _1574699] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1574695, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1574695, tc_HOL_Obool), _1574697)), _1574699) = c_Orderings_Obot__class_Obot(tc_fun(_1574695, tc_HOL_Obool)), 40516 ^ _779308 : [(40517 ^ _779308) ^ [_1574830] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1574695, tc_HOL_Obool)), _1574830), _1574697)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1574695, tc_HOL_Obool)), _1574830), _1574699) = c_Orderings_Obot__class_Obot(tc_fun(_1574695, tc_HOL_Obool)))]]], (40532 ^ _779308) ^ [_1575226, _1575228, _1575230] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1575226, tc_HOL_Obool)), _1575228), _1575230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575226, tc_HOL_Obool)), _1575228), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1575226, tc_HOL_Obool), _1575230))))], (40538 ^ _779308) ^ [_1575357, _1575359, _1575361] : [class_Complete__Lattice_Ocomplete__lattice(_1575357), class_Orderings_Olinorder(_1575357), 40545 ^ _779308 : [(40546 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575357), _1575359), c_Complete__Lattice_OSup__class_OSup(_1575357, _1575361))), 40550 ^ _779308 : [(40551 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1575357), 40549 ^ [_1575357, _1575359, _1575361]), _1575361)))], (40553 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575357), _1575359), 40549 ^ [_1575357, _1575359, _1575361])))]]], (40555 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575357), _1575359), c_Complete__Lattice_OSup__class_OSup(_1575357, _1575361)))), 40556 ^ _779308 : [(40557 ^ _779308) ^ [_1575663] : [hBOOL(hAPP(hAPP(c_member(_1575357), _1575663), _1575361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575357), _1575359), _1575663))]]]]], (40565 ^ _779308) ^ [_1575817, _1575819, _1575821] : [class_Complete__Lattice_Ocomplete__lattice(_1575817), class_Orderings_Olinorder(_1575817), 40572 ^ _779308 : [(40573 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575817), c_Complete__Lattice_OInf__class_OInf(_1575817, _1575819)), _1575821)), 40577 ^ _779308 : [(40578 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1575817), 40576 ^ [_1575817, _1575819, _1575821]), _1575819)))], (40580 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575817), 40576 ^ [_1575817, _1575819, _1575821]), _1575821)))]]], (40582 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575817), c_Complete__Lattice_OInf__class_OInf(_1575817, _1575819)), _1575821))), 40583 ^ _779308 : [(40584 ^ _779308) ^ [_1576123] : [hBOOL(hAPP(hAPP(c_member(_1575817), _1576123), _1575819)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1575817), _1576123), _1575821))]]]]], (40592 ^ _779308) ^ [_1576277, _1576279, _1576281] : [class_Complete__Lattice_Ocomplete__lattice(_1576277), 40595 ^ _779308 : [(40606 ^ _779308) ^ [] : [40608 ^ _779308 : [(40609 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576277), 40607 ^ [_1576277, _1576279, _1576281]), _1576281)))], (40611 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576277), _1576279), 40607 ^ [_1576277, _1576279, _1576281]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576277), _1576279), c_Complete__Lattice_OInf__class_OInf(_1576277, _1576281))))], (40596 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576277), _1576279), c_Complete__Lattice_OInf__class_OInf(_1576277, _1576281))), 40599 ^ _779308 : [(40600 ^ _779308) ^ [_1576435] : [hBOOL(hAPP(hAPP(c_member(_1576277), _1576435), _1576281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576277), _1576279), _1576435)))]]]]], (40615 ^ _779308) ^ [_1576711, _1576713, _1576715] : [class_Complete__Lattice_Ocomplete__lattice(_1576711), 40618 ^ _779308 : [(40629 ^ _779308) ^ [] : [40631 ^ _779308 : [(40632 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576711), 40630 ^ [_1576711, _1576713, _1576715]), _1576713)))], (40634 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576711), 40630 ^ [_1576711, _1576713, _1576715]), _1576715))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576711), c_Complete__Lattice_OSup__class_OSup(_1576711, _1576713)), _1576715)))], (40619 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576711), c_Complete__Lattice_OSup__class_OSup(_1576711, _1576713)), _1576715)), 40622 ^ _779308 : [(40623 ^ _779308) ^ [_1576869] : [hBOOL(hAPP(hAPP(c_member(_1576711), _1576869), _1576713)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1576711), _1576869), _1576715)))]]]]], (40638 ^ _779308) ^ [_1577145, _1577147] : [-(hAPP(c_Relation_OField(_1577145), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1577145, _1577145), tc_HOL_Obool), _1577147)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577145, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1577145, _1577145), tc_HOL_Obool), tc_fun(_1577145, tc_HOL_Obool), c_Relation_OField(_1577145)), _1577147)))], (40640 ^ _779308) ^ [_1577208, _1577210] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577208, tc_HOL_Obool), hAPP(c_Set_OPow(_1577208), _1577210)) = _1577210)], (40642 ^ _779308) ^ [_1577244, _1577246, _1577248, _1577250] : [-(hAPP(c_Set_Oimage(_1577244, _1577246, _1577248), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577244, tc_HOL_Obool), _1577250)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577244, tc_HOL_Obool), tc_fun(_1577246, tc_HOL_Obool)), _1577250), c_Set_Oimage(_1577244, _1577246, _1577248)))], (40644 ^ _779308) ^ [_1577305, _1577307, _1577309, _1577311] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1577305, _1577307), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577305, tc_HOL_Obool), _1577309)), _1577311) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577305, tc_HOL_Obool), tc_fun(tc_prod(_1577305, _1577307), tc_HOL_Obool)), _1577309), hAPP(hAPP(c_COMBC(tc_fun(_1577305, tc_HOL_Obool), tc_fun(_1577305, tc_fun(_1577307, tc_HOL_Obool)), tc_fun(tc_prod(_1577305, _1577307), tc_HOL_Obool)), c_Product__Type_OSigma(_1577305, _1577307)), _1577311)))], (40646 ^ _779308) ^ [_1577395, _1577397, _1577399, _1577401] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577395, tc_HOL_Obool), tc_fun(_1577397, tc_HOL_Obool)), _1577399), hAPP(hAPP(c_COMBC(tc_fun(_1577395, tc_HOL_Obool), tc_fun(_1577395, tc_fun(_1577397, tc_HOL_Obool)), tc_fun(_1577397, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577395, tc_fun(_1577397, tc_HOL_Obool))), _1577401)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577395, tc_fun(_1577397, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577395, tc_HOL_Obool), _1577399)), _1577401))], (40648 ^ _779308) ^ [_1577485, _1577487, _1577489, _1577491] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577485, tc_fun(_1577487, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577485, tc_HOL_Obool), _1577489)), _1577491) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577485, tc_HOL_Obool), tc_fun(_1577487, tc_HOL_Obool)), _1577489), hAPP(hAPP(c_COMBC(tc_fun(_1577485, tc_HOL_Obool), tc_fun(_1577485, tc_fun(_1577487, tc_HOL_Obool)), tc_fun(_1577487, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577485, tc_fun(_1577487, tc_HOL_Obool))), _1577491)))], (40650 ^ _779308) ^ [_1577575, _1577577, _1577579] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577575, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577575, tc_HOL_Obool), _1577577)), _1577579) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577575, tc_HOL_Obool), tc_fun(_1577575, tc_HOL_Obool)), _1577577), hAPP(hAPP(c_COMBC(tc_fun(_1577575, tc_HOL_Obool), tc_fun(_1577575, tc_HOL_Obool), tc_fun(_1577575, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577575, tc_HOL_Obool))), _1577579)))], (40652 ^ _779308) ^ [_1577658, _1577660, _1577662] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577658, tc_HOL_Obool)), _1577660), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577658, tc_HOL_Obool), _1577662)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577658, tc_HOL_Obool), tc_fun(_1577658, tc_HOL_Obool)), _1577662), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1577658, tc_HOL_Obool)), _1577660)))], (40654 ^ _779308) ^ [_1577725, _1577727, _1577729] : [-(hAPP(c_Relation_ORange(_1577725, _1577727), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1577725, _1577727), tc_HOL_Obool), _1577729)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1577725, _1577727), tc_HOL_Obool), tc_fun(_1577727, tc_HOL_Obool)), _1577729), c_Relation_ORange(_1577725, _1577727)))], (40656 ^ _779308) ^ [_1577788, _1577790, _1577792] : [-(hAPP(c_Relation_ODomain(_1577788, _1577790), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1577788, _1577790), tc_HOL_Obool), _1577792)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1577788, _1577790), tc_HOL_Obool), tc_fun(_1577788, tc_HOL_Obool)), _1577792), c_Relation_ODomain(_1577788, _1577790)))], (40658 ^ _779308) ^ [_1577851, _1577853, _1577855, _1577857] : [-(hAPP(c_Set_Ovimage(_1577851, _1577853, _1577855), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1577853, tc_HOL_Obool), _1577857)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1577853, tc_HOL_Obool), tc_fun(_1577851, tc_HOL_Obool)), _1577857), c_Set_Ovimage(_1577851, _1577853, _1577855)))], (40660 ^ _779308) ^ [_1577912, _1577914] : [class_Complete__Lattice_Ocomplete__lattice(_1577912), -(c_Complete__Lattice_OInf__class_OInf(_1577912, _1577914) = c_Complete__Lattice_OSup__class_OSup(_1577912, hAPP(c_Set_OCollect(_1577912), hAPP(hAPP(c_COMBB(tc_fun(_1577912, tc_HOL_Obool), tc_HOL_Obool, _1577912), c_HOL_OAll(_1577912)), hAPP(hAPP(c_COMBB(tc_fun(_1577912, tc_HOL_Obool), tc_fun(_1577912, tc_HOL_Obool), _1577912), hAPP(c_COMBS(_1577912, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1577912), c_fimplies), hAPP(hAPP(c_COMBC(_1577912, tc_fun(_1577912, tc_HOL_Obool), tc_HOL_Obool), c_member(_1577912)), _1577914)))), c_Orderings_Oord__class_Oless__eq(_1577912))))))], (40666 ^ _779308) ^ [_1578139, _1578141] : [class_Complete__Lattice_Ocomplete__lattice(_1578139), -(c_Complete__Lattice_OSup__class_OSup(_1578139, _1578141) = c_Complete__Lattice_OInf__class_OInf(_1578139, hAPP(c_Set_OCollect(_1578139), hAPP(hAPP(c_COMBB(tc_fun(_1578139, tc_HOL_Obool), tc_HOL_Obool, _1578139), c_HOL_OAll(_1578139)), hAPP(hAPP(c_COMBB(tc_fun(_1578139, tc_HOL_Obool), tc_fun(_1578139, tc_HOL_Obool), _1578139), hAPP(c_COMBS(_1578139, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578139), c_fimplies), hAPP(hAPP(c_COMBC(_1578139, tc_fun(_1578139, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578139)), _1578141)))), hAPP(c_COMBC(_1578139, _1578139, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1578139)))))))], (40672 ^ _779308) ^ [_1578380, _1578382, _1578384] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1578380, tc_HOL_Obool)), _1578382), _1578384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578380, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1578380, tc_HOL_Obool), _1578384)), _1578382)))], (40678 ^ _779308) ^ [_1578511] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578511, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1578511, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1578511, tc_HOL_Obool)))], (40680 ^ _779308) ^ [_1578553, _1578555, _1578557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1578553, tc_HOL_Obool), tc_HOL_Obool)), _1578555), _1578557)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1578553, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578553, tc_HOL_Obool), _1578555)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578553, tc_HOL_Obool), _1578557))))], (40686 ^ _779308) ^ [_1578702, _1578704, _1578706] : [c_Equiv__Relations_Oequiv(_1578702, _1578704, _1578706), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578702, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1578702), _1578704), _1578706)) = _1578704)], (40692 ^ _779308) ^ [_1578811, _1578813, _1578815] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578811, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1578811, tc_HOL_Obool)), _1578813), _1578815)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1578811, tc_HOL_Obool)), _1578813), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578811, tc_HOL_Obool), _1578815)))], (40694 ^ _779308) ^ [_1578872, _1578874] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1578872), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578872, tc_HOL_Obool), _1578874))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1578872, tc_HOL_Obool)), _1578874)))], (40700 ^ _779308) ^ [_1578983, _1578985] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1578983, tc_HOL_Obool), tc_HOL_Obool)), _1578985), hAPP(c_Set_OPow(_1578983), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1578983, tc_HOL_Obool), _1578985)))))], (40702 ^ _779308) ^ [_1579032, _1579034, _1579036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1579032, tc_HOL_Obool), tc_HOL_Obool)), _1579034), _1579036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579032, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579032, tc_HOL_Obool), _1579036)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579032, tc_HOL_Obool), _1579034))))], (40708 ^ _779308) ^ [_1579181] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579181, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1579181, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1579181, tc_HOL_Obool)))], (40710 ^ _779308) ^ [_1579223, _1579225] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579223, tc_HOL_Obool), _1579225) = hAPP(c_Set_OCollect(_1579223), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1579223, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1579223), c_HOL_OAll(tc_fun(_1579223, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1579223, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1579223, tc_HOL_Obool), tc_HOL_Obool), _1579223), hAPP(c_COMBS(tc_fun(_1579223, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1579223, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1579223, tc_HOL_Obool), tc_fun(tc_fun(_1579223, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1579223, tc_HOL_Obool))), _1579225)))), c_member(_1579223)))))], (40712 ^ _779308) ^ [_1579351] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579351, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1579351, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1579351, tc_HOL_Obool)))], (40714 ^ _779308) ^ [_1579393, _1579395, _1579397] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579393, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1579393, tc_HOL_Obool), tc_HOL_Obool)), _1579395), _1579397)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1579393, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579393, tc_HOL_Obool), _1579395)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579393, tc_HOL_Obool), _1579397)))], (40716 ^ _779308) ^ [_1579463, _1579465, _1579467] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579463, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1579463, tc_HOL_Obool)), _1579465), _1579467)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1579463, tc_HOL_Obool)), _1579465), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579463, tc_HOL_Obool), _1579467)))], (40718 ^ _779308) ^ [_1579524, _1579526, _1579528, _1579530] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1579524, tc_fun(_1579526, tc_HOL_Obool)), _1579528), _1579530) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579526, tc_HOL_Obool), hAPP(c_Set_Oimage(_1579524, tc_fun(_1579526, tc_HOL_Obool), _1579530), _1579528)))], (40720 ^ _779308) ^ [_1579581, _1579583, _1579585, _1579587] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1579581, tc_HOL_Obool), hAPP(c_Set_Oimage(_1579583, tc_fun(_1579581, tc_HOL_Obool), _1579585), _1579587)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1579583, tc_fun(_1579581, tc_HOL_Obool)), _1579587), _1579585))], (40722 ^ _779308) ^ [_1579638, _1579640, _1579642] : [class_Complete__Lattice_Ocomplete__lattice(_1579638), hBOOL(hAPP(hAPP(c_member(_1579638), _1579640), _1579642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1579638), _1579640), c_Complete__Lattice_OSup__class_OSup(_1579638, _1579642))))], (40732 ^ _779308) ^ [_1579803] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1579803, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1579803, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1579803, tc_HOL_Obool)))], (40734 ^ _779308) ^ [_1579845, _1579847, _1579849] : [class_Complete__Lattice_Ocomplete__lattice(_1579845), hBOOL(hAPP(hAPP(c_member(_1579845), _1579847), _1579849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1579845), c_Complete__Lattice_OInf__class_OInf(_1579845, _1579849)), _1579847)))], (40744 ^ _779308) ^ [_1580010] : [class_Complete__Lattice_Ocomplete__lattice(_1580010), -(c_Complete__Lattice_OSup__class_OSup(_1580010, c_Orderings_Obot__class_Obot(tc_fun(_1580010, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1580010))], (40750 ^ _779308) ^ [_1580103, _1580105, _1580107] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1580103, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1580103, tc_HOL_Obool), tc_HOL_Obool)), _1580105), _1580107)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1580103, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1580103, tc_HOL_Obool), _1580105)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1580103, tc_HOL_Obool), _1580107)))], (40752 ^ _779308) ^ [_1580173, _1580175] : [class_Complete__Lattice_Ocomplete__lattice(_1580173), -(c_Complete__Lattice_OSup__class_OSup(_1580173, hAPP(hAPP(c_Set_Oinsert(_1580173), _1580175), c_Orderings_Obot__class_Obot(tc_fun(_1580173, tc_HOL_Obool)))) = _1580175)], (40758 ^ _779308) ^ [_1580280, _1580282, _1580284] : [class_Complete__Lattice_Ocomplete__lattice(_1580280), -(c_Complete__Lattice_OSup__class_OSup(_1580280, hAPP(hAPP(c_Set_Oinsert(_1580280), _1580282), _1580284)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1580280), _1580282), c_Complete__Lattice_OSup__class_OSup(_1580280, _1580284)))], (40764 ^ _779308) ^ [_1580401, _1580403, _1580405, _1580407, _1580409] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1580401, tc_fun(_1580403, tc_HOL_Obool)), _1580405), hAPP(hAPP(c_COMBS(_1580401, tc_fun(_1580403, tc_HOL_Obool), tc_fun(_1580403, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1580403, tc_HOL_Obool), tc_fun(tc_fun(_1580403, tc_HOL_Obool), tc_fun(_1580403, tc_HOL_Obool)), _1580401), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1580403, tc_HOL_Obool))), _1580407)), _1580409)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1580403, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1580403, tc_HOL_Obool), hAPP(c_Set_Oimage(_1580401, tc_fun(_1580403, tc_HOL_Obool), _1580407), _1580405))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1580403, tc_HOL_Obool), hAPP(c_Set_Oimage(_1580401, tc_fun(_1580403, tc_HOL_Obool), _1580409), _1580405))))], (40766 ^ _779308) ^ [_1580530, _1580532] : [class_Complete__Lattice_Ocomplete__lattice(_1580530), -(c_Complete__Lattice_OInf__class_OInf(_1580530, hAPP(hAPP(c_Set_Oinsert(_1580530), _1580532), c_Orderings_Obot__class_Obot(tc_fun(_1580530, tc_HOL_Obool)))) = _1580532)], (40772 ^ _779308) ^ [_1580637] : [class_Complete__Lattice_Ocomplete__lattice(_1580637), -(c_Complete__Lattice_OSup__class_OSup(_1580637, c_Orderings_Otop__class_Otop(tc_fun(_1580637, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1580637))], (40778 ^ _779308) ^ [_1580730] : [class_Complete__Lattice_Ocomplete__lattice(_1580730), -(c_Complete__Lattice_OInf__class_OInf(_1580730, c_Orderings_Obot__class_Obot(tc_fun(_1580730, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1580730))], (40784 ^ _779308) ^ [_1580823] : [class_Complete__Lattice_Ocomplete__lattice(_1580823), -(c_Complete__Lattice_OInf__class_OInf(_1580823, c_Orderings_Otop__class_Otop(tc_fun(_1580823, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1580823))], (40790 ^ _779308) ^ [_1580916, _1580918, _1580920] : [class_Complete__Lattice_Ocomplete__lattice(_1580916), -(c_Complete__Lattice_OInf__class_OInf(_1580916, hAPP(hAPP(c_Set_Oinsert(_1580916), _1580918), _1580920)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1580916), _1580918), c_Complete__Lattice_OInf__class_OInf(_1580916, _1580920)))], (40796 ^ _779308) ^ [_1581037, _1581039, _1581041] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1581037, tc_HOL_Obool)), _1581039), _1581041) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581037, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1581037, tc_HOL_Obool)), _1581039), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1581037, tc_HOL_Obool)), _1581041), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1581037, tc_HOL_Obool), tc_HOL_Obool))))))], (40798 ^ _779308) ^ [_1581111, _1581113, _1581115, _1581117, _1581119] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1581111, tc_fun(_1581113, tc_HOL_Obool)), _1581115), hAPP(hAPP(c_COMBS(_1581111, tc_fun(_1581113, tc_HOL_Obool), tc_fun(_1581113, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581113, tc_HOL_Obool), tc_fun(tc_fun(_1581113, tc_HOL_Obool), tc_fun(_1581113, tc_HOL_Obool)), _1581111), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1581113, tc_HOL_Obool))), _1581117)), _1581119)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1581113, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581113, tc_HOL_Obool), hAPP(c_Set_Oimage(_1581111, tc_fun(_1581113, tc_HOL_Obool), _1581117), _1581115))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581113, tc_HOL_Obool), hAPP(c_Set_Oimage(_1581111, tc_fun(_1581113, tc_HOL_Obool), _1581119), _1581115))))], (40800 ^ _779308) ^ [_1581240, _1581242, _1581244] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1581240, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581240, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1581240, tc_HOL_Obool), tc_HOL_Obool)), _1581242), _1581244))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1581240, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581240, tc_HOL_Obool), _1581242)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1581240, tc_HOL_Obool), _1581244)))))], (40802 ^ _779308) ^ [_1581320, _1581322, _1581324] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1581320, tc_HOL_Obool)), _1581322), _1581324) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1581320, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1581320, tc_HOL_Obool)), _1581322), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1581320, tc_HOL_Obool)), _1581324), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1581320, tc_HOL_Obool), tc_HOL_Obool))))))], (40804 ^ _779308) ^ [_1581394, _1581396, _1581398] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1581394, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1581394, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1581394, tc_HOL_Obool), _1581396)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1581394, tc_HOL_Obool), _1581398))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1581394, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1581394, tc_HOL_Obool), tc_HOL_Obool)), _1581396), _1581398)))))], (40806 ^ _779308) ^ [_1581474, _1581476, _1581478] : [class_Complete__Lattice_Ocomplete__lattice(_1581474), -(c_Complete__Lattice_OSup__class_OSup(_1581474, hAPP(hAPP(c_Set_Oinsert(_1581474), _1581476), hAPP(hAPP(c_Set_Oinsert(_1581474), _1581478), c_Orderings_Obot__class_Obot(tc_fun(_1581474, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1581474), _1581476), _1581478))], (40812 ^ _779308) ^ [_1581615, _1581617, _1581619] : [class_Complete__Lattice_Ocomplete__lattice(_1581615), -(c_Complete__Lattice_OInf__class_OInf(_1581615, hAPP(hAPP(c_Set_Oinsert(_1581615), _1581617), hAPP(hAPP(c_Set_Oinsert(_1581615), _1581619), c_Orderings_Obot__class_Obot(tc_fun(_1581615, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1581615), _1581617), _1581619))], (40818 ^ _779308) ^ [_1581756, _1581758, _1581760] : [class_Complete__Lattice_Ocomplete__lattice(_1581756), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581756), _1581758)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1581756), _1581760), c_Complete__Lattice_OSup__class_OSup(_1581756, _1581758)) = hAPP(hAPP(c_Finite__Set_Ofold(_1581756, _1581756, c_Lattices_Osemilattice__sup__class_Osup(_1581756)), _1581760), _1581758))], (40828 ^ _779308) ^ [_1581941, _1581943] : [class_Complete__Lattice_Ocomplete__lattice(_1581941), hBOOL(hAPP(c_Finite__Set_Ofinite(_1581941), _1581943)), -(_1581943 = c_Orderings_Obot__class_Obot(tc_fun(_1581941, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1581941, _1581943) = c_Complete__Lattice_OSup__class_OSup(_1581941, _1581943))], (40842 ^ _779308) ^ [_1582113, _1582115, _1582117] : [class_Complete__Lattice_Ocomplete__lattice(_1582113), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582113), _1582115)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1582113), _1582117), c_Complete__Lattice_OInf__class_OInf(_1582113, _1582115)) = hAPP(hAPP(c_Finite__Set_Ofold(_1582113, _1582113, c_Lattices_Osemilattice__inf__class_Oinf(_1582113)), _1582117), _1582115))], (40852 ^ _779308) ^ [_1582298, _1582300] : [class_Complete__Lattice_Ocomplete__lattice(_1582298), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582298), _1582300)), -(_1582300 = c_Orderings_Obot__class_Obot(tc_fun(_1582298, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1582298, _1582300) = c_Complete__Lattice_OInf__class_OInf(_1582298, _1582300))], (40866 ^ _779308) ^ [_1582470, _1582472, _1582474, _1582476, _1582478, _1582480, _1582482, _1582484] : [c_Fun_Oinj__on(_1582470, _1582472, _1582474, _1582476), 40872 ^ _779308 : [(40873 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1582478), 40871 ^ [_1582470, _1582472, _1582474, _1582476, _1582478, _1582480, _1582482, _1582484]), _1582480)))], (40875 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1582470, tc_HOL_Obool)), hAPP(_1582482, 40871 ^ [_1582470, _1582472, _1582474, _1582476, _1582478, _1582480, _1582482, _1582484])), _1582476))]], hBOOL(hAPP(hAPP(c_member(_1582478), _1582484), _1582480)), -(hAPP(c_Set_Oimage(_1582470, _1582472, _1582474), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1582478, tc_fun(_1582470, tc_HOL_Obool)), _1582480), _1582482)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1582478, tc_fun(_1582472, tc_HOL_Obool)), _1582480), hAPP(hAPP(c_COMBB(tc_fun(_1582470, tc_HOL_Obool), tc_fun(_1582472, tc_HOL_Obool), _1582478), c_Set_Oimage(_1582470, _1582472, _1582474)), _1582482)))], (40883 ^ _779308) ^ [_1582959, _1582961, _1582963] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1582959, tc_HOL_Obool)), _1582961)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1582959), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1582959, tc_HOL_Obool), _1582961))), 40893 ^ _779308 : [(40894 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1582959, tc_HOL_Obool)), 40892 ^ [_1582959, _1582961, _1582963]), _1582961)))], (40896 ^ _779308) ^ [] : [hAPP(c_Finite__Set_Ocard(_1582959), 40892 ^ [_1582959, _1582961, _1582963]) = _1582963]], 40900 ^ _779308 : [(40901 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1582959, tc_HOL_Obool)), 40899 ^ [_1582959, _1582961, _1582963]), _1582961)))], (40904 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1582959, tc_HOL_Obool)), 40902 ^ [_1582959, _1582961, _1582963]), _1582961)))], (40906 ^ _779308) ^ [] : [40899 ^ [_1582959, _1582961, _1582963] = 40902 ^ [_1582959, _1582961, _1582963]], (40908 ^ _779308) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1582959, tc_HOL_Obool)), 40899 ^ [_1582959, _1582961, _1582963]), 40902 ^ [_1582959, _1582961, _1582963]) = c_Orderings_Obot__class_Obot(tc_fun(_1582959, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1582963), hAPP(c_Finite__Set_Ocard(tc_fun(_1582959, tc_HOL_Obool)), _1582961)) = hAPP(c_Finite__Set_Ocard(_1582959), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1582959, tc_HOL_Obool), _1582961)))], (40912 ^ _779308) ^ [_1583741, _1583743] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1583741, tc_HOL_Obool), _1583743) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1583741, tc_HOL_Obool), tc_fun(_1583741, tc_HOL_Obool)), _1583743), c_COMBI(tc_fun(_1583741, tc_HOL_Obool))))], (40914 ^ _779308) ^ [_1583792, _1583794] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1583792, tc_HOL_Obool), _1583794) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1583792, tc_HOL_Obool), tc_fun(_1583792, tc_HOL_Obool)), _1583794), c_COMBI(tc_fun(_1583792, tc_HOL_Obool))))], (40916 ^ _779308) ^ [_1583843, _1583845] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1583843, tc_HOL_Obool)), _1583845)), 40922 ^ _779308 : [(40923 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1583843, tc_HOL_Obool)), 40921 ^ [_1583843, _1583845]), _1583845)))], (40925 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1583843), 40921 ^ [_1583843, _1583845]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1583843), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1583843, tc_HOL_Obool), _1583845))))], (40929 ^ _779308) ^ [_1584101, _1584103, _1584105] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1584101, tc_HOL_Obool)), _1584103), _1584105))), 40935 ^ _779308 : [(40936 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1584101, tc_HOL_Obool)), 40934 ^ [_1584101, _1584103, _1584105]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1584101, tc_HOL_Obool)), _1584103), _1584105))))], (40939 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1584101, tc_HOL_Obool)), 40937 ^ [_1584101, _1584103, _1584105]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1584101, tc_HOL_Obool)), _1584103), _1584105))))], (40941 ^ _779308) ^ [] : [40934 ^ [_1584101, _1584103, _1584105] = 40937 ^ [_1584101, _1584103, _1584105]], (40943 ^ _779308) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1584101, tc_HOL_Obool)), 40934 ^ [_1584101, _1584103, _1584105]), 40937 ^ [_1584101, _1584103, _1584105]) = c_Orderings_Obot__class_Obot(tc_fun(_1584101, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1584101, tc_HOL_Obool)), _1584103), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1584101, tc_HOL_Obool), _1584105)) = c_Orderings_Obot__class_Obot(tc_fun(_1584101, tc_HOL_Obool)))], (40947 ^ _779308) ^ [_1584694, _1584696, _1584698, _1584700] : [-(_1584694 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1584696, tc_HOL_Obool), tc_HOL_Obool))), 40953 ^ _779308 : [(40954 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1584696, tc_HOL_Obool)), 40952 ^ [_1584694, _1584696, _1584698, _1584700]), _1584694)))], (40956 ^ _779308) ^ [] : [c_Fun_Oinj__on(_1584696, _1584698, _1584700, 40952 ^ [_1584694, _1584696, _1584698, _1584700])]], -(c_Fun_Oinj__on(_1584696, _1584698, _1584700, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1584696, tc_HOL_Obool), _1584694)))], (40960 ^ _779308) ^ [_1584955, _1584957, _1584959] : [40962 ^ _779308 : [(40963 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1584955, tc_HOL_Obool)), 40961 ^ [_1584955, _1584957, _1584959]), _1584957)))], (40965 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1584955, tc_HOL_Obool)), 40961 ^ [_1584955, _1584957, _1584959]), _1584959))]], -(_1584957 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1584955, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1584955, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1584955, tc_HOL_Obool), _1584957)), _1584959)))], (40973 ^ _779308) ^ [_1585216, _1585218, _1585220, _1585222, _1585224, _1585226] : [-(_1585216 = c_Orderings_Obot__class_Obot(tc_fun(_1585218, tc_HOL_Obool))), 40979 ^ _779308 : [(40980 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1585218), 40978 ^ [_1585216, _1585218, _1585220, _1585222, _1585224, _1585226]), _1585216)))], (40982 ^ _779308) ^ [] : [c_Fun_Oinj__on(_1585220, _1585222, _1585224, hAPP(_1585226, 40978 ^ [_1585216, _1585218, _1585220, _1585222, _1585224, _1585226]))]], -(c_Fun_Oinj__on(_1585220, _1585222, _1585224, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1585218, tc_fun(_1585220, tc_HOL_Obool)), _1585216), _1585226)))], (40986 ^ _779308) ^ [_1585508, _1585510, _1585512, _1585514, _1585516, _1585518, _1585520] : [c_Finite__Set_Ofun__left__comm(_1585508, _1585510, _1585512), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1585508, _1585510, _1585512, _1585514, hAPP(hAPP(c_Set_Oinsert(_1585508), _1585516), _1585518)), _1585520)), -(hBOOL(hAPP(hAPP(c_member(_1585508), _1585516), _1585518))), 40998 ^ _779308 : [(40999 ^ _779308) ^ [] : [-(_1585520 = hAPP(hAPP(_1585512, _1585516), 40997 ^ [_1585508, _1585510, _1585512, _1585514, _1585516, _1585518, _1585520]))], (41001 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1585508, _1585510, _1585512, _1585514, _1585518), 40997 ^ [_1585508, _1585510, _1585512, _1585514, _1585516, _1585518, _1585520])))]]], (41003 ^ _779308) ^ [_1585834, _1585836, _1585838, _1585840] : [class_Orderings_Olinorder(_1585834), hBOOL(hAPP(c_Finite__Set_Ofinite(_1585834), _1585836)), 41013 ^ _779308 : [(41014 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1585834), 41012 ^ [_1585834, _1585836, _1585838, _1585840]), _1585836)))], (41016 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1585834), 41012 ^ [_1585834, _1585836, _1585838, _1585840]), _1585838))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1585834), hAPP(hAPP(c_Finite__Set_Ofold(_1585834, _1585834, c_Orderings_Oord__class_Omax(_1585834)), _1585840), _1585836)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1585834), _1585838), _1585840))))], (41020 ^ _779308) ^ [_1586198, _1586200, _1586202, _1586204] : [class_Orderings_Olinorder(_1586198), hBOOL(hAPP(c_Finite__Set_Ofinite(_1586198), _1586200)), 41030 ^ _779308 : [(41031 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1586198), 41029 ^ [_1586198, _1586200, _1586202, _1586204]), _1586200)))], (41033 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1586198), _1586202), 41029 ^ [_1586198, _1586200, _1586202, _1586204]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1586198), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1586198), _1586202), _1586204)), hAPP(hAPP(c_Finite__Set_Ofold(_1586198, _1586198, c_Orderings_Oord__class_Omin(_1586198)), _1586204), _1586200))))], (41037 ^ _779308) ^ [_1586562, _1586564, _1586566] : [41039 ^ _779308 : [(41040 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1586562, tc_HOL_Obool)), 41038 ^ [_1586562, _1586564, _1586566]), _1586564)))], (41042 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1586562), _1586566), 41038 ^ [_1586562, _1586564, _1586566]))]], -(hBOOL(hAPP(hAPP(c_member(_1586562), _1586566), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1586562, tc_HOL_Obool), _1586564))))], (41046 ^ _779308) ^ [_1586778, _1586780, _1586782, _1586784] : [class_Lattices_Osemilattice__inf(_1586778), hBOOL(hAPP(c_Finite__Set_Ofinite(_1586778), _1586780)), 41056 ^ _779308 : [(41057 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1586778), 41055 ^ [_1586778, _1586780, _1586782, _1586784]), _1586780)))], (41059 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1586778), _1586782), 41055 ^ [_1586778, _1586780, _1586782, _1586784]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1586778), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1586778), _1586782), _1586784)), hAPP(hAPP(c_Finite__Set_Ofold(_1586778, _1586778, c_Lattices_Osemilattice__inf__class_Oinf(_1586778)), _1586784), _1586780))))], (41063 ^ _779308) ^ [_1587142, _1587144, _1587146, _1587148] : [class_Lattices_Osemilattice__sup(_1587142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1587142), _1587144)), 41073 ^ _779308 : [(41074 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1587142), 41072 ^ [_1587142, _1587144, _1587146, _1587148]), _1587144)))], (41076 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1587142), 41072 ^ [_1587142, _1587144, _1587146, _1587148]), _1587146))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1587142), hAPP(hAPP(c_Finite__Set_Ofold(_1587142, _1587142, c_Lattices_Osemilattice__sup__class_Osup(_1587142)), _1587148), _1587144)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1587142), _1587146), _1587148))))], (41080 ^ _779308) ^ [_1587506, _1587508, _1587510] : [class_Divides_Osemiring__div(_1587506), -(_1587508 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1587506), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1587506), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1587506), _1587508), _1587510)), _1587510)), c_Divides_Odiv__class_Omod(_1587506, _1587508, _1587510)))], (41103 ^ _779308) ^ [_1588173, _1588175] : [-(c_Wellfounded_Owf(_1588173, _1588175)), 41106 ^ _779308 : [(41107 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588173), 41105 ^ [_1588173, _1588175]), 41104 ^ [_1588173, _1588175])))], (41109 ^ _779308) ^ [_1588393] : [hBOOL(hAPP(hAPP(c_member(_1588173), _1588393), 41104 ^ [_1588173, _1588175])), 41113 ^ _779308 : [(41114 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588173, _1588173)), hAPP(hAPP(c_Product__Type_OPair(_1588173, _1588173), 41112 ^ [_1588173, _1588175, _1588393]), _1588393)), _1588175)))], (41116 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588173), 41112 ^ [_1588173, _1588175, _1588393]), 41104 ^ [_1588173, _1588175])))]]]]], (41086 ^ _779308) ^ [_1587654, _1587656] : [c_Wellfounded_Owf(_1587654, _1587656), 41089 ^ _779308 : [(41090 ^ _779308) ^ [_1587786] : [41091 ^ _779308 : [(41092 ^ _779308) ^ [_1587891] : [hBOOL(hAPP(hAPP(c_member(_1587654), _1587891), _1587786))]], 41094 ^ _779308 : [(41095 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1587654), 41093 ^ [_1587654, _1587656, _1587786]), _1587786)))], (41097 ^ _779308) ^ [_1588013] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587654, _1587654)), hAPP(hAPP(c_Product__Type_OPair(_1587654, _1587654), _1588013), 41093 ^ [_1587654, _1587656, _1587786])), _1587656)), hBOOL(hAPP(hAPP(c_member(_1587654), _1588013), _1587786))]]]]], (41120 ^ _779308) ^ [_1588649, _1588651] : [-(hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), _1588649)) = hAPP(c_Set_OCollect(tc_Int_Oint), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Int_Oint), c_fconj), hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), _1588651))), 41122 ^ _779308 : [(41123 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 41121 ^ [_1588649, _1588651])))], (41125 ^ _779308) ^ [] : [41126 ^ _779308 : [(41127 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1588649, 41121 ^ [_1588649, _1588651])))], (41129 ^ _779308) ^ [] : [hBOOL(hAPP(_1588651, 41121 ^ [_1588649, _1588651]))]], 41130 ^ _779308 : [(41131 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1588651, 41121 ^ [_1588649, _1588651])))], (41133 ^ _779308) ^ [] : [hBOOL(hAPP(_1588649, 41121 ^ [_1588649, _1588651]))]]]]], (41137 ^ _779308) ^ [_1588970, _1588972, _1588974, _1588976, _1588978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1588970, tc_HOL_Obool)), _1588972), _1588974)), 41143 ^ _779308 : [(41144 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1588970), 41142 ^ [_1588970, _1588972, _1588974, _1588976, _1588978]), _1588972)))], (41146 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1588976, 41142 ^ [_1588970, _1588972, _1588974, _1588976, _1588978])))], (41148 ^ _779308) ^ [] : [hBOOL(hAPP(_1588978, 41142 ^ [_1588970, _1588972, _1588974, _1588976, _1588978]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1588970, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1588970, tc_HOL_Obool)), _1588972), hAPP(c_Set_OCollect(_1588970), _1588976))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1588970, tc_HOL_Obool)), _1588974), hAPP(c_Set_OCollect(_1588970), _1588978)))))], (41152 ^ _779308) ^ [_1589370, _1589372, _1589374] : [hBOOL(hAPP(hAPP(c_member(_1589370), _1589372), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1589370, tc_HOL_Obool), _1589374))), 41156 ^ _779308 : [(41157 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1589370), _1589372), 41155 ^ [_1589370, _1589372, _1589374])))], (41159 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1589370, tc_HOL_Obool)), 41155 ^ [_1589370, _1589372, _1589374]), _1589374)))]]], (41161 ^ _779308) ^ [_1589562, _1589564, _1589566, _1589568] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589562, _1589564)), _1589566), hAPP(c_Relation_Oconverse(_1589564, _1589562), _1589568))), 41166 ^ _779308 : [(41167 ^ _779308) ^ [] : [-(_1589566 = hAPP(hAPP(c_Product__Type_OPair(_1589562, _1589564), 41165 ^ [_1589562, _1589564, _1589566, _1589568]), 41164 ^ [_1589562, _1589564, _1589566, _1589568]))], (41169 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589564, _1589562)), hAPP(hAPP(c_Product__Type_OPair(_1589564, _1589562), 41164 ^ [_1589562, _1589564, _1589566, _1589568]), 41165 ^ [_1589562, _1589564, _1589566, _1589568])), _1589568)))]]], (41171 ^ _779308) ^ [_1589815, _1589817, _1589819, _1589821, _1589823, _1589825] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589815, _1589817)), _1589819), hAPP(hAPP(c_Relation_Orel__comp(_1589815, _1589821, _1589817), _1589823), _1589825))), 41177 ^ _779308 : [(41178 ^ _779308) ^ [] : [-(_1589819 = hAPP(hAPP(c_Product__Type_OPair(_1589815, _1589817), 41174 ^ [_1589815, _1589817, _1589819, _1589821, _1589823, _1589825]), 41176 ^ [_1589815, _1589817, _1589819, _1589821, _1589823, _1589825]))], (41180 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589815, _1589821)), hAPP(hAPP(c_Product__Type_OPair(_1589815, _1589821), 41174 ^ [_1589815, _1589817, _1589819, _1589821, _1589823, _1589825]), 41175 ^ [_1589815, _1589817, _1589819, _1589821, _1589823, _1589825])), _1589823)))], (41182 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589821, _1589817)), hAPP(hAPP(c_Product__Type_OPair(_1589821, _1589817), 41175 ^ [_1589815, _1589817, _1589819, _1589821, _1589823, _1589825]), 41176 ^ [_1589815, _1589817, _1589819, _1589821, _1589823, _1589825])), _1589825)))]]], (41184 ^ _779308) ^ [_1590193, _1590195, _1590197] : [-(c_Nitpick_Oplus__frac(_1590193, _1590195, _1590197) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1590193), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1590193), _1590195), hAPP(c_Nitpick_Odenom(_1590193), _1590197))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1590193), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1590193), tc_Int_Oint), c_Nitpick_Ofrac(_1590193)), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint)), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1590193), _1590195))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint)), hAPP(c_Nitpick_Odenom(_1590193), _1590195))))), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1590193), _1590197))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint)), hAPP(c_Nitpick_Odenom(_1590193), _1590197)))))), c_COMBI(tc_Int_Oint))))], (41186 ^ _779308) ^ [_1590324, _1590326, _1590328, _1590330] : [class_Rings_Olinordered__semidom(_1590324), 41192 ^ _779308 : [(41193 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590326), 41191 ^ [_1590324, _1590326, _1590328, _1590330]), _1590328)))], (41195 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1590324), c_Groups_Ozero__class_Ozero(_1590324)), hAPP(_1590330, 41191 ^ [_1590324, _1590326, _1590328, _1590330])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1590324), c_Groups_Ozero__class_Ozero(_1590324)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1590326, _1590324), _1590330), _1590328))))], (41199 ^ _779308) ^ [_1590620, _1590622, _1590624] : [-(c_Nitpick_Otimes__frac(_1590620, _1590622, _1590624) = hAPP(hAPP(c_Nitpick_Ofrac(_1590620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1590620), _1590622)), hAPP(c_Nitpick_Onum(_1590620), _1590624))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1590620), _1590622)), hAPP(c_Nitpick_Odenom(_1590620), _1590624))))], (41201 ^ _779308) ^ [_1590691, _1590693, _1590695] : [-(c_Nitpick_Oof__frac(_1590693, _1590691, _1590695) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1590691), hAPP(c_Int_Oring__1__class_Oof__int(_1590691), hAPP(c_Nitpick_Onum(_1590693), _1590695))), hAPP(c_Int_Oring__1__class_Oof__int(_1590691), hAPP(c_Nitpick_Odenom(_1590693), _1590695)))), class_Rings_Oinverse(_1590691), class_Rings_Oring__1(_1590691)], (41211 ^ _779308) ^ [_1590884, _1590886] : [-(c_Nitpick_Oinverse__frac(_1590884, _1590886) = hAPP(hAPP(c_Nitpick_Ofrac(_1590884), hAPP(c_Nitpick_Odenom(_1590884), _1590886)), hAPP(c_Nitpick_Onum(_1590884), _1590886)))], (41213 ^ _779308) ^ [_1590930, _1590932] : [-(c_Nitpick_Ouminus__frac(_1590930, _1590932) = c_Nitpick_OAbs__Frac(_1590930, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1590930), _1590932))), hAPP(c_Nitpick_Odenom(_1590930), _1590932))))], (41215 ^ _779308) ^ [_1590998, _1591000, _1591002] : [c_Nitpick_Oless__frac(_1590998, _1591000, _1591002), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1590998), c_Nitpick_Oplus__frac(_1590998, _1591000, c_Nitpick_Ouminus__frac(_1590998, _1591002)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41221 ^ _779308) ^ [_1591109, _1591111, _1591113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591109), c_Nitpick_Oplus__frac(_1591109, _1591111, c_Nitpick_Ouminus__frac(_1591109, _1591113)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1591109, _1591111, _1591113))], (41227 ^ _779308) ^ [_1591244, _1591246, _1591248] : [c_Nitpick_Oless__eq__frac(_1591244, _1591246, _1591248), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591244), c_Nitpick_Oplus__frac(_1591244, _1591246, c_Nitpick_Ouminus__frac(_1591244, _1591248)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41233 ^ _779308) ^ [_1591355, _1591357, _1591359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591355), c_Nitpick_Oplus__frac(_1591355, _1591357, c_Nitpick_Ouminus__frac(_1591355, _1591359)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1591355, _1591357, _1591359))], (41239 ^ _779308) ^ [_1591472] : [-(c_Nitpick_Odenom(_1591472) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1591472, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1591472)))], (41241 ^ _779308) ^ [_1591507] : [-(c_Nitpick_Onum(_1591507) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1591507, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1591507)))], (41243 ^ _779308) ^ [_1591542, _1591544, _1591546] : [-(c_Product__Type_Ointernal__split(_1591542, _1591544, _1591546) = c_Product__Type_Oprod_Oprod__case(_1591542, _1591544, _1591546))], (41245 ^ _779308) ^ [_1591577, _1591579, _1591581, _1591583] : [class_Rings_Olinordered__semidom(_1591577), 41251 ^ _779308 : [(41252 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1591579), 41250 ^ [_1591577, _1591579, _1591581, _1591583]), _1591581)))], (41254 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1591577), c_Groups_Ozero__class_Ozero(_1591577)), hAPP(_1591583, 41250 ^ [_1591577, _1591579, _1591581, _1591583])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1591577), c_Groups_Ozero__class_Ozero(_1591577)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1591579, _1591577), _1591583), _1591581))))], (41258 ^ _779308) ^ [_1591873, _1591875, _1591877, _1591879, _1591881, _1591883] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1591873, _1591875, _1591877), _1591879), hAPP(hAPP(c_Product__Type_OPair(_1591873, _1591875), _1591881), _1591883)) = hAPP(hAPP(_1591879, _1591881), _1591883))], (41260 ^ _779308) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41262 ^ _779308) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41264 ^ _779308) ^ [_1591967, _1591969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41265 ^ [_1591967, _1591969]), hAPP(_1591967, 41265 ^ [_1591967, _1591969]))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), _1591967)), _1591969)))))], (41271 ^ _779308) ^ [_1592127, _1592129] : [-(c_List_Olenlex(_1592127, _1592129) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1592127)), tc_List_Olist(_1592127)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1592127), c_Wellfounded_Oless__than, c_List_Olex(_1592127, _1592129))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1592127), tc_List_Olist(_1592127), tc_prod(tc_Nat_Onat, tc_List_Olist(_1592127))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1592127), tc_prod(tc_Nat_Onat, tc_List_Olist(_1592127))), tc_List_Olist(_1592127)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1592127))), c_Nat_Osize__class_Osize(tc_List_Olist(_1592127)))), c_COMBI(tc_List_Olist(_1592127)))))], (41273 ^ _779308) ^ [_1592234, _1592236, _1592238] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592234)), _1592236) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592234)), _1592238)), _1592236 = _1592238], (41279 ^ _779308) ^ [_1592326, _1592328, _1592330, _1592332, _1592334] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1592326), tc_List_Olist(_1592326))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1592326), tc_List_Olist(_1592326)), _1592328), _1592330)), hAPP(c_List_Olexn(_1592326, _1592332), _1592334))), 41282 ^ _779308 : [(41283 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592326)), _1592328) = _1592334)], (41285 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592326)), _1592330) = _1592334)]]], (41287 ^ _779308) ^ [_1592529, _1592531] : [-(c_List_Olenlex(_1592529, _1592531) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1592529), tc_List_Olist(_1592529))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1592529), tc_List_Olist(_1592529), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1592529), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592529), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool)), tc_List_Olist(_1592529)), c_COMBS(tc_List_Olist(_1592529), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592529), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1592529)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1592529)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592529), tc_fun(tc_List_Olist(_1592529), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1592529), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool)), tc_List_Olist(_1592529)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1592529))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1592529)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1592529))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1592529)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1592529), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592529), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool)), tc_List_Olist(_1592529)), c_COMBS(tc_List_Olist(_1592529), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592529), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1592529)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1592529)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592529), tc_fun(tc_List_Olist(_1592529), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1592529), tc_Nat_Onat), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool)), tc_List_Olist(_1592529)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1592529))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1592529)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1592529))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1592529)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592529), tc_fun(tc_prod(tc_List_Olist(_1592529), tc_List_Olist(_1592529)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592529), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592529), tc_List_Olist(_1592529)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592529), tc_List_Olist(_1592529)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592529), tc_HOL_Obool)), tc_List_Olist(_1592529)), c_COMBC(tc_List_Olist(_1592529), tc_fun(tc_prod(tc_List_Olist(_1592529), tc_List_Olist(_1592529)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592529), tc_prod(tc_List_Olist(_1592529), tc_List_Olist(_1592529))), tc_fun(tc_List_Olist(_1592529), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592529), tc_List_Olist(_1592529)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1592529)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1592529), tc_List_Olist(_1592529)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1592529), tc_List_Olist(_1592529)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1592529)), c_member(tc_prod(tc_List_Olist(_1592529), tc_List_Olist(_1592529))))), c_Product__Type_OPair(tc_List_Olist(_1592529), tc_List_Olist(_1592529))))), c_List_Olex(_1592529, _1592531)))))))], (41289 ^ _779308) ^ [_1593085, _1593087, _1593089] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593085)), c_List_Osublist(_1593085, _1593087, _1593089)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593085)), _1593087)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1593089)))))], (41291 ^ _779308) ^ [_1593151, _1593153, _1593155] : [-(hAPP(c_List_Olexn(_1593151, _1593153), hAPP(c_Nat_OSuc, _1593155)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1593151), tc_List_Olist(_1593151)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1593151, tc_List_Olist(_1593151)), tc_prod(_1593151, tc_List_Olist(_1593151))), tc_prod(tc_List_Olist(_1593151), tc_List_Olist(_1593151)), c_Product__Type_Omap__pair(tc_prod(_1593151, tc_List_Olist(_1593151)), tc_List_Olist(_1593151), tc_prod(_1593151, tc_List_Olist(_1593151)), tc_List_Olist(_1593151), hAPP(c_Product__Type_Oprod_Oprod__case(_1593151, tc_List_Olist(_1593151), tc_List_Olist(_1593151)), c_List_Olist_OCons(_1593151)), hAPP(c_Product__Type_Oprod_Oprod__case(_1593151, tc_List_Olist(_1593151), tc_List_Olist(_1593151)), c_List_Olist_OCons(_1593151)))), c_Wellfounded_Olex__prod(_1593151, tc_List_Olist(_1593151), _1593153, hAPP(c_List_Olexn(_1593151, _1593153), _1593155)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1593151), tc_List_Olist(_1593151))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1593151), tc_List_Olist(_1593151), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593151), tc_fun(tc_List_Olist(_1593151), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593151), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1593151), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593151), tc_HOL_Obool)), tc_List_Olist(_1593151)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1593151))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1593151)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593151), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593151)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593151)))), hAPP(c_Nat_OSuc, _1593155))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593151), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593151)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593151)))), hAPP(c_Nat_OSuc, _1593155)))))))], (41293 ^ _779308) ^ [_1593442, _1593444, _1593446, _1593448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593442)), _1593444)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593442)), _1593446))), _1593444 = hAPP(hAPP(c_List_Olist_OCons(_1593442), _1593448), _1593446)], (41299 ^ _779308) ^ [_1593593, _1593595, _1593597] : [_1593593 = hAPP(hAPP(c_List_Olist_OCons(_1593595), _1593597), _1593593)], (41301 ^ _779308) ^ [_1593643, _1593645, _1593647] : [hAPP(hAPP(c_List_Olist_OCons(_1593643), _1593645), _1593647) = _1593647], (41303 ^ _779308) ^ [_1593702, _1593704, _1593706, _1593708, _1593710] : [hAPP(hAPP(c_List_Olist_OCons(_1593702), _1593704), _1593706) = hAPP(hAPP(c_List_Olist_OCons(_1593702), _1593708), _1593710), 41306 ^ _779308 : [(41307 ^ _779308) ^ [] : [-(_1593704 = _1593708)], (41309 ^ _779308) ^ [] : [-(_1593706 = _1593710)]]], (41311 ^ _779308) ^ [_1593839, _1593841, _1593843, _1593845, _1593847] : [-(hAPP(hAPP(c_List_Olist_OCons(_1593839), _1593841), _1593843) = hAPP(hAPP(c_List_Olist_OCons(_1593839), _1593845), _1593847)), _1593841 = _1593845, _1593843 = _1593847], (41321 ^ _779308) ^ [_1594014, _1594016, _1594018] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594014)), hAPP(hAPP(c_List_Olist_OCons(_1594014), _1594016), _1594018)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594014)), _1594018)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41323 ^ _779308) ^ [_1594096, _1594098, _1594100, _1594102, _1594104, _1594106] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594096), tc_List_Olist(_1594096))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594096), tc_List_Olist(_1594096)), hAPP(hAPP(c_List_Olist_OCons(_1594096), _1594098), _1594100)), hAPP(hAPP(c_List_Olist_OCons(_1594096), _1594102), _1594104))), c_List_Olex(_1594096, _1594106))), 41328 ^ _779308 : [(41329 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594096, _1594096)), hAPP(hAPP(c_Product__Type_OPair(_1594096, _1594096), _1594098), _1594102)), _1594106)))], (41331 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594096)), _1594100) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594096)), _1594104))]], 41332 ^ _779308 : [(41333 ^ _779308) ^ [] : [-(_1594098 = _1594102)], (41335 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594096), tc_List_Olist(_1594096))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594096), tc_List_Olist(_1594096)), _1594100), _1594104)), c_List_Olex(_1594096, _1594106))))]]], (41337 ^ _779308) ^ [_1594494, _1594496, _1594498, _1594500, _1594502, _1594504] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594494), tc_List_Olist(_1594494))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594494), tc_List_Olist(_1594494)), hAPP(hAPP(c_List_Olist_OCons(_1594494), _1594496), _1594498)), hAPP(hAPP(c_List_Olist_OCons(_1594494), _1594500), _1594502))), c_List_Olex(_1594494, _1594504)))), 41338 ^ _779308 : [(41339 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594494, _1594494)), hAPP(hAPP(c_Product__Type_OPair(_1594494, _1594494), _1594496), _1594500)), _1594504)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594494)), _1594498) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594494)), _1594502)], (41345 ^ _779308) ^ [] : [_1594496 = _1594500, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594494), tc_List_Olist(_1594494))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594494), tc_List_Olist(_1594494)), _1594498), _1594502)), c_List_Olex(_1594494, _1594504)))]]], (41353 ^ _779308) ^ [_1594950, _1594952, _1594954] : [-(c_List_Oset__Cons(_1594950, _1594952, _1594954) = hAPP(c_Set_OCollect(tc_List_Olist(_1594950)), hAPP(hAPP(c_COMBB(tc_fun(_1594950, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1594950)), c_HOL_OEx(_1594950)), hAPP(hAPP(c_COMBB(tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool)), tc_fun(_1594950, tc_HOL_Obool), tc_List_Olist(_1594950)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool), tc_HOL_Obool, _1594950), c_HOL_OEx(tc_List_Olist(_1594950)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1594950), tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool)), tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1594950, tc_fun(tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool), tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool))), tc_fun(tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool)), tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool))), tc_List_Olist(_1594950)), c_COMBS(_1594950, tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool), tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1594950, tc_fun(tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool), tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool))), tc_List_Olist(_1594950)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1594950), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool), tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool)), _1594950), c_COMBS(tc_List_Olist(_1594950), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool)), tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1594950)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool), tc_fun(tc_List_Olist(_1594950), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1594950), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1594950)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1594950), tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_List_Olist(_1594950))), tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1594950), tc_List_Olist(_1594950)), tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool)), tc_fun(tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_List_Olist(_1594950))), tc_fun(_1594950, tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool))), tc_List_Olist(_1594950)), c_COMBB(tc_fun(tc_List_Olist(_1594950), tc_List_Olist(_1594950)), tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool), _1594950)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1594950), tc_List_Olist(_1594950)), tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool)), tc_List_Olist(_1594950)), c_COMBB(tc_List_Olist(_1594950), tc_HOL_Obool, tc_List_Olist(_1594950))), c_fequal))), c_List_Olist_OCons(_1594950)))))), hAPP(hAPP(c_COMBC(_1594950, tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool), tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool), tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool)), _1594950), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1594950))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1594950), c_fconj), hAPP(hAPP(c_COMBC(_1594950, tc_fun(_1594950, tc_HOL_Obool), tc_HOL_Obool), c_member(_1594950)), _1594952)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1594950), tc_fun(tc_List_Olist(_1594950), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1594950))), _1594954)))))))], (41355 ^ _779308) ^ [_1595500, _1595502, _1595504, _1595506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1595500), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1595502), _1595504))), -(hAPP(c_Random_Opick(_1595502, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1595502)), _1595504), _1595506)), _1595500) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1595502), _1595504))], (41361 ^ _779308) ^ [_1595643, _1595645, _1595647, _1595649] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1595643), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1595645), _1595647)))), -(hAPP(c_Random_Opick(_1595645, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1595645)), _1595647), _1595649)), _1595643) = hAPP(c_Random_Opick(_1595645, _1595649), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1595643), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1595645), _1595647))))], (41367 ^ _779308) ^ [_1595731, _1595733, _1595735] : [-(c_Random_Oselect__weight(_1595731, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1595731)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1595731), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1595733)), _1595735)) = c_Random_Oselect__weight(_1595731, _1595735))], (41369 ^ _779308) ^ [_1595811, _1595813, _1595815, _1595817, _1595819, _1595821] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595811), tc_List_Olist(_1595811))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595811), tc_List_Olist(_1595811)), hAPP(hAPP(c_List_Olist_OCons(_1595811), _1595813), _1595815)), hAPP(hAPP(c_List_Olist_OCons(_1595811), _1595817), _1595819))), c_List_Olexord(_1595811, _1595821))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595811, _1595811)), hAPP(hAPP(c_Product__Type_OPair(_1595811, _1595811), _1595813), _1595817)), _1595821))), 41376 ^ _779308 : [(41377 ^ _779308) ^ [] : [-(_1595813 = _1595817)], (41379 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595811), tc_List_Olist(_1595811))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595811), tc_List_Olist(_1595811)), _1595815), _1595819)), c_List_Olexord(_1595811, _1595821))))]]], (41381 ^ _779308) ^ [_1596138, _1596140, _1596142, _1596144, _1596146, _1596148] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596138), tc_List_Olist(_1596138))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596138), tc_List_Olist(_1596138)), hAPP(hAPP(c_List_Olist_OCons(_1596138), _1596140), _1596142)), hAPP(hAPP(c_List_Olist_OCons(_1596138), _1596144), _1596146))), c_List_Olexord(_1596138, _1596148)))), 41382 ^ _779308 : [(41383 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596138, _1596138)), hAPP(hAPP(c_Product__Type_OPair(_1596138, _1596138), _1596140), _1596144)), _1596148))], (41385 ^ _779308) ^ [] : [_1596140 = _1596144, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596138), tc_List_Olist(_1596138))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596138), tc_List_Olist(_1596138)), _1596142), _1596146)), c_List_Olexord(_1596138, _1596148)))]]], (41393 ^ _779308) ^ [_1596532, _1596534, _1596536, _1596538] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596532), tc_List_Olist(_1596532))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596532), tc_List_Olist(_1596532)), _1596534), _1596536)), c_List_Olex(_1596532, _1596538))), 41396 ^ _779308 : [(41397 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596532), tc_List_Olist(_1596532))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596532), tc_List_Olist(_1596532)), _1596534), _1596536)), c_List_Olexord(_1596532, _1596538))))], (41399 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596532)), _1596534) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596532)), _1596536))]]], (41401 ^ _779308) ^ [_1596783, _1596785, _1596787, _1596789] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596783), tc_List_Olist(_1596783))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596783), tc_List_Olist(_1596783)), _1596785), _1596787)), c_List_Olex(_1596783, _1596789)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596783), tc_List_Olist(_1596783))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596783), tc_List_Olist(_1596783)), _1596785), _1596787)), c_List_Olexord(_1596783, _1596789))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596783)), _1596785) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596783)), _1596787)], (41411 ^ _779308) ^ [_1597070, _1597072, _1597074, _1597076, _1597078, _1597080] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597070, _1597070)), hAPP(hAPP(c_Product__Type_OPair(_1597070, _1597070), _1597072), _1597074)), c_Transitive__Closure_Ortrancl(_1597070, _1597076))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597070), tc_List_Olist(_1597070))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597070), tc_List_Olist(_1597070)), _1597078), _1597080)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597070), c_List_Olistrel1(_1597070, _1597076)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597070), tc_List_Olist(_1597070))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597070), tc_List_Olist(_1597070)), hAPP(hAPP(c_List_Olist_OCons(_1597070), _1597072), _1597078)), hAPP(hAPP(c_List_Olist_OCons(_1597070), _1597074), _1597080))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597070), c_List_Olistrel1(_1597070, _1597076)))))], (41421 ^ _779308) ^ [_1597431, _1597433, _1597435, _1597437] : [-(c_List_Olist_Olist__size(_1597431, _1597433, hAPP(hAPP(c_List_Olist_OCons(_1597431), _1597435), _1597437)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1597433, _1597435)), c_List_Olist_Olist__size(_1597431, _1597433, _1597437))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41423 ^ _779308) ^ [_1597491, _1597493, _1597495, _1597497] : [hBOOL(hAPP(hAPP(c_member(_1597491), _1597493), c_Wellfounded_Oacc(_1597491, _1597495))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1597491)), _1597497), c_Wellfounded_Oacc(tc_List_Olist(_1597491), c_List_Olistrel1(_1597491, _1597495)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1597491)), hAPP(hAPP(c_List_Olist_OCons(_1597491), _1597493), _1597497)), c_Wellfounded_Oacc(tc_List_Olist(_1597491), c_List_Olistrel1(_1597491, _1597495)))))], (41433 ^ _779308) ^ [_1597732, _1597734] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1597732), tc_List_Olist(_1597732)), tc_HOL_Obool)), c_List_Olistrel1(_1597732, c_Transitive__Closure_Ortrancl(_1597732, _1597734))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1597732), c_List_Olistrel1(_1597732, _1597734)))))], (41435 ^ _779308) ^ [_1597788, _1597790] : [-(c_List_Olistrel1(_1597788, hAPP(c_Relation_Oconverse(_1597788, _1597788), _1597790)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1597788), tc_List_Olist(_1597788)), c_List_Olistrel1(_1597788, _1597790)))], (41437 ^ _779308) ^ [_1597835, _1597837, _1597839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1597835, _1597835), tc_HOL_Obool)), _1597837), _1597839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1597835), tc_List_Olist(_1597835)), tc_HOL_Obool)), c_List_Olistrel1(_1597835, _1597837)), c_List_Olistrel1(_1597835, _1597839))))], (41443 ^ _779308) ^ [_1597986, _1597988, _1597990, _1597992, _1597994] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597986), tc_List_Olist(_1597986))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597986), tc_List_Olist(_1597986)), _1597988), _1597990)), c_List_Olistrel1(_1597986, _1597992))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597986), tc_List_Olist(_1597986))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597986), tc_List_Olist(_1597986)), hAPP(hAPP(c_List_Olist_OCons(_1597986), _1597994), _1597988)), hAPP(hAPP(c_List_Olist_OCons(_1597986), _1597994), _1597990))), c_List_Olistrel1(_1597986, _1597992))))], (41449 ^ _779308) ^ [_1598221, _1598223, _1598225, _1598227, _1598229] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598221), tc_List_Olist(_1598221))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598221), tc_List_Olist(_1598221)), _1598223), _1598225)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598221), c_List_Olistrel1(_1598221, _1598227)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598221), tc_List_Olist(_1598221))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598221), tc_List_Olist(_1598221)), hAPP(hAPP(c_List_Olist_OCons(_1598221), _1598229), _1598223)), hAPP(hAPP(c_List_Olist_OCons(_1598221), _1598229), _1598225))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598221), c_List_Olistrel1(_1598221, _1598227)))))], (41455 ^ _779308) ^ [_1598476, _1598478, _1598480, _1598482] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598476), tc_List_Olist(_1598476))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598476), tc_List_Olist(_1598476)), _1598478), _1598480)), c_List_Olistrel1(_1598476, _1598482))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598476)), _1598478) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598476)), _1598480))], (41461 ^ _779308) ^ [_1598645, _1598647, _1598649, _1598651] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598645), tc_List_Olist(_1598645))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598645), tc_List_Olist(_1598645)), _1598647), _1598649)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598645), c_List_Olistrel1(_1598645, _1598651)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598645)), _1598647) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598645)), _1598649))], (41467 ^ _779308) ^ [_1598845, _1598847, _1598849, _1598851] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598845), tc_List_Olist(_1598845))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598845), tc_List_Olist(_1598845)), _1598847), _1598849)), c_List_Olistrel1(_1598845, hAPP(c_Relation_Oconverse(_1598845, _1598845), _1598851)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598845), tc_List_Olist(_1598845))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598845), tc_List_Olist(_1598845)), _1598847), _1598849)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1598845), tc_List_Olist(_1598845)), c_List_Olistrel1(_1598845, _1598851)))))], (41473 ^ _779308) ^ [_1599074, _1599076, _1599078, _1599080] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599074), tc_List_Olist(_1599074))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599074), tc_List_Olist(_1599074)), _1599076), _1599078)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1599074), tc_List_Olist(_1599074)), c_List_Olistrel1(_1599074, _1599080)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599074), tc_List_Olist(_1599074))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599074), tc_List_Olist(_1599074)), _1599076), _1599078)), c_List_Olistrel1(_1599074, hAPP(c_Relation_Oconverse(_1599074, _1599074), _1599080)))))], (41479 ^ _779308) ^ [_1599336, _1599338, _1599340, _1599342, _1599344, _1599346] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599336), tc_List_Olist(_1599336))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599336), tc_List_Olist(_1599336)), hAPP(hAPP(c_List_Olist_OCons(_1599336), _1599338), _1599340)), hAPP(hAPP(c_List_Olist_OCons(_1599336), _1599342), _1599344))), c_List_Olistrel1(_1599336, _1599346))), 41484 ^ _779308 : [(41485 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599336, _1599336)), hAPP(hAPP(c_Product__Type_OPair(_1599336, _1599336), _1599338), _1599342)), _1599346)))], (41487 ^ _779308) ^ [] : [-(_1599340 = _1599344)]], 41488 ^ _779308 : [(41489 ^ _779308) ^ [] : [-(_1599338 = _1599342)], (41491 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599336), tc_List_Olist(_1599336))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599336), tc_List_Olist(_1599336)), _1599340), _1599344)), c_List_Olistrel1(_1599336, _1599346))))]]], (41493 ^ _779308) ^ [_1599706, _1599708, _1599710, _1599712, _1599714, _1599716] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599706), tc_List_Olist(_1599706))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599706), tc_List_Olist(_1599706)), hAPP(hAPP(c_List_Olist_OCons(_1599706), _1599708), _1599710)), hAPP(hAPP(c_List_Olist_OCons(_1599706), _1599712), _1599714))), c_List_Olistrel1(_1599706, _1599716)))), 41494 ^ _779308 : [(41495 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599706, _1599706)), hAPP(hAPP(c_Product__Type_OPair(_1599706, _1599706), _1599708), _1599712)), _1599716)), _1599710 = _1599714], (41501 ^ _779308) ^ [] : [_1599708 = _1599712, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599706), tc_List_Olist(_1599706))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599706), tc_List_Olist(_1599706)), _1599710), _1599714)), c_List_Olistrel1(_1599706, _1599716)))]]], (41509 ^ _779308) ^ [_1600134, _1600136, _1600138, _1600140, _1600142] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600134, _1600134)), hAPP(hAPP(c_Product__Type_OPair(_1600134, _1600134), _1600136), _1600138)), _1600140)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600134), tc_List_Olist(_1600134))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600134), tc_List_Olist(_1600134)), hAPP(hAPP(c_List_Olist_OCons(_1600134), _1600136), _1600142)), hAPP(hAPP(c_List_Olist_OCons(_1600134), _1600138), _1600142))), c_List_Olistrel1(_1600134, _1600140))))], (41515 ^ _779308) ^ [_1600347, _1600349, _1600351, _1600353] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1600347), tc_List_Olist(_1600347), c_List_Olistrel(_1600347, _1600349)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1600347)), hAPP(hAPP(c_List_Olist_OCons(_1600347), _1600351), _1600353)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1600347), tc_HOL_Obool)))) = c_List_Oset__Cons(_1600347, hAPP(c_Relation_OImage(_1600347, _1600347, _1600349), hAPP(hAPP(c_Set_Oinsert(_1600347), _1600351), c_Orderings_Obot__class_Obot(tc_fun(_1600347, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1600347), tc_List_Olist(_1600347), c_List_Olistrel(_1600347, _1600349)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1600347)), _1600353), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1600347), tc_HOL_Obool))))))], (41517 ^ _779308) ^ [_1600470, _1600472, _1600474, _1600476] : [41520 ^ _779308 : [(41521 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600470, _1600470)), hAPP(hAPP(c_Product__Type_OPair(_1600470, _1600470), 41518 ^ [_1600470, _1600472, _1600474, _1600476]), 41519 ^ [_1600470, _1600472, _1600474, _1600476])), _1600472))], (41523 ^ _779308) ^ [] : [41518 ^ [_1600470, _1600472, _1600474, _1600476] = 41519 ^ [_1600470, _1600472, _1600474, _1600476]], (41525 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600470, _1600470)), hAPP(hAPP(c_Product__Type_OPair(_1600470, _1600470), 41519 ^ [_1600470, _1600472, _1600474, _1600476]), 41518 ^ [_1600470, _1600472, _1600474, _1600476])), _1600472))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600470), tc_List_Olist(_1600470))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600470), tc_List_Olist(_1600470)), _1600474), _1600476)), c_List_Olexord(_1600470, _1600472)))), -(_1600474 = _1600476), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600470), tc_List_Olist(_1600470))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600470), tc_List_Olist(_1600470)), _1600476), _1600474)), c_List_Olexord(_1600470, _1600472))))], (41537 ^ _779308) ^ [_1601017, _1601019, _1601021] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601017), tc_List_Olist(_1601017))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601017), tc_List_Olist(_1601017)), _1601019), _1601019)), c_List_Olistrel(_1601017, c_Transitive__Closure_Ortrancl(_1601017, _1601021)))))], (41539 ^ _779308) ^ [_1601077, _1601079, _1601081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1601077, _1601077), tc_HOL_Obool)), _1601079), _1601081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1601077), tc_List_Olist(_1601077)), tc_HOL_Obool)), c_List_Olistrel(_1601077, _1601079)), c_List_Olistrel(_1601077, _1601081))))], (41545 ^ _779308) ^ [_1601228, _1601230] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1601228), tc_List_Olist(_1601228)), tc_HOL_Obool)), c_List_Olistrel(_1601228, _1601230)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1601228), c_List_Olistrel1(_1601228, _1601230)))))], (41547 ^ _779308) ^ [_1601281, _1601283, _1601285, _1601287] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601281), tc_List_Olist(_1601281))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601281), tc_List_Olist(_1601281)), _1601283), _1601285)), c_List_Olistrel(_1601281, _1601287))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601281)), _1601283) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601281)), _1601285))], (41553 ^ _779308) ^ [_1601450, _1601452, _1601454, _1601456, _1601458] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601450), tc_List_Olist(_1601450))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601450), tc_List_Olist(_1601450)), _1601452), _1601454)), c_List_Olistrel(_1601450, c_Transitive__Closure_Ortrancl(_1601450, _1601456)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601450), tc_List_Olist(_1601450))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601450), tc_List_Olist(_1601450)), _1601454), _1601458)), c_List_Olistrel(_1601450, c_Transitive__Closure_Ortrancl(_1601450, _1601456)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601450), tc_List_Olist(_1601450))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601450), tc_List_Olist(_1601450)), _1601452), _1601458)), c_List_Olistrel(_1601450, c_Transitive__Closure_Ortrancl(_1601450, _1601456)))))], (41563 ^ _779308) ^ [_1601789, _1601791] : [-(c_List_Olistrel(_1601789, c_Transitive__Closure_Ortrancl(_1601789, _1601791)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1601789), c_List_Olistrel1(_1601789, _1601791)))], (41565 ^ _779308) ^ [_1601828, _1601830, _1601832, _1601834] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601828), tc_List_Olist(_1601828))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601828), tc_List_Olist(_1601828)), _1601830), _1601832)), c_List_Olistrel1(_1601828, _1601834))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601828), tc_List_Olist(_1601828))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601828), tc_List_Olist(_1601828)), _1601830), _1601832)), c_List_Olistrel(_1601828, c_Transitive__Closure_Ortrancl(_1601828, _1601834)))))], (41571 ^ _779308) ^ [_1602035, _1602037, _1602039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602035, _1602035), tc_HOL_Obool)), _1602037), _1602039)), c_Relation_Orefl__on(_1602035, c_Orderings_Otop__class_Otop(tc_fun(_1602035, tc_HOL_Obool)), _1602039), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1602035), tc_List_Olist(_1602035)), tc_HOL_Obool)), c_List_Olistrel1(_1602035, _1602037)), c_List_Olistrel(_1602035, _1602039))))], (41581 ^ _779308) ^ [_1602252, _1602254, _1602256, _1602258] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602252), tc_List_Olist(_1602252))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602252), tc_List_Olist(_1602252)), _1602254), _1602256)), c_List_Olistrel(_1602252, _1602258))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602252), tc_List_Olist(_1602252))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602252), tc_List_Olist(_1602252)), _1602254), _1602256)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1602252), c_List_Olistrel1(_1602252, _1602258)))))], (41587 ^ _779308) ^ [_1602463, _1602465, _1602467, _1602469, _1602471, _1602473] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602463, _1602463)), hAPP(hAPP(c_Product__Type_OPair(_1602463, _1602463), _1602465), _1602467)), _1602469)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602463), tc_List_Olist(_1602463))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602463), tc_List_Olist(_1602463)), _1602471), _1602473)), c_List_Olistrel(_1602463, _1602469))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602463), tc_List_Olist(_1602463))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602463), tc_List_Olist(_1602463)), hAPP(hAPP(c_List_Olist_OCons(_1602463), _1602465), _1602471)), hAPP(hAPP(c_List_Olist_OCons(_1602463), _1602467), _1602473))), c_List_Olistrel(_1602463, _1602469))))], (41597 ^ _779308) ^ [_1602819, _1602821, _1602823, _1602825] : [c_List_Olistrelp(_1602819, hAPP(hAPP(c_COMBC(_1602819, tc_fun(tc_prod(_1602819, _1602819), tc_HOL_Obool), tc_fun(_1602819, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602819, tc_fun(tc_fun(tc_prod(_1602819, _1602819), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1602819, _1602819), tc_HOL_Obool), tc_fun(_1602819, tc_HOL_Obool)), _1602819), c_COMBC(_1602819, tc_fun(tc_prod(_1602819, _1602819), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602819, tc_prod(_1602819, _1602819)), tc_fun(_1602819, tc_fun(tc_fun(tc_prod(_1602819, _1602819), tc_HOL_Obool), tc_HOL_Obool)), _1602819), hAPP(c_COMBB(tc_prod(_1602819, _1602819), tc_fun(tc_fun(tc_prod(_1602819, _1602819), tc_HOL_Obool), tc_HOL_Obool), _1602819), c_member(tc_prod(_1602819, _1602819)))), c_Product__Type_OPair(_1602819, _1602819)))), _1602821), _1602823, _1602825), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602819), tc_List_Olist(_1602819))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602819), tc_List_Olist(_1602819)), _1602823), _1602825)), c_List_Olistrel(_1602819, _1602821))))], (41603 ^ _779308) ^ [_1603196, _1603198, _1603200, _1603202] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603196), tc_List_Olist(_1603196))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603196), tc_List_Olist(_1603196)), _1603200), _1603202)), c_List_Olistrel(_1603196, _1603198))), -(c_List_Olistrelp(_1603196, hAPP(hAPP(c_COMBC(_1603196, tc_fun(tc_prod(_1603196, _1603196), tc_HOL_Obool), tc_fun(_1603196, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603196, tc_fun(tc_fun(tc_prod(_1603196, _1603196), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1603196, _1603196), tc_HOL_Obool), tc_fun(_1603196, tc_HOL_Obool)), _1603196), c_COMBC(_1603196, tc_fun(tc_prod(_1603196, _1603196), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603196, tc_prod(_1603196, _1603196)), tc_fun(_1603196, tc_fun(tc_fun(tc_prod(_1603196, _1603196), tc_HOL_Obool), tc_HOL_Obool)), _1603196), hAPP(c_COMBB(tc_prod(_1603196, _1603196), tc_fun(tc_fun(tc_prod(_1603196, _1603196), tc_HOL_Obool), tc_HOL_Obool), _1603196), c_member(tc_prod(_1603196, _1603196)))), c_Product__Type_OPair(_1603196, _1603196)))), _1603198), _1603200, _1603202))], (41609 ^ _779308) ^ [_1603579, _1603581, _1603583, _1603585, _1603587] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603579), tc_List_Olist(_1603579))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603579), tc_List_Olist(_1603579)), hAPP(hAPP(c_List_Olist_OCons(_1603579), _1603581), _1603583)), _1603585)), c_List_Olistrel(_1603579, _1603587))), 41614 ^ _779308 : [(41615 ^ _779308) ^ [] : [-(_1603585 = hAPP(hAPP(c_List_Olist_OCons(_1603579), 41612 ^ [_1603579, _1603581, _1603583, _1603585, _1603587]), 41613 ^ [_1603579, _1603581, _1603583, _1603585, _1603587]))], (41617 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603579, _1603579)), hAPP(hAPP(c_Product__Type_OPair(_1603579, _1603579), _1603581), 41612 ^ [_1603579, _1603581, _1603583, _1603585, _1603587])), _1603587)))], (41619 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603579), tc_List_Olist(_1603579))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603579), tc_List_Olist(_1603579)), _1603583), 41613 ^ [_1603579, _1603581, _1603583, _1603585, _1603587])), c_List_Olistrel(_1603579, _1603587))))]]], (41621 ^ _779308) ^ [_1603968, _1603970, _1603972, _1603974, _1603976, _1603978] : [hBOOL(hAPP(hAPP(_1603968, _1603970), _1603972)), c_List_Olistrelp(_1603974, _1603968, _1603976, _1603978), -(c_List_Olistrelp(_1603974, _1603968, hAPP(hAPP(c_List_Olist_OCons(_1603974), _1603970), _1603976), hAPP(hAPP(c_List_Olist_OCons(_1603974), _1603972), _1603978)))], (41631 ^ _779308) ^ [_1604190, _1604192, _1604194, _1604196, _1604198, _1604200] : [c_List_Olistrelp(_1604190, _1604192, hAPP(hAPP(c_List_Olist_OCons(_1604190), _1604194), _1604196), hAPP(hAPP(c_List_Olist_OCons(_1604190), _1604198), _1604200)), 41634 ^ _779308 : [(41635 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1604192, _1604194), _1604198)))], (41637 ^ _779308) ^ [] : [-(c_List_Olistrelp(_1604190, _1604192, _1604196, _1604200))]]], (41639 ^ _779308) ^ [_1604347, _1604349, _1604351, _1604353, _1604355, _1604357] : [-(c_List_Olistrelp(_1604347, _1604349, hAPP(hAPP(c_List_Olist_OCons(_1604347), _1604351), _1604353), hAPP(hAPP(c_List_Olist_OCons(_1604347), _1604355), _1604357))), hBOOL(hAPP(hAPP(_1604349, _1604351), _1604355)), c_List_Olistrelp(_1604347, _1604349, _1604353, _1604357)], (41649 ^ _779308) ^ [_1604544, _1604546, _1604548, _1604550, _1604552] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604544), tc_List_Olist(_1604544))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604544), tc_List_Olist(_1604544)), _1604546), hAPP(hAPP(c_List_Olist_OCons(_1604544), _1604548), _1604550))), c_List_Olistrel(_1604544, _1604552))), 41654 ^ _779308 : [(41655 ^ _779308) ^ [] : [-(_1604546 = hAPP(hAPP(c_List_Olist_OCons(_1604544), 41652 ^ [_1604544, _1604546, _1604548, _1604550, _1604552]), 41653 ^ [_1604544, _1604546, _1604548, _1604550, _1604552]))], (41657 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604544, _1604544)), hAPP(hAPP(c_Product__Type_OPair(_1604544, _1604544), 41652 ^ [_1604544, _1604546, _1604548, _1604550, _1604552]), _1604548)), _1604552)))], (41659 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604544), tc_List_Olist(_1604544))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604544), tc_List_Olist(_1604544)), 41653 ^ [_1604544, _1604546, _1604548, _1604550, _1604552]), _1604550)), c_List_Olistrel(_1604544, _1604552))))]]], (41661 ^ _779308) ^ [_1604933, _1604935, _1604937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1604933, _1604933), tc_HOL_Obool)), _1604935), hAPP(hAPP(c_Product__Type_OSigma(_1604933, _1604933), _1604937), hAPP(c_COMBK(tc_fun(_1604933, tc_HOL_Obool), _1604933), _1604937)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1604933), tc_List_Olist(_1604933)), tc_HOL_Obool)), c_List_Olistrel(_1604933, _1604935)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1604933), tc_List_Olist(_1604933)), c_List_Olists(_1604933, _1604937)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1604933), tc_HOL_Obool), tc_List_Olist(_1604933)), c_List_Olists(_1604933, _1604937))))))], (41667 ^ _779308) ^ [_1605178] : [-(c_List_Olists(_1605178, c_Orderings_Otop__class_Otop(tc_fun(_1605178, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1605178), tc_HOL_Obool)))], (41669 ^ _779308) ^ [_1605216, _1605218, _1605220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605216, tc_HOL_Obool)), _1605218), _1605220)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1605216), tc_HOL_Obool)), c_List_Olists(_1605216, _1605218)), c_List_Olists(_1605216, _1605220))))], (41675 ^ _779308) ^ [_1605351, _1605353, _1605355] : [c_Equiv__Relations_Oequiv(_1605351, _1605353, _1605355), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1605351), c_List_Olists(_1605351, _1605353), c_List_Olistrel(_1605351, _1605355)))], (41681 ^ _779308) ^ [_1605450, _1605452, _1605454] : [c_Relation_Orefl__on(_1605450, _1605452, _1605454), -(c_Relation_Orefl__on(tc_List_Olist(_1605450), c_List_Olists(_1605450, _1605452), c_List_Olistrel(_1605450, _1605454)))], (41687 ^ _779308) ^ [_1605570, _1605572, _1605574, _1605576] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605570)), hAPP(hAPP(c_List_Olist_OCons(_1605570), _1605572), _1605574)), c_List_Olists(_1605570, _1605576))), 41690 ^ _779308 : [(41691 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1605570), _1605572), _1605576)))], (41693 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605570)), _1605574), c_List_Olists(_1605570, _1605576))))]]], (41695 ^ _779308) ^ [_1605751, _1605753, _1605755, _1605757] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605751)), hAPP(hAPP(c_List_Olist_OCons(_1605751), _1605753), _1605755)), c_List_Olists(_1605751, _1605757)))), hBOOL(hAPP(hAPP(c_member(_1605751), _1605753), _1605757)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605751)), _1605755), c_List_Olists(_1605751, _1605757)))], (41705 ^ _779308) ^ [_1605968, _1605970, _1605972] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605968)), _1605970), c_List_Olists(_1605968, c_Wellfounded_Oacc(_1605968, _1605972)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1605968)), _1605970), c_Wellfounded_Oacc(tc_List_Olist(_1605968), c_List_Olistrel1(_1605968, _1605972)))))], (41711 ^ _779308) ^ [_1606111, _1606113, _1606115] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606111)), _1606113), c_Wellfounded_Oacc(tc_List_Olist(_1606111), c_List_Olistrel1(_1606111, _1606115)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606111)), _1606113), c_List_Olists(_1606111, c_Wellfounded_Oacc(_1606111, _1606115)))))], (41717 ^ _779308) ^ [_1606275, _1606277, _1606279, _1606281] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606275), tc_List_Olist(_1606275))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606275), tc_List_Olist(_1606275)), _1606277), _1606279)), c_List_Olistrel(_1606275, _1606281))), 41720 ^ _779308 : [(41721 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606275)), _1606277) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606275)), _1606279))], (41723 ^ _779308) ^ [_1606504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1606504), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606275)), _1606277))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606275, _1606275)), hAPP(hAPP(c_Product__Type_OPair(_1606275, _1606275), hAPP(hAPP(c_List_Onth(_1606275), _1606277), _1606504)), hAPP(hAPP(c_List_Onth(_1606275), _1606279), _1606504))), _1606281)))]]], (41729 ^ _779308) ^ [_1606683, _1606685, _1606687, _1606689] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606683), tc_List_Olist(_1606683))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606683), tc_List_Olist(_1606683)), _1606685), _1606687)), c_List_Olistrel(_1606683, _1606689)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606683)), _1606685) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606683)), _1606687), 41735 ^ _779308 : [(41736 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41734 ^ [_1606683, _1606685, _1606687, _1606689]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606683)), _1606685))))], (41738 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606683, _1606683)), hAPP(hAPP(c_Product__Type_OPair(_1606683, _1606683), hAPP(hAPP(c_List_Onth(_1606683), _1606685), 41734 ^ [_1606683, _1606685, _1606687, _1606689])), hAPP(hAPP(c_List_Onth(_1606683), _1606687), 41734 ^ [_1606683, _1606685, _1606687, _1606689]))), _1606689))]]], (41742 ^ _779308) ^ [_1607126, _1607128, _1607130] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607126, _1607126)), hAPP(hAPP(c_Product__Type_OPair(_1607126, _1607126), 41743 ^ [_1607126, _1607128, _1607130]), 41743 ^ [_1607126, _1607128, _1607130])), _1607128))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607126), tc_List_Olist(_1607126))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607126), tc_List_Olist(_1607126)), _1607130), _1607130)), c_List_Olexord(_1607126, _1607128)))], (41749 ^ _779308) ^ [_1607310] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1607310)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1607310), tc_HOL_Obool))))], (41751 ^ _779308) ^ [_1607364, _1607366, _1607368] : [_1607364 = _1607366, 41754 ^ _779308 : [(41755 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607368)), _1607364) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607368)), _1607366))], (41757 ^ _779308) ^ [_1607512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1607512), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607368)), _1607364))), -(hAPP(hAPP(c_List_Onth(_1607368), _1607364), _1607512) = hAPP(hAPP(c_List_Onth(_1607368), _1607366), _1607512))]]], (41763 ^ _779308) ^ [_1607651, _1607653, _1607655] : [-(_1607651 = _1607653), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607655)), _1607651) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607655)), _1607653), 41769 ^ _779308 : [(41770 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41768 ^ [_1607651, _1607653, _1607655]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607655)), _1607651))))], (41772 ^ _779308) ^ [] : [hAPP(hAPP(c_List_Onth(_1607655), _1607651), 41768 ^ [_1607651, _1607653, _1607655]) = hAPP(hAPP(c_List_Onth(_1607655), _1607653), 41768 ^ [_1607651, _1607653, _1607655])]]], (41776 ^ _779308) ^ [_1607966, _1607968, _1607970] : [-(hAPP(hAPP(c_List_Onth(_1607966), hAPP(hAPP(c_List_Olist_OCons(_1607966), _1607968), _1607970)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1607968)], (41778 ^ _779308) ^ [_1608009, _1608011, _1608013, _1608015] : [-(hAPP(hAPP(c_List_Onth(_1608009), hAPP(hAPP(c_List_Olist_OCons(_1608009), _1608011), _1608013)), hAPP(c_Nat_OSuc, _1608015)) = hAPP(hAPP(c_List_Onth(_1608009), _1608013), _1608015))], (41780 ^ _779308) ^ [_1608065, _1608067, _1608069, _1608071] : [-(hAPP(hAPP(c_List_Onth(_1608065), hAPP(hAPP(c_List_Olist_OCons(_1608065), _1608067), _1608069)), _1608071) = c_Nat_Onat_Onat__case(_1608065, _1608067, hAPP(c_List_Onth(_1608065), _1608069), _1608071))], (41782 ^ _779308) ^ [_1608135, _1608137, _1608139, _1608141] : [_1608135 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1608137), hAPP(hAPP(c_List_Olist_OCons(_1608137), _1608139), _1608141)), _1608135) = _1608139)], (41788 ^ _779308) ^ [_1608242, _1608244, _1608246, _1608248] : [-(_1608242 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1608244), hAPP(hAPP(c_List_Olist_OCons(_1608244), _1608246), _1608248)), _1608242) = hAPP(hAPP(c_List_Onth(_1608244), _1608248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1608242), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41794 ^ _779308) ^ [_1608329, _1608331, _1608333, _1608335] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608329) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1608331), hAPP(hAPP(c_List_Olist_OCons(_1608331), _1608333), _1608335)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608329)) = _1608333)], (41800 ^ _779308) ^ [_1608448, _1608450, _1608452, _1608454] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608448) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1608450), hAPP(hAPP(c_List_Olist_OCons(_1608450), _1608452), _1608454)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608448)) = hAPP(hAPP(c_List_Onth(_1608450), _1608454), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1608448)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41806 ^ _779308) ^ [_1608550, _1608552, _1608554, _1608556] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608550), tc_List_Olist(_1608550))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608550), tc_List_Olist(_1608550)), _1608552), _1608554)), c_List_Olexord(_1608550, _1608556))), 41811 ^ _779308 : [(41812 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608550)), _1608552)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608550)), _1608554))))], (41814 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1608550), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608550)), _1608552)), _1608554) = _1608552)]], 41816 ^ _779308 : [(41817 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41815 ^ [_1608550, _1608552, _1608554, _1608556]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608550)), _1608552)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608550)), _1608554)))))], (41819 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1608550), 41815 ^ [_1608550, _1608552, _1608554, _1608556]), _1608552) = hAPP(hAPP(c_List_Otake(_1608550), 41815 ^ [_1608550, _1608552, _1608554, _1608556]), _1608554))], (41821 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608550, _1608550)), hAPP(hAPP(c_Product__Type_OPair(_1608550, _1608550), hAPP(hAPP(c_List_Onth(_1608550), _1608552), 41815 ^ [_1608550, _1608552, _1608554, _1608556])), hAPP(hAPP(c_List_Onth(_1608550), _1608554), 41815 ^ [_1608550, _1608552, _1608554, _1608556]))), _1608556)))]]], (41823 ^ _779308) ^ [_1609090, _1609092, _1609094, _1609096] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609090), tc_List_Olist(_1609090))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609090), tc_List_Olist(_1609090)), _1609092), _1609094)), c_List_Olexord(_1609090, _1609096)))), 41824 ^ _779308 : [(41825 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609090)), _1609092)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609090)), _1609094))), hAPP(hAPP(c_List_Otake(_1609090), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609090)), _1609092)), _1609094) = _1609092], (41831 ^ _779308) ^ [_1609397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1609397), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609090)), _1609092)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609090)), _1609094)))), hAPP(hAPP(c_List_Otake(_1609090), _1609397), _1609092) = hAPP(hAPP(c_List_Otake(_1609090), _1609397), _1609094), hBOOL(hAPP(hAPP(c_member(tc_prod(_1609090, _1609090)), hAPP(hAPP(c_Product__Type_OPair(_1609090, _1609090), hAPP(hAPP(c_List_Onth(_1609090), _1609092), _1609397)), hAPP(hAPP(c_List_Onth(_1609090), _1609094), _1609397))), _1609096))]]], (41843 ^ _779308) ^ [_1609751, _1609753, _1609755] : [-(hAPP(c_List_Oset(_1609751), c_List_Osublist(_1609751, _1609753, _1609755)) = hAPP(c_Set_OCollect(_1609751), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1609751), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1609751, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1609751), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1609751), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1609751, tc_fun(tc_Nat_Onat, _1609751), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1609751, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1609751), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1609751), c_COMBB(_1609751, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1609751), _1609753))))), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609751)), _1609753)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1609755))))))], (41845 ^ _779308) ^ [_1609895, _1609897] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1609895), hAPP(c_List_Oset(_1609895), _1609897))))], (41847 ^ _779308) ^ [_1609929, _1609931, _1609933] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1609929, tc_HOL_Obool)), hAPP(c_List_Oset(_1609929), _1609931)), hAPP(c_List_Oset(_1609929), hAPP(hAPP(c_List_Olist_OCons(_1609929), _1609933), _1609931)))))], (41849 ^ _779308) ^ [_1609984, _1609986, _1609988] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609984)), _1609986)), _1609988)), -(hAPP(hAPP(c_List_Otake(_1609984), _1609988), _1609986) = _1609986)], (41855 ^ _779308) ^ [_1610103, _1610105, _1610107, _1610109] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1610103), _1610105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610107, tc_HOL_Obool)), hAPP(c_List_Oset(_1610107), hAPP(hAPP(c_List_Otake(_1610107), _1610103), _1610109))), hAPP(c_List_Oset(_1610107), hAPP(hAPP(c_List_Otake(_1610107), _1610105), _1610109)))))], (41861 ^ _779308) ^ [_1610266, _1610268, _1610270] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610266, tc_HOL_Obool)), hAPP(c_List_Oset(_1610266), hAPP(hAPP(c_List_Otake(_1610266), _1610268), _1610270))), hAPP(c_List_Oset(_1610266), _1610270))))], (41863 ^ _779308) ^ [_1610321, _1610323, _1610325] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610321, tc_HOL_Obool)), hAPP(c_List_Oset(_1610321), c_List_Osublist(_1610321, _1610323, _1610325))), hAPP(c_List_Oset(_1610321), _1610323))))], (41865 ^ _779308) ^ [_1610372, _1610374, _1610376, _1610378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610372), _1610374)), -(hAPP(hAPP(c_List_Onth(_1610376), hAPP(hAPP(c_List_Otake(_1610376), _1610374), _1610378)), _1610372) = hAPP(hAPP(c_List_Onth(_1610376), _1610378), _1610372))], (41871 ^ _779308) ^ [_1610510, _1610512, _1610514, _1610516] : [-(hBOOL(hAPP(hAPP(c_member(_1610510), _1610512), hAPP(c_List_Oset(_1610510), _1610514)))), hBOOL(hAPP(hAPP(c_member(_1610510), _1610512), hAPP(c_List_Oset(_1610510), c_List_Osublist(_1610510, _1610514, _1610516))))], (41877 ^ _779308) ^ [_1610634, _1610636, _1610638, _1610640] : [hBOOL(hAPP(hAPP(c_member(_1610634), _1610636), hAPP(c_List_Oset(_1610634), hAPP(hAPP(c_List_Otake(_1610634), _1610638), _1610640)))), -(hBOOL(hAPP(hAPP(c_member(_1610634), _1610636), hAPP(c_List_Oset(_1610634), _1610640))))], (41883 ^ _779308) ^ [_1610779, _1610781, _1610783, _1610785] : [hBOOL(hAPP(hAPP(c_member(_1610779), _1610781), hAPP(c_List_Oset(_1610779), c_List_Osublist(_1610779, _1610783, _1610785)))), -(hBOOL(hAPP(hAPP(c_member(_1610779), _1610781), hAPP(c_List_Oset(_1610779), _1610783))))], (41889 ^ _779308) ^ [_1610916, _1610918, _1610920, _1610922] : [hBOOL(hAPP(hAPP(c_member(_1610916), _1610918), hAPP(c_List_Oset(_1610916), hAPP(hAPP(c_List_Olist_OCons(_1610916), _1610920), _1610922)))), -(_1610918 = _1610920), -(hBOOL(hAPP(hAPP(c_member(_1610916), _1610918), hAPP(c_List_Oset(_1610916), _1610922))))], (41899 ^ _779308) ^ [_1611074, _1611076, _1611078, _1611080] : [-(hAPP(hAPP(c_List_Otake(_1611074), hAPP(c_Nat_OSuc, _1611076)), hAPP(hAPP(c_List_Olist_OCons(_1611074), _1611078), _1611080)) = hAPP(hAPP(c_List_Olist_OCons(_1611074), _1611078), hAPP(hAPP(c_List_Otake(_1611074), _1611076), _1611080)))], (41901 ^ _779308) ^ [_1611138, _1611140, _1611142] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611138)), hAPP(hAPP(c_List_Otake(_1611138), _1611140), _1611142)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611138)), _1611142)), _1611140))], (41903 ^ _779308) ^ [_1611193, _1611195, _1611197, _1611199] : [-(hAPP(hAPP(c_List_Otake(_1611193), _1611195), hAPP(hAPP(c_List_Otake(_1611193), _1611197), _1611199)) = hAPP(hAPP(c_List_Otake(_1611193), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1611195), _1611197)), _1611199))], (41905 ^ _779308) ^ [_1611252, _1611254, _1611256] : [-(hAPP(c_List_Oset(_1611252), hAPP(hAPP(c_List_Olist_OCons(_1611252), _1611254), _1611256)) = hAPP(hAPP(c_Set_Oinsert(_1611252), _1611254), hAPP(c_List_Oset(_1611252), _1611256)))], (41907 ^ _779308) ^ [_1611305, _1611307, _1611309] : [-(c_List_Osublist(_1611305, _1611307, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1611309)) = hAPP(hAPP(c_List_Otake(_1611305), _1611309), _1611307))], (41909 ^ _779308) ^ [_1611347, _1611349] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1611347), hAPP(c_List_Oset(_1611347), _1611349))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611347)), _1611349))))], (41911 ^ _779308) ^ [_1611412, _1611414, _1611416] : [41913 ^ _779308 : [(41914 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1611412), 41912 ^ [_1611412, _1611414, _1611416]), hAPP(c_List_Oset(_1611412), _1611414))))], (41916 ^ _779308) ^ [] : [hBOOL(hAPP(_1611416, 41912 ^ [_1611412, _1611414, _1611416]))]], 41917 ^ _779308 : [(41918 ^ _779308) ^ [_1611596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1611596), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611412)), _1611414))), -(hBOOL(hAPP(_1611416, hAPP(hAPP(c_List_Onth(_1611412), _1611414), _1611596))))]]], (41924 ^ _779308) ^ [_1611723, _1611725, _1611727] : [41926 ^ _779308 : [(41927 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41925 ^ [_1611723, _1611725, _1611727]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1611723)), _1611725))))], (41929 ^ _779308) ^ [] : [hBOOL(hAPP(_1611727, hAPP(hAPP(c_List_Onth(_1611723), _1611725), 41925 ^ [_1611723, _1611725, _1611727])))]], 41930 ^ _779308 : [(41931 ^ _779308) ^ [_1611925] : [hBOOL(hAPP(hAPP(c_member(_1611723), _1611925), hAPP(c_List_Oset(_1611723), _1611725))), -(hBOOL(hAPP(_1611727, _1611925)))]]], (41937 ^ _779308) ^ [_1612042, _1612044, _1612046, _1612048, _1612050] : [hBOOL(hAPP(hAPP(c_member(_1612042), _1612044), hAPP(c_List_Oset(_1612042), _1612046))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612048), hAPP(_1612050, _1612044))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612048), c_List_Olist_Olist__size(_1612042, _1612050, _1612046))))], (41947 ^ _779308) ^ [_1612241, _1612243, _1612245, _1612247, _1612249] : [hBOOL(hAPP(hAPP(c_member(_1612241), _1612243), hAPP(c_List_Oset(_1612241), _1612245))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1612247), hAPP(_1612249, _1612243))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1612247), c_List_Olist_Olist__size(_1612241, _1612249, _1612245))))], (41967 ^ _779308) ^ [_1612685, _1612687, _1612689] : [41969 ^ _779308 : [(41970 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612685), 41968 ^ [_1612685, _1612687, _1612689]), hAPP(c_List_Oset(_1612685), _1612687))))], (41972 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1612685), 41968 ^ [_1612685, _1612687, _1612689]), _1612689))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612685)), _1612687), c_List_Olists(_1612685, _1612689))))], (41957 ^ _779308) ^ [_1612458, _1612460, _1612462] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1612458)), _1612460), c_List_Olists(_1612458, _1612462))), 41960 ^ _779308 : [(41961 ^ _779308) ^ [_1612566] : [hBOOL(hAPP(hAPP(c_member(_1612458), _1612566), hAPP(c_List_Oset(_1612458), _1612460))), -(hBOOL(hAPP(hAPP(c_member(_1612458), _1612566), _1612462)))]]], (41976 ^ _779308) ^ [_1612905, _1612907, _1612909] : [hBOOL(hAPP(hAPP(c_member(_1612905), _1612907), hAPP(c_List_Oset(_1612905), _1612909))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612905)), _1612909))))], (41982 ^ _779308) ^ [_1613044, _1613046, _1613048] : [hBOOL(hAPP(hAPP(c_member(_1613044), _1613046), hAPP(c_List_Oset(_1613044), _1613048))), 41986 ^ _779308 : [(41987 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41985 ^ [_1613044, _1613046, _1613048]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613044)), _1613048))))], (41989 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1613044), _1613048), 41985 ^ [_1613044, _1613046, _1613048]) = _1613046)]]], (41991 ^ _779308) ^ [_1613232, _1613234, _1613236] : [-(hBOOL(hAPP(hAPP(c_member(_1613232), _1613234), hAPP(c_List_Oset(_1613232), _1613236)))), 41992 ^ _779308 : [(41993 ^ _779308) ^ [_1613306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613306), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613232)), _1613236))), hAPP(hAPP(c_List_Onth(_1613232), _1613236), _1613306) = _1613234]]], (42001 ^ _779308) ^ [_1613468, _1613470, _1613472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1613468), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613470)), _1613472))), -(hBOOL(hAPP(hAPP(c_member(_1613470), hAPP(hAPP(c_List_Onth(_1613470), _1613472), _1613468)), hAPP(c_List_Oset(_1613470), _1613472))))], (42007 ^ _779308) ^ [_1613611, _1613613] : [-(c_List_Olists(_1613611, _1613613) = hAPP(c_Set_OCollect(tc_List_Olist(_1613611)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613611), tc_fun(_1613611, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1613611, tc_HOL_Obool), tc_fun(tc_fun(_1613611, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1613611)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1613611, tc_HOL_Obool))), c_List_Oset(_1613611))), _1613613)))], (42009 ^ _779308) ^ [_1613689, _1613691] : [-(hAPP(c_List_Oset(_1613689), _1613691) = hAPP(c_Set_OCollect(_1613689), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1613689), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1613689, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1613689), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1613689), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1613689, tc_fun(tc_Nat_Onat, _1613689), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1613689, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1613689), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1613689), c_COMBB(_1613689, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1613689), _1613691))))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613689)), _1613691))))))], (42011 ^ _779308) ^ [_1613815, _1613817, _1613819] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1613815), _1613817)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1613815)), hAPP(c_Set_OCollect(tc_List_Olist(_1613815)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1613815), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1613815)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613815), tc_fun(_1613815, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1613815, tc_HOL_Obool), tc_fun(tc_fun(_1613815, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1613815)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1613815, tc_HOL_Obool))), c_List_Oset(_1613815))), _1613817))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1613815), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1613815)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1613815)))), _1613819))))))], (42017 ^ _779308) ^ [_1614118, _1614120, _1614122] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1614118), _1614120)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1614118)), hAPP(c_Set_OCollect(tc_List_Olist(_1614118)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1614118), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1614118)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614118), tc_fun(_1614118, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614118, tc_HOL_Obool), tc_fun(tc_fun(_1614118, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614118)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614118, tc_HOL_Obool))), c_List_Oset(_1614118))), _1614120))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614118), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1614118)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1614118)))), _1614122))))))], (42023 ^ _779308) ^ [_1614442, _1614444, _1614446, _1614448] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614442), tc_List_Olist(_1614442))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614442), tc_List_Olist(_1614442)), _1614444), _1614446)), c_List_Olistrel(_1614442, _1614448))), 42026 ^ _779308 : [(42027 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614442)), _1614444) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614442)), _1614446))], (42029 ^ _779308) ^ [_1614778] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1614442, _1614442)), _1614778), hAPP(c_List_Oset(tc_prod(_1614442, _1614442)), hAPP(hAPP(c_List_Ozip(_1614442, _1614442), _1614444), _1614446)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1614442, _1614442, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1614442, tc_fun(tc_prod(_1614442, _1614442), tc_HOL_Obool), tc_fun(_1614442, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614442, tc_fun(tc_fun(tc_prod(_1614442, _1614442), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1614442, _1614442), tc_HOL_Obool), tc_fun(_1614442, tc_HOL_Obool)), _1614442), c_COMBC(_1614442, tc_fun(tc_prod(_1614442, _1614442), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614442, tc_prod(_1614442, _1614442)), tc_fun(_1614442, tc_fun(tc_fun(tc_prod(_1614442, _1614442), tc_HOL_Obool), tc_HOL_Obool)), _1614442), hAPP(c_COMBB(tc_prod(_1614442, _1614442), tc_fun(tc_fun(tc_prod(_1614442, _1614442), tc_HOL_Obool), tc_HOL_Obool), _1614442), c_member(tc_prod(_1614442, _1614442)))), c_Product__Type_OPair(_1614442, _1614442)))), _1614448)), _1614778)))]]], (42035 ^ _779308) ^ [_1615171, _1615173, _1615175, _1615177] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615171), tc_List_Olist(_1615171))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615171), tc_List_Olist(_1615171)), _1615173), _1615175)), c_List_Olistrel(_1615171, _1615177)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615171)), _1615173) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615171)), _1615175), 42041 ^ _779308 : [(42042 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615171, _1615171)), 42040 ^ [_1615171, _1615173, _1615175, _1615177]), hAPP(c_List_Oset(tc_prod(_1615171, _1615171)), hAPP(hAPP(c_List_Ozip(_1615171, _1615171), _1615173), _1615175)))))], (42044 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1615171, _1615171, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1615171, tc_fun(tc_prod(_1615171, _1615171), tc_HOL_Obool), tc_fun(_1615171, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615171, tc_fun(tc_fun(tc_prod(_1615171, _1615171), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1615171, _1615171), tc_HOL_Obool), tc_fun(_1615171, tc_HOL_Obool)), _1615171), c_COMBC(_1615171, tc_fun(tc_prod(_1615171, _1615171), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615171, tc_prod(_1615171, _1615171)), tc_fun(_1615171, tc_fun(tc_fun(tc_prod(_1615171, _1615171), tc_HOL_Obool), tc_HOL_Obool)), _1615171), hAPP(c_COMBB(tc_prod(_1615171, _1615171), tc_fun(tc_fun(tc_prod(_1615171, _1615171), tc_HOL_Obool), tc_HOL_Obool), _1615171), c_member(tc_prod(_1615171, _1615171)))), c_Product__Type_OPair(_1615171, _1615171)))), _1615177)), 42040 ^ [_1615171, _1615173, _1615175, _1615177]))]]], (42048 ^ _779308) ^ [_1615909, _1615911, _1615913, _1615915] : [-(hAPP(c_List_Oset(tc_prod(_1615909, _1615911)), hAPP(hAPP(c_List_Ozip(_1615909, _1615911), _1615913), _1615915)) = hAPP(c_Set_OCollect(tc_prod(_1615909, _1615911)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1615909, _1615911)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1615909, _1615911), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1615909, _1615911)), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_prod(_1615909, _1615911)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(tc_prod(_1615909, _1615911), tc_fun(tc_Nat_Onat, tc_prod(_1615909, _1615911)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1615909, _1615911), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1615909, _1615911)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1615909, _1615911)), c_COMBB(tc_prod(_1615909, _1615911), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1615911, tc_prod(_1615909, _1615911)), hAPP(hAPP(c_COMBB(_1615909, tc_fun(_1615911, tc_prod(_1615909, _1615911)), tc_Nat_Onat), c_Product__Type_OPair(_1615909, _1615911)), hAPP(c_List_Onth(_1615909), _1615913))), hAPP(c_List_Onth(_1615911), _1615915)))))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615909)), _1615913)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615911)), _1615915)))))))], (42050 ^ _779308) ^ [_1616134, _1616136, _1616138, _1616140, _1616142] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1616134, _1616136)), _1616138), hAPP(hAPP(c_List_Ozip(_1616134, _1616136), _1616140), _1616142)) = hAPP(hAPP(c_List_Ozip(_1616134, _1616136), hAPP(hAPP(c_List_Otake(_1616134), _1616138), _1616140)), hAPP(hAPP(c_List_Otake(_1616136), _1616138), _1616142)))], (42052 ^ _779308) ^ [_1616210, _1616212, _1616214, _1616216] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1616210, _1616212))), hAPP(hAPP(c_List_Ozip(_1616210, _1616212), _1616214), _1616216)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616210)), _1616214)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616212)), _1616216)))], (42054 ^ _779308) ^ [_1616278, _1616280, _1616282, _1616284, _1616286, _1616288] : [-(hAPP(hAPP(c_List_Ozip(_1616278, _1616280), hAPP(hAPP(c_List_Olist_OCons(_1616278), _1616282), _1616284)), hAPP(hAPP(c_List_Olist_OCons(_1616280), _1616286), _1616288)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1616278, _1616280)), hAPP(hAPP(c_Product__Type_OPair(_1616278, _1616280), _1616282), _1616286)), hAPP(hAPP(c_List_Ozip(_1616278, _1616280), _1616284), _1616288)))], (42056 ^ _779308) ^ [_1616383, _1616385, _1616387] : [_1616383 = _1616385, 42059 ^ _779308 : [(42060 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616387)), _1616383) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616387)), _1616385))], (42062 ^ _779308) ^ [_1616539] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616387, _1616387)), _1616539), hAPP(c_List_Oset(tc_prod(_1616387, _1616387)), hAPP(hAPP(c_List_Ozip(_1616387, _1616387), _1616383), _1616385)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1616387, _1616387, tc_HOL_Obool), c_fequal), _1616539)))]]], (42068 ^ _779308) ^ [_1616694, _1616696, _1616698] : [-(_1616694 = _1616696), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616698)), _1616694) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616698)), _1616696), 42074 ^ _779308 : [(42075 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616698, _1616698)), 42073 ^ [_1616694, _1616696, _1616698]), hAPP(c_List_Oset(tc_prod(_1616698, _1616698)), hAPP(hAPP(c_List_Ozip(_1616698, _1616698), _1616694), _1616696)))))], (42077 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1616698, _1616698, tc_HOL_Obool), c_fequal), 42073 ^ [_1616694, _1616696, _1616698]))]]], (42081 ^ _779308) ^ [_1617008, _1617010, _1617012, _1617014, _1617016, _1617018] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617008, _1617010)), hAPP(hAPP(c_Product__Type_OPair(_1617008, _1617010), _1617012), _1617014)), hAPP(c_List_Oset(tc_prod(_1617008, _1617010)), hAPP(hAPP(c_List_Ozip(_1617008, _1617010), _1617016), _1617018)))), 42084 ^ _779308 : [(42085 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617008), _1617012), hAPP(c_List_Oset(_1617008), _1617016))))], (42087 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617010), _1617014), hAPP(c_List_Oset(_1617010), _1617018))))]]], (42089 ^ _779308) ^ [_1617243, _1617245, _1617247, _1617249, _1617251, _1617253] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617243, _1617245)), hAPP(hAPP(c_Product__Type_OPair(_1617243, _1617245), _1617247), _1617249)), hAPP(c_List_Oset(tc_prod(_1617243, _1617245)), hAPP(hAPP(c_List_Ozip(_1617243, _1617245), _1617251), _1617253)))), -(hBOOL(hAPP(hAPP(c_member(_1617245), _1617249), hAPP(c_List_Oset(_1617245), _1617253))))], (42095 ^ _779308) ^ [_1617424, _1617426, _1617428, _1617430, _1617432, _1617434] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617424, _1617426)), hAPP(hAPP(c_Product__Type_OPair(_1617424, _1617426), _1617428), _1617430)), hAPP(c_List_Oset(tc_prod(_1617424, _1617426)), hAPP(hAPP(c_List_Ozip(_1617424, _1617426), _1617432), _1617434)))), -(hBOOL(hAPP(hAPP(c_member(_1617424), _1617428), hAPP(c_List_Oset(_1617424), _1617432))))], (42101 ^ _779308) ^ [_1617626, _1617628, _1617630, _1617632] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617626, _1617626)), hAPP(hAPP(c_Product__Type_OPair(_1617626, _1617626), _1617628), _1617630)), hAPP(c_List_Oset(tc_prod(_1617626, _1617626)), hAPP(hAPP(c_List_Ozip(_1617626, _1617626), _1617632), _1617632)))), 42104 ^ _779308 : [(42105 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617626), _1617628), hAPP(c_List_Oset(_1617626), _1617632))))], (42107 ^ _779308) ^ [] : [-(_1617628 = _1617630)]]], (42109 ^ _779308) ^ [_1617825, _1617827, _1617829, _1617831] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617825, _1617825)), hAPP(hAPP(c_Product__Type_OPair(_1617825, _1617825), _1617827), _1617829)), hAPP(c_List_Oset(tc_prod(_1617825, _1617825)), hAPP(hAPP(c_List_Ozip(_1617825, _1617825), _1617831), _1617831))))), hBOOL(hAPP(hAPP(c_member(_1617825), _1617827), hAPP(c_List_Oset(_1617825), _1617831))), _1617827 = _1617829], (42119 ^ _779308) ^ [_1618060, _1618062, _1618064, _1618066, _1618068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618060), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618062)), _1618064))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618060), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618066)), _1618068))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1618062, _1618066)), hAPP(hAPP(c_List_Ozip(_1618062, _1618066), _1618064), _1618068)), _1618060) = hAPP(hAPP(c_Product__Type_OPair(_1618062, _1618066), hAPP(hAPP(c_List_Onth(_1618062), _1618064), _1618060)), hAPP(hAPP(c_List_Onth(_1618066), _1618068), _1618060)))], (42129 ^ _779308) ^ [_1618339, _1618341] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1618339, _1618341) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1618339), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1618341), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42131 ^ _779308) ^ [_1618386, _1618388] : [class_Groups_Ocomm__monoid__add(_1618386), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1618386), _1618388) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1618386), hAPP(c_List_Onth(_1618386), _1618388)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618386)), _1618388))))], (42137 ^ _779308) ^ [_1618519, _1618521] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1618519, _1618521)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1618519, _1618521))], (42139 ^ _779308) ^ [_1618554, _1618556] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1618554, _1618556) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1618554, _1618556)))], (42151 ^ _779308) ^ [_1618769] : [42153 ^ _779308 : [(42154 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42152 ^ [_1618769]), hAPP(c_List_Oset(tc_Nat_Onat), _1618769))))], (42156 ^ _779308) ^ [] : [42152 ^ [_1618769] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1618769) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42141 ^ _779308) ^ [_1618601] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1618601) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42144 ^ _779308 : [(42145 ^ _779308) ^ [_1618676] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1618676), hAPP(c_List_Oset(tc_Nat_Onat), _1618601))), -(_1618676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (42160 ^ _779308) ^ [_1618925, _1618927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1618925), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1618927))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1618927), _1618925)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1618927))))], (42166 ^ _779308) ^ [_1619046, _1619048, _1619050] : [class_Groups_Omonoid__add(_1619046), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1619046), hAPP(hAPP(c_List_Olist_OCons(_1619046), _1619048), _1619050)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1619046), _1619048), hAPP(c_List_Omonoid__add__class_Olistsum(_1619046), _1619050)))], (42172 ^ _779308) ^ [_1619175, _1619177] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1619175), _1619177) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619175, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1619177), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42174 ^ _779308) ^ [_1619218, _1619220] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1619218, _1619220) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1619218), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1619220)))], (42176 ^ _779308) ^ [_1619271] : [c_List_Onat__list(_1619271), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1619271)))], (42182 ^ _779308) ^ [_1619344] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1619344)), -(c_List_Onat__list(_1619344))], (42188 ^ _779308) ^ [_1619423, _1619425, _1619427, _1619429] : [42190 ^ _779308 : [(42191 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1619423), 42189 ^ [_1619423, _1619425, _1619427, _1619429]), hAPP(c_List_Oset(_1619423), _1619425))))], (42193 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1619427, 42189 ^ [_1619423, _1619425, _1619427, _1619429])), hAPP(_1619429, 42189 ^ [_1619423, _1619425, _1619427, _1619429])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1619423, _1619427, _1619425)), c_List_Olist_Olist__size(_1619423, _1619429, _1619425))))], (42197 ^ _779308) ^ [_1619673, _1619675, _1619677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619673), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1619675))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1619675), _1619673), _1619677)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619675)), _1619677)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1619675), _1619673)))], (42203 ^ _779308) ^ [_1619834, _1619836, _1619838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1619834), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619836)), _1619838))), -(c_List_Obutlast(_1619836, hAPP(hAPP(c_List_Otake(_1619836), _1619834), _1619838)) = hAPP(hAPP(c_List_Otake(_1619836), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1619834), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1619838))], (42209 ^ _779308) ^ [_1619987, _1619989, _1619991, _1619993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619987)), _1619989)), _1619991)), -(hAPP(hAPP(c_List_Olist__update(_1619987, _1619989), _1619991), _1619993) = _1619989)], (42215 ^ _779308) ^ [_1620106, _1620108, _1620110, _1620112, _1620114] : [-(_1620106 = _1620108), -(hAPP(hAPP(c_List_Onth(_1620110), hAPP(hAPP(c_List_Olist__update(_1620110, _1620112), _1620106), _1620114)), _1620108) = hAPP(hAPP(c_List_Onth(_1620110), _1620112), _1620108))], (42221 ^ _779308) ^ [_1620173, _1620175, _1620177] : [-(hAPP(hAPP(c_List_Olist__update(_1620173, _1620175), _1620177), hAPP(hAPP(c_List_Onth(_1620173), _1620175), _1620177)) = _1620175)], (42223 ^ _779308) ^ [_1620232, _1620234, _1620236, _1620238] : [_1620232 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620234)), _1620236)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1620234, hAPP(hAPP(c_List_Olist__update(_1620234, _1620236), _1620232), _1620238)) = c_List_Obutlast(_1620234, _1620236))], (42229 ^ _779308) ^ [_1620363, _1620365, _1620367, _1620369] : [-(_1620363 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620365)), _1620367)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1620365, hAPP(hAPP(c_List_Olist__update(_1620365, _1620367), _1620363), _1620369)) = hAPP(hAPP(c_List_Olist__update(_1620365, c_List_Obutlast(_1620365, _1620367)), _1620363), _1620369))], (42235 ^ _779308) ^ [_1620442, _1620444, _1620446, _1620448] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620442)), hAPP(hAPP(c_List_Olist__update(_1620442, _1620444), _1620446), _1620448)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620442)), _1620444))], (42237 ^ _779308) ^ [_1620494, _1620496, _1620498, _1620500, _1620502, _1620504, _1620506] : [-(hAPP(hAPP(c_List_Ozip(_1620494, _1620496), hAPP(hAPP(c_List_Olist__update(_1620494, _1620498), _1620500), _1620502)), hAPP(hAPP(c_List_Olist__update(_1620496, _1620504), _1620500), _1620506)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1620494, _1620496), hAPP(hAPP(c_List_Ozip(_1620494, _1620496), _1620498), _1620504)), _1620500), hAPP(hAPP(c_Product__Type_OPair(_1620494, _1620496), _1620502), _1620506)))], (42239 ^ _779308) ^ [_1620586, _1620588, _1620590, _1620592, _1620594, _1620596] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1620586, _1620588), hAPP(hAPP(c_List_Ozip(_1620586, _1620588), _1620590), _1620592)), _1620594), _1620596) = hAPP(hAPP(c_List_Ozip(_1620586, _1620588), hAPP(hAPP(c_List_Olist__update(_1620586, _1620590), _1620594), hAPP(c_Product__Type_Ofst(_1620586, _1620588), _1620596))), hAPP(hAPP(c_List_Olist__update(_1620588, _1620592), _1620594), hAPP(c_Product__Type_Osnd(_1620586, _1620588), _1620596))))], (42241 ^ _779308) ^ [_1620679, _1620681, _1620683, _1620685, _1620687] : [-(hAPP(hAPP(c_List_Olist__update(_1620679, hAPP(hAPP(c_List_Olist__update(_1620679, _1620681), _1620683), _1620685)), _1620683), _1620687) = hAPP(hAPP(c_List_Olist__update(_1620679, _1620681), _1620683), _1620687))], (42243 ^ _779308) ^ [_1620733, _1620735, _1620737, _1620739, _1620741, _1620743] : [-(_1620733 = _1620735), -(hAPP(hAPP(c_List_Olist__update(_1620737, hAPP(hAPP(c_List_Olist__update(_1620737, _1620739), _1620733), _1620741)), _1620735), _1620743) = hAPP(hAPP(c_List_Olist__update(_1620737, hAPP(hAPP(c_List_Olist__update(_1620737, _1620739), _1620735), _1620743)), _1620733), _1620741))], (42249 ^ _779308) ^ [_1620813, _1620815, _1620817, _1620819, _1620821] : [-(hAPP(hAPP(c_List_Olist__update(_1620813, hAPP(hAPP(c_List_Olist_OCons(_1620813), _1620815), _1620817)), _1620819), _1620821) = c_Nat_Onat_Onat__case(tc_List_Olist(_1620813), hAPP(hAPP(c_List_Olist_OCons(_1620813), _1620821), _1620817), hAPP(hAPP(c_COMBB(tc_List_Olist(_1620813), tc_List_Olist(_1620813), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1620813), _1620815)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1620813, tc_List_Olist(_1620813)), c_List_Olist__update(_1620813, _1620817)), _1620821)), _1620819))], (42251 ^ _779308) ^ [_1620910, _1620912, _1620914, _1620916] : [-(hAPP(hAPP(c_List_Olist__update(_1620910, hAPP(hAPP(c_List_Olist_OCons(_1620910), _1620912), _1620914)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1620916) = hAPP(hAPP(c_List_Olist_OCons(_1620910), _1620916), _1620914))], (42253 ^ _779308) ^ [_1620964, _1620966, _1620968, _1620970, _1620972] : [-(hAPP(hAPP(c_List_Olist__update(_1620964, hAPP(hAPP(c_List_Olist_OCons(_1620964), _1620966), _1620968)), hAPP(c_Nat_OSuc, _1620970)), _1620972) = hAPP(hAPP(c_List_Olist_OCons(_1620964), _1620966), hAPP(hAPP(c_List_Olist__update(_1620964, _1620968), _1620970), _1620972)))], (42255 ^ _779308) ^ [_1621032, _1621034, _1621036] : [hBOOL(hAPP(hAPP(c_member(_1621032), _1621034), hAPP(c_List_Oset(_1621032), c_List_Obutlast(_1621032, _1621036)))), -(hBOOL(hAPP(hAPP(c_member(_1621032), _1621034), hAPP(c_List_Oset(_1621032), _1621036))))], (42261 ^ _779308) ^ [_1621165, _1621167, _1621169, _1621171, _1621173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621165, tc_HOL_Obool)), hAPP(c_List_Oset(_1621165), _1621167)), _1621169)), hBOOL(hAPP(hAPP(c_member(_1621165), _1621171), _1621169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621165, tc_HOL_Obool)), hAPP(c_List_Oset(_1621165), hAPP(hAPP(c_List_Olist__update(_1621165, _1621167), _1621173), _1621171))), _1621169)))], (42271 ^ _779308) ^ [_1621398, _1621400, _1621402, _1621404] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1621398, tc_HOL_Obool)), hAPP(c_List_Oset(_1621398), hAPP(hAPP(c_List_Olist__update(_1621398, _1621400), _1621402), _1621404))), hAPP(hAPP(c_Set_Oinsert(_1621398), _1621404), hAPP(c_List_Oset(_1621398), _1621400)))))], (42273 ^ _779308) ^ [_1621464, _1621466, _1621468, _1621470, _1621472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1621464), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621466)), _1621468))), 42276 ^ _779308 : [(42277 ^ _779308) ^ [] : [_1621464 = _1621470, -(hAPP(hAPP(c_List_Onth(_1621466), hAPP(hAPP(c_List_Olist__update(_1621466, _1621468), _1621464), _1621472)), _1621470) = _1621472)], (42283 ^ _779308) ^ [] : [-(_1621464 = _1621470), -(hAPP(hAPP(c_List_Onth(_1621466), hAPP(hAPP(c_List_Olist__update(_1621466, _1621468), _1621464), _1621472)), _1621470) = hAPP(hAPP(c_List_Onth(_1621466), _1621468), _1621470))]]], (42289 ^ _779308) ^ [_1621760, _1621762, _1621764, _1621766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1621760), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621762)), _1621764))), 42292 ^ _779308 : [(42293 ^ _779308) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1621762, _1621764), _1621760), _1621766) = _1621764, -(hAPP(hAPP(c_List_Onth(_1621762), _1621764), _1621760) = _1621766)], (42299 ^ _779308) ^ [] : [hAPP(hAPP(c_List_Onth(_1621762), _1621764), _1621760) = _1621766, -(hAPP(hAPP(c_List_Olist__update(_1621762, _1621764), _1621760), _1621766) = _1621764)]]], (42305 ^ _779308) ^ [_1622054, _1622056, _1622058, _1622060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622054), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622056)), _1622058))), -(hAPP(hAPP(c_List_Onth(_1622056), hAPP(hAPP(c_List_Olist__update(_1622056, _1622058), _1622054), _1622060)), _1622054) = _1622060)], (42311 ^ _779308) ^ [_1622193, _1622195, _1622197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622193), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622195)), _1622197))), -(hAPP(hAPP(c_List_Otake(_1622195), _1622193), c_List_Obutlast(_1622195, _1622197)) = hAPP(hAPP(c_List_Otake(_1622195), _1622193), _1622197))], (42317 ^ _779308) ^ [_1622334, _1622336] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622334)), c_List_Obutlast(_1622334, _1622336)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622334)), _1622336)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42319 ^ _779308) ^ [_1622382, _1622384, _1622386, _1622388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622382), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622384)), _1622386))), -(hBOOL(hAPP(hAPP(c_member(_1622384), _1622388), hAPP(c_List_Oset(_1622384), hAPP(hAPP(c_List_Olist__update(_1622384, _1622386), _1622382), _1622388)))))], (42325 ^ _779308) ^ [_1622529, _1622531] : [-(c_List_Obutlast(_1622529, _1622531) = hAPP(hAPP(c_List_Otake(_1622529), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622529)), _1622531)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1622531))], (42327 ^ _779308) ^ [_1622599, _1622601, _1622603, _1622605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622599), tc_List_Olist(_1622599))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622599), tc_List_Olist(_1622599)), _1622601), _1622603)), c_List_Olistrel1(_1622599, _1622605))), 42332 ^ _779308 : [(42333 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622599, _1622599)), hAPP(hAPP(c_Product__Type_OPair(_1622599, _1622599), hAPP(hAPP(c_List_Onth(_1622599), _1622601), 42331 ^ [_1622599, _1622601, _1622603, _1622605])), 42330 ^ [_1622599, _1622601, _1622603, _1622605])), _1622605)))], (42335 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42331 ^ [_1622599, _1622601, _1622603, _1622605]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622599)), _1622601))))], (42337 ^ _779308) ^ [] : [-(_1622603 = hAPP(hAPP(c_List_Olist__update(_1622599, _1622601), 42331 ^ [_1622599, _1622601, _1622603, _1622605]), 42330 ^ [_1622599, _1622601, _1622603, _1622605]))]]], (42339 ^ _779308) ^ [_1622947, _1622949, _1622951, _1622953] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622947), tc_List_Olist(_1622947))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622947), tc_List_Olist(_1622947)), _1622949), _1622951)), c_List_Olistrel1(_1622947, _1622953)))), 42340 ^ _779308 : [(42341 ^ _779308) ^ [_1623080, _1623082] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622947, _1622947)), hAPP(hAPP(c_Product__Type_OPair(_1622947, _1622947), hAPP(hAPP(c_List_Onth(_1622947), _1622949), _1623080)), _1623082)), _1622953)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623080), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622947)), _1622949))), _1622951 = hAPP(hAPP(c_List_Olist__update(_1622947, _1622949), _1623080), _1623082)]]], (42353 ^ _779308) ^ [_1623380, _1623382, _1623384, _1623386] : [hBOOL(hAPP(c_List_Odistinct(_1623380), _1623382)), -(hBOOL(hAPP(hAPP(c_member(_1623380), _1623384), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1623380, tc_HOL_Obool)), hAPP(c_List_Oset(_1623380), _1623382)), hAPP(hAPP(c_Set_Oinsert(_1623380), hAPP(hAPP(c_List_Onth(_1623380), _1623382), _1623386)), c_Orderings_Obot__class_Obot(tc_fun(_1623380, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1623380), hAPP(hAPP(c_List_Olist__update(_1623380, _1623382), _1623386), _1623384))))], (42363 ^ _779308) ^ [_1623598, _1623600] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1623598, _1623600))))], (42365 ^ _779308) ^ [_1623628, _1623630, _1623632] : [hBOOL(hAPP(c_List_Odistinct(_1623628), _1623630)), -(hBOOL(hAPP(c_List_Odistinct(_1623628), hAPP(hAPP(c_List_Otake(_1623628), _1623632), _1623630))))], (42371 ^ _779308) ^ [_1623739, _1623741, _1623743] : [hBOOL(hAPP(c_List_Odistinct(_1623739), _1623741)), -(hBOOL(hAPP(c_List_Odistinct(_1623739), c_List_Osublist(_1623739, _1623741, _1623743))))], (42377 ^ _779308) ^ [_1623842, _1623844, _1623846, _1623848] : [hBOOL(hAPP(c_List_Odistinct(_1623842), _1623844)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1623842, _1623846)), hAPP(hAPP(c_List_Ozip(_1623842, _1623846), _1623844), _1623848))))], (42383 ^ _779308) ^ [_1623963, _1623965, _1623967, _1623969] : [hBOOL(hAPP(c_List_Odistinct(_1623963), _1623965)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1623967, _1623963)), hAPP(hAPP(c_List_Ozip(_1623967, _1623963), _1623969), _1623965))))], (42389 ^ _779308) ^ [_1624102, _1624104, _1624106] : [hBOOL(hAPP(c_List_Odistinct(_1624102), hAPP(hAPP(c_List_Olist_OCons(_1624102), _1624104), _1624106))), 42392 ^ _779308 : [(42393 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1624102), _1624104), hAPP(c_List_Oset(_1624102), _1624106)))], (42395 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1624102), _1624106)))]]], (42397 ^ _779308) ^ [_1624269, _1624271, _1624273] : [-(hBOOL(hAPP(c_List_Odistinct(_1624269), hAPP(hAPP(c_List_Olist_OCons(_1624269), _1624271), _1624273)))), -(hBOOL(hAPP(hAPP(c_member(_1624269), _1624271), hAPP(c_List_Oset(_1624269), _1624273)))), hBOOL(hAPP(c_List_Odistinct(_1624269), _1624273))], (42407 ^ _779308) ^ [_1624463, _1624465] : [hAPP(c_Finite__Set_Ocard(_1624463), hAPP(c_List_Oset(_1624463), _1624465)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624463)), _1624465), -(hBOOL(hAPP(c_List_Odistinct(_1624463), _1624465)))], (42413 ^ _779308) ^ [_1624582, _1624584] : [hBOOL(hAPP(c_List_Odistinct(_1624582), _1624584)), -(hAPP(c_Finite__Set_Ocard(_1624582), hAPP(c_List_Oset(_1624582), _1624584)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624582)), _1624584))], (42437 ^ _779308) ^ [_1625176, _1625178] : [42439 ^ _779308 : [(42440 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42438 ^ [_1625176, _1625178]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625176)), _1625178))))], (42443 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42441 ^ [_1625176, _1625178]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625176)), _1625178))))], (42445 ^ _779308) ^ [] : [42438 ^ [_1625176, _1625178] = 42441 ^ [_1625176, _1625178]], (42447 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1625176), _1625178), 42438 ^ [_1625176, _1625178]) = hAPP(hAPP(c_List_Onth(_1625176), _1625178), 42441 ^ [_1625176, _1625178]))]], -(hBOOL(hAPP(c_List_Odistinct(_1625176), _1625178)))], (42419 ^ _779308) ^ [_1624716, _1624718] : [hBOOL(hAPP(c_List_Odistinct(_1624716), _1624718)), 42422 ^ _779308 : [(42423 ^ _779308) ^ [_1624848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624848), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624716)), _1624718))), 42426 ^ _779308 : [(42427 ^ _779308) ^ [_1624975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624975), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624716)), _1624718))), -(_1624848 = _1624975), hAPP(hAPP(c_List_Onth(_1624716), _1624718), _1624848) = hAPP(hAPP(c_List_Onth(_1624716), _1624718), _1624975)]]]]], (42451 ^ _779308) ^ [_1625608, _1625610, _1625612, _1625614] : [hBOOL(hAPP(c_List_Odistinct(_1625608), _1625610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625612), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625608)), _1625610))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625614), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625608)), _1625610))), 42462 ^ _779308 : [(42463 ^ _779308) ^ [] : [hAPP(hAPP(c_List_Onth(_1625608), _1625610), _1625612) = hAPP(hAPP(c_List_Onth(_1625608), _1625610), _1625614), -(_1625612 = _1625614)], (42469 ^ _779308) ^ [] : [_1625612 = _1625614, -(hAPP(hAPP(c_List_Onth(_1625608), _1625610), _1625612) = hAPP(hAPP(c_List_Onth(_1625608), _1625610), _1625614))]]], (42475 ^ _779308) ^ [_1626043, _1626045] : [class_Groups_Ocomm__monoid__add(_1626043), hBOOL(hAPP(c_List_Odistinct(_1626043), _1626045)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1626043), _1626045) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1626043, _1626043), c_COMBI(_1626043)), hAPP(c_List_Oset(_1626043), _1626045)))], (42485 ^ _779308) ^ [_1626229, _1626231] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1626229), _1626231)), -(c_Nitpick_Ocard_H(_1626229, _1626231) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626229)), c_Hilbert__Choice_OEps(tc_List_Olist(_1626229), hAPP(hAPP(c_COMBS(tc_List_Olist(_1626229), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1626229)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1626229), tc_fun(_1626229, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1626229, tc_HOL_Obool), tc_fun(tc_fun(_1626229, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1626229)), c_fequal), c_List_Oset(_1626229))), _1626231))), c_List_Odistinct(_1626229)))))], (42491 ^ _779308) ^ [_1626466, _1626468] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1626466), _1626468))), -(c_Nitpick_Ocard_H(_1626466, _1626468) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42497 ^ _779308) ^ [_1626511, _1626513, _1626515, _1626517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1626511), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626513)), _1626515))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1626511), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626513)), _1626517))), 42507 ^ _779308 : [(42508 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42506 ^ [_1626511, _1626513, _1626515, _1626517]), _1626511)))], (42510 ^ _779308) ^ [] : [hAPP(hAPP(c_List_Onth(_1626513), _1626515), 42506 ^ [_1626511, _1626513, _1626515, _1626517]) = hAPP(hAPP(c_List_Onth(_1626513), _1626517), 42506 ^ [_1626511, _1626513, _1626515, _1626517])]], -(hAPP(hAPP(c_List_Otake(_1626513), _1626511), _1626515) = hAPP(hAPP(c_List_Otake(_1626513), _1626511), _1626517))], (42514 ^ _779308) ^ [_1626928, _1626930, _1626932] : [hBOOL(hAPP(c_List_Odistinct(_1626928), _1626930)), -(hAPP(c_List_Oset(_1626928), c_List_Oremove1(_1626928, _1626932, _1626930)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1626928, tc_HOL_Obool)), hAPP(c_List_Oset(_1626928), _1626930)), hAPP(hAPP(c_Set_Oinsert(_1626928), _1626932), c_Orderings_Obot__class_Obot(tc_fun(_1626928, tc_HOL_Obool)))))], (42520 ^ _779308) ^ [_1627106, _1627108, _1627110, _1627112] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627106) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1627108), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627106)), hAPP(hAPP(c_List_Olist_OCons(_1627108), _1627110), _1627112)) = c_List_Olist_ONil(_1627108))], (42526 ^ _779308) ^ [_1627229, _1627231, _1627233, _1627235] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627229) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1627231), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627229)), hAPP(hAPP(c_List_Olist_OCons(_1627231), _1627233), _1627235)) = hAPP(hAPP(c_List_Olist_OCons(_1627231), _1627233), hAPP(hAPP(c_List_Otake(_1627231), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1627229)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1627235)))], (42532 ^ _779308) ^ [_1627318, _1627320] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1627318)), c_List_Olist_ONil(_1627318)), c_List_Olists(_1627318, _1627320))))], (42534 ^ _779308) ^ [_1627357, _1627359, _1627361] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627357), tc_List_Olist(_1627357))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627357), tc_List_Olist(_1627357)), _1627359), c_List_Olist_ONil(_1627357))), c_List_Olistrel(_1627357, _1627361))), -(_1627359 = c_List_Olist_ONil(_1627357))], (42540 ^ _779308) ^ [_1627504, _1627506, _1627508] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627504), tc_List_Olist(_1627504))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627504), tc_List_Olist(_1627504)), c_List_Olist_ONil(_1627504)), _1627506)), c_List_Olistrel(_1627504, _1627508))), -(_1627506 = c_List_Olist_ONil(_1627504))], (42546 ^ _779308) ^ [_1627650, _1627652] : [-(_1627650 = c_List_Olist_ONil(_1627652)), hBOOL(hAPP(c_List_Odistinct(_1627652), _1627650)), -(hBOOL(hAPP(c_List_Odistinct(_1627652), c_List_Obutlast(_1627652, _1627650))))], (42556 ^ _779308) ^ [_1627801, _1627803, _1627805] : [hBOOL(hAPP(c_List_Odistinct(_1627801), _1627803)), -(hBOOL(hAPP(c_List_Odistinct(_1627801), c_List_Oremove1(_1627801, _1627805, _1627803))))], (42562 ^ _779308) ^ [_1627904] : [-(hBOOL(hAPP(c_List_Odistinct(_1627904), c_List_Olist_ONil(_1627904))))], (42564 ^ _779308) ^ [_1627933] : [-(c_List_Obutlast(_1627933, c_List_Olist_ONil(_1627933)) = c_List_Olist_ONil(_1627933))], (42566 ^ _779308) ^ [_1627975, _1627977, _1627979] : [_1627975 = c_List_Olist_ONil(_1627977), -(c_List_Obutlast(_1627977, hAPP(hAPP(c_List_Olist_OCons(_1627977), _1627979), _1627975)) = c_List_Olist_ONil(_1627977))], (42572 ^ _779308) ^ [_1628078, _1628080, _1628082] : [-(_1628078 = c_List_Olist_ONil(_1628080)), -(c_List_Obutlast(_1628080, hAPP(hAPP(c_List_Olist_OCons(_1628080), _1628082), _1628078)) = hAPP(hAPP(c_List_Olist_OCons(_1628080), _1628082), c_List_Obutlast(_1628080, _1628078)))], (42578 ^ _779308) ^ [_1628157, _1628159, _1628161] : [c_List_Olist_ONil(_1628157) = hAPP(hAPP(c_List_Olist_OCons(_1628157), _1628159), _1628161)], (42580 ^ _779308) ^ [_1628209, _1628211, _1628213] : [hAPP(hAPP(c_List_Olist_OCons(_1628209), _1628211), _1628213) = c_List_Olist_ONil(_1628209)], (42582 ^ _779308) ^ [_1628261, _1628263, _1628265, _1628267] : [_1628261 = _1628263, -(c_List_Oremove1(_1628265, _1628261, hAPP(hAPP(c_List_Olist_OCons(_1628265), _1628263), _1628267)) = _1628267)], (42588 ^ _779308) ^ [_1628360, _1628362, _1628364, _1628366] : [-(_1628360 = _1628362), -(c_List_Oremove1(_1628364, _1628360, hAPP(hAPP(c_List_Olist_OCons(_1628364), _1628362), _1628366)) = hAPP(hAPP(c_List_Olist_OCons(_1628364), _1628362), c_List_Oremove1(_1628364, _1628360, _1628366)))], (42594 ^ _779308) ^ [_1628426, _1628428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1628426), _1628428)), -(c_List_Oupto(_1628428, _1628426) = c_List_Olist_ONil(tc_Int_Oint))], (42610 ^ _779308) ^ [_1628649, _1628651, _1628653] : [42611 ^ _779308 : [(42612 ^ _779308) ^ [] : [_1628651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42614 ^ _779308) ^ [] : [_1628653 = c_List_Olist_ONil(_1628649)]], -(hAPP(hAPP(c_List_Otake(_1628649), _1628651), _1628653) = c_List_Olist_ONil(_1628649))], (42600 ^ _779308) ^ [_1628537, _1628539, _1628541] : [hAPP(hAPP(c_List_Otake(_1628537), _1628539), _1628541) = c_List_Olist_ONil(_1628537), -(_1628539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1628541 = c_List_Olist_ONil(_1628537))], (42618 ^ _779308) ^ [_1628792, _1628794] : [-(hAPP(hAPP(c_List_Otake(_1628792), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1628794) = c_List_Olist_ONil(_1628792))], (42620 ^ _779308) ^ [_1628827, _1628829] : [-(hAPP(hAPP(c_List_Otake(_1628827), _1628829), c_List_Olist_ONil(_1628827)) = c_List_Olist_ONil(_1628827))], (42622 ^ _779308) ^ [_1628864, _1628866] : [-(c_List_Osublist(_1628864, c_List_Olist_ONil(_1628864), _1628866) = c_List_Olist_ONil(_1628864))], (42624 ^ _779308) ^ [_1628897, _1628899, _1628901, _1628903] : [-(c_List_Oremove1(_1628897, _1628899, c_List_Oremove1(_1628897, _1628901, _1628903)) = c_List_Oremove1(_1628897, _1628901, c_List_Oremove1(_1628897, _1628899, _1628903)))], (42626 ^ _779308) ^ [_1628942, _1628944] : [-(c_List_Oremove1(_1628942, _1628944, c_List_Olist_ONil(_1628942)) = c_List_Olist_ONil(_1628942))], (42628 ^ _779308) ^ [_1628975, _1628977] : [-(c_List_Olistrelp(_1628975, _1628977, c_List_Olist_ONil(_1628975), c_List_Olist_ONil(_1628975)))], (42630 ^ _779308) ^ [_1629006, _1629008] : [-(c_List_Olistrelp(_1629006, _1629008, c_List_Olist_ONil(_1629006), c_List_Olist_ONil(_1629006)))], (42632 ^ _779308) ^ [_1629037, _1629039, _1629041] : [-(hAPP(hAPP(c_List_Ozip(_1629037, _1629039), c_List_Olist_ONil(_1629037)), _1629041) = c_List_Olist_ONil(tc_prod(_1629037, _1629039)))], (42634 ^ _779308) ^ [_1629080, _1629082, _1629084] : [-(hAPP(hAPP(c_List_Ozip(_1629080, _1629082), _1629084), c_List_Olist_ONil(_1629082)) = c_List_Olist_ONil(tc_prod(_1629080, _1629082)))], (42636 ^ _779308) ^ [_1629123] : [class_Groups_Omonoid__add(_1629123), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1629123), c_List_Olist_ONil(_1629123)) = c_Groups_Ozero__class_Ozero(_1629123))], (42642 ^ _779308) ^ [_1629229, _1629231] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629229)), _1629231) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1629231 = c_List_Olist_ONil(_1629229))], (42648 ^ _779308) ^ [_1629320, _1629322] : [_1629322 = c_List_Olist_ONil(_1629320), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629320)), _1629322) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42654 ^ _779308) ^ [_1629417] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629417)), c_List_Olist_ONil(_1629417)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42656 ^ _779308) ^ [_1629464, _1629466] : [hAPP(c_List_Oset(_1629464), _1629466) = c_Orderings_Obot__class_Obot(tc_fun(_1629464, tc_HOL_Obool)), -(_1629466 = c_List_Olist_ONil(_1629464))], (42662 ^ _779308) ^ [_1629561, _1629563] : [_1629563 = c_List_Olist_ONil(_1629561), -(hAPP(c_List_Oset(_1629561), _1629563) = c_Orderings_Obot__class_Obot(tc_fun(_1629561, tc_HOL_Obool)))], (42668 ^ _779308) ^ [_1629679, _1629681] : [c_Orderings_Obot__class_Obot(tc_fun(_1629679, tc_HOL_Obool)) = hAPP(c_List_Oset(_1629679), _1629681), -(_1629681 = c_List_Olist_ONil(_1629679))], (42674 ^ _779308) ^ [_1629776, _1629778] : [_1629778 = c_List_Olist_ONil(_1629776), -(c_Orderings_Obot__class_Obot(tc_fun(_1629776, tc_HOL_Obool)) = hAPP(c_List_Oset(_1629776), _1629778))], (42680 ^ _779308) ^ [_1629879] : [-(hAPP(c_List_Oset(_1629879), c_List_Olist_ONil(_1629879)) = c_Orderings_Obot__class_Obot(tc_fun(_1629879, tc_HOL_Obool)))], (42682 ^ _779308) ^ [_1629914, _1629916, _1629918] : [-(hAPP(hAPP(c_List_Olist__update(_1629914, c_List_Olist_ONil(_1629914)), _1629916), _1629918) = c_List_Olist_ONil(_1629914))], (42684 ^ _779308) ^ [_1629954, _1629956, _1629958] : [-(hAPP(hAPP(c_List_Olist__update(_1629954, c_List_Olist_ONil(_1629954)), _1629956), _1629958) = c_List_Olist_ONil(_1629954))], (42686 ^ _779308) ^ [_1630015, _1630017, _1630019, _1630021] : [hAPP(hAPP(c_List_Olist__update(_1630015, _1630017), _1630019), _1630021) = c_List_Olist_ONil(_1630015), -(_1630017 = c_List_Olist_ONil(_1630015))], (42692 ^ _779308) ^ [_1630118, _1630120, _1630122, _1630124] : [_1630120 = c_List_Olist_ONil(_1630118), -(hAPP(hAPP(c_List_Olist__update(_1630118, _1630120), _1630122), _1630124) = c_List_Olist_ONil(_1630118))], (42698 ^ _779308) ^ [_1630227, _1630229] : [-(c_List_Olist_Olist__size(_1630227, _1630229, c_List_Olist_ONil(_1630227)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42700 ^ _779308) ^ [_1630254, _1630256, _1630258] : [-(hBOOL(hAPP(hAPP(c_member(_1630254), _1630256), hAPP(c_List_Oset(_1630254), _1630258)))), -(c_List_Oremove1(_1630254, _1630256, _1630258) = _1630258)], (42706 ^ _779308) ^ [_1630307, _1630309, _1630311, _1630313] : [-(hBOOL(hAPP(hAPP(c_member(_1630307), _1630309), hAPP(c_List_Oset(_1630307), _1630311)))), hBOOL(hAPP(hAPP(c_member(_1630307), _1630309), hAPP(c_List_Oset(_1630307), c_List_Oremove1(_1630307, _1630313, _1630311))))], (42712 ^ _779308) ^ [_1630430, _1630432, _1630434, _1630436] : [-(_1630430 = _1630432), 42715 ^ _779308 : [(42716 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630434), _1630430), hAPP(c_List_Oset(_1630434), c_List_Oremove1(_1630434, _1630432, _1630436)))), -(hBOOL(hAPP(hAPP(c_member(_1630434), _1630430), hAPP(c_List_Oset(_1630434), _1630436))))], (42722 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630434), _1630430), hAPP(c_List_Oset(_1630434), _1630436))), -(hBOOL(hAPP(hAPP(c_member(_1630434), _1630430), hAPP(c_List_Oset(_1630434), c_List_Oremove1(_1630434, _1630432, _1630436)))))]]], (42728 ^ _779308) ^ [_1630731, _1630733] : [-(c_List_Osublist(_1630731, _1630733, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1630731))], (42730 ^ _779308) ^ [_1630762, _1630764, _1630766] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1630762, tc_HOL_Obool)), hAPP(c_List_Oset(_1630762), c_List_Oremove1(_1630762, _1630764, _1630766))), hAPP(c_List_Oset(_1630762), _1630766))))], (42732 ^ _779308) ^ [_1630828, _1630830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630828)), _1630830))), _1630830 = c_List_Olist_ONil(_1630828)], (42738 ^ _779308) ^ [_1630922, _1630924] : [-(_1630924 = c_List_Olist_ONil(_1630922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630922)), _1630924))))], (42744 ^ _779308) ^ [_1630971, _1630973, _1630975] : [-(hAPP(hAPP(c_List_Otake(_1630971), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1630971), _1630973), _1630975)) = hAPP(hAPP(c_List_Olist_OCons(_1630971), _1630973), c_List_Olist_ONil(_1630971)))], (42746 ^ _779308) ^ [_1631039, _1631041, _1631043] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631039), tc_List_Olist(_1631039))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631039), tc_List_Olist(_1631039)), _1631041), c_List_Olist_ONil(_1631039))), c_List_Olistrel1(_1631039, _1631043)))], (42748 ^ _779308) ^ [_1631113, _1631115, _1631117] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631113), tc_List_Olist(_1631113))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631113), tc_List_Olist(_1631113)), c_List_Olist_ONil(_1631113)), _1631115)), c_List_Olistrel1(_1631113, _1631117)))], (42750 ^ _779308) ^ [_1631172, _1631174] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631172), tc_List_Olist(_1631172))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631172), tc_List_Olist(_1631172)), c_List_Olist_ONil(_1631172)), c_List_Olist_ONil(_1631172))), c_List_Olistrel(_1631172, _1631174))))], (42752 ^ _779308) ^ [_1631246, _1631248, _1631250] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631246), tc_List_Olist(_1631246))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631246), tc_List_Olist(_1631246)), _1631248), c_List_Olist_ONil(_1631246))), c_List_Olexord(_1631246, _1631250)))], (42754 ^ _779308) ^ [_1631320, _1631322, _1631324] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631320), tc_List_Olist(_1631320))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631320), tc_List_Olist(_1631320)), _1631322), c_List_Olist_ONil(_1631320))), c_List_Olex(_1631320, _1631324)))], (42756 ^ _779308) ^ [_1631394, _1631396, _1631398] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631394), tc_List_Olist(_1631394))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631394), tc_List_Olist(_1631394)), c_List_Olist_ONil(_1631394)), _1631396)), c_List_Olex(_1631394, _1631398)))], (42758 ^ _779308) ^ [_1631453, _1631455, _1631457, _1631459] : [-(hAPP(hAPP(c_List_Otake(_1631453), _1631455), hAPP(hAPP(c_List_Olist_OCons(_1631453), _1631457), _1631459)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1631453), c_List_Olist_ONil(_1631453), hAPP(hAPP(c_COMBB(tc_List_Olist(_1631453), tc_List_Olist(_1631453), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1631453), _1631457)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1631453), tc_List_Olist(_1631453)), c_List_Otake(_1631453)), _1631459)), _1631455))], (42760 ^ _779308) ^ [_1631551, _1631553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1631551), _1631553)), -(c_List_Oupto(_1631551, _1631553) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1631551), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1631551), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1631553)))], (42766 ^ _779308) ^ [_1631668, _1631670] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1631668), _1631670))), -(c_List_Oupto(_1631668, _1631670) = c_List_Olist_ONil(tc_Int_Oint))], (42772 ^ _779308) ^ [_1631726, _1631728, _1631730] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1631726)), -(c_List_Osublist(_1631728, hAPP(hAPP(c_List_Olist_OCons(_1631728), _1631730), c_List_Olist_ONil(_1631728)), _1631726) = hAPP(hAPP(c_List_Olist_OCons(_1631728), _1631730), c_List_Olist_ONil(_1631728)))], (42778 ^ _779308) ^ [_1631851, _1631853, _1631855] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1631851))), -(c_List_Osublist(_1631853, hAPP(hAPP(c_List_Olist_OCons(_1631853), _1631855), c_List_Olist_ONil(_1631853)), _1631851) = c_List_Olist_ONil(_1631853))], (42784 ^ _779308) ^ [_1631909] : [-(c_List_Olists(_1631909, c_Orderings_Obot__class_Obot(tc_fun(_1631909, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1631909)), c_List_Olist_ONil(_1631909)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1631909), tc_HOL_Obool))))], (42786 ^ _779308) ^ [_1631974, _1631976, _1631978, _1631980] : [_1631974 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1631976), _1631974), hAPP(hAPP(c_List_Olist_OCons(_1631976), _1631978), _1631980)) = c_List_Olist_ONil(_1631976))], (42792 ^ _779308) ^ [_1632085, _1632087, _1632089, _1632091] : [-(_1632085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1632087), _1632085), hAPP(hAPP(c_List_Olist_OCons(_1632087), _1632089), _1632091)) = hAPP(hAPP(c_List_Olist_OCons(_1632087), _1632089), hAPP(hAPP(c_List_Otake(_1632087), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1632085), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1632091)))], (42798 ^ _779308) ^ [_1632174, _1632176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632174)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632176))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632174), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632176)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632174)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632174)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632176))))], (42804 ^ _779308) ^ [_1632333, _1632335] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632333)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632335)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632333), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1632335)) = c_List_Olist_ONil(tc_Int_Oint))], (42810 ^ _779308) ^ [_1632391, _1632393] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1632391), tc_List_Olist(_1632391), c_List_Olistrel(_1632391, _1632393)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632391)), c_List_Olist_ONil(_1632391)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632391), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632391)), c_List_Olist_ONil(_1632391)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632391), tc_HOL_Obool))))], (42812 ^ _779308) ^ [_1632468, _1632470] : [-(c_List_Oset__Cons(_1632468, _1632470, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632468)), c_List_Olist_ONil(_1632468)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632468), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1632468, tc_List_Olist(_1632468), hAPP(hAPP(c_COMBC(_1632468, tc_List_Olist(_1632468), tc_List_Olist(_1632468)), c_List_Olist_OCons(_1632468)), c_List_Olist_ONil(_1632468))), _1632470))], (42814 ^ _779308) ^ [_1632555, _1632557, _1632559] : [hBOOL(hAPP(hAPP(c_member(_1632555), _1632557), hAPP(c_List_Oset(_1632555), _1632559))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632555)), c_List_Oremove1(_1632555, _1632557, _1632559)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632555)), _1632559)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42820 ^ _779308) ^ [_1632700, _1632702, _1632704] : [-(hBOOL(hAPP(hAPP(c_member(_1632700), _1632702), hAPP(c_List_Oset(_1632700), _1632704)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632700)), c_List_Oremove1(_1632700, _1632702, _1632704)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632700)), _1632704))], (42826 ^ _779308) ^ [_1632770, _1632772] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_List_Oupto__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1632770), _1632772))), 42829 ^ _779308 : [(42830 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1632770), _1632772)), -(c_List_Oupto(_1632770, _1632772) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1632770), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1632770), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1632772)))], (42836 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1632770), _1632772))), -(c_List_Oupto(_1632770, _1632772) = c_List_Olist_ONil(tc_Int_Oint))]]], (42842 ^ _779308) ^ [_1633020, _1633022, _1633024] : [-(_1633020 = c_List_Olist_ONil(_1633022)), -(hBOOL(hAPP(hAPP(c_member(_1633022), hAPP(c_Product__Type_Ofst(_1633022, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1633022, _1633020), _1633024))), hAPP(c_List_Oset(_1633022), _1633020))))], (42848 ^ _779308) ^ [_1633084] : [-(c_List_Olistset(_1633084, c_List_Olist_ONil(tc_fun(_1633084, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633084)), c_List_Olist_ONil(_1633084)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633084), tc_HOL_Obool))))], (42850 ^ _779308) ^ [_1633134, _1633136, _1633138, _1633140, _1633142] : [-(hAPP(hAPP(c_List_Ozip(_1633134, _1633136), _1633138), hAPP(hAPP(c_List_Olist_OCons(_1633136), _1633140), _1633142)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1633134, _1633136)), _1633134, c_List_Olist_ONil(tc_prod(_1633134, _1633136)), hAPP(hAPP(c_COMBC(_1633134, tc_fun(tc_List_Olist(_1633134), tc_List_Olist(tc_prod(_1633134, _1633136))), tc_fun(tc_List_Olist(_1633134), tc_List_Olist(tc_prod(_1633134, _1633136)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1633134, _1633136)), tc_List_Olist(tc_prod(_1633134, _1633136))), tc_fun(tc_fun(tc_List_Olist(_1633134), tc_List_Olist(tc_prod(_1633134, _1633136))), tc_fun(tc_List_Olist(_1633134), tc_List_Olist(tc_prod(_1633134, _1633136)))), _1633134), c_COMBB(tc_List_Olist(tc_prod(_1633134, _1633136)), tc_List_Olist(tc_prod(_1633134, _1633136)), tc_List_Olist(_1633134))), hAPP(hAPP(c_COMBB(tc_prod(_1633134, _1633136), tc_fun(tc_List_Olist(tc_prod(_1633134, _1633136)), tc_List_Olist(tc_prod(_1633134, _1633136))), _1633134), c_List_Olist_OCons(tc_prod(_1633134, _1633136))), hAPP(hAPP(c_COMBC(_1633134, _1633136, tc_prod(_1633134, _1633136)), c_Product__Type_OPair(_1633134, _1633136)), _1633140)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1633134), tc_List_Olist(_1633136), tc_List_Olist(tc_prod(_1633134, _1633136))), c_List_Ozip(_1633134, _1633136)), _1633142))), _1633138))], (42852 ^ _779308) ^ [_1633361, _1633363, _1633365, _1633367, _1633369, _1633371] : [-(hAPP(c_List_Olist_Olist__case(_1633361, _1633363, _1633365, _1633367), hAPP(hAPP(c_List_Olist_OCons(_1633363), _1633369), _1633371)) = hAPP(hAPP(_1633367, _1633369), _1633371))], (42854 ^ _779308) ^ [_1633416, _1633418, _1633420, _1633422] : [-(hAPP(c_List_Olist_Olist__case(_1633416, _1633418, _1633420, _1633422), c_List_Olist_ONil(_1633418)) = _1633420)], (42856 ^ _779308) ^ [_1633455, _1633457, _1633459] : [-(c_List_Olistset(_1633455, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1633455, tc_HOL_Obool)), _1633457), _1633459)) = c_List_Oset__Cons(_1633455, _1633457, c_List_Olistset(_1633455, _1633459)))], (42858 ^ _779308) ^ [_1633503, _1633505, _1633507, _1633509, _1633511] : [-(hAPP(hAPP(c_List_Ozip(_1633503, _1633505), hAPP(hAPP(c_List_Olist_OCons(_1633503), _1633507), _1633509)), _1633511) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1633503, _1633505)), _1633505, c_List_Olist_ONil(tc_prod(_1633503, _1633505)), hAPP(hAPP(c_COMBC(_1633505, tc_fun(tc_List_Olist(_1633505), tc_List_Olist(tc_prod(_1633503, _1633505))), tc_fun(tc_List_Olist(_1633505), tc_List_Olist(tc_prod(_1633503, _1633505)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1633503, _1633505)), tc_List_Olist(tc_prod(_1633503, _1633505))), tc_fun(tc_fun(tc_List_Olist(_1633505), tc_List_Olist(tc_prod(_1633503, _1633505))), tc_fun(tc_List_Olist(_1633505), tc_List_Olist(tc_prod(_1633503, _1633505)))), _1633505), c_COMBB(tc_List_Olist(tc_prod(_1633503, _1633505)), tc_List_Olist(tc_prod(_1633503, _1633505)), tc_List_Olist(_1633505))), hAPP(hAPP(c_COMBB(tc_prod(_1633503, _1633505), tc_fun(tc_List_Olist(tc_prod(_1633503, _1633505)), tc_List_Olist(tc_prod(_1633503, _1633505))), _1633505), c_List_Olist_OCons(tc_prod(_1633503, _1633505))), hAPP(c_Product__Type_OPair(_1633503, _1633505), _1633507)))), hAPP(c_List_Ozip(_1633503, _1633505), _1633509))), _1633511))], (42860 ^ _779308) ^ [_1633704, _1633706, _1633708] : [class_Orderings_Olinorder(_1633704), hBOOL(hAPP(c_Finite__Set_Ofinite(_1633704), _1633706)), -(c_List_Olinorder__class_Osorted__list__of__set(_1633704, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1633704, tc_HOL_Obool)), _1633706), hAPP(hAPP(c_Set_Oinsert(_1633704), _1633708), c_Orderings_Obot__class_Obot(tc_fun(_1633704, tc_HOL_Obool))))) = c_List_Oremove1(_1633704, _1633708, c_List_Olinorder__class_Osorted__list__of__set(_1633704, _1633706)))], (42870 ^ _779308) ^ [_1633911, _1633913, _1633915] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_List_Oupto__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1633911), _1633913))), -(hBOOL(hAPP(hAPP(_1633915, _1633911), _1633913))), 42877 ^ _779308 : [(42878 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_List_Oupto__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 42875 ^ [_1633911, _1633913, _1633915]), 42876 ^ [_1633911, _1633913, _1633915]))))], (42886 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1633915, 42875 ^ [_1633911, _1633913, _1633915]), 42876 ^ [_1633911, _1633913, _1633915]))], (42880 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 42875 ^ [_1633911, _1633913, _1633915]), 42876 ^ [_1633911, _1633913, _1633915])), -(hBOOL(hAPP(hAPP(_1633915, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 42875 ^ [_1633911, _1633913, _1633915]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 42876 ^ [_1633911, _1633913, _1633915])))]]], (42890 ^ _779308) ^ [_1634402] : [class_Orderings_Olinorder(_1634402), -(c_List_Olinorder__class_Osorted__list__of__set(_1634402, c_Orderings_Obot__class_Obot(tc_fun(_1634402, tc_HOL_Obool))) = c_List_Olist_ONil(_1634402))], (42896 ^ _779308) ^ [_1634513, _1634515, _1634517, _1634519, _1634521] : [_1634513 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1634515, _1634517, _1634519), _1634513), _1634521) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634517), _1634515), c_List_Olist_ONil(_1634517)), _1634521))], (42902 ^ _779308) ^ [_1634636, _1634638, _1634640, _1634642, _1634644] : [-(_1634636 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1634638, _1634640, _1634642), _1634636), _1634644) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1634640), _1634638), tc_prod(_1634640, _1634638), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634640), _1634638), c_List_Olist_ONil(_1634640)), _1634644), hAPP(c_Product__Type_Oprod_Oprod__case(_1634640, _1634638, tc_prod(tc_List_Olist(_1634640), _1634638)), hAPP(hAPP(c_COMBC(_1634640, tc_fun(_1634638, tc_prod(tc_List_Olist(_1634640), _1634638)), tc_fun(_1634638, tc_prod(tc_List_Olist(_1634640), _1634638))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1634640), _1634638), tc_prod(tc_List_Olist(_1634640), _1634638)), tc_fun(tc_fun(_1634638, tc_prod(tc_List_Olist(_1634640), _1634638)), tc_fun(_1634638, tc_prod(tc_List_Olist(_1634640), _1634638))), _1634640), c_COMBB(tc_prod(tc_List_Olist(_1634640), _1634638), tc_prod(tc_List_Olist(_1634640), _1634638), _1634638)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1634640), tc_fun(_1634638, tc_prod(tc_List_Olist(_1634640), _1634638))), tc_fun(tc_prod(tc_List_Olist(_1634640), _1634638), tc_prod(tc_List_Olist(_1634640), _1634638)), _1634640), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1634640), _1634638, tc_prod(tc_List_Olist(_1634640), _1634638))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1634640), tc_List_Olist(_1634640)), tc_fun(tc_List_Olist(_1634640), tc_fun(_1634638, tc_prod(tc_List_Olist(_1634640), _1634638))), _1634640), hAPP(c_COMBB(tc_List_Olist(_1634640), tc_fun(_1634638, tc_prod(tc_List_Olist(_1634640), _1634638)), tc_List_Olist(_1634640)), c_Product__Type_OPair(tc_List_Olist(_1634640), _1634638))), c_List_Olist_OCons(_1634640))))), hAPP(c_Lazy__Sequence_Oanamorph(_1634638, _1634640, _1634642), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1634636), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1634642, _1634644)))], (42908 ^ _779308) ^ [_1634930, _1634932, _1634934, _1634936] : [-(c_List_Osublist(_1634930, hAPP(hAPP(c_List_Olist_OCons(_1634930), _1634932), _1634934), _1634936) = hAPP(hAPP(c_List_Oappend(_1634930), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1634930)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1634936)), hAPP(hAPP(c_List_Olist_OCons(_1634930), _1634932), c_List_Olist_ONil(_1634930))), c_List_Olist_ONil(_1634930))), c_List_Osublist(_1634930, _1634934, hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_Nat_Onat), c_member(tc_Nat_Onat)), c_Nat_OSuc)), _1634936)))))], (42910 ^ _779308) ^ [_1635041, _1635043, _1635045, _1635047, _1635049] : [hAPP(hAPP(c_List_Oappend(_1635041), _1635043), _1635045) = hAPP(hAPP(c_List_Olist_OCons(_1635041), _1635047), _1635049), 42915 ^ _779308 : [(42916 ^ _779308) ^ [] : [-(_1635043 = c_List_Olist_ONil(_1635041))], (42918 ^ _779308) ^ [] : [-(_1635045 = hAPP(hAPP(c_List_Olist_OCons(_1635041), _1635047), _1635049))]], 42920 ^ _779308 : [(42921 ^ _779308) ^ [] : [-(_1635043 = hAPP(hAPP(c_List_Olist_OCons(_1635041), _1635047), 42919 ^ [_1635041, _1635043, _1635045, _1635047, _1635049]))], (42923 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1635041), 42919 ^ [_1635041, _1635043, _1635045, _1635047, _1635049]), _1635045) = _1635049)]]], (42925 ^ _779308) ^ [_1635334, _1635336, _1635338, _1635340, _1635342] : [-(hAPP(hAPP(c_List_Oappend(_1635334), _1635336), _1635338) = hAPP(hAPP(c_List_Olist_OCons(_1635334), _1635340), _1635342)), 42926 ^ _779308 : [(42927 ^ _779308) ^ [] : [_1635336 = c_List_Olist_ONil(_1635334), _1635338 = hAPP(hAPP(c_List_Olist_OCons(_1635334), _1635340), _1635342)], (42933 ^ _779308) ^ [_1635517] : [_1635336 = hAPP(hAPP(c_List_Olist_OCons(_1635334), _1635340), _1635517), hAPP(hAPP(c_List_Oappend(_1635334), _1635517), _1635338) = _1635342]]], (42941 ^ _779308) ^ [_1635705, _1635707, _1635709, _1635711, _1635713] : [hAPP(hAPP(c_List_Olist_OCons(_1635705), _1635707), _1635709) = hAPP(hAPP(c_List_Oappend(_1635705), _1635711), _1635713), 42946 ^ _779308 : [(42947 ^ _779308) ^ [] : [-(_1635711 = c_List_Olist_ONil(_1635705))], (42949 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1635705), _1635707), _1635709) = _1635713)]], 42951 ^ _779308 : [(42952 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1635705), _1635707), 42950 ^ [_1635705, _1635707, _1635709, _1635711, _1635713]) = _1635711)], (42954 ^ _779308) ^ [] : [-(_1635709 = hAPP(hAPP(c_List_Oappend(_1635705), 42950 ^ [_1635705, _1635707, _1635709, _1635711, _1635713]), _1635713))]]], (42956 ^ _779308) ^ [_1635998, _1636000, _1636002, _1636004, _1636006] : [-(hAPP(hAPP(c_List_Olist_OCons(_1635998), _1636000), _1636002) = hAPP(hAPP(c_List_Oappend(_1635998), _1636004), _1636006)), 42957 ^ _779308 : [(42958 ^ _779308) ^ [] : [_1636004 = c_List_Olist_ONil(_1635998), hAPP(hAPP(c_List_Olist_OCons(_1635998), _1636000), _1636002) = _1636006], (42964 ^ _779308) ^ [_1636181] : [hAPP(hAPP(c_List_Olist_OCons(_1635998), _1636000), _1636181) = _1636004, _1636002 = hAPP(hAPP(c_List_Oappend(_1635998), _1636181), _1636006)]]], (42972 ^ _779308) ^ [_1636369, _1636371, _1636373, _1636375, _1636377] : [hAPP(hAPP(c_List_Oappend(_1636369), _1636371), hAPP(hAPP(c_List_Olist_OCons(_1636369), _1636373), c_List_Olist_ONil(_1636369))) = hAPP(hAPP(c_List_Oappend(_1636369), _1636375), hAPP(hAPP(c_List_Olist_OCons(_1636369), _1636377), c_List_Olist_ONil(_1636369))), 42975 ^ _779308 : [(42976 ^ _779308) ^ [] : [-(_1636371 = _1636375)], (42978 ^ _779308) ^ [] : [-(_1636373 = _1636377)]]], (42980 ^ _779308) ^ [_1636546, _1636548, _1636550, _1636552, _1636554] : [-(hAPP(hAPP(c_List_Oappend(_1636546), _1636548), hAPP(hAPP(c_List_Olist_OCons(_1636546), _1636550), c_List_Olist_ONil(_1636546))) = hAPP(hAPP(c_List_Oappend(_1636546), _1636552), hAPP(hAPP(c_List_Olist_OCons(_1636546), _1636554), c_List_Olist_ONil(_1636546)))), _1636548 = _1636552, _1636550 = _1636554], (42990 ^ _779308) ^ [_1636761, _1636763, _1636765, _1636767] : [-(hAPP(hAPP(c_List_Oappend(_1636761), hAPP(hAPP(c_List_Olist_OCons(_1636761), _1636763), _1636765)), _1636767) = hAPP(hAPP(c_List_Olist_OCons(_1636761), _1636763), hAPP(hAPP(c_List_Oappend(_1636761), _1636765), _1636767)))], (42992 ^ _779308) ^ [_1636822, _1636824, _1636826, _1636828, _1636830, _1636832] : [hAPP(hAPP(c_List_Olist_OCons(_1636822), _1636824), _1636826) = _1636828, _1636830 = hAPP(hAPP(c_List_Oappend(_1636822), _1636826), _1636832), -(hAPP(hAPP(c_List_Olist_OCons(_1636822), _1636824), _1636830) = hAPP(hAPP(c_List_Oappend(_1636822), _1636828), _1636832))], (43002 ^ _779308) ^ [_1637052, _1637054, _1637056, _1637058] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637052)), hAPP(hAPP(c_List_Oappend(_1637052), _1637054), _1637056)), c_List_Olists(_1637052, _1637058))), 43005 ^ _779308 : [(43006 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637052)), _1637054), c_List_Olists(_1637052, _1637058))))], (43008 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637052)), _1637056), c_List_Olists(_1637052, _1637058))))]]], (43010 ^ _779308) ^ [_1637243, _1637245, _1637247, _1637249] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637243)), hAPP(hAPP(c_List_Oappend(_1637243), _1637245), _1637247)), c_List_Olists(_1637243, _1637249)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637243)), _1637245), c_List_Olists(_1637243, _1637249))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637243)), _1637247), c_List_Olists(_1637243, _1637249)))], (43020 ^ _779308) ^ [_1637470, _1637472, _1637474, _1637476, _1637478, _1637480] : [hAPP(hAPP(c_List_Oappend(_1637470), _1637472), _1637474) = _1637476, _1637478 = hAPP(hAPP(c_List_Oappend(_1637470), _1637474), _1637480), -(hAPP(hAPP(c_List_Oappend(_1637470), _1637472), _1637478) = hAPP(hAPP(c_List_Oappend(_1637470), _1637476), _1637480))], (43030 ^ _779308) ^ [_1637700, _1637702, _1637704, _1637706] : [hAPP(hAPP(c_List_Oappend(_1637700), _1637702), _1637704) = hAPP(hAPP(c_List_Oappend(_1637700), _1637706), _1637704), -(_1637702 = _1637706)], (43036 ^ _779308) ^ [_1637809, _1637811, _1637813, _1637815] : [_1637811 = _1637815, -(hAPP(hAPP(c_List_Oappend(_1637809), _1637811), _1637813) = hAPP(hAPP(c_List_Oappend(_1637809), _1637815), _1637813))], (43042 ^ _779308) ^ [_1637945, _1637947, _1637949, _1637951] : [hAPP(hAPP(c_List_Oappend(_1637945), _1637947), _1637949) = hAPP(hAPP(c_List_Oappend(_1637945), _1637947), _1637951), -(_1637949 = _1637951)], (43048 ^ _779308) ^ [_1638054, _1638056, _1638058, _1638060] : [_1638058 = _1638060, -(hAPP(hAPP(c_List_Oappend(_1638054), _1638056), _1638058) = hAPP(hAPP(c_List_Oappend(_1638054), _1638056), _1638060))], (43054 ^ _779308) ^ [_1638193, _1638195, _1638197, _1638199, _1638201] : [hAPP(hAPP(c_List_Oappend(_1638193), _1638195), _1638197) = hAPP(hAPP(c_List_Oappend(_1638193), _1638199), _1638201), 43060 ^ _779308 : [(43061 ^ _779308) ^ [] : [-(_1638195 = hAPP(hAPP(c_List_Oappend(_1638193), _1638199), 43057 ^ [_1638193, _1638195, _1638197, _1638199, _1638201]))], (43063 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1638193), 43057 ^ [_1638193, _1638195, _1638197, _1638199, _1638201]), _1638197) = _1638201)]], 43064 ^ _779308 : [(43065 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1638193), _1638195), 43057 ^ [_1638193, _1638195, _1638197, _1638199, _1638201]) = _1638199)], (43067 ^ _779308) ^ [] : [-(_1638197 = hAPP(hAPP(c_List_Oappend(_1638193), 43057 ^ [_1638193, _1638195, _1638197, _1638199, _1638201]), _1638201))]]], (43069 ^ _779308) ^ [_1638524, _1638526, _1638528, _1638530, _1638532] : [-(hAPP(hAPP(c_List_Oappend(_1638524), _1638526), _1638528) = hAPP(hAPP(c_List_Oappend(_1638524), _1638530), _1638532)), 43070 ^ _779308 : [(43071 ^ _779308) ^ [_1638636] : [_1638526 = hAPP(hAPP(c_List_Oappend(_1638524), _1638530), _1638636), hAPP(hAPP(c_List_Oappend(_1638524), _1638636), _1638528) = _1638532], (43077 ^ _779308) ^ [_1638748] : [hAPP(hAPP(c_List_Oappend(_1638524), _1638526), _1638748) = _1638530, _1638528 = hAPP(hAPP(c_List_Oappend(_1638524), _1638748), _1638532)]]], (43085 ^ _779308) ^ [_1638912, _1638914, _1638916, _1638918] : [-(hAPP(hAPP(c_List_Oappend(_1638912), hAPP(hAPP(c_List_Oappend(_1638912), _1638914), _1638916)), _1638918) = hAPP(hAPP(c_List_Oappend(_1638912), _1638914), hAPP(hAPP(c_List_Oappend(_1638912), _1638916), _1638918)))], (43087 ^ _779308) ^ [_1638973, _1638975, _1638977] : [class_Groups_Omonoid__add(_1638973), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1638973), hAPP(hAPP(c_List_Oappend(_1638973), _1638975), _1638977)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1638973), hAPP(c_List_Omonoid__add__class_Olistsum(_1638973), _1638975)), hAPP(c_List_Omonoid__add__class_Olistsum(_1638973), _1638977)))], (43093 ^ _779308) ^ [_1639112, _1639114, _1639116] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639112)), hAPP(hAPP(c_List_Oappend(_1639112), _1639114), _1639116)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639112)), _1639114)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639112)), _1639116)))], (43095 ^ _779308) ^ [_1639174, _1639176, _1639178, _1639180, _1639182, _1639184] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639174)), _1639176) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639178)), _1639180), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639174)), _1639182) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639178)), _1639184), -(hAPP(hAPP(c_List_Ozip(_1639174, _1639178), hAPP(hAPP(c_List_Oappend(_1639174), _1639176), _1639182)), hAPP(hAPP(c_List_Oappend(_1639178), _1639180), _1639184)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1639174, _1639178)), hAPP(hAPP(c_List_Ozip(_1639174, _1639178), _1639176), _1639180)), hAPP(hAPP(c_List_Ozip(_1639174, _1639178), _1639182), _1639184)))], (43105 ^ _779308) ^ [_1639483, _1639485, _1639487] : [-(hAPP(c_List_Oset(_1639483), hAPP(hAPP(c_List_Oappend(_1639483), _1639485), _1639487)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1639483, tc_HOL_Obool)), hAPP(c_List_Oset(_1639483), _1639485)), hAPP(c_List_Oset(_1639483), _1639487)))], (43107 ^ _779308) ^ [_1639544, _1639546] : [-(hAPP(hAPP(c_List_Oappend(_1639544), c_List_Olist_ONil(_1639544)), _1639546) = _1639546)], (43109 ^ _779308) ^ [_1639597, _1639599, _1639601] : [c_List_Olist_ONil(_1639597) = hAPP(hAPP(c_List_Oappend(_1639597), _1639599), _1639601), 43112 ^ _779308 : [(43113 ^ _779308) ^ [] : [-(_1639599 = c_List_Olist_ONil(_1639597))], (43115 ^ _779308) ^ [] : [-(_1639601 = c_List_Olist_ONil(_1639597))]]], (43117 ^ _779308) ^ [_1639726, _1639728, _1639730] : [-(c_List_Olist_ONil(_1639726) = hAPP(hAPP(c_List_Oappend(_1639726), _1639728), _1639730)), _1639728 = c_List_Olist_ONil(_1639726), _1639730 = c_List_Olist_ONil(_1639726)], (43127 ^ _779308) ^ [_1639889, _1639891] : [-(hAPP(hAPP(c_List_Oappend(_1639889), _1639891), c_List_Olist_ONil(_1639889)) = _1639891)], (43129 ^ _779308) ^ [_1639942, _1639944, _1639946] : [_1639942 = hAPP(hAPP(c_List_Oappend(_1639944), _1639942), _1639946), -(_1639946 = c_List_Olist_ONil(_1639944))], (43135 ^ _779308) ^ [_1640037, _1640039, _1640041] : [_1640041 = c_List_Olist_ONil(_1640039), -(_1640037 = hAPP(hAPP(c_List_Oappend(_1640039), _1640037), _1640041))], (43141 ^ _779308) ^ [_1640156, _1640158, _1640160] : [_1640156 = hAPP(hAPP(c_List_Oappend(_1640158), _1640160), _1640156), -(_1640160 = c_List_Olist_ONil(_1640158))], (43147 ^ _779308) ^ [_1640251, _1640253, _1640255] : [_1640255 = c_List_Olist_ONil(_1640253), -(_1640251 = hAPP(hAPP(c_List_Oappend(_1640253), _1640255), _1640251))], (43153 ^ _779308) ^ [_1640370, _1640372, _1640374] : [hAPP(hAPP(c_List_Oappend(_1640370), _1640372), _1640374) = c_List_Olist_ONil(_1640370), 43156 ^ _779308 : [(43157 ^ _779308) ^ [] : [-(_1640372 = c_List_Olist_ONil(_1640370))], (43159 ^ _779308) ^ [] : [-(_1640374 = c_List_Olist_ONil(_1640370))]]], (43161 ^ _779308) ^ [_1640499, _1640501, _1640503] : [-(hAPP(hAPP(c_List_Oappend(_1640499), _1640501), _1640503) = c_List_Olist_ONil(_1640499)), _1640501 = c_List_Olist_ONil(_1640499), _1640503 = c_List_Olist_ONil(_1640499)], (43171 ^ _779308) ^ [_1640680, _1640682, _1640684] : [hAPP(hAPP(c_List_Oappend(_1640680), _1640682), _1640684) = _1640682, -(_1640684 = c_List_Olist_ONil(_1640680))], (43177 ^ _779308) ^ [_1640775, _1640777, _1640779] : [_1640779 = c_List_Olist_ONil(_1640775), -(hAPP(hAPP(c_List_Oappend(_1640775), _1640777), _1640779) = _1640777)], (43183 ^ _779308) ^ [_1640894, _1640896, _1640898] : [hAPP(hAPP(c_List_Oappend(_1640894), _1640896), _1640898) = _1640898, -(_1640896 = c_List_Olist_ONil(_1640894))], (43189 ^ _779308) ^ [_1640989, _1640991, _1640993] : [_1640991 = c_List_Olist_ONil(_1640989), -(hAPP(hAPP(c_List_Oappend(_1640989), _1640991), _1640993) = _1640993)], (43195 ^ _779308) ^ [_1641090, _1641092, _1641094] : [_1641090 = _1641092, -(_1641090 = hAPP(hAPP(c_List_Oappend(_1641094), c_List_Olist_ONil(_1641094)), _1641092))], (43201 ^ _779308) ^ [_1641201, _1641203, _1641205] : [_1641201 = c_List_Olist_ONil(_1641203), -(c_List_Obutlast(_1641203, hAPP(hAPP(c_List_Oappend(_1641203), _1641205), _1641201)) = c_List_Obutlast(_1641203, _1641205))], (43207 ^ _779308) ^ [_1641306, _1641308, _1641310] : [-(_1641306 = c_List_Olist_ONil(_1641308)), -(c_List_Obutlast(_1641308, hAPP(hAPP(c_List_Oappend(_1641308), _1641310), _1641306)) = hAPP(hAPP(c_List_Oappend(_1641308), _1641310), c_List_Obutlast(_1641308, _1641306)))], (43213 ^ _779308) ^ [_1641370, _1641372, _1641374, _1641376] : [-(hAPP(hAPP(c_List_Onth(_1641370), hAPP(hAPP(c_List_Oappend(_1641370), _1641372), hAPP(hAPP(c_List_Olist_OCons(_1641370), _1641374), _1641376))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641370)), _1641372)) = _1641374)], (43215 ^ _779308) ^ [_1641430, _1641432, _1641434, _1641436] : [-(hAPP(hAPP(c_List_Onth(_1641430), hAPP(hAPP(c_List_Oappend(_1641430), _1641432), _1641434)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641430)), _1641432)), _1641436)) = hAPP(hAPP(c_List_Onth(_1641430), _1641434), _1641436))], (43217 ^ _779308) ^ [_1641496, _1641498, _1641500, _1641502] : [-(hAPP(hAPP(c_List_Otake(_1641496), _1641498), hAPP(hAPP(c_List_Oappend(_1641496), _1641500), _1641502)) = hAPP(hAPP(c_List_Oappend(_1641496), hAPP(hAPP(c_List_Otake(_1641496), _1641498), _1641500)), hAPP(hAPP(c_List_Otake(_1641496), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1641498), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641496)), _1641500))), _1641502)))], (43219 ^ _779308) ^ [_1641578, _1641580, _1641582, _1641584, _1641586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641578), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641580)), _1641582))), -(hAPP(hAPP(c_List_Olist__update(_1641580, hAPP(hAPP(c_List_Oappend(_1641580), _1641582), _1641584)), _1641578), _1641586) = hAPP(hAPP(c_List_Oappend(_1641580), hAPP(hAPP(c_List_Olist__update(_1641580, _1641582), _1641578), _1641586)), _1641584))], (43225 ^ _779308) ^ [_1641753, _1641755, _1641757, _1641759, _1641761] : [-(hAPP(hAPP(c_List_Olist__update(_1641753, hAPP(hAPP(c_List_Oappend(_1641753), _1641755), hAPP(hAPP(c_List_Olist_OCons(_1641753), _1641757), _1641759))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641753)), _1641755)), _1641761) = hAPP(hAPP(c_List_Oappend(_1641753), _1641755), hAPP(hAPP(c_List_Olist_OCons(_1641753), _1641761), _1641759)))], (43227 ^ _779308) ^ [_1641847, _1641849, _1641851, _1641853] : [hBOOL(hAPP(hAPP(c_member(_1641847), _1641849), hAPP(c_List_Oset(_1641847), _1641851))), -(c_List_Oremove1(_1641847, _1641849, hAPP(hAPP(c_List_Oappend(_1641847), _1641851), _1641853)) = hAPP(hAPP(c_List_Oappend(_1641847), c_List_Oremove1(_1641847, _1641849, _1641851)), _1641853))], (43233 ^ _779308) ^ [_1641994, _1641996, _1641998, _1642000] : [-(hBOOL(hAPP(hAPP(c_member(_1641994), _1641996), hAPP(c_List_Oset(_1641994), _1641998)))), -(c_List_Oremove1(_1641994, _1641996, hAPP(hAPP(c_List_Oappend(_1641994), _1641998), _1642000)) = hAPP(hAPP(c_List_Oappend(_1641994), _1641998), c_List_Oremove1(_1641994, _1641996, _1642000)))], (43239 ^ _779308) ^ [_1642072, _1642074, _1642076, _1642078] : [43240 ^ _779308 : [(43241 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642072), _1642074), hAPP(c_List_Oset(_1642072), c_List_Obutlast(_1642072, _1642076))))], (43243 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1642072), _1642074), hAPP(c_List_Oset(_1642072), c_List_Obutlast(_1642072, _1642078))))]], -(hBOOL(hAPP(hAPP(c_member(_1642072), _1642074), hAPP(c_List_Oset(_1642072), c_List_Obutlast(_1642072, hAPP(hAPP(c_List_Oappend(_1642072), _1642076), _1642078))))))], (43247 ^ _779308) ^ [_1642297, _1642299, _1642301] : [-(c_List_Obutlast(_1642297, hAPP(hAPP(c_List_Oappend(_1642297), _1642299), hAPP(hAPP(c_List_Olist_OCons(_1642297), _1642301), c_List_Olist_ONil(_1642297)))) = _1642299)], (43249 ^ _779308) ^ [_1642345, _1642347, _1642349, _1642351, _1642353, _1642355] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642345), tc_List_Olist(_1642345))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642345), tc_List_Olist(_1642345)), hAPP(hAPP(c_List_Oappend(_1642345), _1642347), _1642353)), hAPP(hAPP(c_List_Oappend(_1642345), _1642349), _1642355))), c_List_Olistrel1(_1642345, _1642351)))), 43250 ^ _779308 : [(43251 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642345), tc_List_Olist(_1642345))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642345), tc_List_Olist(_1642345)), _1642347), _1642349)), c_List_Olistrel1(_1642345, _1642351))), _1642353 = _1642355], (43257 ^ _779308) ^ [] : [_1642347 = _1642349, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642345), tc_List_Olist(_1642345))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642345), tc_List_Olist(_1642345)), _1642353), _1642355)), c_List_Olistrel1(_1642345, _1642351)))]]], (43265 ^ _779308) ^ [_1642793, _1642795, _1642797, _1642799, _1642801] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642793), tc_List_Olist(_1642793))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642793), tc_List_Olist(_1642793)), _1642795), _1642797)), c_List_Olexord(_1642793, _1642799))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642793), tc_List_Olist(_1642793))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642793), tc_List_Olist(_1642793)), hAPP(hAPP(c_List_Oappend(_1642793), _1642801), _1642795)), hAPP(hAPP(c_List_Oappend(_1642793), _1642801), _1642797))), c_List_Olexord(_1642793, _1642799))))], (43271 ^ _779308) ^ [_1643046, _1643048, _1643050] : [hBOOL(hAPP(c_List_Odistinct(_1643046), hAPP(hAPP(c_List_Oappend(_1643046), _1643048), _1643050))), 43274 ^ _779308 : [(43275 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643046), _1643048)))], (43277 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643046), _1643050)))], (43279 ^ _779308) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1643046, tc_HOL_Obool)), hAPP(c_List_Oset(_1643046), _1643048)), hAPP(c_List_Oset(_1643046), _1643050)) = c_Orderings_Obot__class_Obot(tc_fun(_1643046, tc_HOL_Obool)))]]], (43281 ^ _779308) ^ [_1643263, _1643265, _1643267] : [-(hBOOL(hAPP(c_List_Odistinct(_1643263), hAPP(hAPP(c_List_Oappend(_1643263), _1643265), _1643267)))), hBOOL(hAPP(c_List_Odistinct(_1643263), _1643265)), hBOOL(hAPP(c_List_Odistinct(_1643263), _1643267)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1643263, tc_HOL_Obool)), hAPP(c_List_Oset(_1643263), _1643265)), hAPP(c_List_Oset(_1643263), _1643267)) = c_Orderings_Obot__class_Obot(tc_fun(_1643263, tc_HOL_Obool))], (43295 ^ _779308) ^ [_1643559, _1643561, _1643563, _1643565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1643559), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643561)), _1643563))), -(hAPP(hAPP(c_List_Onth(_1643561), hAPP(hAPP(c_List_Oappend(_1643561), _1643563), _1643565)), _1643559) = hAPP(hAPP(c_List_Onth(_1643561), _1643563), _1643559))], (43301 ^ _779308) ^ [_1643706, _1643708, _1643710, _1643712] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1643706), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643708)), _1643710)))), -(hAPP(hAPP(c_List_Onth(_1643708), hAPP(hAPP(c_List_Oappend(_1643708), _1643710), _1643712)), _1643706) = hAPP(hAPP(c_List_Onth(_1643708), _1643712), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1643706), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643708)), _1643710))))], (43307 ^ _779308) ^ [_1643815, _1643817, _1643819, _1643821, _1643823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1643815), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643817)), _1643819))), -(hAPP(hAPP(c_List_Olist__update(_1643817, hAPP(hAPP(c_List_Oappend(_1643817), _1643819), _1643821)), _1643815), _1643823) = hAPP(hAPP(c_List_Oappend(_1643817), hAPP(hAPP(c_List_Olist__update(_1643817, _1643819), _1643815), _1643823)), _1643821))], (43313 ^ _779308) ^ [_1643984, _1643986, _1643988, _1643990, _1643992] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1643984), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643986)), _1643988)))), -(hAPP(hAPP(c_List_Olist__update(_1643986, hAPP(hAPP(c_List_Oappend(_1643986), _1643988), _1643990)), _1643984), _1643992) = hAPP(hAPP(c_List_Oappend(_1643986), _1643988), hAPP(hAPP(c_List_Olist__update(_1643986, _1643990), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1643984), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643986)), _1643988))), _1643992)))], (43319 ^ _779308) ^ [_1644087, _1644089, _1644091, _1644093] : [-(c_List_Osublist(_1644087, hAPP(hAPP(c_List_Oappend(_1644087), _1644089), _1644091), _1644093) = hAPP(hAPP(c_List_Oappend(_1644087), c_List_Osublist(_1644087, _1644089, _1644093)), c_List_Osublist(_1644087, _1644091, hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_Nat_Onat), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644087)), _1644089)))), _1644093)))))], (43321 ^ _779308) ^ [_1644166, _1644168, _1644170, _1644172, _1644174, _1644176, _1644178, _1644180] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644166, _1644166)), hAPP(hAPP(c_Product__Type_OPair(_1644166, _1644166), _1644168), _1644170)), _1644172)), _1644174 = hAPP(hAPP(c_List_Oappend(_1644166), _1644176), hAPP(hAPP(c_List_Olist_OCons(_1644166), _1644168), _1644178)), _1644180 = hAPP(hAPP(c_List_Oappend(_1644166), _1644176), hAPP(hAPP(c_List_Olist_OCons(_1644166), _1644170), _1644178)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644166), tc_List_Olist(_1644166))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644166), tc_List_Olist(_1644166)), _1644174), _1644180)), c_List_Olistrel1(_1644166, _1644172))))], (43335 ^ _779308) ^ [_1644545, _1644547, _1644549, _1644551, _1644553, _1644555, _1644557] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644545, _1644545)), hAPP(hAPP(c_Product__Type_OPair(_1644545, _1644545), _1644547), _1644549)), _1644551)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644545), tc_List_Olist(_1644545))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644545), tc_List_Olist(_1644545)), hAPP(hAPP(c_List_Oappend(_1644545), _1644553), hAPP(hAPP(c_List_Olist_OCons(_1644545), _1644547), _1644555))), hAPP(hAPP(c_List_Oappend(_1644545), _1644553), hAPP(hAPP(c_List_Olist_OCons(_1644545), _1644549), _1644557)))), c_List_Olexord(_1644545, _1644551))))], (43341 ^ _779308) ^ [_1644794, _1644796, _1644798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644794), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644796)), _1644798))), -(hAPP(hAPP(c_List_Otake(_1644796), hAPP(c_Nat_OSuc, _1644794)), _1644798) = hAPP(hAPP(c_List_Oappend(_1644796), hAPP(hAPP(c_List_Otake(_1644796), _1644794), _1644798)), hAPP(hAPP(c_List_Olist_OCons(_1644796), hAPP(hAPP(c_List_Onth(_1644796), _1644798), _1644794)), c_List_Olist_ONil(_1644796))))], (43347 ^ _779308) ^ [_1645014, _1645016, _1645018, _1645020, _1645022, _1645024] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645014), tc_List_Olist(_1645014))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645014), tc_List_Olist(_1645014)), hAPP(hAPP(c_List_Oappend(_1645014), _1645016), hAPP(hAPP(c_List_Olist_OCons(_1645014), _1645018), c_List_Olist_ONil(_1645014)))), hAPP(hAPP(c_List_Oappend(_1645014), _1645020), hAPP(hAPP(c_List_Olist_OCons(_1645014), _1645022), c_List_Olist_ONil(_1645014))))), c_List_Olistrel1(_1645014, _1645024))), 43352 ^ _779308 : [(43353 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645014), tc_List_Olist(_1645014))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645014), tc_List_Olist(_1645014)), _1645016), _1645020)), c_List_Olistrel1(_1645014, _1645024))))], (43355 ^ _779308) ^ [] : [-(_1645018 = _1645022)]], 43356 ^ _779308 : [(43357 ^ _779308) ^ [] : [-(_1645016 = _1645020)], (43359 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1645014, _1645014)), hAPP(hAPP(c_Product__Type_OPair(_1645014, _1645014), _1645018), _1645022)), _1645024)))]]], (43361 ^ _779308) ^ [_1645424, _1645426, _1645428, _1645430, _1645432, _1645434] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645424), tc_List_Olist(_1645424))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645424), tc_List_Olist(_1645424)), hAPP(hAPP(c_List_Oappend(_1645424), _1645426), hAPP(hAPP(c_List_Olist_OCons(_1645424), _1645428), c_List_Olist_ONil(_1645424)))), hAPP(hAPP(c_List_Oappend(_1645424), _1645430), hAPP(hAPP(c_List_Olist_OCons(_1645424), _1645432), c_List_Olist_ONil(_1645424))))), c_List_Olistrel1(_1645424, _1645434)))), 43362 ^ _779308 : [(43363 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645424), tc_List_Olist(_1645424))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645424), tc_List_Olist(_1645424)), _1645426), _1645430)), c_List_Olistrel1(_1645424, _1645434))), _1645428 = _1645432], (43369 ^ _779308) ^ [] : [_1645426 = _1645430, hBOOL(hAPP(hAPP(c_member(tc_prod(_1645424, _1645424)), hAPP(hAPP(c_Product__Type_OPair(_1645424, _1645424), _1645428), _1645432)), _1645434))]]], (43377 ^ _779308) ^ [_1645892, _1645894, _1645896, _1645898] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645892), tc_List_Olist(_1645892))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645892), tc_List_Olist(_1645892)), _1645894), _1645896)), c_List_Olistrel1(_1645892, _1645898))), 43382 ^ _779308 : [(43383 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1645892, _1645892)), hAPP(hAPP(c_Product__Type_OPair(_1645892, _1645892), 43380 ^ [_1645892, _1645894, _1645896, _1645898]), 43381 ^ [_1645892, _1645894, _1645896, _1645898])), _1645898)))], (43387 ^ _779308) ^ [] : [-(_1645894 = hAPP(hAPP(c_List_Oappend(_1645892), 43384 ^ [_1645892, _1645894, _1645896, _1645898]), hAPP(hAPP(c_List_Olist_OCons(_1645892), 43380 ^ [_1645892, _1645894, _1645896, _1645898]), 43385 ^ [_1645892, _1645894, _1645896, _1645898])))], (43389 ^ _779308) ^ [] : [-(_1645896 = hAPP(hAPP(c_List_Oappend(_1645892), 43384 ^ [_1645892, _1645894, _1645896, _1645898]), hAPP(hAPP(c_List_Olist_OCons(_1645892), 43381 ^ [_1645892, _1645894, _1645896, _1645898]), 43385 ^ [_1645892, _1645894, _1645896, _1645898])))]]], (43391 ^ _779308) ^ [_1646297, _1646299, _1646301, _1646303, _1646305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646297), tc_List_Olist(_1646297))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646297), tc_List_Olist(_1646297)), hAPP(hAPP(c_List_Oappend(_1646297), _1646299), _1646301)), hAPP(hAPP(c_List_Oappend(_1646297), _1646299), _1646303))), c_List_Olexord(_1646297, _1646305))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1646297, _1646297)), hAPP(hAPP(c_Product__Type_OPair(_1646297, _1646297), 43396 ^ [_1646297, _1646299, _1646301, _1646303, _1646305]), 43396 ^ [_1646297, _1646299, _1646301, _1646303, _1646305])), _1646305))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646297), tc_List_Olist(_1646297))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646297), tc_List_Olist(_1646297)), _1646301), _1646303)), c_List_Olexord(_1646297, _1646305))))], (43402 ^ _779308) ^ [_1646616, _1646618] : [-(hAPP(c_List_Orotate1(_1646616), _1646618) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1646616), _1646616, c_List_Olist_ONil(_1646616), hAPP(hAPP(c_COMBB(tc_List_Olist(_1646616), tc_fun(tc_List_Olist(_1646616), tc_List_Olist(_1646616)), _1646616), hAPP(c_COMBC(tc_List_Olist(_1646616), tc_List_Olist(_1646616), tc_List_Olist(_1646616)), c_List_Oappend(_1646616))), hAPP(hAPP(c_COMBC(_1646616, tc_List_Olist(_1646616), tc_List_Olist(_1646616)), c_List_Olist_OCons(_1646616)), c_List_Olist_ONil(_1646616)))), _1646618))], (43404 ^ _779308) ^ [_1646710, _1646712, _1646714, _1646716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1646710), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646712)), _1646714))), -(hAPP(hAPP(c_List_Olist__update(_1646712, _1646714), _1646710), _1646716) = hAPP(hAPP(c_List_Oappend(_1646712), hAPP(hAPP(c_List_Otake(_1646712), _1646710), _1646714)), hAPP(hAPP(c_List_Olist_OCons(_1646712), _1646716), hAPP(hAPP(c_List_Odrop(_1646712), hAPP(c_Nat_OSuc, _1646710)), _1646714))))], (43410 ^ _779308) ^ [_1646903, _1646905, _1646907] : [-(hAPP(hAPP(c_List_Oappend(_1646903), hAPP(hAPP(c_List_Otake(_1646903), _1646905), _1646907)), hAPP(hAPP(c_List_Odrop(_1646903), _1646905), _1646907)) = _1646907)], (43412 ^ _779308) ^ [_1646954, _1646956, _1646958, _1646960] : [-(hAPP(hAPP(c_List_Odrop(_1646954), hAPP(c_Nat_OSuc, _1646956)), hAPP(hAPP(c_List_Olist_OCons(_1646954), _1646958), _1646960)) = hAPP(hAPP(c_List_Odrop(_1646954), _1646956), _1646960))], (43414 ^ _779308) ^ [_1647010, _1647012, _1647014] : [-(hAPP(hAPP(c_List_Odrop(_1647010), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1647010), _1647012), _1647014)) = _1647014)], (43416 ^ _779308) ^ [_1647053, _1647055, _1647057, _1647059, _1647061] : [hAPP(hAPP(c_List_Odrop(_1647053), _1647055), _1647057) = hAPP(hAPP(c_List_Olist_OCons(_1647053), _1647059), _1647061), -(hAPP(hAPP(c_List_Onth(_1647053), _1647057), _1647055) = _1647059)], (43422 ^ _779308) ^ [_1647184, _1647186, _1647188] : [hBOOL(hAPP(c_List_Odistinct(_1647184), _1647186)), -(hBOOL(hAPP(c_List_Odistinct(_1647184), hAPP(hAPP(c_List_Odrop(_1647184), _1647188), _1647186))))], (43428 ^ _779308) ^ [_1647310, _1647312] : [hBOOL(hAPP(c_List_Odistinct(_1647310), hAPP(c_List_Orotate1(_1647310), _1647312))), -(hBOOL(hAPP(c_List_Odistinct(_1647310), _1647312)))], (43434 ^ _779308) ^ [_1647409, _1647411] : [hBOOL(hAPP(c_List_Odistinct(_1647409), _1647411)), -(hBOOL(hAPP(c_List_Odistinct(_1647409), hAPP(c_List_Orotate1(_1647409), _1647411))))], (43440 ^ _779308) ^ [_1647514, _1647516, _1647518] : [-(c_List_Obutlast(_1647514, hAPP(hAPP(c_List_Odrop(_1647514), _1647516), _1647518)) = hAPP(hAPP(c_List_Odrop(_1647514), _1647516), c_List_Obutlast(_1647514, _1647518)))], (43442 ^ _779308) ^ [_1647563, _1647565, _1647567] : [-(hAPP(hAPP(c_List_Odrop(_1647563), _1647565), c_List_Obutlast(_1647563, _1647567)) = c_List_Obutlast(_1647563, hAPP(hAPP(c_List_Odrop(_1647563), _1647565), _1647567)))], (43444 ^ _779308) ^ [_1647612, _1647614, _1647616, _1647618] : [-(hAPP(hAPP(c_List_Otake(_1647612), _1647614), hAPP(hAPP(c_List_Odrop(_1647612), _1647616), _1647618)) = hAPP(hAPP(c_List_Odrop(_1647612), _1647616), hAPP(hAPP(c_List_Otake(_1647612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1647614), _1647616)), _1647618)))], (43446 ^ _779308) ^ [_1647679, _1647681, _1647683, _1647685] : [-(hAPP(hAPP(c_List_Odrop(_1647679), _1647681), hAPP(hAPP(c_List_Otake(_1647679), _1647683), _1647685)) = hAPP(hAPP(c_List_Otake(_1647679), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1647683), _1647681)), hAPP(hAPP(c_List_Odrop(_1647679), _1647681), _1647685)))], (43448 ^ _779308) ^ [_1647746, _1647748, _1647750, _1647752] : [-(hAPP(hAPP(c_List_Odrop(_1647746), _1647748), hAPP(hAPP(c_List_Odrop(_1647746), _1647750), _1647752)) = hAPP(hAPP(c_List_Odrop(_1647746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1647748), _1647750)), _1647752))], (43450 ^ _779308) ^ [_1647805, _1647807] : [-(hAPP(hAPP(c_List_Odrop(_1647805), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1647807) = _1647807)], (43452 ^ _779308) ^ [_1647838, _1647840, _1647842, _1647844, _1647846] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1647838, _1647840)), _1647842), hAPP(hAPP(c_List_Ozip(_1647838, _1647840), _1647844), _1647846)) = hAPP(hAPP(c_List_Ozip(_1647838, _1647840), hAPP(hAPP(c_List_Odrop(_1647838), _1647842), _1647844)), hAPP(hAPP(c_List_Odrop(_1647840), _1647842), _1647846)))], (43454 ^ _779308) ^ [_1647914, _1647916] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647914)), hAPP(c_List_Orotate1(_1647914), _1647916)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647914)), _1647916))], (43456 ^ _779308) ^ [_1647958, _1647960, _1647962] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647958)), hAPP(hAPP(c_List_Odrop(_1647958), _1647960), _1647962)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647958)), _1647962)), _1647960))], (43458 ^ _779308) ^ [_1648013, _1648015] : [-(hAPP(c_List_Oset(_1648013), hAPP(c_List_Orotate1(_1648013), _1648015)) = hAPP(c_List_Oset(_1648013), _1648015))], (43460 ^ _779308) ^ [_1648053, _1648055, _1648057, _1648059] : [hBOOL(hAPP(hAPP(c_member(_1648053), _1648055), hAPP(c_List_Oset(_1648053), hAPP(hAPP(c_List_Odrop(_1648053), _1648057), _1648059)))), -(hBOOL(hAPP(hAPP(c_member(_1648053), _1648055), hAPP(c_List_Oset(_1648053), _1648059))))], (43466 ^ _779308) ^ [_1648198, _1648200, _1648202] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648198, tc_HOL_Obool)), hAPP(c_List_Oset(_1648198), hAPP(hAPP(c_List_Odrop(_1648198), _1648200), _1648202))), hAPP(c_List_Oset(_1648198), _1648202))))], (43468 ^ _779308) ^ [_1648253, _1648255] : [-(hAPP(hAPP(c_List_Odrop(_1648253), _1648255), c_List_Olist_ONil(_1648253)) = c_List_Olist_ONil(_1648253))], (43470 ^ _779308) ^ [_1648305, _1648307] : [hAPP(c_List_Orotate1(_1648305), _1648307) = c_List_Olist_ONil(_1648305), -(_1648307 = c_List_Olist_ONil(_1648305))], (43476 ^ _779308) ^ [_1648396, _1648398] : [_1648398 = c_List_Olist_ONil(_1648396), -(hAPP(c_List_Orotate1(_1648396), _1648398) = c_List_Olist_ONil(_1648396))], (43482 ^ _779308) ^ [_1648493, _1648495, _1648497, _1648499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1648493), _1648495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1648497, tc_HOL_Obool)), hAPP(c_List_Oset(_1648497), hAPP(hAPP(c_List_Odrop(_1648497), _1648495), _1648499))), hAPP(c_List_Oset(_1648497), hAPP(hAPP(c_List_Odrop(_1648497), _1648493), _1648499)))))], (43488 ^ _779308) ^ [_1648674, _1648676, _1648678] : [hAPP(hAPP(c_List_Odrop(_1648674), _1648676), _1648678) = c_List_Olist_ONil(_1648674), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648674)), _1648678)), _1648676)))], (43494 ^ _779308) ^ [_1648793, _1648795, _1648797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648793)), _1648797)), _1648795)), -(hAPP(hAPP(c_List_Odrop(_1648793), _1648795), _1648797) = c_List_Olist_ONil(_1648793))], (43500 ^ _779308) ^ [_1648918, _1648920, _1648922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648918)), _1648920)), _1648922)), -(hAPP(hAPP(c_List_Odrop(_1648918), _1648922), _1648920) = c_List_Olist_ONil(_1648918))], (43506 ^ _779308) ^ [_1649041, _1649043, _1649045, _1649047] : [-(hAPP(hAPP(c_List_Odrop(_1649041), _1649043), hAPP(hAPP(c_List_Oappend(_1649041), _1649045), _1649047)) = hAPP(hAPP(c_List_Oappend(_1649041), hAPP(hAPP(c_List_Odrop(_1649041), _1649043), _1649045)), hAPP(hAPP(c_List_Odrop(_1649041), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1649043), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649041)), _1649045))), _1649047)))], (43508 ^ _779308) ^ [_1649144, _1649146, _1649148, _1649150] : [hAPP(hAPP(c_List_Oappend(_1649144), _1649146), _1649148) = _1649150, 43511 ^ _779308 : [(43512 ^ _779308) ^ [] : [-(_1649146 = hAPP(hAPP(c_List_Otake(_1649144), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649144)), _1649146)), _1649150))], (43514 ^ _779308) ^ [] : [-(_1649148 = hAPP(hAPP(c_List_Odrop(_1649144), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649144)), _1649146)), _1649150))]]], (43516 ^ _779308) ^ [_1649323, _1649325, _1649327, _1649329] : [-(hAPP(hAPP(c_List_Oappend(_1649323), _1649325), _1649327) = _1649329), _1649325 = hAPP(hAPP(c_List_Otake(_1649323), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649323)), _1649325)), _1649329), _1649327 = hAPP(hAPP(c_List_Odrop(_1649323), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649323)), _1649325)), _1649329)], (43526 ^ _779308) ^ [_1649538, _1649540, _1649542, _1649544] : [-(hAPP(hAPP(c_List_Odrop(_1649538), _1649540), hAPP(hAPP(c_List_Olist_OCons(_1649538), _1649542), _1649544)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1649538), hAPP(hAPP(c_List_Olist_OCons(_1649538), _1649542), _1649544), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1649538), tc_List_Olist(_1649538)), c_List_Odrop(_1649538)), _1649544), _1649540))], (43528 ^ _779308) ^ [_1649629, _1649631, _1649633, _1649635] : [_1649629 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1649631), _1649629), hAPP(hAPP(c_List_Olist_OCons(_1649631), _1649633), _1649635)) = hAPP(hAPP(c_List_Olist_OCons(_1649631), _1649633), _1649635))], (43534 ^ _779308) ^ [_1649752, _1649754, _1649756, _1649758] : [-(_1649752 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1649754), _1649752), hAPP(hAPP(c_List_Olist_OCons(_1649754), _1649756), _1649758)) = hAPP(hAPP(c_List_Odrop(_1649754), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1649752), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1649758))], (43540 ^ _779308) ^ [_1649824, _1649826, _1649828, _1649830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1649824), _1649826)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649828)), _1649830))), -(hAPP(hAPP(c_List_Onth(_1649828), hAPP(hAPP(c_List_Odrop(_1649828), _1649824), _1649830)), _1649826) = hAPP(hAPP(c_List_Onth(_1649828), _1649830), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1649824), _1649826)))], (43546 ^ _779308) ^ [_1650025, _1650027, _1650029, _1650031, _1650033] : [hAPP(hAPP(c_List_Oappend(_1650025), _1650027), _1650029) = hAPP(hAPP(c_List_Oappend(_1650025), _1650031), _1650033), 43549 ^ _779308 : [(43550 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650025)), _1650027)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650025)), _1650031))), 43553 ^ _779308 : [(43554 ^ _779308) ^ [] : [-(_1650027 = hAPP(hAPP(c_List_Otake(_1650025), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650025)), _1650027)), _1650031))], (43556 ^ _779308) ^ [] : [-(_1650029 = hAPP(hAPP(c_List_Oappend(_1650025), hAPP(hAPP(c_List_Odrop(_1650025), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650025)), _1650027)), _1650031)), _1650033))]]], (43558 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650025)), _1650027)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650025)), _1650031)))), 43561 ^ _779308 : [(43562 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1650025), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650025)), _1650031)), _1650027) = _1650031)], (43564 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1650025), hAPP(hAPP(c_List_Odrop(_1650025), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650025)), _1650031)), _1650027)), _1650029) = _1650033)]]]]], (43566 ^ _779308) ^ [_1650538, _1650540, _1650542, _1650544, _1650546] : [-(hAPP(hAPP(c_List_Oappend(_1650538), _1650540), _1650542) = hAPP(hAPP(c_List_Oappend(_1650538), _1650544), _1650546)), 43569 ^ _779308 : [(43570 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650538)), _1650540)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650538)), _1650544))))], (43572 ^ _779308) ^ [] : [_1650540 = hAPP(hAPP(c_List_Otake(_1650538), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650538)), _1650540)), _1650544), _1650542 = hAPP(hAPP(c_List_Oappend(_1650538), hAPP(hAPP(c_List_Odrop(_1650538), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650538)), _1650540)), _1650544)), _1650546)]], 43577 ^ _779308 : [(43578 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650538)), _1650540)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650538)), _1650544)))], (43580 ^ _779308) ^ [] : [hAPP(hAPP(c_List_Otake(_1650538), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650538)), _1650544)), _1650540) = _1650544, hAPP(hAPP(c_List_Oappend(_1650538), hAPP(hAPP(c_List_Odrop(_1650538), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650538)), _1650544)), _1650540)), _1650542) = _1650546]]], (43588 ^ _779308) ^ [_1651126, _1651128, _1651130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1651126), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651128)), _1651130))), -(hAPP(hAPP(c_List_Olist_OCons(_1651128), hAPP(hAPP(c_List_Onth(_1651128), _1651130), _1651126)), hAPP(hAPP(c_List_Odrop(_1651128), hAPP(c_Nat_OSuc, _1651126)), _1651130)) = hAPP(hAPP(c_List_Odrop(_1651128), _1651126), _1651130))], (43594 ^ _779308) ^ [_1651297, _1651299, _1651301, _1651303] : [-(hAPP(c_List_Orotate1(_1651297), c_List_Olist_ONil(_1651297)) = c_List_Olist_ONil(_1651297))], (43596 ^ _779308) ^ [_1651332, _1651334, _1651336, _1651338] : [-(hAPP(c_List_Orotate1(_1651334), hAPP(hAPP(c_List_Olist_OCons(_1651334), _1651336), _1651338)) = hAPP(hAPP(c_List_Oappend(_1651334), _1651338), hAPP(hAPP(c_List_Olist_OCons(_1651334), _1651336), c_List_Olist_ONil(_1651334))))], (43598 ^ _779308) ^ [_1651409, _1651411, _1651413, _1651415] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651409) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1651411), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651409)), hAPP(hAPP(c_List_Olist_OCons(_1651411), _1651413), _1651415)) = hAPP(hAPP(c_List_Olist_OCons(_1651411), _1651413), _1651415))], (43604 ^ _779308) ^ [_1651544, _1651546, _1651548, _1651550] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651544) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1651546), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651544)), hAPP(hAPP(c_List_Olist_OCons(_1651546), _1651548), _1651550)) = hAPP(hAPP(c_List_Odrop(_1651546), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1651544)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1651550))], (43610 ^ _779308) ^ [_1651625, _1651627, _1651629, _1651631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1651625), _1651627)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651629)), _1651631))), -(hAPP(hAPP(c_List_Otake(_1651629), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1651625), _1651627)), _1651631) = hAPP(hAPP(c_List_Oappend(_1651629), hAPP(hAPP(c_List_Otake(_1651629), _1651625), _1651631)), hAPP(hAPP(c_List_Otake(_1651629), _1651627), hAPP(hAPP(c_List_Odrop(_1651629), _1651625), _1651631))))], (43616 ^ _779308) ^ [_1651834, _1651836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651834)), _1651836)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1651834), _1651836) = _1651836)], (43622 ^ _779308) ^ [_1651945, _1651947, _1651949, _1651951, _1651953] : [-(hAPP(hAPP(c_List_Ozip(_1651945, _1651947), hAPP(hAPP(c_List_Oappend(_1651945), _1651949), _1651951)), _1651953) = hAPP(hAPP(c_List_Oappend(tc_prod(_1651945, _1651947)), hAPP(hAPP(c_List_Ozip(_1651945, _1651947), _1651949), hAPP(hAPP(c_List_Otake(_1651947), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651945)), _1651949)), _1651953))), hAPP(hAPP(c_List_Ozip(_1651945, _1651947), _1651951), hAPP(hAPP(c_List_Odrop(_1651947), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651945)), _1651949)), _1651953))))], (43624 ^ _779308) ^ [_1652052, _1652054, _1652056, _1652058, _1652060] : [-(hAPP(hAPP(c_List_Ozip(_1652052, _1652054), _1652056), hAPP(hAPP(c_List_Oappend(_1652054), _1652058), _1652060)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1652052, _1652054)), hAPP(hAPP(c_List_Ozip(_1652052, _1652054), hAPP(hAPP(c_List_Otake(_1652052), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652054)), _1652058)), _1652056)), _1652058)), hAPP(hAPP(c_List_Ozip(_1652052, _1652054), hAPP(hAPP(c_List_Odrop(_1652052), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652054)), _1652058)), _1652056)), _1652060)))], (43626 ^ _779308) ^ [_1652159, _1652161, _1652163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652159), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652161)), _1652163))), -(_1652163 = hAPP(hAPP(c_List_Oappend(_1652161), hAPP(hAPP(c_List_Otake(_1652161), _1652159), _1652163)), hAPP(hAPP(c_List_Olist_OCons(_1652161), hAPP(hAPP(c_List_Onth(_1652161), _1652163), _1652159)), hAPP(hAPP(c_List_Odrop(_1652161), hAPP(c_Nat_OSuc, _1652159)), _1652163))))], (43632 ^ _779308) ^ [_1652348, _1652350, _1652352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652348), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652350)), _1652352))), -(hAPP(hAPP(c_List_Oappend(_1652350), hAPP(hAPP(c_List_Otake(_1652350), _1652348), _1652352)), hAPP(hAPP(c_List_Olist_OCons(_1652350), hAPP(c_List_Ohd(_1652350), hAPP(hAPP(c_List_Odrop(_1652350), _1652348), _1652352))), c_List_Olist_ONil(_1652350))) = hAPP(hAPP(c_List_Otake(_1652350), hAPP(c_Nat_OSuc, _1652348)), _1652352))], (43638 ^ _779308) ^ [_1652550, _1652552, _1652554] : [-(_1652550 = c_List_Olist_ONil(_1652552)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652554), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652552)), _1652550))), -(hAPP(c_List_Ohd(_1652552), hAPP(hAPP(c_List_Odrop(_1652552), _1652554), _1652550)) = hAPP(hAPP(c_List_Onth(_1652552), _1652550), _1652554))], (43648 ^ _779308) ^ [_1652749, _1652751, _1652753] : [-(hAPP(c_List_Ohd(_1652749), hAPP(hAPP(c_List_Olist_OCons(_1652749), _1652751), _1652753)) = _1652751)], (43650 ^ _779308) ^ [_1652785, _1652787, _1652789] : [-(_1652785 = c_List_Olist_ONil(_1652787)), -(hAPP(c_List_Ohd(_1652787), hAPP(hAPP(c_List_Oappend(_1652787), _1652785), _1652789)) = hAPP(c_List_Ohd(_1652787), _1652785))], (43656 ^ _779308) ^ [_1652855, _1652857, _1652859] : [_1652855 = c_List_Olist_ONil(_1652857), -(hAPP(c_List_Ohd(_1652857), hAPP(hAPP(c_List_Oappend(_1652857), _1652855), _1652859)) = hAPP(c_List_Ohd(_1652857), _1652859))], (43662 ^ _779308) ^ [_1652968, _1652970, _1652972] : [-(_1652968 = c_List_Olist_ONil(_1652970)), -(hAPP(c_List_Ohd(_1652970), hAPP(hAPP(c_List_Oappend(_1652970), _1652968), _1652972)) = hAPP(c_List_Ohd(_1652970), _1652968))], (43668 ^ _779308) ^ [_1653024, _1653026] : [-(_1653024 = c_List_Olist_ONil(_1653026)), -(hBOOL(hAPP(hAPP(c_member(_1653026), hAPP(c_List_Ohd(_1653026), _1653024)), hAPP(c_List_Oset(_1653026), _1653024))))], (43674 ^ _779308) ^ [_1653075, _1653077] : [-(_1653075 = c_List_Olist_ONil(_1653077)), -(hAPP(c_List_Ohd(_1653077), _1653075) = hAPP(hAPP(c_List_Onth(_1653077), _1653075), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (43680 ^ _779308) ^ [_1653122, _1653124] : [-(_1653122 = c_List_Olist_ONil(_1653124)), -(hAPP(c_List_Orotate1(_1653124), _1653122) = hAPP(hAPP(c_List_Oappend(_1653124), hAPP(c_List_Otl(_1653124), _1653122)), hAPP(hAPP(c_List_Olist_OCons(_1653124), hAPP(c_List_Ohd(_1653124), _1653122)), c_List_Olist_ONil(_1653124))))], (43686 ^ _779308) ^ [_1653189, _1653191, _1653193] : [-(_1653189 = c_List_Olist_ONil(_1653191)), -(hAPP(c_List_Ohd(_1653191), hAPP(c_List_Orotate(_1653191, _1653193), _1653189)) = hAPP(hAPP(c_List_Onth(_1653191), _1653189), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1653193, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653191)), _1653189))))], (43692 ^ _779308) ^ [_1653259, _1653261, _1653263] : [-(hAPP(hAPP(c_List_Odrop(_1653259), _1653261), hAPP(c_List_Otl(_1653259), _1653263)) = hAPP(c_List_Otl(_1653259), hAPP(hAPP(c_List_Odrop(_1653259), _1653261), _1653263)))], (43694 ^ _779308) ^ [_1653312, _1653314, _1653316] : [-(hAPP(c_List_Otl(_1653312), hAPP(hAPP(c_List_Odrop(_1653312), _1653314), _1653316)) = hAPP(hAPP(c_List_Odrop(_1653312), _1653314), hAPP(c_List_Otl(_1653312), _1653316)))], (43696 ^ _779308) ^ [_1653365, _1653367, _1653369] : [-(hAPP(c_List_Otl(_1653365), hAPP(hAPP(c_List_Olist_OCons(_1653365), _1653367), _1653369)) = _1653369)], (43698 ^ _779308) ^ [_1653405, _1653407] : [hBOOL(hAPP(c_List_Odistinct(_1653405), _1653407)), -(hBOOL(hAPP(c_List_Odistinct(_1653405), hAPP(c_List_Otl(_1653405), _1653407))))], (43704 ^ _779308) ^ [_1653526, _1653528, _1653530] : [hBOOL(hAPP(c_List_Odistinct(_1653526), hAPP(c_List_Orotate(_1653526, _1653528), _1653530))), -(hBOOL(hAPP(c_List_Odistinct(_1653526), _1653530)))], (43710 ^ _779308) ^ [_1653629, _1653631, _1653633] : [hBOOL(hAPP(c_List_Odistinct(_1653629), _1653633)), -(hBOOL(hAPP(c_List_Odistinct(_1653629), hAPP(c_List_Orotate(_1653629, _1653631), _1653633))))], (43716 ^ _779308) ^ [_1653738, _1653740, _1653742] : [-(c_List_Orotate(_1653738, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1653740), _1653742)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1653738), tc_List_Olist(_1653738), tc_List_Olist(_1653738), c_List_Orotate(_1653738, _1653740)), c_List_Orotate(_1653738, _1653742)))], (43718 ^ _779308) ^ [_1653794, _1653796, _1653798, _1653800] : [-(hAPP(c_List_Orotate(_1653794, _1653796), hAPP(c_List_Orotate(_1653794, _1653798), _1653800)) = hAPP(c_List_Orotate(_1653794, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1653796), _1653798)), _1653800))], (43720 ^ _779308) ^ [_1653847] : [-(c_List_Orotate(_1653847, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1653847)))], (43722 ^ _779308) ^ [_1653877, _1653879, _1653881] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653877)), hAPP(c_List_Orotate(_1653877, _1653879), _1653881)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653877)), _1653881))], (43724 ^ _779308) ^ [_1653924, _1653926, _1653928] : [-(hAPP(c_List_Oset(_1653924), hAPP(c_List_Orotate(_1653924, _1653926), _1653928)) = hAPP(c_List_Oset(_1653924), _1653928))], (43726 ^ _779308) ^ [_1653967] : [-(hAPP(c_List_Otl(_1653967), c_List_Olist_ONil(_1653967)) = c_List_Olist_ONil(_1653967))], (43728 ^ _779308) ^ [_1654017, _1654019, _1654021] : [hAPP(c_List_Orotate(_1654017, _1654019), _1654021) = c_List_Olist_ONil(_1654017), -(_1654021 = c_List_Olist_ONil(_1654017))], (43734 ^ _779308) ^ [_1654112, _1654114, _1654116] : [_1654116 = c_List_Olist_ONil(_1654112), -(hAPP(c_List_Orotate(_1654112, _1654114), _1654116) = c_List_Olist_ONil(_1654112))], (43740 ^ _779308) ^ [_1654213, _1654215, _1654217] : [-(hAPP(c_List_Orotate1(_1654213), hAPP(c_List_Orotate(_1654213, _1654215), _1654217)) = hAPP(c_List_Orotate(_1654213, _1654215), hAPP(c_List_Orotate1(_1654213), _1654217)))], (43742 ^ _779308) ^ [_1654262, _1654264] : [-(c_List_Orotate(_1654262, _1654264) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1654262), tc_List_Olist(_1654262)), _1654264), c_List_Orotate1(_1654262)))], (43744 ^ _779308) ^ [_1654301, _1654303, _1654305] : [-(_1654301 = c_List_Olist_ONil(_1654303)), -(hAPP(c_List_Otl(_1654303), hAPP(hAPP(c_List_Oappend(_1654303), _1654301), _1654305)) = hAPP(hAPP(c_List_Oappend(_1654303), hAPP(c_List_Otl(_1654303), _1654301)), _1654305))], (43750 ^ _779308) ^ [_1654367, _1654369, _1654371] : [-(hAPP(hAPP(c_List_Otake(_1654367), _1654369), hAPP(c_List_Otl(_1654367), _1654371)) = hAPP(c_List_Otl(_1654367), hAPP(hAPP(c_List_Otake(_1654367), hAPP(c_Nat_OSuc, _1654369)), _1654371)))], (43752 ^ _779308) ^ [_1654423, _1654425, _1654427] : [-(hAPP(c_List_Orotate(_1654423, _1654425), _1654427) = hAPP(c_List_Orotate(_1654423, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1654425, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654423)), _1654427))), _1654427))], (43754 ^ _779308) ^ [_1654473, _1654475, _1654477] : [-(hAPP(hAPP(c_List_Odrop(_1654473), hAPP(c_Nat_OSuc, _1654475)), _1654477) = hAPP(hAPP(c_List_Odrop(_1654473), _1654475), hAPP(c_List_Otl(_1654473), _1654477)))], (43756 ^ _779308) ^ [_1654524, _1654526, _1654528] : [-(hAPP(c_List_Orotate(_1654524, hAPP(c_Nat_OSuc, _1654526)), _1654528) = hAPP(c_List_Orotate1(_1654524), hAPP(c_List_Orotate(_1654524, _1654526), _1654528)))], (43758 ^ _779308) ^ [_1654571, _1654573, _1654575] : [-(hAPP(c_List_Otl(_1654571), hAPP(hAPP(c_List_Oappend(_1654571), _1654573), _1654575)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1654571), _1654571, hAPP(c_List_Otl(_1654571), _1654575), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1654571), tc_List_Olist(_1654571)), _1654571), hAPP(hAPP(c_COMBC(tc_List_Olist(_1654571), tc_List_Olist(_1654571), tc_List_Olist(_1654571)), c_List_Oappend(_1654571)), _1654575))), _1654573))], (43760 ^ _779308) ^ [_1654657, _1654659, _1654661] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1654657, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654659)), _1654661)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1654659, _1654657), _1654661) = _1654661)], (43766 ^ _779308) ^ [_1654770, _1654772, _1654774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654770)), _1654772)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1654770, _1654774), _1654772) = _1654772)], (43772 ^ _779308) ^ [_1654885, _1654887] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654885)), hAPP(c_List_Otl(_1654885), _1654887)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654885)), _1654887)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43774 ^ _779308) ^ [_1654935, _1654937, _1654939] : [-(hAPP(c_List_Otl(_1654935), hAPP(hAPP(c_List_Otake(_1654935), _1654937), _1654939)) = hAPP(hAPP(c_List_Otake(_1654935), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1654937), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1654935), _1654939)))], (43776 ^ _779308) ^ [_1654990, _1654992, _1654994] : [-(_1654990 = c_List_Olist_ONil(_1654992)), -(hAPP(hAPP(c_List_Otake(_1654992), hAPP(c_Nat_OSuc, _1654994)), _1654990) = hAPP(hAPP(c_List_Olist_OCons(_1654992), hAPP(c_List_Ohd(_1654992), _1654990)), hAPP(hAPP(c_List_Otake(_1654992), _1654994), hAPP(c_List_Otl(_1654992), _1654990))))], (43782 ^ _779308) ^ [_1655067, _1655069, _1655071] : [-(hAPP(c_List_Orotate(_1655067, _1655069), _1655071) = hAPP(hAPP(c_List_Oappend(_1655067), hAPP(hAPP(c_List_Odrop(_1655067), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655069, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655067)), _1655071))), _1655071)), hAPP(hAPP(c_List_Otake(_1655067), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655069, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655067)), _1655071))), _1655071)))], (43784 ^ _779308) ^ [_1655146, _1655148] : [class_Lattices_Oab__semigroup__idem__mult(_1655146), -(_1655148 = c_List_Olist_ONil(_1655146)), -(hAPP(c_Finite__Set_Ofold1(_1655146, c_Groups_Otimes__class_Otimes(_1655146)), hAPP(c_List_Oset(_1655146), _1655148)) = hAPP(c_List_Ofoldl(_1655146, _1655146, c_Groups_Otimes__class_Otimes(_1655146), hAPP(c_List_Ohd(_1655146), _1655148)), hAPP(c_List_Otl(_1655146), _1655148)))], (43794 ^ _779308) ^ [_1655306, _1655308, _1655310, _1655312] : [43795 ^ _779308 : [(43796 ^ _779308) ^ [_1655403, _1655405] : [_1655306 = hAPP(hAPP(c_List_Olist_OCons(_1655308), _1655405), _1655403)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655308), tc_List_Olist(_1655308))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655308), tc_List_Olist(_1655308)), _1655310), hAPP(hAPP(c_List_Oappend(_1655308), _1655310), _1655306))), c_List_Olexord(_1655308, _1655312))))], (43800 ^ _779308) ^ [_1655502, _1655504, _1655506, _1655508] : [-(hAPP(c_List_Ofoldl(_1655502, _1655504, _1655506, _1655508), c_List_Olist_ONil(_1655504)) = _1655508)], (43802 ^ _779308) ^ [_1655541, _1655543, _1655545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1655541), _1655543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1655541), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1655543), _1655545))))], (43808 ^ _779308) ^ [_1655656, _1655658, _1655660] : [class_Groups_Omonoid__add(_1655656), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1655656), _1655658), hAPP(c_List_Ofoldl(_1655656, _1655656, c_Groups_Oplus__class_Oplus(_1655656), c_Groups_Ozero__class_Ozero(_1655656)), _1655660)) = hAPP(c_List_Ofoldl(_1655656, _1655656, c_Groups_Oplus__class_Oplus(_1655656), _1655658), _1655660))], (43814 ^ _779308) ^ [_1655793, _1655795, _1655797, _1655799] : [class_Groups_Osemigroup__add(_1655793), -(hAPP(c_List_Ofoldl(_1655793, _1655793, c_Groups_Oplus__class_Oplus(_1655793), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1655793), _1655795), _1655797)), _1655799) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1655793), _1655795), hAPP(c_List_Ofoldl(_1655793, _1655793, c_Groups_Oplus__class_Oplus(_1655793), _1655797), _1655799)))], (43820 ^ _779308) ^ [_1655944, _1655946, _1655948, _1655950, _1655952, _1655954] : [-(hAPP(c_List_Ofoldl(_1655944, _1655946, _1655948, _1655950), hAPP(hAPP(c_List_Olist_OCons(_1655946), _1655952), _1655954)) = hAPP(c_List_Ofoldl(_1655944, _1655946, _1655948, hAPP(hAPP(_1655948, _1655950), _1655952)), _1655954))], (43822 ^ _779308) ^ [_1656007, _1656009, _1656011, _1656013, _1656015, _1656017] : [-(hAPP(c_List_Ofoldl(_1656007, _1656009, _1656011, _1656013), hAPP(hAPP(c_List_Oappend(_1656009), _1656015), _1656017)) = hAPP(c_List_Ofoldl(_1656007, _1656009, _1656011, hAPP(c_List_Ofoldl(_1656007, _1656009, _1656011, _1656013), _1656015)), _1656017))], (43824 ^ _779308) ^ [_1656072] : [class_Groups_Omonoid__add(_1656072), -(c_List_Omonoid__add__class_Olistsum(_1656072) = c_List_Ofoldl(_1656072, _1656072, c_Groups_Oplus__class_Oplus(_1656072), c_Groups_Ozero__class_Ozero(_1656072)))], (43830 ^ _779308) ^ [_1656182, _1656184] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656182), _1656184) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43833 ^ _779308 : [(43834 ^ _779308) ^ [] : [-(_1656182 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43836 ^ _779308) ^ [_1656296] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1656296), hAPP(c_List_Oset(tc_Nat_Onat), _1656184))), -(_1656296 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43842 ^ _779308) ^ [_1656393, _1656395] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656393), _1656395) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1656393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43848 ^ _779308 : [(43849 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43847 ^ [_1656393, _1656395]), hAPP(c_List_Oset(tc_Nat_Onat), _1656395))))], (43851 ^ _779308) ^ [] : [43847 ^ [_1656393, _1656395] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43855 ^ _779308) ^ [_1656619, _1656621, _1656623, _1656625, _1656627] : [c_Finite__Set_Ofun__left__comm__idem(_1656619, _1656621, _1656623), -(hAPP(hAPP(c_Finite__Set_Ofold(_1656619, _1656621, _1656623), _1656625), hAPP(c_List_Oset(_1656619), _1656627)) = hAPP(c_List_Ofoldl(_1656621, _1656619, hAPP(c_COMBC(_1656619, _1656621, _1656621), _1656623), _1656625), _1656627))], (43861 ^ _779308) ^ [_1656764, _1656766] : [class_Complete__Lattice_Ocomplete__lattice(_1656764), -(c_Complete__Lattice_OSup__class_OSup(_1656764, hAPP(c_List_Oset(_1656764), _1656766)) = hAPP(c_List_Ofoldl(_1656764, _1656764, c_Lattices_Osemilattice__sup__class_Osup(_1656764), c_Orderings_Obot__class_Obot(_1656764)), _1656766))], (43867 ^ _779308) ^ [_1656879, _1656881] : [class_Complete__Lattice_Ocomplete__lattice(_1656879), -(c_Complete__Lattice_OInf__class_OInf(_1656879, hAPP(c_List_Oset(_1656879), _1656881)) = hAPP(c_List_Ofoldl(_1656879, _1656879, c_Lattices_Osemilattice__inf__class_Oinf(_1656879), c_Orderings_Otop__class_Otop(_1656879)), _1656881))], (43873 ^ _779308) ^ [_1656994, _1656996, _1656998] : [class_Lattices_Olattice(_1656994), -(c_Big__Operators_Olattice__class_OSup__fin(_1656994, hAPP(c_List_Oset(_1656994), hAPP(hAPP(c_List_Olist_OCons(_1656994), _1656996), _1656998))) = hAPP(c_List_Ofoldl(_1656994, _1656994, c_Lattices_Osemilattice__sup__class_Osup(_1656994), _1656996), _1656998))], (43879 ^ _779308) ^ [_1657123, _1657125, _1657127] : [class_Lattices_Olattice(_1657123), -(c_Big__Operators_Olattice__class_OInf__fin(_1657123, hAPP(c_List_Oset(_1657123), hAPP(hAPP(c_List_Olist_OCons(_1657123), _1657125), _1657127))) = hAPP(c_List_Ofoldl(_1657123, _1657123, c_Lattices_Osemilattice__inf__class_Oinf(_1657123), _1657125), _1657127))], (43885 ^ _779308) ^ [_1657252, _1657254, _1657256] : [class_Orderings_Olinorder(_1657252), -(c_Big__Operators_Olinorder__class_OMin(_1657252, hAPP(c_List_Oset(_1657252), hAPP(hAPP(c_List_Olist_OCons(_1657252), _1657254), _1657256))) = hAPP(c_List_Ofoldl(_1657252, _1657252, c_Orderings_Oord__class_Omin(_1657252), _1657254), _1657256))], (43891 ^ _779308) ^ [_1657381, _1657383, _1657385] : [class_Orderings_Olinorder(_1657381), -(c_Big__Operators_Olinorder__class_OMax(_1657381, hAPP(c_List_Oset(_1657381), hAPP(hAPP(c_List_Olist_OCons(_1657381), _1657383), _1657385))) = hAPP(c_List_Ofoldl(_1657381, _1657381, c_Orderings_Oord__class_Omax(_1657381), _1657383), _1657385))], (43897 ^ _779308) ^ [_1657510, _1657512, _1657514] : [class_Orderings_Olinorder(_1657510), -(c_Big__Operators_Olattice_OInf__fin(_1657510, c_Orderings_Oord__class_Omin(_1657510), hAPP(c_List_Oset(_1657510), hAPP(hAPP(c_List_Olist_OCons(_1657510), _1657512), _1657514))) = hAPP(c_List_Ofoldl(_1657510, _1657510, c_Orderings_Oord__class_Omin(_1657510), _1657512), _1657514))], (43903 ^ _779308) ^ [_1657645, _1657647, _1657649] : [class_Orderings_Olinorder(_1657645), -(c_Big__Operators_Olattice_OSup__fin(_1657645, c_Orderings_Oord__class_Omax(_1657645), hAPP(c_List_Oset(_1657645), hAPP(hAPP(c_List_Olist_OCons(_1657645), _1657647), _1657649))) = hAPP(c_List_Ofoldl(_1657645, _1657645, c_Orderings_Oord__class_Omax(_1657645), _1657647), _1657649))], (43909 ^ _779308) ^ [_1657780, _1657782, _1657784, _1657786] : [class_Complete__Lattice_Ocomplete__lattice(_1657780), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1657782, _1657780), hAPP(c_List_Oset(_1657782), _1657784)), _1657786) = hAPP(c_List_Ofoldl(_1657780, _1657782, hAPP(c_COMBC(_1657782, _1657780, _1657780), hAPP(hAPP(c_COMBB(_1657780, tc_fun(_1657780, _1657780), _1657782), c_Lattices_Osemilattice__sup__class_Osup(_1657780)), _1657786)), c_Orderings_Obot__class_Obot(_1657780)), _1657784))], (43915 ^ _779308) ^ [_1657951, _1657953, _1657955, _1657957] : [class_Complete__Lattice_Ocomplete__lattice(_1657951), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657953, _1657951), hAPP(c_List_Oset(_1657953), _1657955)), _1657957) = hAPP(c_List_Ofoldl(_1657951, _1657953, hAPP(c_COMBC(_1657953, _1657951, _1657951), hAPP(hAPP(c_COMBB(_1657951, tc_fun(_1657951, _1657951), _1657953), c_Lattices_Osemilattice__inf__class_Oinf(_1657951)), _1657957)), c_Orderings_Otop__class_Otop(_1657951)), _1657955))], (43921 ^ _779308) ^ [_1658122, _1658124] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1658122), hAPP(c_List_Oset(tc_Nat_Onat), _1658124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1658122), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1658124))))], (43927 ^ _779308) ^ [_1658231, _1658233, _1658235] : [class_Orderings_Olinorder(_1658231), hBOOL(hAPP(c_Finite__Set_Ofinite(_1658231), _1658233)), -(c_List_Olinorder__class_Osorted__list__of__set(_1658231, hAPP(hAPP(c_Set_Oinsert(_1658231), _1658235), _1658233)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658231, _1658231, c_COMBI(_1658231)), _1658235), c_List_Olinorder__class_Osorted__list__of__set(_1658231, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1658231, tc_HOL_Obool)), _1658233), hAPP(hAPP(c_Set_Oinsert(_1658231), _1658235), c_Orderings_Obot__class_Obot(tc_fun(_1658231, tc_HOL_Obool)))))))], (43937 ^ _779308) ^ [_1658488, _1658490, _1658492] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658488), tc_List_Olist(_1658488))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658488), tc_List_Olist(_1658488)), c_List_Olist_ONil(_1658488)), _1658490)), c_List_Olexord(_1658488, _1658492))), -(_1658490 = hAPP(hAPP(c_List_Olist_OCons(_1658488), 43940 ^ [_1658488, _1658490, _1658492]), 43941 ^ [_1658488, _1658490, _1658492]))], (43945 ^ _779308) ^ [_1658671, _1658673, _1658675] : [43946 ^ _779308 : [(43947 ^ _779308) ^ [_1658760, _1658762] : [_1658673 = hAPP(hAPP(c_List_Olist_OCons(_1658671), _1658762), _1658760)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658671), tc_List_Olist(_1658671))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658671), tc_List_Olist(_1658671)), c_List_Olist_ONil(_1658671)), _1658673)), c_List_Olexord(_1658671, _1658675))))], (43951 ^ _779308) ^ [_1658855, _1658857, _1658859, _1658861, _1658863, _1658865] : [class_Orderings_Olinorder(_1658855), 43954 ^ _779308 : [(43955 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1658855), hAPP(_1658857, _1658859)), hAPP(_1658857, _1658861))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658863, _1658855, _1658857), _1658859), hAPP(hAPP(c_List_Olist_OCons(_1658863), _1658861), _1658865)) = hAPP(hAPP(c_List_Olist_OCons(_1658863), _1658859), hAPP(hAPP(c_List_Olist_OCons(_1658863), _1658861), _1658865)))], (43961 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1658855), hAPP(_1658857, _1658859)), hAPP(_1658857, _1658861)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658863, _1658855, _1658857), _1658859), hAPP(hAPP(c_List_Olist_OCons(_1658863), _1658861), _1658865)) = hAPP(hAPP(c_List_Olist_OCons(_1658863), _1658861), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1658863, _1658855, _1658857), _1658859), _1658865)))]]], (43967 ^ _779308) ^ [_1659237, _1659239, _1659241, _1659243] : [class_Orderings_Olinorder(_1659237), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659239, _1659237, _1659241), _1659243), c_List_Olist_ONil(_1659239)) = hAPP(hAPP(c_List_Olist_OCons(_1659239), _1659243), c_List_Olist_ONil(_1659239)))], (43973 ^ _779308) ^ [_1659360, _1659362, _1659364, _1659366, _1659368] : [class_Orderings_Olinorder(_1659360), -(hAPP(c_List_Oset(_1659362), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659362, _1659360, _1659364), _1659366), _1659368)) = hAPP(hAPP(c_Set_Oinsert(_1659362), _1659366), hAPP(c_List_Oset(_1659362), _1659368)))], (43979 ^ _779308) ^ [_1659497, _1659499, _1659501, _1659503, _1659505] : [class_Orderings_Olinorder(_1659497), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659499)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659499, _1659497, _1659501), _1659503), _1659505)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659499)), _1659505)))], (43985 ^ _779308) ^ [_1659632] : [class_Orderings_Olinorder(_1659632), -(c_Finite__Set_Ofun__left__comm(_1659632, tc_List_Olist(_1659632), c_List_Olinorder__class_Oinsort__key(_1659632, _1659632, c_COMBI(_1659632))))], (43991 ^ _779308) ^ [_1659723, _1659725, _1659727, _1659729] : [class_Orderings_Olinorder(_1659723), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659723, _1659723, c_COMBI(_1659723)), _1659725), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659723, _1659723, c_COMBI(_1659723)), _1659727), _1659729)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659723, _1659723, c_COMBI(_1659723)), _1659727), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659723, _1659723, c_COMBI(_1659723)), _1659725), _1659729)))], (43997 ^ _779308) ^ [_1659898, _1659900, _1659902, _1659904, _1659906, _1659908] : [class_Orderings_Olinorder(_1659898), -(hAPP(_1659900, _1659902) = hAPP(_1659900, _1659904)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659906, _1659898, _1659900), _1659904), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659906, _1659898, _1659900), _1659902), _1659908)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659906, _1659898, _1659900), _1659902), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659906, _1659898, _1659900), _1659904), _1659908)))], (44007 ^ _779308) ^ [_1660088, _1660090, _1660092] : [class_Orderings_Olinorder(_1660088), -(c_List_Oremove1(_1660088, _1660090, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660088, _1660088, c_COMBI(_1660088)), _1660090), _1660092)) = _1660092)], (44013 ^ _779308) ^ [_1660197, _1660199, _1660201, _1660203, _1660205] : [class_Orderings_Olinorder(_1660197), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660199, _1660197, _1660201), _1660203), _1660205) = c_List_Olist_ONil(_1660199)], (44019 ^ _779308) ^ [_1660303, _1660305, _1660307, _1660309, _1660311] : [class_Orderings_Olinorder(_1660303), 44022 ^ _779308 : [(44023 ^ _779308) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1660305), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660305, _1660303, _1660307), _1660309), _1660311))), 44026 ^ _779308 : [(44027 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1660305), _1660309), hAPP(c_List_Oset(_1660305), _1660311)))], (44029 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1660305), _1660311)))]]], (44031 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1660305), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660305, _1660303, _1660307), _1660309), _1660311)))), -(hBOOL(hAPP(hAPP(c_member(_1660305), _1660309), hAPP(c_List_Oset(_1660305), _1660311)))), hBOOL(hAPP(c_List_Odistinct(_1660305), _1660311))]]], (44041 ^ _779308) ^ [_1660705, _1660707, _1660709, _1660711, _1660713] : [class_Orderings_Olinorder(_1660705), -(hBOOL(hAPP(hAPP(c_member(_1660705), hAPP(_1660707, _1660709)), hAPP(c_Set_Oimage(_1660711, _1660705, _1660707), hAPP(c_List_Oset(_1660711), _1660713))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1660711, _1660705, _1660707, _1660709, _1660713) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660711, _1660705, _1660707), _1660709), _1660713))], (44051 ^ _779308) ^ [_1660877, _1660879, _1660881] : [class_Orderings_Olinorder(_1660877), -(hBOOL(hAPP(hAPP(c_member(_1660877), _1660879), hAPP(c_List_Oset(_1660877), _1660881)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1660877, _1660877, c_COMBI(_1660877), _1660879, _1660881) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660877, _1660877, c_COMBI(_1660877)), _1660879), _1660881))], (44061 ^ _779308) ^ [_1661033, _1661035, _1661037, _1661039, _1661041] : [class_Orderings_Olinorder(_1661033), hBOOL(hAPP(c_List_Odistinct(_1661035), _1661037)), -(hBOOL(hAPP(c_List_Odistinct(_1661035), c_List_Olinorder__class_Oinsort__insert__key(_1661035, _1661033, _1661039, _1661041, _1661037))))], (44071 ^ _779308) ^ [_1661200, _1661202, _1661204] : [class_Orderings_Olinorder(_1661200), hBOOL(hAPP(hAPP(c_member(_1661200), _1661202), hAPP(c_List_Oset(_1661200), _1661204))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661200, _1661200, c_COMBI(_1661200), _1661202, _1661204) = _1661204)], (44081 ^ _779308) ^ [_1661371, _1661373, _1661375] : [class_Orderings_Olinorder(_1661371), -(hAPP(c_List_Oset(_1661371), c_List_Olinorder__class_Oinsort__insert__key(_1661371, _1661371, c_COMBI(_1661371), _1661373, _1661375)) = hAPP(hAPP(c_Set_Oinsert(_1661371), _1661373), hAPP(c_List_Oset(_1661371), _1661375)))], (44087 ^ _779308) ^ [_1661500, _1661502, _1661504, _1661506, _1661508] : [class_Orderings_Olinorder(_1661500), hBOOL(hAPP(hAPP(c_member(_1661500), hAPP(_1661502, _1661504)), hAPP(c_Set_Oimage(_1661506, _1661500, _1661502), hAPP(c_List_Oset(_1661506), _1661508)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661506, _1661500, _1661502, _1661504, _1661508) = _1661508)], (44097 ^ _779308) ^ [_1661694, _1661696, _1661698, _1661700] : [-(_1661694 = c_List_Olist_ONil(_1661696)), 44100 ^ _779308 : [(44101 ^ _779308) ^ [] : [_1661698 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661696)), _1661694)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1661696, hAPP(hAPP(c_List_Olist__update(_1661696, _1661694), _1661698), _1661700)) = _1661700)], (44107 ^ _779308) ^ [] : [-(_1661698 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661696)), _1661694)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1661696, hAPP(hAPP(c_List_Olist__update(_1661696, _1661694), _1661698), _1661700)) = c_List_Olast(_1661696, _1661694))]]], (44113 ^ _779308) ^ [_1661980, _1661982] : [-(_1661980 = c_List_Olist_ONil(_1661982)), -(c_List_Olast(_1661982, _1661980) = hAPP(hAPP(c_List_Onth(_1661982), _1661980), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661982)), _1661980)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (44119 ^ _779308) ^ [_1662054, _1662056, _1662058] : [_1662054 = c_List_Olist_ONil(_1662056), -(c_List_Olast(_1662056, hAPP(hAPP(c_List_Olist_OCons(_1662056), _1662058), _1662054)) = _1662058)], (44125 ^ _779308) ^ [_1662153, _1662155, _1662157] : [-(_1662153 = c_List_Olist_ONil(_1662155)), -(c_List_Olast(_1662155, hAPP(hAPP(c_List_Olist_OCons(_1662155), _1662157), _1662153)) = c_List_Olast(_1662155, _1662153))], (44131 ^ _779308) ^ [_1662205, _1662207, _1662209] : [-(_1662205 = c_List_Olist_ONil(_1662207)), -(c_List_Olast(_1662207, hAPP(hAPP(c_List_Olist_OCons(_1662207), _1662209), _1662205)) = c_List_Olast(_1662207, _1662205))], (44137 ^ _779308) ^ [_1662259, _1662261, _1662263] : [_1662259 = c_List_Olist_ONil(_1662261), -(c_List_Olast(_1662261, hAPP(hAPP(c_List_Olist_OCons(_1662261), _1662263), _1662259)) = _1662263)], (44143 ^ _779308) ^ [_1662376, _1662378, _1662380] : [_1662376 = c_List_Olist_ONil(_1662378), -(c_List_Olast(_1662378, hAPP(hAPP(c_List_Oappend(_1662378), _1662380), _1662376)) = c_List_Olast(_1662378, _1662380))], (44149 ^ _779308) ^ [_1662481, _1662483, _1662485] : [-(_1662481 = c_List_Olist_ONil(_1662483)), -(c_List_Olast(_1662483, hAPP(hAPP(c_List_Oappend(_1662483), _1662485), _1662481)) = c_List_Olast(_1662483, _1662481))], (44155 ^ _779308) ^ [_1662533, _1662535, _1662537] : [-(_1662533 = c_List_Olist_ONil(_1662535)), -(c_List_Olast(_1662535, hAPP(hAPP(c_List_Oappend(_1662535), _1662537), _1662533)) = c_List_Olast(_1662535, _1662533))], (44161 ^ _779308) ^ [_1662587, _1662589, _1662591] : [_1662587 = c_List_Olist_ONil(_1662589), -(c_List_Olast(_1662589, hAPP(hAPP(c_List_Oappend(_1662589), _1662591), _1662587)) = c_List_Olast(_1662589, _1662591))], (44167 ^ _779308) ^ [_1662694, _1662696] : [-(_1662694 = c_List_Olist_ONil(_1662696)), -(hBOOL(hAPP(hAPP(c_member(_1662696), c_List_Olast(_1662696, _1662694)), hAPP(c_List_Oset(_1662696), _1662694))))], (44173 ^ _779308) ^ [_1662747, _1662749, _1662751] : [-(c_List_Olast(_1662747, hAPP(hAPP(c_List_Oappend(_1662747), _1662749), hAPP(hAPP(c_List_Olist_OCons(_1662747), _1662751), c_List_Olist_ONil(_1662747)))) = _1662751)], (44175 ^ _779308) ^ [_1662795, _1662797, _1662799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662795), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662797)), _1662799))), -(c_List_Olast(_1662797, hAPP(hAPP(c_List_Odrop(_1662797), _1662795), _1662799)) = c_List_Olast(_1662797, _1662799))], (44181 ^ _779308) ^ [_1662922, _1662924] : [-(_1662922 = c_List_Olist_ONil(_1662924)), -(hAPP(hAPP(c_List_Oappend(_1662924), c_List_Obutlast(_1662924, _1662922)), hAPP(hAPP(c_List_Olist_OCons(_1662924), c_List_Olast(_1662924, _1662922)), c_List_Olist_ONil(_1662924))) = _1662922)], (44187 ^ _779308) ^ [_1663005, _1663007, _1663009, _1663011] : [hAPP(hAPP(c_List_Oappend(_1663005), _1663007), hAPP(hAPP(c_List_Olist_OCons(_1663005), _1663009), c_List_Olist_ONil(_1663005))) = _1663011, 44190 ^ _779308 : [(44191 ^ _779308) ^ [] : [_1663011 = c_List_Olist_ONil(_1663005)], (44193 ^ _779308) ^ [] : [-(c_List_Obutlast(_1663005, _1663011) = _1663007)], (44195 ^ _779308) ^ [] : [-(c_List_Olast(_1663005, _1663011) = _1663009)]]], (44197 ^ _779308) ^ [_1663194, _1663196, _1663198, _1663200] : [-(hAPP(hAPP(c_List_Oappend(_1663194), _1663196), hAPP(hAPP(c_List_Olist_OCons(_1663194), _1663198), c_List_Olist_ONil(_1663194))) = _1663200), -(_1663200 = c_List_Olist_ONil(_1663194)), c_List_Obutlast(_1663194, _1663200) = _1663196, c_List_Olast(_1663194, _1663200) = _1663198], (44211 ^ _779308) ^ [_1663462, _1663464, _1663466] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663462)), _1663464), c_List_Olists(_1663462, _1663466))), -(_1663464 = c_List_Olist_ONil(_1663462)), 44220 ^ _779308 : [(44221 ^ _779308) ^ [] : [-(_1663464 = hAPP(hAPP(c_List_Olist_OCons(_1663462), 44218 ^ [_1663462, _1663464, _1663466]), 44219 ^ [_1663462, _1663464, _1663466]))], (44223 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1663462), 44218 ^ [_1663462, _1663464, _1663466]), _1663466)))], (44225 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663462)), 44219 ^ [_1663462, _1663464, _1663466]), c_List_Olists(_1663462, _1663466))))]]], (44227 ^ _779308) ^ [_1663745, _1663747, _1663749] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663745)), _1663747), c_List_Olists(_1663745, _1663749)))), 44228 ^ _779308 : [(44229 ^ _779308) ^ [] : [_1663747 = c_List_Olist_ONil(_1663745)], (44231 ^ _779308) ^ [_1663873, _1663875] : [_1663747 = hAPP(hAPP(c_List_Olist_OCons(_1663745), _1663875), _1663873), hBOOL(hAPP(hAPP(c_member(_1663745), _1663875), _1663749)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1663745)), _1663873), c_List_Olists(_1663745, _1663749)))]]], (44243 ^ _779308) ^ [_1664107, _1664109] : [-(_1664107 = c_List_Olist_ONil(_1664109)), -(c_Random_Oselect__weight(_1664109, hAPP(hAPP(c_List_Omap(_1664109, tc_prod(tc_Code__Numeral_Ocode__numeral, _1664109)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1664109), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1664107)) = c_Random_Oselect(_1664109, _1664107))], (44249 ^ _779308) ^ [_1664169, _1664171, _1664173] : [c_Fun_Oinj__on(_1664169, _1664171, _1664173, c_Orderings_Otop__class_Otop(tc_fun(_1664169, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1664169), tc_List_Olist(_1664171), hAPP(c_List_Omap(_1664169, _1664171), _1664173), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1664169), tc_HOL_Obool))))], (44255 ^ _779308) ^ [_1664296, _1664298, _1664300, _1664302] : [-(_1664296 = c_List_Olist_ONil(_1664298)), -(c_List_Olast(_1664300, hAPP(hAPP(c_List_Omap(_1664298, _1664300), _1664302), _1664296)) = hAPP(_1664302, c_List_Olast(_1664298, _1664296)))], (44261 ^ _779308) ^ [_1664356, _1664358, _1664360, _1664362, _1664364, _1664366, _1664368] : [-(hAPP(c_List_Ofoldl(_1664356, _1664358, _1664360, _1664362), hAPP(hAPP(c_List_Omap(_1664364, _1664358), _1664366), _1664368)) = hAPP(c_List_Ofoldl(_1664356, _1664364, hAPP(hAPP(c_COMBC(_1664356, tc_fun(_1664364, _1664358), tc_fun(_1664364, _1664356)), hAPP(hAPP(c_COMBB(tc_fun(_1664358, _1664356), tc_fun(tc_fun(_1664364, _1664358), tc_fun(_1664364, _1664356)), _1664356), c_COMBB(_1664358, _1664356, _1664364)), _1664360)), _1664366), _1664362), _1664368))], (44263 ^ _779308) ^ [_1664458, _1664460, _1664462, _1664464, _1664466] : [-(hAPP(c_List_Orotate(_1664458, _1664460), hAPP(hAPP(c_List_Omap(_1664462, _1664458), _1664464), _1664466)) = hAPP(hAPP(c_List_Omap(_1664462, _1664458), _1664464), hAPP(c_List_Orotate(_1664462, _1664460), _1664466)))], (44265 ^ _779308) ^ [_1664519, _1664521, _1664523, _1664525] : [-(hAPP(hAPP(c_List_Omap(_1664519, _1664521), _1664523), hAPP(c_List_Otl(_1664519), _1664525)) = hAPP(c_List_Otl(_1664521), hAPP(hAPP(c_List_Omap(_1664519, _1664521), _1664523), _1664525)))], (44267 ^ _779308) ^ [_1664576, _1664578, _1664580, _1664582, _1664584, _1664586] : [-(hAPP(hAPP(c_List_Ozip(_1664576, _1664578), _1664580), hAPP(hAPP(c_List_Omap(_1664582, _1664578), _1664584), _1664586)) = hAPP(hAPP(c_List_Omap(tc_prod(_1664576, _1664582), tc_prod(_1664576, _1664578)), hAPP(c_Product__Type_Oprod_Oprod__case(_1664576, _1664582, tc_prod(_1664576, _1664578)), hAPP(hAPP(c_COMBC(_1664576, tc_fun(_1664582, _1664578), tc_fun(_1664582, tc_prod(_1664576, _1664578))), hAPP(hAPP(c_COMBB(tc_fun(_1664578, tc_prod(_1664576, _1664578)), tc_fun(tc_fun(_1664582, _1664578), tc_fun(_1664582, tc_prod(_1664576, _1664578))), _1664576), c_COMBB(_1664578, tc_prod(_1664576, _1664578), _1664582)), c_Product__Type_OPair(_1664576, _1664578))), _1664584))), hAPP(hAPP(c_List_Ozip(_1664576, _1664582), _1664580), _1664586)))], (44269 ^ _779308) ^ [_1664718, _1664720, _1664722, _1664724, _1664726, _1664728, _1664730, _1664732] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1664718, _1664720), _1664722), _1664724), hAPP(hAPP(c_List_Ozip(_1664718, _1664720), _1664726), hAPP(hAPP(c_List_Omap(_1664728, _1664720), _1664730), _1664732))) = hAPP(hAPP(c_List_Omap(tc_prod(_1664718, _1664728), _1664722), hAPP(c_Product__Type_Oprod_Oprod__case(_1664718, _1664728, _1664722), hAPP(hAPP(c_COMBB(tc_fun(_1664728, tc_prod(_1664718, _1664720)), tc_fun(_1664728, _1664722), _1664718), hAPP(c_COMBB(tc_prod(_1664718, _1664720), _1664722, _1664728), _1664724)), hAPP(hAPP(c_COMBC(_1664718, tc_fun(_1664728, _1664720), tc_fun(_1664728, tc_prod(_1664718, _1664720))), hAPP(hAPP(c_COMBB(tc_fun(_1664720, tc_prod(_1664718, _1664720)), tc_fun(tc_fun(_1664728, _1664720), tc_fun(_1664728, tc_prod(_1664718, _1664720))), _1664718), c_COMBB(_1664720, tc_prod(_1664718, _1664720), _1664728)), c_Product__Type_OPair(_1664718, _1664720))), _1664730)))), hAPP(hAPP(c_List_Ozip(_1664718, _1664728), _1664726), _1664732)))], (44271 ^ _779308) ^ [_1664899, _1664901, _1664903, _1664905, _1664907, _1664909, _1664911, _1664913] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1664899, _1664901), _1664903), _1664905), hAPP(hAPP(c_List_Ozip(_1664899, _1664901), hAPP(hAPP(c_List_Omap(_1664907, _1664899), _1664909), _1664911)), _1664913)) = hAPP(hAPP(c_List_Omap(tc_prod(_1664907, _1664901), _1664903), hAPP(c_Product__Type_Oprod_Oprod__case(_1664907, _1664901, _1664903), hAPP(hAPP(c_COMBB(tc_fun(_1664901, tc_prod(_1664899, _1664901)), tc_fun(_1664901, _1664903), _1664907), hAPP(c_COMBB(tc_prod(_1664899, _1664901), _1664903, _1664901), _1664905)), hAPP(hAPP(c_COMBB(_1664899, tc_fun(_1664901, tc_prod(_1664899, _1664901)), _1664907), c_Product__Type_OPair(_1664899, _1664901)), _1664909)))), hAPP(hAPP(c_List_Ozip(_1664907, _1664901), _1664911), _1664913)))], (44273 ^ _779308) ^ [_1665042, _1665044, _1665046, _1665048, _1665050, _1665052] : [-(hAPP(hAPP(c_List_Ozip(_1665042, _1665044), hAPP(hAPP(c_List_Omap(_1665046, _1665042), _1665048), _1665050)), _1665052) = hAPP(hAPP(c_List_Omap(tc_prod(_1665046, _1665044), tc_prod(_1665042, _1665044)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665046, _1665044, tc_prod(_1665042, _1665044)), hAPP(hAPP(c_COMBB(_1665042, tc_fun(_1665044, tc_prod(_1665042, _1665044)), _1665046), c_Product__Type_OPair(_1665042, _1665044)), _1665048))), hAPP(hAPP(c_List_Ozip(_1665046, _1665044), _1665050), _1665052)))], (44275 ^ _779308) ^ [_1665146, _1665148, _1665150, _1665152, _1665154, _1665156, _1665158, _1665160] : [-(hAPP(hAPP(c_List_Ozip(_1665146, _1665148), hAPP(hAPP(c_List_Omap(_1665150, _1665146), _1665152), _1665154)), hAPP(hAPP(c_List_Omap(_1665156, _1665148), _1665158), _1665160)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665150, _1665156), tc_prod(_1665146, _1665148)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665150, _1665156, tc_prod(_1665146, _1665148)), hAPP(hAPP(c_COMBC(_1665150, tc_fun(_1665156, _1665148), tc_fun(_1665156, tc_prod(_1665146, _1665148))), hAPP(hAPP(c_COMBB(tc_fun(_1665148, tc_prod(_1665146, _1665148)), tc_fun(tc_fun(_1665156, _1665148), tc_fun(_1665156, tc_prod(_1665146, _1665148))), _1665150), c_COMBB(_1665148, tc_prod(_1665146, _1665148), _1665156)), hAPP(hAPP(c_COMBB(_1665146, tc_fun(_1665148, tc_prod(_1665146, _1665148)), _1665150), c_Product__Type_OPair(_1665146, _1665148)), _1665152))), _1665158))), hAPP(hAPP(c_List_Ozip(_1665150, _1665156), _1665154), _1665160)))], (44277 ^ _779308) ^ [_1665317, _1665319] : [-(hAPP(hAPP(c_List_Ozip(_1665317, _1665317), _1665319), _1665319) = hAPP(hAPP(c_List_Omap(_1665317, tc_prod(_1665317, _1665317)), hAPP(hAPP(c_COMBS(_1665317, _1665317, tc_prod(_1665317, _1665317)), c_Product__Type_OPair(_1665317, _1665317)), c_COMBI(_1665317))), _1665319))], (44279 ^ _779308) ^ [_1665402, _1665404, _1665406, _1665408] : [hAPP(hAPP(c_List_Omap(_1665402, _1665404), _1665406), _1665408) = c_List_Olist_ONil(_1665404), -(_1665408 = c_List_Olist_ONil(_1665402))], (44285 ^ _779308) ^ [_1665505, _1665507, _1665509, _1665511] : [_1665511 = c_List_Olist_ONil(_1665505), -(hAPP(hAPP(c_List_Omap(_1665505, _1665507), _1665509), _1665511) = c_List_Olist_ONil(_1665507))], (44291 ^ _779308) ^ [_1665614, _1665616, _1665618] : [-(hAPP(hAPP(c_List_Omap(_1665614, _1665616), _1665618), c_List_Olist_ONil(_1665614)) = c_List_Olist_ONil(_1665616))], (44293 ^ _779308) ^ [_1665675, _1665677, _1665679, _1665681] : [c_List_Olist_ONil(_1665675) = hAPP(hAPP(c_List_Omap(_1665677, _1665675), _1665679), _1665681), -(_1665681 = c_List_Olist_ONil(_1665677))], (44299 ^ _779308) ^ [_1665778, _1665780, _1665782, _1665784] : [_1665784 = c_List_Olist_ONil(_1665780), -(c_List_Olist_ONil(_1665778) = hAPP(hAPP(c_List_Omap(_1665780, _1665778), _1665782), _1665784))], (44305 ^ _779308) ^ [_1665887, _1665889, _1665891, _1665893, _1665895, _1665897] : [-(hAPP(hAPP(c_List_Omap(_1665887, _1665889), _1665891), hAPP(hAPP(c_List_Olist__update(_1665887, _1665893), _1665895), _1665897)) = hAPP(hAPP(c_List_Olist__update(_1665889, hAPP(hAPP(c_List_Omap(_1665887, _1665889), _1665891), _1665893)), _1665895), hAPP(_1665891, _1665897)))], (44317 ^ _779308) ^ [_1666227, _1666229, _1666231, _1666233, _1666235] : [44319 ^ _779308 : [(44320 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1666227), 44318 ^ [_1666227, _1666229, _1666231, _1666233, _1666235]), hAPP(c_List_Oset(_1666227), _1666233))))], (44322 ^ _779308) ^ [] : [hAPP(_1666231, 44318 ^ [_1666227, _1666229, _1666231, _1666233, _1666235]) = hAPP(_1666235, 44318 ^ [_1666227, _1666229, _1666231, _1666233, _1666235])]], -(hAPP(hAPP(c_List_Omap(_1666227, _1666229), _1666231), _1666233) = hAPP(hAPP(c_List_Omap(_1666227, _1666229), _1666235), _1666233))], (44307 ^ _779308) ^ [_1665983, _1665985, _1665987, _1665989, _1665991] : [hAPP(hAPP(c_List_Omap(_1665983, _1665985), _1665987), _1665989) = hAPP(hAPP(c_List_Omap(_1665983, _1665985), _1665991), _1665989), 44310 ^ _779308 : [(44311 ^ _779308) ^ [_1666106] : [hBOOL(hAPP(hAPP(c_member(_1665983), _1666106), hAPP(c_List_Oset(_1665983), _1665989))), -(hAPP(_1665987, _1666106) = hAPP(_1665991, _1666106))]]], (44326 ^ _779308) ^ [_1666484, _1666486, _1666488, _1666490] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666484)), hAPP(hAPP(c_List_Omap(_1666486, _1666484), _1666488), _1666490)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666486)), _1666490))], (44328 ^ _779308) ^ [_1666536, _1666538, _1666540, _1666542, _1666544, _1666546, _1666548] : [hAPP(hAPP(c_List_Omap(_1666536, _1666538), _1666540), _1666542) = hAPP(hAPP(c_List_Omap(_1666544, _1666538), _1666546), _1666548), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666536)), _1666542) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1666544)), _1666548))], (44334 ^ _779308) ^ [_1666687, _1666689, _1666691] : [class_Groups_Omonoid__add(_1666687), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1666687), hAPP(hAPP(c_List_Omap(_1666689, _1666687), hAPP(c_COMBK(_1666687, _1666689), c_Groups_Ozero__class_Ozero(_1666687))), _1666691)) = c_Groups_Ozero__class_Ozero(_1666687))], (44340 ^ _779308) ^ [_1666812, _1666814, _1666816, _1666818, _1666820] : [class_Rings_Osemiring__0(_1666812), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1666812), hAPP(hAPP(c_List_Omap(_1666814, _1666812), hAPP(hAPP(c_COMBC(_1666814, _1666812, _1666812), hAPP(hAPP(c_COMBB(_1666812, tc_fun(_1666812, _1666812), _1666814), c_Groups_Otimes__class_Otimes(_1666812)), _1666816)), _1666818)), _1666820)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1666812), hAPP(c_List_Omonoid__add__class_Olistsum(_1666812), hAPP(hAPP(c_List_Omap(_1666814, _1666812), _1666816), _1666820))), _1666818))], (44346 ^ _779308) ^ [_1667015, _1667017, _1667019, _1667021, _1667023] : [class_Rings_Osemiring__0(_1667015), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667015), hAPP(hAPP(c_List_Omap(_1667017, _1667015), hAPP(hAPP(c_COMBB(_1667015, _1667015, _1667017), hAPP(c_Groups_Otimes__class_Otimes(_1667015), _1667019)), _1667021)), _1667023)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1667015), _1667019), hAPP(c_List_Omonoid__add__class_Olistsum(_1667015), hAPP(hAPP(c_List_Omap(_1667017, _1667015), _1667021), _1667023))))], (44352 ^ _779308) ^ [_1667198, _1667200, _1667202, _1667204, _1667206] : [class_Groups_Oab__group__add(_1667198), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667198), hAPP(hAPP(c_List_Omap(_1667200, _1667198), hAPP(hAPP(c_COMBS(_1667200, _1667198, _1667198), hAPP(hAPP(c_COMBB(_1667198, tc_fun(_1667198, _1667198), _1667200), c_Groups_Ominus__class_Ominus(_1667198)), _1667202)), _1667204)), _1667206)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1667198), hAPP(c_List_Omonoid__add__class_Olistsum(_1667198), hAPP(hAPP(c_List_Omap(_1667200, _1667198), _1667202), _1667206))), hAPP(c_List_Omonoid__add__class_Olistsum(_1667198), hAPP(hAPP(c_List_Omap(_1667200, _1667198), _1667204), _1667206))))], (44358 ^ _779308) ^ [_1667429, _1667431, _1667433, _1667435, _1667437] : [class_Groups_Ocomm__monoid__add(_1667429), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667429), hAPP(hAPP(c_List_Omap(_1667431, _1667429), hAPP(hAPP(c_COMBS(_1667431, _1667429, _1667429), hAPP(hAPP(c_COMBB(_1667429, tc_fun(_1667429, _1667429), _1667431), c_Groups_Oplus__class_Oplus(_1667429)), _1667433)), _1667435)), _1667437)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1667429), hAPP(c_List_Omonoid__add__class_Olistsum(_1667429), hAPP(hAPP(c_List_Omap(_1667431, _1667429), _1667433), _1667437))), hAPP(c_List_Omonoid__add__class_Olistsum(_1667429), hAPP(hAPP(c_List_Omap(_1667431, _1667429), _1667435), _1667437))))], (44364 ^ _779308) ^ [_1667660, _1667662, _1667664, _1667666, _1667668] : [hAPP(hAPP(c_List_Omap(_1667660, _1667662), _1667664), _1667666) = hAPP(hAPP(c_List_Omap(_1667660, _1667662), _1667664), _1667668), c_Fun_Oinj__on(_1667660, _1667662, _1667664, c_Orderings_Otop__class_Otop(tc_fun(_1667660, tc_HOL_Obool))), -(_1667666 = _1667668)], (44374 ^ _779308) ^ [_1667851, _1667853, _1667855, _1667857, _1667859] : [c_Fun_Oinj__on(_1667851, _1667853, _1667855, c_Orderings_Otop__class_Otop(tc_fun(_1667851, tc_HOL_Obool))), 44377 ^ _779308 : [(44378 ^ _779308) ^ [] : [hAPP(hAPP(c_List_Omap(_1667851, _1667853), _1667855), _1667857) = hAPP(hAPP(c_List_Omap(_1667851, _1667853), _1667855), _1667859), -(_1667857 = _1667859)], (44384 ^ _779308) ^ [] : [_1667857 = _1667859, -(hAPP(hAPP(c_List_Omap(_1667851, _1667853), _1667855), _1667857) = hAPP(hAPP(c_List_Omap(_1667851, _1667853), _1667855), _1667859))]]], (44390 ^ _779308) ^ [_1668144, _1668146] : [-(hAPP(hAPP(c_List_Omap(_1668144, _1668144), c_COMBI(_1668144)), _1668146) = _1668146)], (44392 ^ _779308) ^ [_1668180, _1668182, _1668184, _1668186, _1668188] : [-(hAPP(hAPP(c_List_Otake(_1668180), _1668182), hAPP(hAPP(c_List_Omap(_1668184, _1668180), _1668186), _1668188)) = hAPP(hAPP(c_List_Omap(_1668184, _1668180), _1668186), hAPP(hAPP(c_List_Otake(_1668184), _1668182), _1668188)))], (44394 ^ _779308) ^ [_1668245, _1668247, _1668249, _1668251] : [-(hAPP(hAPP(c_List_Omap(_1668245, _1668247), _1668249), c_List_Obutlast(_1668245, _1668251)) = c_List_Obutlast(_1668247, hAPP(hAPP(c_List_Omap(_1668245, _1668247), _1668249), _1668251)))], (44396 ^ _779308) ^ [_1668298, _1668300, _1668302, _1668304] : [-(hAPP(c_List_Oset(_1668298), hAPP(hAPP(c_List_Omap(_1668300, _1668298), _1668302), _1668304)) = hAPP(c_Set_Oimage(_1668300, _1668298, _1668302), hAPP(c_List_Oset(_1668300), _1668304)))], (44398 ^ _779308) ^ [_1668353, _1668355, _1668357, _1668359, _1668361] : [-(hAPP(hAPP(c_List_Omap(_1668353, _1668355), _1668357), hAPP(hAPP(c_List_Olist_OCons(_1668353), _1668359), _1668361)) = hAPP(hAPP(c_List_Olist_OCons(_1668355), hAPP(_1668357, _1668359)), hAPP(hAPP(c_List_Omap(_1668353, _1668355), _1668357), _1668361)))], (44400 ^ _779308) ^ [_1668421, _1668423, _1668425, _1668427, _1668429] : [-(hAPP(hAPP(c_List_Omap(_1668421, _1668423), _1668425), hAPP(hAPP(c_List_Oappend(_1668421), _1668427), _1668429)) = hAPP(hAPP(c_List_Oappend(_1668423), hAPP(hAPP(c_List_Omap(_1668421, _1668423), _1668425), _1668427)), hAPP(hAPP(c_List_Omap(_1668421, _1668423), _1668425), _1668429)))], (44402 ^ _779308) ^ [_1668491, _1668493, _1668495, _1668497] : [-(_1668491 = c_List_Olist_ONil(_1668493)), -(hAPP(c_List_Ohd(_1668495), hAPP(hAPP(c_List_Omap(_1668493, _1668495), _1668497), _1668491)) = hAPP(_1668497, hAPP(c_List_Ohd(_1668493), _1668491)))], (44408 ^ _779308) ^ [_1668555, _1668557, _1668559, _1668561, _1668563] : [-(hAPP(hAPP(c_List_Odrop(_1668555), _1668557), hAPP(hAPP(c_List_Omap(_1668559, _1668555), _1668561), _1668563)) = hAPP(hAPP(c_List_Omap(_1668559, _1668555), _1668561), hAPP(hAPP(c_List_Odrop(_1668559), _1668557), _1668563)))], (44410 ^ _779308) ^ [_1668620, _1668622, _1668624, _1668626, _1668628] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1668620), tc_List_Olist(_1668622), tc_List_Olist(_1668624), hAPP(c_List_Omap(_1668620, _1668622), _1668626)), hAPP(c_List_Omap(_1668624, _1668620), _1668628)) = hAPP(c_List_Omap(_1668624, _1668622), hAPP(c_Fun_Ocomp(_1668620, _1668622, _1668624, _1668626), _1668628)))], (44412 ^ _779308) ^ [_1668691, _1668693, _1668695, _1668697, _1668699] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1668691), tc_List_Olist(_1668693), tc_List_Olist(_1668695), hAPP(c_List_Omap(_1668691, _1668693), _1668697)), hAPP(c_List_Omap(_1668695, _1668691), _1668699)) = hAPP(c_List_Omap(_1668695, _1668693), hAPP(c_Fun_Ocomp(_1668691, _1668693, _1668695, _1668697), _1668699)))], (44414 ^ _779308) ^ [_1668762, _1668764, _1668766, _1668768, _1668770, _1668772] : [-(hAPP(hAPP(c_List_Omap(_1668762, _1668764), _1668766), hAPP(hAPP(c_List_Omap(_1668768, _1668762), _1668770), _1668772)) = hAPP(hAPP(c_List_Omap(_1668768, _1668764), hAPP(c_Fun_Ocomp(_1668762, _1668764, _1668768, _1668766), _1668770)), _1668772))], (44416 ^ _779308) ^ [_1668830, _1668832, _1668834, _1668836, _1668838, _1668840] : [-(hAPP(hAPP(c_List_Omap(_1668830, _1668832), _1668834), hAPP(hAPP(c_List_Omap(_1668836, _1668830), _1668838), _1668840)) = hAPP(hAPP(c_List_Omap(_1668836, _1668832), hAPP(c_Fun_Ocomp(_1668830, _1668832, _1668836, _1668834), _1668838)), _1668840))], (44418 ^ _779308) ^ [_1668898] : [-(hAPP(c_List_Omap(_1668898, _1668898), c_COMBI(_1668898)) = c_Fun_Oid(tc_List_Olist(_1668898)))], (44420 ^ _779308) ^ [_1668933, _1668935, _1668937, _1668939, _1668941] : [-(c_List_Olist_Olist__size(_1668933, _1668935, hAPP(hAPP(c_List_Omap(_1668937, _1668933), _1668939), _1668941)) = c_List_Olist_Olist__size(_1668937, hAPP(c_Fun_Ocomp(_1668933, tc_Nat_Onat, _1668937, _1668935), _1668939), _1668941))], (44422 ^ _779308) ^ [_1668989] : [-(hAPP(c_List_Omap(_1668989, _1668989), c_Fun_Oid(_1668989)) = c_Fun_Oid(tc_List_Olist(_1668989)))], (44424 ^ _779308) ^ [_1669024, _1669026, _1669028, _1669030, _1669032] : [c_Fun_Oinj__on(_1669024, _1669026, _1669028, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669024, tc_HOL_Obool)), hAPP(c_List_Oset(_1669024), _1669030)), hAPP(c_List_Oset(_1669024), _1669032))), 44427 ^ _779308 : [(44428 ^ _779308) ^ [] : [hAPP(hAPP(c_List_Omap(_1669024, _1669026), _1669028), _1669030) = hAPP(hAPP(c_List_Omap(_1669024, _1669026), _1669028), _1669032), -(_1669030 = _1669032)], (44434 ^ _779308) ^ [] : [_1669030 = _1669032, -(hAPP(hAPP(c_List_Omap(_1669024, _1669026), _1669028), _1669030) = hAPP(hAPP(c_List_Omap(_1669024, _1669026), _1669028), _1669032))]]], (44440 ^ _779308) ^ [_1669349, _1669351, _1669353, _1669355, _1669357] : [hAPP(hAPP(c_List_Omap(_1669349, _1669351), _1669353), _1669355) = hAPP(hAPP(c_List_Omap(_1669349, _1669351), _1669353), _1669357), c_Fun_Oinj__on(_1669349, _1669351, _1669353, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669349, tc_HOL_Obool)), hAPP(c_List_Oset(_1669349), _1669355)), hAPP(c_List_Oset(_1669349), _1669357))), -(_1669355 = _1669357)], (44450 ^ _779308) ^ [_1669572, _1669574, _1669576, _1669578, _1669580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1669572), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669574)), _1669576))), -(hAPP(hAPP(c_List_Onth(_1669578), hAPP(hAPP(c_List_Omap(_1669574, _1669578), _1669580), _1669576)), _1669572) = hAPP(_1669580, hAPP(hAPP(c_List_Onth(_1669574), _1669576), _1669572)))], (44456 ^ _779308) ^ [_1669731, _1669733, _1669735, _1669737, _1669739, _1669741] : [-(hBOOL(hAPP(hAPP(c_member(_1669731), _1669733), hAPP(c_List_Oset(_1669731), _1669735)))), -(hAPP(hAPP(c_List_Omap(_1669731, _1669737), c_Fun_Ofun__upd(_1669731, _1669737, _1669739, _1669733, _1669741)), _1669735) = hAPP(hAPP(c_List_Omap(_1669731, _1669737), _1669739), _1669735))], (44462 ^ _779308) ^ [_1669832, _1669834, _1669836, _1669838] : [hBOOL(hAPP(c_List_Odistinct(_1669832), hAPP(hAPP(c_List_Omap(_1669834, _1669832), _1669836), _1669838))), 44465 ^ _779308 : [(44466 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1669834), _1669838)))], (44468 ^ _779308) ^ [] : [-(c_Fun_Oinj__on(_1669834, _1669832, _1669836, hAPP(c_List_Oset(_1669834), _1669838)))]]], (44470 ^ _779308) ^ [_1669983, _1669985, _1669987, _1669989] : [-(hBOOL(hAPP(c_List_Odistinct(_1669983), hAPP(hAPP(c_List_Omap(_1669985, _1669983), _1669987), _1669989)))), hBOOL(hAPP(c_List_Odistinct(_1669985), _1669989)), c_Fun_Oinj__on(_1669985, _1669983, _1669987, hAPP(c_List_Oset(_1669985), _1669989))], (44480 ^ _779308) ^ [_1670170, _1670172] : [class_Groups_Oordered__ab__group__add__abs(_1670170), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1670170), hAPP(c_Groups_Oabs__class_Oabs(_1670170), hAPP(c_List_Omonoid__add__class_Olistsum(_1670170), _1670172))), hAPP(c_List_Omonoid__add__class_Olistsum(_1670170), hAPP(hAPP(c_List_Omap(_1670170, _1670170), c_Groups_Oabs__class_Oabs(_1670170)), _1670172)))))], (44486 ^ _779308) ^ [_1670311, _1670313, _1670315, _1670317] : [class_Groups_Oab__group__add(_1670311), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1670311), hAPP(c_List_Omonoid__add__class_Olistsum(_1670311), hAPP(hAPP(c_List_Omap(_1670313, _1670311), _1670315), _1670317))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1670311), hAPP(hAPP(c_List_Omap(_1670313, _1670311), hAPP(c_Fun_Ocomp(_1670311, _1670311, _1670313, c_Groups_Ouminus__class_Ouminus(_1670311)), _1670315)), _1670317)))], (44492 ^ _779308) ^ [_1670476, _1670478, _1670480, _1670482] : [c_Fun_Oinj__on(_1670476, _1670478, _1670480, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1670476, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1670476), tc_fun(_1670476, tc_HOL_Obool), c_List_Oset(_1670476)), _1670482))), -(c_Fun_Oinj__on(tc_List_Olist(_1670476), tc_List_Olist(_1670478), hAPP(c_List_Omap(_1670476, _1670478), _1670480), _1670482))], (44498 ^ _779308) ^ [_1670643, _1670645, _1670647] : [c_Fun_Oinj__on(tc_List_Olist(_1670643), tc_List_Olist(_1670645), hAPP(c_List_Omap(_1670643, _1670645), _1670647), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1670643), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1670643, _1670645, _1670647, c_Orderings_Otop__class_Otop(tc_fun(_1670643, tc_HOL_Obool))))], (44504 ^ _779308) ^ [_1670770, _1670772, _1670774] : [c_Fun_Oinj__on(_1670770, _1670772, _1670774, c_Orderings_Otop__class_Otop(tc_fun(_1670770, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1670770), tc_List_Olist(_1670772), hAPP(c_List_Omap(_1670770, _1670772), _1670774), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1670770), tc_HOL_Obool))))], (44510 ^ _779308) ^ [_1670903, _1670905, _1670907] : [c_Fun_Oinj__on(tc_List_Olist(_1670903), tc_List_Olist(_1670905), hAPP(c_List_Omap(_1670903, _1670905), _1670907), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1670903), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1670903, _1670905, _1670907, c_Orderings_Otop__class_Otop(tc_fun(_1670903, tc_HOL_Obool))))], (44516 ^ _779308) ^ [_1671034, _1671036, _1671038, _1671040] : [class_Groups_Ocomm__monoid__add(_1671034), hBOOL(hAPP(c_List_Odistinct(_1671036), _1671038)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671034), hAPP(hAPP(c_List_Omap(_1671036, _1671034), _1671040), _1671038)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1671036, _1671034), _1671040), hAPP(c_List_Oset(_1671036), _1671038)))], (44526 ^ _779308) ^ [_1671233, _1671235, _1671237, _1671239] : [class_Rings_Osemiring__1(_1671233), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671233), hAPP(hAPP(c_List_Omap(_1671235, _1671233), hAPP(c_COMBK(_1671233, _1671235), _1671237)), _1671239)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1671233), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1671233), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671235)), _1671239))), _1671237))], (44532 ^ _779308) ^ [_1671392, _1671394, _1671396, _1671398, _1671400] : [class_Groups_Ocomm__monoid__add(_1671392), hBOOL(hAPP(hAPP(c_member(_1671394), _1671396), hAPP(c_List_Oset(_1671394), _1671398))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671392), hAPP(hAPP(c_List_Omap(_1671394, _1671392), _1671400), _1671398)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1671392), hAPP(_1671400, _1671396)), hAPP(c_List_Omonoid__add__class_Olistsum(_1671392), hAPP(hAPP(c_List_Omap(_1671394, _1671392), _1671400), c_List_Oremove1(_1671394, _1671396, _1671398)))))], (44542 ^ _779308) ^ [_1671641, _1671643, _1671645, _1671647] : [class_Groups_Ocomm__monoid__add(_1671641), 44545 ^ _779308 : [(44546 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1671643), _1671645)), -(c_Nitpick_Osetsum_H(_1671643, _1671641, _1671647, _1671645) = hAPP(c_List_Omonoid__add__class_Olistsum(_1671641), hAPP(hAPP(c_List_Omap(_1671643, _1671641), _1671647), c_Hilbert__Choice_OEps(tc_List_Olist(_1671643), hAPP(hAPP(c_COMBS(tc_List_Olist(_1671643), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1671643)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1671643), tc_fun(_1671643, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1671643, tc_HOL_Obool), tc_fun(tc_fun(_1671643, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1671643)), c_fequal), c_List_Oset(_1671643))), _1671645))), c_List_Odistinct(_1671643))))))], (44552 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1671643), _1671645))), -(c_Nitpick_Osetsum_H(_1671643, _1671641, _1671647, _1671645) = c_Groups_Ozero__class_Ozero(_1671641))]]], (44558 ^ _779308) ^ [_1672029, _1672031, _1672033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672029), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672031)), _1672033))), -(hAPP(c_Random_Opick(_1672031, hAPP(hAPP(c_List_Omap(_1672031, tc_prod(tc_Code__Numeral_Ocode__numeral, _1672031)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1672031), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1672033)), hAPP(c_Code__Numeral_Oof__nat, _1672029)) = hAPP(hAPP(c_List_Onth(_1672031), _1672033), _1672029))], (44564 ^ _779308) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44566 ^ _779308) ^ [_1672220, _1672222] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1672220)), hAPP(c_Code__Numeral_Oof__nat, _1672222)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1672220), _1672222)))], (44568 ^ _779308) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (44570 ^ _779308) ^ [_1672299, _1672301] : [hAPP(c_Code__Numeral_Oof__nat, _1672299) = hAPP(c_Code__Numeral_Oof__nat, _1672301), -(_1672299 = _1672301)], (44576 ^ _779308) ^ [_1672384, _1672386] : [_1672384 = _1672386, -(hAPP(c_Code__Numeral_Oof__nat, _1672384) = hAPP(c_Code__Numeral_Oof__nat, _1672386))], (44582 ^ _779308) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44584 ^ _779308) ^ [_1672508, _1672510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1672508)), hAPP(c_Code__Numeral_Oof__nat, _1672510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672508), _1672510)))], (44590 ^ _779308) ^ [_1672613, _1672615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672613), _1672615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1672613)), hAPP(c_Code__Numeral_Oof__nat, _1672615))))], (44596 ^ _779308) ^ [_1672724, _1672726] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1672724), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1672726), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 44603 ^ _779308 : [(44604 ^ _779308) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1672724) = hAPP(c_Code__Numeral_Oof__nat, _1672726), -(_1672724 = _1672726)], (44610 ^ _779308) ^ [] : [_1672724 = _1672726, -(hAPP(c_Code__Numeral_Oof__nat, _1672724) = hAPP(c_Code__Numeral_Oof__nat, _1672726))]]], (44616 ^ _779308) ^ [_1673021, _1673023, _1673025, _1673027] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673021)), _1673023) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673025)), _1673027), -(hAPP(hAPP(c_List_Omap(tc_prod(_1673021, _1673025), _1673021), c_Product__Type_Ofst(_1673021, _1673025)), hAPP(hAPP(c_List_Ozip(_1673021, _1673025), _1673023), _1673027)) = _1673023)], (44622 ^ _779308) ^ [_1673178, _1673180, _1673182, _1673184] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673178)), _1673180) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673182)), _1673184), -(hAPP(hAPP(c_List_Omap(tc_prod(_1673178, _1673182), _1673182), c_Product__Type_Osnd(_1673178, _1673182)), hAPP(hAPP(c_List_Ozip(_1673178, _1673182), _1673180), _1673184)) = _1673184)], (44628 ^ _779308) ^ [] : [-(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Code__Numeral_Ocode__numeral, tc_Int_Oint, c_Code__Numeral_Oof__nat), c_Int_Onat))], (44630 ^ _779308) ^ [_1673353, _1673355, _1673357] : [-(hAPP(hAPP(c_List_Ozip(_1673353, _1673355), hAPP(hAPP(c_List_Omap(tc_prod(_1673353, _1673355), _1673353), c_Product__Type_Ofst(_1673353, _1673355)), _1673357)), hAPP(hAPP(c_List_Omap(tc_prod(_1673353, _1673355), _1673355), c_Product__Type_Osnd(_1673353, _1673355)), _1673357)) = _1673357)], (44632 ^ _779308) ^ [_1673419, _1673421] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673419)), hAPP(c_Code__Numeral_Oof__nat, _1673421)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1673419), _1673421)))], (44634 ^ _779308) ^ [_1673480, _1673482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673480)), hAPP(c_Code__Numeral_Oof__nat, _1673482))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1673480), _1673482)))], (44640 ^ _779308) ^ [_1673585, _1673587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1673585), _1673587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673585)), hAPP(c_Code__Numeral_Oof__nat, _1673587))))], (44646 ^ _779308) ^ [_1673696, _1673698, _1673700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1673696), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1673698), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1673698)), _1673700)))), -(hBOOL(hAPP(hAPP(c_member(_1673698), hAPP(c_Random_Opick(_1673698, _1673700), _1673696)), hAPP(c_List_Oset(_1673698), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1673698), _1673698), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1673698)), _1673700)))))], (44652 ^ _779308) ^ [_1673887, _1673889, _1673891, _1673893, _1673895] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673887)), _1673889) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673891)), _1673893), 44655 ^ _779308 : [(44656 ^ _779308) ^ [] : [hAPP(hAPP(c_List_Ozip(_1673887, _1673891), _1673889), _1673893) = _1673895, 44659 ^ _779308 : [(44660 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1673887, _1673891), _1673887), c_Product__Type_Ofst(_1673887, _1673891)), _1673895) = _1673889)], (44662 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1673887, _1673891), _1673891), c_Product__Type_Osnd(_1673887, _1673891)), _1673895) = _1673893)]]], (44664 ^ _779308) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1673887, _1673891), _1673889), _1673893) = _1673895), hAPP(hAPP(c_List_Omap(tc_prod(_1673887, _1673891), _1673887), c_Product__Type_Ofst(_1673887, _1673891)), _1673895) = _1673889, hAPP(hAPP(c_List_Omap(tc_prod(_1673887, _1673891), _1673891), c_Product__Type_Osnd(_1673887, _1673891)), _1673895) = _1673893]]], (44674 ^ _779308) ^ [_1674335, _1674337, _1674339] : [-(c_List_Olist_Olist__size(_1674335, _1674337, _1674339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(_1674335, tc_Nat_Onat), _1674337), _1674339))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674335)), _1674339)))], (44676 ^ _779308) ^ [_1674397] : [-(_1674397 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1674397)))], (44682 ^ _779308) ^ [_1674429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1674429)), _1674429 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44688 ^ _779308) ^ [_1674511, _1674513, _1674515, _1674517] : [class_Groups_Ocomm__monoid__add(_1674511), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1674511), _1674513), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1674515, _1674517))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1674511), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1674511), _1674513), c_List_Oupto(_1674515, _1674517))))], (44694 ^ _779308) ^ [_1674654, _1674656, _1674658, _1674660] : [class_Groups_Ocomm__monoid__add(_1674654), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1674654), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1674654), _1674656), c_List_Oupto(_1674658, _1674660))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1674654), _1674656), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1674658, _1674660))))], (44700 ^ _779308) ^ [_1674797, _1674799, _1674801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674797), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1674797)), _1674799)))), -(hBOOL(hAPP(hAPP(c_member(_1674797), hAPP(c_Product__Type_Ofst(_1674797, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1674797, _1674799), _1674801))), hAPP(c_List_Oset(_1674797), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674797), _1674797), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1674797)), _1674799)))))], (44706 ^ _779308) ^ [_1674994, _1674996] : [-(c_Random_Oselect__weight(_1674994, _1674996) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1674994, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674994), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1674994)), _1674996)))), hAPP(hAPP(c_COMBB(_1674994, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1674994, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1674994, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1674994, _1674996))))], (44708 ^ _779308) ^ [_1675078, _1675080] : [-(c_Random_Oselect(_1675078, _1675080) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_Code__Numeral_Ocode__numeral, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1675078, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Orange(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675078)), _1675080)))), hAPP(hAPP(c_COMBB(_1675078, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1675078, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1675078, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1675078, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1675078), _1675080)), c_Code__Numeral_Onat__of))))], (44710 ^ _779308) ^ [_1675166, _1675168] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1675166)), hAPP(c_Code__Numeral_Oof__nat, _1675168)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1675166), _1675168)))], (44712 ^ _779308) ^ [_1675212] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1675212)) = _1675212)], (44714 ^ _779308) ^ [_1675241] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1675241)) = _1675241)], (44716 ^ _779308) ^ [_1675270] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1675270)) = _1675270)], (44718 ^ _779308) ^ [_1675314, _1675316] : [hAPP(c_Code__Numeral_Onat__of, _1675314) = hAPP(c_Code__Numeral_Onat__of, _1675316), -(_1675314 = _1675316)], (44724 ^ _779308) ^ [_1675399, _1675401] : [_1675399 = _1675401, -(hAPP(c_Code__Numeral_Onat__of, _1675399) = hAPP(c_Code__Numeral_Onat__of, _1675401))], (44730 ^ _779308) ^ [_1675505, _1675507] : [hAPP(c_Code__Numeral_Onat__of, _1675505) = hAPP(c_Code__Numeral_Onat__of, _1675507), -(_1675505 = _1675507)], (44736 ^ _779308) ^ [_1675590, _1675592] : [_1675590 = _1675592, -(hAPP(c_Code__Numeral_Onat__of, _1675590) = hAPP(c_Code__Numeral_Onat__of, _1675592))], (44742 ^ _779308) ^ [_1675681, _1675683] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1675681), _1675683) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1675681)), hAPP(c_Code__Numeral_Onat__of, _1675683))))], (44744 ^ _779308) ^ [] : [-(c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral, tc_Nat_Onat, c_Code__Numeral_Onat__of, c_Code__Numeral_Oof__nat, c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (44746 ^ _779308) ^ [_1675760, _1675762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1675760), _1675762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1675760)), hAPP(c_Code__Numeral_Onat__of, _1675762))))], (44752 ^ _779308) ^ [_1675865, _1675867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1675865)), hAPP(c_Code__Numeral_Onat__of, _1675867))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1675865), _1675867)))], (44758 ^ _779308) ^ [_1675976] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1675976)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (44760 ^ _779308) ^ [_1676007] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1676007)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1676007))], (44762 ^ _779308) ^ [] : [-(c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat, tc_Int_Oint, tc_Code__Numeral_Ocode__numeral, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), c_Code__Numeral_Onat__of))], (44764 ^ _779308) ^ [_1676072, _1676074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1676072), _1676074)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676072)), hAPP(c_Code__Numeral_Onat__of, _1676074))))], (44770 ^ _779308) ^ [_1676177, _1676179] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676177)), hAPP(c_Code__Numeral_Onat__of, _1676179))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1676177), _1676179)))], (44776 ^ _779308) ^ [_1676288] : [-(hAPP(c_Code__Numeral_Onat__of, _1676288) = c_Code__Numeral_Onat__of__aux(_1676288, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44778 ^ _779308) ^ [_1676317, _1676319] : [-(c_Code__Numeral_Onat__of__aux(_1676317, _1676319) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676317)), _1676319))], (44780 ^ _779308) ^ [_1676354] : [-(c_Code__Numeral_OSuc__code__numeral(_1676354) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1676354))))], (44782 ^ _779308) ^ [_1676388, _1676390] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1676388), _1676390) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676388)), hAPP(c_Code__Numeral_Onat__of, _1676390))))], (44784 ^ _779308) ^ [_1676434] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1676434), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1676434)) = _1676434)], (44790 ^ _779308) ^ [_1676531, _1676533] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1676531), _1676533) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676531)), hAPP(c_Code__Numeral_Onat__of, _1676533))))], (44792 ^ _779308) ^ [_1676577, _1676579] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1676577), _1676579) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676577)), hAPP(c_Code__Numeral_Onat__of, _1676579))))], (44794 ^ _779308) ^ [_1676623, _1676625] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1676623), _1676625) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1676623), _1676625))], (44796 ^ _779308) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (44798 ^ _779308) ^ [_1676678, _1676680] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1676678, _1676680) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1676678), hAPP(c_Code__Numeral_Onat__of, _1676680))))], (44800 ^ _779308) ^ [_1676716] : [-(_1676716 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1676716)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1676716))))], (44806 ^ _779308) ^ [_1676767, _1676769, _1676771, _1676773, _1676775] : [class_Groups_Omonoid__add(_1676767), class_Groups_Oordered__ab__semigroup__add(_1676767), 44816 ^ _779308 : [(44817 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676769), 44815 ^ [_1676767, _1676769, _1676771, _1676773, _1676775]), hAPP(c_List_Oset(_1676769), _1676771))))], (44819 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676767), hAPP(_1676773, 44815 ^ [_1676767, _1676769, _1676771, _1676773, _1676775])), hAPP(_1676775, 44815 ^ [_1676767, _1676769, _1676771, _1676773, _1676775])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676767), hAPP(c_List_Omonoid__add__class_Olistsum(_1676767), hAPP(hAPP(c_List_Omap(_1676769, _1676767), _1676773), _1676771))), hAPP(c_List_Omonoid__add__class_Olistsum(_1676767), hAPP(hAPP(c_List_Omap(_1676769, _1676767), _1676775), _1676771)))))], (44823 ^ _779308) ^ [_1677191, _1677193] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1677191), _1677193) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1677191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))), _1677193))))], (44825 ^ _779308) ^ [_1677229, _1677231, _1677233, _1677235, _1677237] : [c_List_Opartition(_1677229, _1677231, _1677233) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1677229), tc_List_Olist(_1677229)), _1677235), _1677237), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1677229, tc_HOL_Obool)), hAPP(c_List_Oset(_1677229), _1677235)), hAPP(c_List_Oset(_1677229), _1677237)) = hAPP(c_List_Oset(_1677229), _1677233))], (44831 ^ _779308) ^ [_1677398, _1677400, _1677402] : [-(c_List_Olistsp(_1677398, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1677398, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1677398, tc_fun(_1677398, tc_HOL_Obool), tc_HOL_Obool), c_member(_1677398)), _1677400)), hAPP(hAPP(c_COMBC(_1677398, tc_fun(_1677398, tc_HOL_Obool), tc_HOL_Obool), c_member(_1677398)), _1677402))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1677398), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677398), tc_fun(tc_List_Olist(_1677398), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1677398))), c_List_Olists(_1677398, _1677400))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677398), tc_fun(tc_List_Olist(_1677398), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1677398))), c_List_Olists(_1677398, _1677402))))], (44833 ^ _779308) ^ [_1677530, _1677532] : [-(hBOOL(hAPP(c_List_Olistsp(_1677530, _1677532), c_List_Olist_ONil(_1677530))))], (44835 ^ _779308) ^ [_1677562, _1677564] : [-(hBOOL(hAPP(c_List_Olistsp(_1677562, _1677564), c_List_Olist_ONil(_1677562))))], (44847 ^ _779308) ^ [_1677810, _1677812, _1677814] : [44849 ^ _779308 : [(44850 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1677810), 44848 ^ [_1677810, _1677812, _1677814]), hAPP(c_List_Oset(_1677810), _1677814))))], (44852 ^ _779308) ^ [] : [hBOOL(hAPP(_1677812, 44848 ^ [_1677810, _1677812, _1677814]))]], -(hBOOL(hAPP(c_List_Olistsp(_1677810, _1677812), _1677814)))], (44837 ^ _779308) ^ [_1677612, _1677614, _1677616] : [hBOOL(hAPP(c_List_Olistsp(_1677612, _1677614), _1677616)), 44840 ^ _779308 : [(44841 ^ _779308) ^ [_1677701] : [hBOOL(hAPP(hAPP(c_member(_1677612), _1677701), hAPP(c_List_Oset(_1677612), _1677616))), -(hBOOL(hAPP(_1677614, _1677701)))]]], (44856 ^ _779308) ^ [_1678021, _1678023, _1678025, _1678027] : [hBOOL(hAPP(c_List_Olistsp(_1678021, hAPP(hAPP(c_COMBS(_1678021, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1678021), c_fconj), _1678023)), _1678025)), _1678027)), 44859 ^ _779308 : [(44860 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1678021, _1678023), _1678027)))], (44862 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1678021, _1678025), _1678027)))]]], (44864 ^ _779308) ^ [_1678194, _1678196, _1678198, _1678200] : [-(hBOOL(hAPP(c_List_Olistsp(_1678194, hAPP(hAPP(c_COMBS(_1678194, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1678194), c_fconj), _1678196)), _1678198)), _1678200))), hBOOL(hAPP(c_List_Olistsp(_1678194, _1678196), _1678200)), hBOOL(hAPP(c_List_Olistsp(_1678194, _1678198), _1678200))], (44874 ^ _779308) ^ [_1678403, _1678405, _1678407] : [-(c_List_Olistsp(_1678403, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1678403, tc_HOL_Obool)), _1678405), _1678407)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1678403), tc_HOL_Obool)), c_List_Olistsp(_1678403, _1678405)), c_List_Olistsp(_1678403, _1678407)))], (44876 ^ _779308) ^ [_1678463, _1678465, _1678467, _1678469] : [hBOOL(hAPP(c_List_Olistsp(_1678463, _1678465), _1678467)), hBOOL(hAPP(c_List_Olistsp(_1678463, _1678469), _1678467)), -(hBOOL(hAPP(c_List_Olistsp(_1678463, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1678463, tc_HOL_Obool)), _1678465), _1678469)), _1678467)))], (44886 ^ _779308) ^ [_1678673, _1678675, _1678677, _1678679] : [hBOOL(hAPP(c_List_Olistsp(_1678673, _1678675), hAPP(hAPP(c_List_Olist_OCons(_1678673), _1678677), _1678679))), 44889 ^ _779308 : [(44890 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1678675, _1678677)))], (44892 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1678673, _1678675), _1678679)))]]], (44894 ^ _779308) ^ [_1678816, _1678818, _1678820, _1678822] : [-(hBOOL(hAPP(c_List_Olistsp(_1678816, _1678818), hAPP(hAPP(c_List_Olist_OCons(_1678816), _1678820), _1678822)))), hBOOL(hAPP(_1678818, _1678820)), hBOOL(hAPP(c_List_Olistsp(_1678816, _1678818), _1678822))], (44904 ^ _779308) ^ [_1679016, _1679018, _1679020, _1679022] : [hBOOL(hAPP(c_List_Olistsp(_1679016, _1679018), hAPP(hAPP(c_List_Oappend(_1679016), _1679020), _1679022))), 44907 ^ _779308 : [(44908 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1679016, _1679018), _1679020)))], (44910 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1679016, _1679018), _1679022)))]]], (44912 ^ _779308) ^ [_1679165, _1679167, _1679169, _1679171] : [-(hBOOL(hAPP(c_List_Olistsp(_1679165, _1679167), hAPP(hAPP(c_List_Oappend(_1679165), _1679169), _1679171)))), hBOOL(hAPP(c_List_Olistsp(_1679165, _1679167), _1679169)), hBOOL(hAPP(c_List_Olistsp(_1679165, _1679167), _1679171))], (44922 ^ _779308) ^ [_1679350, _1679352, _1679354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1679350, tc_HOL_Obool)), _1679352), _1679354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1679350), tc_HOL_Obool)), c_List_Olistsp(_1679350, _1679352)), c_List_Olistsp(_1679350, _1679354))))], (44928 ^ _779308) ^ [_1679485, _1679487, _1679489, _1679491, _1679493] : [c_List_Opartition(_1679485, _1679487, _1679489) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679485), tc_List_Olist(_1679485)), _1679491), _1679493), 44931 ^ _779308 : [(44932 ^ _779308) ^ [_1679638] : [hBOOL(hAPP(hAPP(c_member(_1679485), _1679638), hAPP(c_List_Oset(_1679485), _1679491))), -(hBOOL(hAPP(_1679487, _1679638)))], (44938 ^ _779308) ^ [_1679747] : [hBOOL(hAPP(hAPP(c_member(_1679485), _1679747), hAPP(c_List_Oset(_1679485), _1679493))), hBOOL(hAPP(_1679487, _1679747))]]], (44944 ^ _779308) ^ [_1679867, _1679869] : [-(c_List_Opartition(_1679867, _1679869, c_List_Olist_ONil(_1679867)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679867), tc_List_Olist(_1679867)), c_List_Olist_ONil(_1679867)), c_List_Olist_ONil(_1679867)))], (44946 ^ _779308) ^ [_1679933, _1679935, _1679937] : [hBOOL(hAPP(c_List_Olistsp(_1679933, hAPP(hAPP(c_COMBC(_1679933, tc_fun(_1679933, tc_HOL_Obool), tc_HOL_Obool), c_member(_1679933)), _1679935)), _1679937)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1679933)), _1679937), c_List_Olists(_1679933, _1679935))))], (44952 ^ _779308) ^ [_1680072, _1680074, _1680076] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680072)), _1680076), c_List_Olists(_1680072, _1680074))), -(hBOOL(hAPP(c_List_Olistsp(_1680072, hAPP(hAPP(c_COMBC(_1680072, tc_fun(_1680072, tc_HOL_Obool), tc_HOL_Obool), c_member(_1680072)), _1680074)), _1680076)))], (44958 ^ _779308) ^ [_1680217, _1680219, _1680221, _1680223] : [-(c_List_Opartition(_1680217, _1680219, hAPP(hAPP(c_List_Olist_OCons(_1680217), _1680221), _1680223)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1680217), tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1680217), tc_fun(tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217))), tc_fun(tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1680217), tc_fun(tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)))), tc_fun(tc_fun(tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217))), tc_fun(tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)))), tc_List_Olist(_1680217)), c_COMBS(tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217))), tc_fun(tc_List_Olist(_1680217), tc_fun(tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)))), tc_List_Olist(_1680217)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)), tc_fun(tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217))), tc_List_Olist(_1680217)), hAPP(c_If(tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217))), hAPP(_1680219, _1680221)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1680217), tc_fun(tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217))), tc_List_Olist(_1680217)), c_Product__Type_OPair(tc_List_Olist(_1680217), tc_List_Olist(_1680217))), hAPP(c_List_Olist_OCons(_1680217), _1680221))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1680217), tc_fun(tc_List_Olist(_1680217), tc_List_Olist(_1680217)), tc_fun(tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217))), tc_fun(tc_fun(tc_List_Olist(_1680217), tc_List_Olist(_1680217)), tc_fun(tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)))), tc_List_Olist(_1680217)), c_COMBB(tc_List_Olist(_1680217), tc_prod(tc_List_Olist(_1680217), tc_List_Olist(_1680217)), tc_List_Olist(_1680217))), c_Product__Type_OPair(tc_List_Olist(_1680217), tc_List_Olist(_1680217)))), hAPP(c_List_Olist_OCons(_1680217), _1680221)))), c_List_Opartition(_1680217, _1680219, _1680223)))], (44960 ^ _779308) ^ [_1680636, _1680638, _1680640, _1680642] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680636)), _1680638), c_List_Olists(_1680636, _1680640))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1680636)), _1680638), c_List_Olists(_1680636, _1680642))), -(hBOOL(hAPP(c_List_Olistsp(_1680636, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680636, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1680636, tc_fun(_1680636, tc_HOL_Obool), tc_HOL_Obool), c_member(_1680636)), _1680640)), hAPP(hAPP(c_COMBC(_1680636, tc_fun(_1680636, tc_HOL_Obool), tc_HOL_Obool), c_member(_1680636)), _1680642))), _1680638)))], (44970 ^ _779308) ^ [_1680913, _1680915, _1680917, _1680919, _1680921] : [-(c_Enum_Oproduct(_1680913, _1680915, hAPP(hAPP(c_List_Olist_OCons(_1680913), _1680917), _1680919), _1680921) = hAPP(hAPP(c_List_Oappend(tc_prod(_1680913, _1680915)), hAPP(hAPP(c_List_Omap(_1680915, tc_prod(_1680913, _1680915)), hAPP(c_Product__Type_OPair(_1680913, _1680915), _1680917)), _1680921)), c_Enum_Oproduct(_1680913, _1680915, _1680919, _1680921)))], (44972 ^ _779308) ^ [_1681015, _1681017, _1681019, _1681021, _1681023] : [c_List_Olist__all2(_1681015, _1681017, _1681019, _1681021, _1681023), 44975 ^ _779308 : [(44976 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681015)), _1681021) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681017)), _1681023))], (44978 ^ _779308) ^ [_1681181] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681015, _1681017)), _1681181), hAPP(c_List_Oset(tc_prod(_1681015, _1681017)), hAPP(hAPP(c_List_Ozip(_1681015, _1681017), _1681021), _1681023)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1681015, _1681017, tc_HOL_Obool), _1681019), _1681181)))]]], (44984 ^ _779308) ^ [_1681340, _1681342, _1681344, _1681346, _1681348] : [-(c_List_Olist__all2(_1681340, _1681342, _1681344, _1681346, _1681348)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681340)), _1681346) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681342)), _1681348), 44990 ^ _779308 : [(44991 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1681340, _1681342)), 44989 ^ [_1681340, _1681342, _1681344, _1681346, _1681348]), hAPP(c_List_Oset(tc_prod(_1681340, _1681342)), hAPP(hAPP(c_List_Ozip(_1681340, _1681342), _1681346), _1681348)))))], (44993 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1681340, _1681342, tc_HOL_Obool), _1681344), 44989 ^ [_1681340, _1681342, _1681344, _1681346, _1681348]))]]], (44997 ^ _779308) ^ [_1681711, _1681713, _1681715, _1681717, _1681719, _1681721, _1681723] : [c_List_Olist__all2(_1681711, _1681713, _1681715, hAPP(hAPP(c_List_Omap(_1681717, _1681711), _1681719), _1681721), _1681723), -(c_List_Olist__all2(_1681717, _1681713, hAPP(hAPP(c_COMBB(_1681711, tc_fun(_1681713, tc_HOL_Obool), _1681717), _1681715), _1681719), _1681721, _1681723))], (45003 ^ _779308) ^ [_1681850, _1681852, _1681854, _1681856, _1681858, _1681860, _1681862] : [c_List_Olist__all2(_1681856, _1681852, hAPP(hAPP(c_COMBB(_1681850, tc_fun(_1681852, tc_HOL_Obool), _1681856), _1681854), _1681858), _1681860, _1681862), -(c_List_Olist__all2(_1681850, _1681852, _1681854, hAPP(hAPP(c_List_Omap(_1681856, _1681850), _1681858), _1681860), _1681862))], (45009 ^ _779308) ^ [_1682025, _1682027, _1682029, _1682031, _1682033, _1682035, _1682037] : [c_List_Olist__all2(_1682025, _1682027, _1682029, _1682031, hAPP(hAPP(c_List_Omap(_1682033, _1682027), _1682035), _1682037)), -(c_List_Olist__all2(_1682025, _1682033, hAPP(hAPP(c_COMBC(_1682025, tc_fun(_1682033, _1682027), tc_fun(_1682033, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1682027, tc_HOL_Obool), tc_fun(tc_fun(_1682033, _1682027), tc_fun(_1682033, tc_HOL_Obool)), _1682025), c_COMBB(_1682027, tc_HOL_Obool, _1682033)), _1682029)), _1682035), _1682031, _1682037))], (45015 ^ _779308) ^ [_1682222, _1682224, _1682226, _1682228, _1682230, _1682232, _1682234] : [c_List_Olist__all2(_1682222, _1682230, hAPP(hAPP(c_COMBC(_1682222, tc_fun(_1682230, _1682224), tc_fun(_1682230, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1682224, tc_HOL_Obool), tc_fun(tc_fun(_1682230, _1682224), tc_fun(_1682230, tc_HOL_Obool)), _1682222), c_COMBB(_1682224, tc_HOL_Obool, _1682230)), _1682226)), _1682232), _1682228, _1682234), -(c_List_Olist__all2(_1682222, _1682224, _1682226, _1682228, hAPP(hAPP(c_List_Omap(_1682230, _1682224), _1682232), _1682234)))], (45021 ^ _779308) ^ [_1682425, _1682427, _1682429, _1682431, _1682433, _1682435] : [c_List_Olist__all2(_1682425, _1682427, _1682429, _1682431, _1682433), -(c_List_Olist__all2(_1682425, _1682427, _1682429, hAPP(hAPP(c_List_Odrop(_1682425), _1682435), _1682431), hAPP(hAPP(c_List_Odrop(_1682427), _1682435), _1682433)))], (45027 ^ _779308) ^ [_1682554, _1682556, _1682558, _1682560, _1682562, _1682564, _1682566] : [c_List_Olist__all2(_1682554, _1682556, _1682558, _1682560, _1682562), c_List_Olist__all2(_1682554, _1682556, _1682558, _1682564, _1682566), -(c_List_Olist__all2(_1682554, _1682556, _1682558, hAPP(hAPP(c_List_Oappend(_1682554), _1682560), _1682564), hAPP(hAPP(c_List_Oappend(_1682556), _1682562), _1682566)))], (45037 ^ _779308) ^ [_1682753, _1682755, _1682757, _1682759, _1682761, _1682763, _1682765] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682753)), _1682755) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682757)), _1682759), 45040 ^ _779308 : [(45041 ^ _779308) ^ [] : [c_List_Olist__all2(_1682753, _1682757, _1682761, hAPP(hAPP(c_List_Oappend(_1682753), _1682755), _1682763), hAPP(hAPP(c_List_Oappend(_1682757), _1682759), _1682765)), 45044 ^ _779308 : [(45045 ^ _779308) ^ [] : [-(c_List_Olist__all2(_1682753, _1682757, _1682761, _1682755, _1682759))], (45047 ^ _779308) ^ [] : [-(c_List_Olist__all2(_1682753, _1682757, _1682761, _1682763, _1682765))]]], (45049 ^ _779308) ^ [] : [-(c_List_Olist__all2(_1682753, _1682757, _1682761, hAPP(hAPP(c_List_Oappend(_1682753), _1682755), _1682763), hAPP(hAPP(c_List_Oappend(_1682757), _1682759), _1682765))), c_List_Olist__all2(_1682753, _1682757, _1682761, _1682755, _1682759), c_List_Olist__all2(_1682753, _1682757, _1682761, _1682763, _1682765)]]], (45059 ^ _779308) ^ [_1683205, _1683207, _1683209, _1683211, _1683213, _1683215, _1683217] : [c_List_Olist__all2(_1683205, _1683207, _1683209, hAPP(hAPP(c_List_Olist_OCons(_1683205), _1683211), _1683213), hAPP(hAPP(c_List_Olist_OCons(_1683207), _1683215), _1683217)), 45062 ^ _779308 : [(45063 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1683209, _1683211), _1683215)))], (45065 ^ _779308) ^ [] : [-(c_List_Olist__all2(_1683205, _1683207, _1683209, _1683213, _1683217))]]], (45067 ^ _779308) ^ [_1683368, _1683370, _1683372, _1683374, _1683376, _1683378, _1683380] : [-(c_List_Olist__all2(_1683368, _1683370, _1683372, hAPP(hAPP(c_List_Olist_OCons(_1683368), _1683374), _1683376), hAPP(hAPP(c_List_Olist_OCons(_1683370), _1683378), _1683380))), hBOOL(hAPP(hAPP(_1683372, _1683374), _1683378)), c_List_Olist__all2(_1683368, _1683370, _1683372, _1683376, _1683380)], (45077 ^ _779308) ^ [_1683573, _1683575, _1683577, _1683579, _1683581, _1683583] : [c_List_Olist__all2(_1683573, _1683575, _1683577, _1683579, _1683581), -(c_List_Olist__all2(_1683573, _1683575, _1683577, hAPP(hAPP(c_List_Otake(_1683573), _1683583), _1683579), hAPP(hAPP(c_List_Otake(_1683575), _1683583), _1683581)))], (45083 ^ _779308) ^ [_1683720, _1683722, _1683724] : [_1683720 = _1683722, -(c_List_Olist__all2(_1683724, _1683724, c_fequal, _1683720, _1683722))], (45089 ^ _779308) ^ [_1683801, _1683803, _1683805] : [c_List_Olist__all2(_1683805, _1683805, c_fequal, _1683801, _1683803), -(_1683801 = _1683803)], (45095 ^ _779308) ^ [_1683888, _1683890, _1683892, _1683894, _1683896] : [c_List_Olist__all2(_1683888, _1683890, _1683892, _1683894, _1683896), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683888)), _1683894) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683890)), _1683896))], (45101 ^ _779308) ^ [_1684026, _1684028, _1684030, _1684032] : [c_List_Olist__all2(_1684026, _1684028, _1684030, c_List_Olist_ONil(_1684026), _1684032), -(_1684032 = c_List_Olist_ONil(_1684028))], (45107 ^ _779308) ^ [_1684117, _1684119, _1684121, _1684123] : [_1684123 = c_List_Olist_ONil(_1684119), -(c_List_Olist__all2(_1684117, _1684119, _1684121, c_List_Olist_ONil(_1684117), _1684123))], (45113 ^ _779308) ^ [_1684235, _1684237, _1684239, _1684241] : [c_List_Olist__all2(_1684235, _1684237, _1684239, _1684241, c_List_Olist_ONil(_1684237)), -(_1684241 = c_List_Olist_ONil(_1684235))], (45119 ^ _779308) ^ [_1684326, _1684328, _1684330, _1684332] : [_1684332 = c_List_Olist_ONil(_1684326), -(c_List_Olist__all2(_1684326, _1684328, _1684330, _1684332, c_List_Olist_ONil(_1684328)))], (45125 ^ _779308) ^ [_1684423, _1684425, _1684427] : [-(c_Enum_Oproduct(_1684423, _1684425, c_List_Olist_ONil(_1684423), _1684427) = c_List_Olist_ONil(tc_prod(_1684423, _1684425)))], (45127 ^ _779308) ^ [_1684486, _1684488, _1684490, _1684492, _1684494] : [c_List_Olist__all2(_1684486, _1684488, _1684490, _1684492, _1684494), 45130 ^ _779308 : [(45131 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684486)), _1684492) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684488)), _1684494))], (45133 ^ _779308) ^ [_1684649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1684649), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684486)), _1684492))), -(hBOOL(hAPP(hAPP(_1684490, hAPP(hAPP(c_List_Onth(_1684486), _1684492), _1684649)), hAPP(hAPP(c_List_Onth(_1684488), _1684494), _1684649))))]]], (45139 ^ _779308) ^ [_1684802, _1684804, _1684806, _1684808, _1684810] : [-(c_List_Olist__all2(_1684802, _1684804, _1684806, _1684808, _1684810)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684802)), _1684808) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684804)), _1684810), 45145 ^ _779308 : [(45146 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45144 ^ [_1684802, _1684804, _1684806, _1684808, _1684810]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684802)), _1684808))))], (45148 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1684806, hAPP(hAPP(c_List_Onth(_1684802), _1684808), 45144 ^ [_1684802, _1684804, _1684806, _1684808, _1684810])), hAPP(hAPP(c_List_Onth(_1684804), _1684810), 45144 ^ [_1684802, _1684804, _1684806, _1684808, _1684810])))]]], (45152 ^ _779308) ^ [_1685162, _1685164, _1685166, _1685168, _1685170, _1685172] : [c_List_Olist__all2(_1685162, _1685164, _1685166, _1685168, _1685170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685172), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685162)), _1685168))), -(hBOOL(hAPP(hAPP(_1685166, hAPP(hAPP(c_List_Onth(_1685162), _1685168), _1685172)), hAPP(hAPP(c_List_Onth(_1685164), _1685170), _1685172))))], (45162 ^ _779308) ^ [_1685379, _1685381, _1685383, _1685385, _1685387, _1685389] : [c_List_Olist__all2(_1685379, _1685381, _1685383, _1685385, _1685387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685389), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685381)), _1685387))), -(hBOOL(hAPP(hAPP(_1685383, hAPP(hAPP(c_List_Onth(_1685379), _1685385), _1685389)), hAPP(hAPP(c_List_Onth(_1685381), _1685387), _1685389))))], (45172 ^ _779308) ^ [_1685596, _1685598, _1685600, _1685602, _1685604, _1685606, _1685608, _1685610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685596), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685598)), _1685600))), c_List_Olist__all2(_1685598, _1685602, _1685604, _1685600, _1685606), hBOOL(hAPP(hAPP(_1685604, _1685608), _1685610)), -(c_List_Olist__all2(_1685598, _1685602, _1685604, hAPP(hAPP(c_List_Olist__update(_1685598, _1685600), _1685596), _1685608), hAPP(hAPP(c_List_Olist__update(_1685602, _1685606), _1685596), _1685610)))], (45186 ^ _779308) ^ [_1685895, _1685897, _1685899, _1685901, _1685903, _1685905, _1685907, _1685909] : [c_List_Olist__all2(_1685895, _1685897, _1685899, _1685901, _1685903), hBOOL(hAPP(hAPP(_1685899, _1685905), _1685907)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685909), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685897)), _1685903))), -(c_List_Olist__all2(_1685895, _1685897, _1685899, hAPP(hAPP(c_List_Olist__update(_1685895, _1685901), _1685909), _1685905), hAPP(hAPP(c_List_Olist__update(_1685897, _1685903), _1685909), _1685907)))], (45200 ^ _779308) ^ [_1686194, _1686196, _1686198, _1686200] : [hBOOL(hAPP(c_List_Odistinct(_1686194), _1686196)), hBOOL(hAPP(c_List_Odistinct(_1686198), _1686200)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1686194, _1686198)), c_Enum_Oproduct(_1686194, _1686198, _1686196, _1686200))))], (45210 ^ _779308) ^ [_1686371, _1686373, _1686375, _1686377] : [-(hAPP(c_List_Oset(tc_prod(_1686371, _1686373)), c_Enum_Oproduct(_1686371, _1686373, _1686375, _1686377)) = hAPP(hAPP(c_Product__Type_OSigma(_1686371, _1686373), hAPP(c_List_Oset(_1686371), _1686375)), hAPP(c_COMBK(tc_fun(_1686373, tc_HOL_Obool), _1686371), hAPP(c_List_Oset(_1686373), _1686377))))], (45212 ^ _779308) ^ [_1686441, _1686443] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1686441), tc_fun(_1686441, tc_HOL_Obool), c_List_Oset(_1686441)), hAPP(c_List_Oset(tc_List_Olist(_1686441)), c_Enum_Osublists(_1686441, _1686443))) = hAPP(c_Set_OPow(_1686441), hAPP(c_List_Oset(_1686441), _1686443)))], (45214 ^ _779308) ^ [_1686500, _1686502] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1686500))), c_Enum_Osublists(_1686500, _1686502)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686500)), _1686502)))], (45216 ^ _779308) ^ [_1686547] : [-(c_Enum_Osublists(_1686547, c_List_Olist_ONil(_1686547)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1686547)), c_List_Olist_ONil(_1686547)), c_List_Olist_ONil(tc_List_Olist(_1686547))))], (45218 ^ _779308) ^ [_1686591, _1686593, _1686595] : [-(c_Enum_Osublists(_1686591, hAPP(hAPP(c_List_Olist_OCons(_1686591), _1686593), _1686595)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1686591)), tc_List_Olist(tc_List_Olist(_1686591))), c_Enum_Osublists(_1686591, _1686595)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1686591)), tc_List_Olist(tc_List_Olist(_1686591)), tc_List_Olist(tc_List_Olist(_1686591))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1686591)), tc_fun(tc_List_Olist(tc_List_Olist(_1686591)), tc_List_Olist(tc_List_Olist(_1686591))), tc_List_Olist(tc_List_Olist(_1686591))), c_List_Oappend(tc_List_Olist(_1686591))), hAPP(c_List_Omap(tc_List_Olist(_1686591), tc_List_Olist(_1686591)), hAPP(c_List_Olist_OCons(_1686591), _1686593)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1686591))))))], (45220 ^ _779308) ^ [_1686725, _1686727] : [hBOOL(hAPP(c_List_Odistinct(_1686725), _1686727)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1686725, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1686725), tc_fun(_1686725, tc_HOL_Obool)), c_List_Oset(_1686725)), c_Enum_Osublists(_1686725, _1686727)))))], (45226 ^ _779308) ^ [_1686862, _1686864, _1686866] : [-(hAPP(c_List_Oset(tc_List_Olist(_1686862)), c_Enum_On__lists(_1686862, _1686864, _1686866)) = hAPP(c_Set_OCollect(tc_List_Olist(_1686862)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1686862), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1686862)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1686862), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1686862)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1686862)))), _1686864))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1686862), tc_fun(_1686862, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1686862, tc_HOL_Obool), tc_fun(tc_fun(_1686862, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1686862)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1686862, tc_HOL_Obool))), c_List_Oset(_1686862))), hAPP(c_List_Oset(_1686862), _1686866)))))], (45228 ^ _779308) ^ [_1687007, _1687009] : [-(c_Enum_Oenum__the(_1687007, _1687009) = c_HOL_OThe(_1687007, _1687009))], (45230 ^ _779308) ^ [_1687038, _1687040, _1687042] : [hBOOL(hAPP(c_List_Odistinct(_1687038), _1687040)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1687038)), c_Enum_On__lists(_1687038, _1687042, _1687040))))], (45236 ^ _779308) ^ [_1687154, _1687156] : [_1687154 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1687156, _1687154, c_List_Olist_ONil(_1687156)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687156)), c_List_Olist_ONil(_1687156)), c_List_Olist_ONil(tc_List_Olist(_1687156))))], (45242 ^ _779308) ^ [_1687269, _1687271] : [-(_1687269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1687271, _1687269, c_List_Olist_ONil(_1687271)) = c_List_Olist_ONil(tc_List_Olist(_1687271)))], (45248 ^ _779308) ^ [_1687317, _1687319] : [-(c_Enum_On__lists(_1687317, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1687319) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687317)), c_List_Olist_ONil(_1687317)), c_List_Olist_ONil(tc_List_Olist(_1687317))))], (45250 ^ _779308) ^ [_1687362, _1687364, _1687366] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1687362))), c_Enum_On__lists(_1687362, _1687364, _1687366)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687362)), _1687366)), _1687364))], (45252 ^ _779308) ^ [_1687415, _1687417, _1687419, _1687421] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1687415)), _1687417), hAPP(c_List_Oset(tc_List_Olist(_1687415)), c_Enum_On__lists(_1687415, _1687419, _1687421)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687415)), _1687417) = _1687419)], (45258 ^ _779308) ^ [_1687550, _1687552, _1687554, _1687556, _1687558] : [45260 ^ _779308 : [(45261 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1687550, _1687552)), 45259 ^ [_1687550, _1687552, _1687554, _1687556, _1687558]), hAPP(c_List_Oset(tc_prod(_1687550, _1687552)), hAPP(hAPP(c_List_Ozip(_1687550, _1687552), _1687554), _1687556)))))], (45263 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1687550, _1687552, tc_HOL_Obool), _1687558), 45259 ^ [_1687550, _1687552, _1687554, _1687556, _1687558]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687550)), _1687554) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687552)), _1687556), -(c_List_Olist__all2(_1687550, _1687552, _1687558, _1687554, _1687556))], (45271 ^ _779308) ^ [_1687889, _1687891, _1687893, _1687895] : [45273 ^ _779308 : [(45274 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45272 ^ [_1687889, _1687891, _1687893, _1687895]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687889)), _1687891))))], (45276 ^ _779308) ^ [] : [hBOOL(hAPP(_1687893, hAPP(hAPP(c_List_Onth(_1687889), _1687891), 45272 ^ [_1687889, _1687891, _1687893, _1687895])))]], hBOOL(hAPP(hAPP(c_member(_1687889), _1687895), hAPP(c_List_Oset(_1687889), _1687891))), -(hBOOL(hAPP(_1687893, _1687895)))], (45284 ^ _779308) ^ [_1688185, _1688187, _1688189, _1688191, _1688193] : [c_Finite__Set_Ofun__left__comm(_1688185, _1688187, _1688189), -(hAPP(hAPP(c_Finite__Set_Ofold(_1688185, _1688187, _1688189), _1688191), hAPP(c_List_Oset(_1688185), _1688193)) = hAPP(c_List_Ofoldl(_1688187, _1688185, hAPP(c_COMBC(_1688185, _1688187, _1688187), _1688189), _1688191), c_List_Oremdups(_1688185, _1688193)))], (45290 ^ _779308) ^ [_1688336, _1688338, _1688340, _1688342, _1688344] : [c_Fun_Oinj__on(_1688336, _1688338, _1688340, hAPP(hAPP(c_Set_Oinsert(_1688336), _1688342), hAPP(c_List_Oset(_1688336), _1688344))), -(hAPP(hAPP(c_List_Omap(_1688336, _1688338), _1688340), hAPP(c_List_OremoveAll(_1688336, _1688342), _1688344)) = hAPP(c_List_OremoveAll(_1688338, hAPP(_1688340, _1688342)), hAPP(hAPP(c_List_Omap(_1688336, _1688338), _1688340), _1688344)))], (45296 ^ _779308) ^ [_1688515, _1688517] : [-(hBOOL(hAPP(c_List_Odistinct(_1688515), c_List_Oremdups(_1688515, _1688517))))], (45298 ^ _779308) ^ [_1688547, _1688549] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688547)), c_List_Oremdups(_1688547, _1688549))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688547)), _1688549))))], (45300 ^ _779308) ^ [_1688594, _1688596] : [hBOOL(hAPP(c_List_Odistinct(_1688594), _1688596)), -(c_List_Oremdups(_1688594, _1688596) = _1688596)], (45306 ^ _779308) ^ [_1688685, _1688687, _1688689] : [hBOOL(hAPP(c_List_Odistinct(_1688685), _1688687)), -(hBOOL(hAPP(c_List_Odistinct(_1688685), hAPP(c_List_OremoveAll(_1688685, _1688689), _1688687))))], (45312 ^ _779308) ^ [_1688807, _1688809] : [c_List_Oremdups(_1688807, _1688809) = _1688809, -(hBOOL(hAPP(c_List_Odistinct(_1688807), _1688809)))], (45318 ^ _779308) ^ [_1688894, _1688896] : [hBOOL(hAPP(c_List_Odistinct(_1688894), _1688896)), -(c_List_Oremdups(_1688894, _1688896) = _1688896)], (45324 ^ _779308) ^ [_1688987, _1688989] : [-(hAPP(c_List_Oset(_1688987), c_List_Oremdups(_1688987, _1688989)) = hAPP(c_List_Oset(_1688987), _1688989))], (45326 ^ _779308) ^ [_1689040, _1689042] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689040)), c_List_Oremdups(_1689040, _1689042)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689040)), _1689042), -(c_List_Oremdups(_1689040, _1689042) = _1689042)], (45332 ^ _779308) ^ [_1689153, _1689155] : [c_List_Oremdups(_1689153, _1689155) = _1689155, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689153)), c_List_Oremdups(_1689153, _1689155)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689153)), _1689155))], (45338 ^ _779308) ^ [_1689272, _1689274] : [-(c_List_Oremdups(_1689272, c_List_Oremdups(_1689272, _1689274)) = c_List_Oremdups(_1689272, _1689274))], (45340 ^ _779308) ^ [_1689321, _1689323] : [c_List_Oremdups(_1689321, _1689323) = c_List_Olist_ONil(_1689321), -(_1689323 = c_List_Olist_ONil(_1689321))], (45346 ^ _779308) ^ [_1689408, _1689410] : [_1689410 = c_List_Olist_ONil(_1689408), -(c_List_Oremdups(_1689408, _1689410) = c_List_Olist_ONil(_1689408))], (45352 ^ _779308) ^ [_1689501, _1689503] : [-(hAPP(c_List_OremoveAll(_1689501, _1689503), c_List_Olist_ONil(_1689501)) = c_List_Olist_ONil(_1689501))], (45354 ^ _779308) ^ [_1689551, _1689553] : [c_List_Olist_ONil(_1689551) = c_List_Oremdups(_1689551, _1689553), -(_1689553 = c_List_Olist_ONil(_1689551))], (45360 ^ _779308) ^ [_1689638, _1689640] : [_1689640 = c_List_Olist_ONil(_1689638), -(c_List_Olist_ONil(_1689638) = c_List_Oremdups(_1689638, _1689640))], (45366 ^ _779308) ^ [_1689731] : [-(c_List_Oremdups(_1689731, c_List_Olist_ONil(_1689731)) = c_List_Olist_ONil(_1689731))], (45368 ^ _779308) ^ [_1689776, _1689778, _1689780, _1689782] : [_1689776 = _1689778, -(hAPP(c_List_OremoveAll(_1689780, _1689776), hAPP(hAPP(c_List_Olist_OCons(_1689780), _1689778), _1689782)) = hAPP(c_List_OremoveAll(_1689780, _1689776), _1689782))], (45374 ^ _779308) ^ [_1689891, _1689893, _1689895, _1689897] : [-(_1689891 = _1689893), -(hAPP(c_List_OremoveAll(_1689895, _1689891), hAPP(hAPP(c_List_Olist_OCons(_1689895), _1689893), _1689897)) = hAPP(hAPP(c_List_Olist_OCons(_1689895), _1689893), hAPP(c_List_OremoveAll(_1689895, _1689891), _1689897)))], (45380 ^ _779308) ^ [_1689961, _1689963, _1689965, _1689967] : [-(hAPP(c_List_OremoveAll(_1689961, _1689963), hAPP(hAPP(c_List_Oappend(_1689961), _1689965), _1689967)) = hAPP(hAPP(c_List_Oappend(_1689961), hAPP(c_List_OremoveAll(_1689961, _1689963), _1689965)), hAPP(c_List_OremoveAll(_1689961, _1689963), _1689967)))], (45382 ^ _779308) ^ [_1690024, _1690026, _1690028, _1690030] : [-(c_List_Oremdups(_1690024, hAPP(hAPP(c_List_Omap(_1690026, _1690024), _1690028), c_List_Oremdups(_1690026, _1690030))) = c_List_Oremdups(_1690024, hAPP(hAPP(c_List_Omap(_1690026, _1690024), _1690028), _1690030)))], (45384 ^ _779308) ^ [_1690080, _1690082, _1690084] : [hBOOL(hAPP(c_List_Odistinct(_1690080), _1690082)), -(c_List_Oremove1(_1690080, _1690084, c_List_Oremdups(_1690080, _1690082)) = c_List_Oremdups(_1690080, c_List_Oremove1(_1690080, _1690084, _1690082)))], (45390 ^ _779308) ^ [_1690191, _1690193, _1690195] : [-(hBOOL(hAPP(hAPP(c_member(_1690191), _1690193), hAPP(c_List_Oset(_1690191), _1690195)))), -(hAPP(c_List_OremoveAll(_1690191, _1690193), _1690195) = _1690195)], (45396 ^ _779308) ^ [_1690247, _1690249, _1690251] : [hBOOL(hAPP(c_List_Odistinct(_1690247), _1690249)), -(c_List_Oremove1(_1690247, _1690251, _1690249) = hAPP(c_List_OremoveAll(_1690247, _1690251), _1690249))], (45402 ^ _779308) ^ [_1690366, _1690368, _1690370] : [hBOOL(hAPP(hAPP(c_member(_1690366), _1690368), hAPP(c_List_Oset(_1690366), _1690370))), -(c_List_Oremdups(_1690366, hAPP(hAPP(c_List_Olist_OCons(_1690366), _1690368), _1690370)) = c_List_Oremdups(_1690366, _1690370))], (45408 ^ _779308) ^ [_1690491, _1690493, _1690495] : [-(hBOOL(hAPP(hAPP(c_member(_1690491), _1690493), hAPP(c_List_Oset(_1690491), _1690495)))), -(c_List_Oremdups(_1690491, hAPP(hAPP(c_List_Olist_OCons(_1690491), _1690493), _1690495)) = hAPP(hAPP(c_List_Olist_OCons(_1690491), _1690493), c_List_Oremdups(_1690491, _1690495)))], (45414 ^ _779308) ^ [_1690565, _1690567] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690565)), c_List_Oremdups(_1690565, _1690567)) = hAPP(c_Finite__Set_Ocard(_1690565), hAPP(c_List_Oset(_1690565), _1690567)))], (45416 ^ _779308) ^ [_1690610, _1690612, _1690614, _1690616, _1690618] : [c_Fun_Oinj__on(_1690610, _1690612, _1690614, c_Orderings_Otop__class_Otop(tc_fun(_1690610, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1690610, _1690612), _1690614), hAPP(c_List_OremoveAll(_1690610, _1690616), _1690618)) = hAPP(c_List_OremoveAll(_1690612, hAPP(_1690614, _1690616)), hAPP(hAPP(c_List_Omap(_1690610, _1690612), _1690614), _1690618)))], (45422 ^ _779308) ^ [_1690773, _1690775, _1690777] : [-(hAPP(c_List_Oset(_1690773), hAPP(c_List_OremoveAll(_1690773, _1690775), _1690777)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1690773, tc_HOL_Obool)), hAPP(c_List_Oset(_1690773), _1690777)), hAPP(hAPP(c_Set_Oinsert(_1690773), _1690775), c_Orderings_Obot__class_Obot(tc_fun(_1690773, tc_HOL_Obool)))))], (45424 ^ _779308) ^ [_1690840, _1690842] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690840)), c_List_Oremdups(_1690840, c_List_Oconcat(_1690840, _1690842))) = hAPP(c_Finite__Set_Ocard(_1690840), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1690840), tc_fun(_1690840, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1690840)), _1690842)), c_List_Oset(_1690840))))], (45426 ^ _779308) ^ [_1690906, _1690908] : [class_Orderings_Olinorder(_1690906), -(c_List_Olinorder__class_Osorted__list__of__set(_1690906, hAPP(c_List_Oset(_1690906), _1690908)) = c_List_Olinorder__class_Osort__key(_1690906, _1690906, c_COMBI(_1690906), c_List_Oremdups(_1690906, _1690908)))], (45432 ^ _779308) ^ [_1691017, _1691019] : [-(c_List_Oconcat(_1691017, _1691019) = hAPP(c_List_Ofoldl(tc_List_Olist(_1691017), tc_List_Olist(_1691017), c_List_Oappend(_1691017), c_List_Olist_ONil(_1691017)), _1691019))], (45434 ^ _779308) ^ [_1691061, _1691063, _1691065] : [class_Orderings_Olinorder(_1691061), -(c_List_Olinorder__class_Osort__key(_1691063, _1691061, _1691065, c_List_Olist_ONil(_1691063)) = c_List_Olist_ONil(_1691063))], (45440 ^ _779308) ^ [_1691156, _1691158, _1691160] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1691156), tc_List_Olist(_1691156), c_List_Oappend(_1691156), _1691158), _1691160) = hAPP(hAPP(c_List_Oappend(_1691156), _1691158), c_List_Oconcat(_1691156, _1691160)))], (45442 ^ _779308) ^ [_1691208, _1691210, _1691212, _1691214] : [class_Orderings_Olinorder(_1691208), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691210)), c_List_Olinorder__class_Osort__key(_1691210, _1691208, _1691212, _1691214)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691210)), _1691214))], (45448 ^ _779308) ^ [_1691325, _1691327, _1691329, _1691331] : [class_Orderings_Olinorder(_1691325), -(hAPP(c_List_Oset(_1691327), c_List_Olinorder__class_Osort__key(_1691327, _1691325, _1691329, _1691331)) = hAPP(c_List_Oset(_1691327), _1691331))], (45454 ^ _779308) ^ [_1691434, _1691436, _1691438, _1691440] : [class_Orderings_Olinorder(_1691434), 45457 ^ _779308 : [(45458 ^ _779308) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1691436), c_List_Olinorder__class_Osort__key(_1691436, _1691434, _1691438, _1691440))), -(hBOOL(hAPP(c_List_Odistinct(_1691436), _1691440)))], (45464 ^ _779308) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1691436), _1691440)), -(hBOOL(hAPP(c_List_Odistinct(_1691436), c_List_Olinorder__class_Osort__key(_1691436, _1691434, _1691438, _1691440))))]]], (45470 ^ _779308) ^ [_1691690] : [-(c_List_Oconcat(_1691690, c_List_Olist_ONil(tc_List_Olist(_1691690))) = c_List_Olist_ONil(_1691690))], (45472 ^ _779308) ^ [_1691722, _1691724, _1691726] : [-(c_List_Oconcat(_1691722, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1691722)), _1691724), _1691726)) = hAPP(hAPP(c_List_Oappend(_1691722), _1691724), c_List_Oconcat(_1691722, _1691726)))], (45484 ^ _779308) ^ [_1691994, _1691996] : [45486 ^ _779308 : [(45487 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1691994)), 45485 ^ [_1691994, _1691996]), hAPP(c_List_Oset(tc_List_Olist(_1691994)), _1691996))))], (45489 ^ _779308) ^ [] : [45485 ^ [_1691994, _1691996] = c_List_Olist_ONil(_1691994)]], -(c_List_Oconcat(_1691994, _1691996) = c_List_Olist_ONil(_1691994))], (45474 ^ _779308) ^ [_1691788, _1691790] : [c_List_Oconcat(_1691788, _1691790) = c_List_Olist_ONil(_1691788), 45477 ^ _779308 : [(45478 ^ _779308) ^ [_1691879] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1691788)), _1691879), hAPP(c_List_Oset(tc_List_Olist(_1691788)), _1691790))), -(_1691879 = c_List_Olist_ONil(_1691788))]]], (45503 ^ _779308) ^ [_1692406, _1692408] : [45505 ^ _779308 : [(45506 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692406)), 45504 ^ [_1692406, _1692408]), hAPP(c_List_Oset(tc_List_Olist(_1692406)), _1692408))))], (45508 ^ _779308) ^ [] : [45504 ^ [_1692406, _1692408] = c_List_Olist_ONil(_1692406)]], -(c_List_Olist_ONil(_1692406) = c_List_Oconcat(_1692406, _1692408))], (45493 ^ _779308) ^ [_1692200, _1692202] : [c_List_Olist_ONil(_1692200) = c_List_Oconcat(_1692200, _1692202), 45496 ^ _779308 : [(45497 ^ _779308) ^ [_1692291] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692200)), _1692291), hAPP(c_List_Oset(tc_List_Olist(_1692200)), _1692202))), -(_1692291 = c_List_Olist_ONil(_1692200))]]], (45512 ^ _779308) ^ [_1692597, _1692599, _1692601, _1692603] : [-(hAPP(hAPP(c_List_Omap(_1692597, _1692599), _1692601), c_List_Oconcat(_1692597, _1692603)) = c_List_Oconcat(_1692599, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1692597), tc_List_Olist(_1692599)), hAPP(c_List_Omap(_1692597, _1692599), _1692601)), _1692603)))], (45514 ^ _779308) ^ [_1692660, _1692662] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692660)), c_List_Oconcat(_1692660, _1692662)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1692660), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1692660))), _1692662)))], (45516 ^ _779308) ^ [_1692713, _1692715] : [-(hAPP(c_List_Oset(_1692713), c_List_Oconcat(_1692713, _1692715)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1692713), tc_fun(_1692713, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1692713)), _1692715)), c_List_Oset(_1692713)))], (45518 ^ _779308) ^ [_1692769, _1692771, _1692773, _1692775, _1692777] : [class_Orderings_Olinorder(_1692769), -(c_List_Olinorder__class_Osort__key(_1692771, _1692769, _1692773, hAPP(hAPP(c_List_Olist_OCons(_1692771), _1692775), _1692777)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1692771, _1692769, _1692773), _1692775), c_List_Olinorder__class_Osort__key(_1692771, _1692769, _1692773, _1692777)))], (45524 ^ _779308) ^ [_1692906, _1692908, _1692910] : [-(c_List_Oconcat(_1692906, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1692906)), _1692908), _1692910)) = hAPP(hAPP(c_List_Oappend(_1692906), c_List_Oconcat(_1692906, _1692908)), c_List_Oconcat(_1692906, _1692910)))], (45526 ^ _779308) ^ [_1692960, _1692962] : [class_Orderings_Olinorder(_1692960), -(c_List_Olinorder__class_Osort__key(_1692960, _1692960, c_COMBI(_1692960), _1692962) = hAPP(c_List_Ofoldl(tc_List_Olist(_1692960), _1692960, hAPP(c_COMBC(_1692960, tc_List_Olist(_1692960), tc_List_Olist(_1692960)), c_List_Olinorder__class_Oinsort__key(_1692960, _1692960, c_COMBI(_1692960))), c_List_Olist_ONil(_1692960)), _1692962))], (45532 ^ _779308) ^ [_1693107, _1693109, _1693111] : [45534 ^ _779308 : [(45535 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693107), tc_List_Olist(_1693107))), 45533 ^ [_1693107, _1693109, _1693111]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1693107), tc_List_Olist(_1693107))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1693107), tc_List_Olist(_1693107)), _1693109), _1693111)))))], (45537 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1693107), tc_List_Olist(_1693107), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1693107), tc_fun(tc_List_Olist(_1693107), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693107), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1693107), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693107), tc_HOL_Obool)), tc_List_Olist(_1693107)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1693107))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1693107)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1693107))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1693107)))), 45533 ^ [_1693107, _1693109, _1693111]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693107))), _1693109) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693107))), _1693111), 45542 ^ _779308 : [(45543 ^ _779308) ^ [] : [c_List_Oconcat(_1693107, _1693109) = c_List_Oconcat(_1693107, _1693111), -(_1693109 = _1693111)], (45549 ^ _779308) ^ [] : [_1693109 = _1693111, -(c_List_Oconcat(_1693107, _1693109) = c_List_Oconcat(_1693107, _1693111))]]], (45555 ^ _779308) ^ [_1693834, _1693836, _1693838] : [c_List_Oconcat(_1693834, _1693836) = c_List_Oconcat(_1693834, _1693838), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693834))), _1693836) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693834))), _1693838), 45565 ^ _779308 : [(45566 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693834), tc_List_Olist(_1693834))), 45564 ^ [_1693834, _1693836, _1693838]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1693834), tc_List_Olist(_1693834))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1693834), tc_List_Olist(_1693834)), _1693836), _1693838)))))], (45568 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1693834), tc_List_Olist(_1693834), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1693834), tc_fun(tc_List_Olist(_1693834), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693834), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1693834), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693834), tc_HOL_Obool)), tc_List_Olist(_1693834)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1693834))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1693834)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1693834))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1693834)))), 45564 ^ [_1693834, _1693836, _1693838]))]], -(_1693836 = _1693838)], (45572 ^ _779308) ^ [_1694475, _1694477, _1694479, _1694481] : [-(c_List_Oconcat(_1694475, hAPP(hAPP(c_List_Omap(_1694477, tc_List_Olist(_1694475)), hAPP(hAPP(c_COMBC(_1694477, tc_List_Olist(_1694475), tc_List_Olist(_1694475)), hAPP(hAPP(c_COMBB(_1694475, tc_fun(tc_List_Olist(_1694475), tc_List_Olist(_1694475)), _1694477), c_List_Olist_OCons(_1694475)), _1694479)), c_List_Olist_ONil(_1694475))), _1694481)) = hAPP(hAPP(c_List_Omap(_1694477, _1694475), _1694479), _1694481))], (45574 ^ _779308) ^ [_1694562, _1694564, _1694566] : [-(c_Enum_On__lists(_1694562, hAPP(c_Nat_OSuc, _1694564), _1694566) = c_List_Oconcat(tc_List_Olist(_1694562), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694562), tc_List_Olist(tc_List_Olist(_1694562))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694562), tc_List_Olist(_1694562), tc_List_Olist(tc_List_Olist(_1694562))), hAPP(hAPP(c_COMBB(tc_fun(_1694562, tc_List_Olist(_1694562)), tc_fun(tc_List_Olist(_1694562), tc_List_Olist(tc_List_Olist(_1694562))), tc_List_Olist(_1694562)), c_List_Omap(_1694562, tc_List_Olist(_1694562))), hAPP(c_COMBC(_1694562, tc_List_Olist(_1694562), tc_List_Olist(_1694562)), c_List_Olist_OCons(_1694562)))), _1694566)), c_Enum_On__lists(_1694562, _1694564, _1694566))))], (45576 ^ _779308) ^ [_1694682, _1694684, _1694686, _1694688] : [-(c_List_Otranspose(_1694682, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1694682)), hAPP(hAPP(c_List_Olist_OCons(_1694682), _1694684), _1694686)), _1694688)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1694682)), hAPP(hAPP(c_List_Olist_OCons(_1694682), _1694684), c_List_Oconcat(_1694682, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694682), tc_List_Olist(_1694682)), c_List_Olist_Olist__case(tc_List_Olist(_1694682), _1694682, c_List_Olist_ONil(_1694682), hAPP(hAPP(c_COMBB(tc_List_Olist(_1694682), tc_fun(tc_List_Olist(_1694682), tc_List_Olist(_1694682)), _1694682), c_COMBK(tc_List_Olist(_1694682), tc_List_Olist(_1694682))), hAPP(hAPP(c_COMBC(_1694682, tc_List_Olist(_1694682), tc_List_Olist(_1694682)), c_List_Olist_OCons(_1694682)), c_List_Olist_ONil(_1694682))))), _1694688)))), c_List_Otranspose(_1694682, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1694682)), _1694686), c_List_Oconcat(tc_List_Olist(_1694682), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694682), tc_List_Olist(tc_List_Olist(_1694682))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1694682)), _1694682, c_List_Olist_ONil(tc_List_Olist(_1694682)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1694682), tc_List_Olist(tc_List_Olist(_1694682))), _1694682), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694682), tc_List_Olist(tc_List_Olist(_1694682)), tc_List_Olist(tc_List_Olist(_1694682))), c_List_Olist_OCons(tc_List_Olist(_1694682))), c_List_Olist_ONil(tc_List_Olist(_1694682)))))), _1694688))))))], (45578 ^ _779308) ^ [_1694908, _1694910] : [-(c_List_Oconcat(_1694908, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694908), tc_List_Olist(_1694908)), c_List_Olist_Olist__case(tc_List_Olist(_1694908), _1694908, c_List_Olist_ONil(_1694908), hAPP(hAPP(c_COMBB(tc_List_Olist(_1694908), tc_fun(tc_List_Olist(_1694908), tc_List_Olist(_1694908)), _1694908), c_COMBK(tc_List_Olist(_1694908), tc_List_Olist(_1694908))), hAPP(hAPP(c_COMBC(_1694908, tc_List_Olist(_1694908), tc_List_Olist(_1694908)), c_List_Olist_OCons(_1694908)), c_List_Olist_ONil(_1694908))))), _1694910)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694908), _1694908), c_List_Ohd(_1694908)), hAPP(c_List_Ofilter(tc_List_Olist(_1694908), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1694908)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694908), tc_List_Olist(_1694908), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1694908)))), _1694910)))], (45580 ^ _779308) ^ [_1695051, _1695053, _1695055] : [-(hAPP(c_List_Ofilter(_1695051, _1695053), c_List_Oconcat(_1695051, _1695055)) = c_List_Oconcat(_1695051, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695051), tc_List_Olist(_1695051)), c_List_Ofilter(_1695051, _1695053)), _1695055)))], (45582 ^ _779308) ^ [_1695106, _1695108, _1695110, _1695112, _1695114] : [class_Orderings_Olinorder(_1695106), -(hAPP(c_List_Ofilter(_1695108, _1695110), c_List_Olinorder__class_Osort__key(_1695108, _1695106, _1695112, _1695114)) = c_List_Olinorder__class_Osort__key(_1695108, _1695106, _1695112, hAPP(c_List_Ofilter(_1695108, _1695110), _1695114)))], (45588 ^ _779308) ^ [_1695231, _1695233, _1695235] : [hBOOL(hAPP(c_List_Odistinct(_1695231), _1695233)), -(hBOOL(hAPP(c_List_Odistinct(_1695231), hAPP(c_List_Ofilter(_1695231, _1695235), _1695233))))], (45594 ^ _779308) ^ [_1695338, _1695340, _1695342] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695338)), hAPP(c_List_Ofilter(_1695338, _1695340), _1695342))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695338)), hAPP(c_List_Ofilter(_1695338, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1695338), c_fNot), _1695340)), _1695342))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695338)), _1695342))], (45596 ^ _779308) ^ [_1695414, _1695416, _1695418] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1695414, tc_HOL_Obool)), hAPP(c_List_Oset(_1695414), hAPP(c_List_Ofilter(_1695414, _1695416), _1695418))), hAPP(c_List_Oset(_1695414), _1695418))))], (45608 ^ _779308) ^ [_1695685, _1695687, _1695689] : [45610 ^ _779308 : [(45611 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1695685), 45609 ^ [_1695685, _1695687, _1695689]), hAPP(c_List_Oset(_1695685), _1695689))))], (45613 ^ _779308) ^ [] : [hBOOL(hAPP(_1695687, 45609 ^ [_1695685, _1695687, _1695689]))]], -(hAPP(c_List_Ofilter(_1695685, _1695687), _1695689) = _1695689)], (45598 ^ _779308) ^ [_1695485, _1695487, _1695489] : [hAPP(c_List_Ofilter(_1695485, _1695487), _1695489) = _1695489, 45601 ^ _779308 : [(45602 ^ _779308) ^ [_1695576] : [hBOOL(hAPP(hAPP(c_member(_1695485), _1695576), hAPP(c_List_Oset(_1695485), _1695489))), -(hBOOL(hAPP(_1695487, _1695576)))]]], (45617 ^ _779308) ^ [_1695877, _1695879, _1695881] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695877)), hAPP(c_List_Ofilter(_1695877, _1695879), _1695881))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695877)), _1695881))))], (45619 ^ _779308) ^ [_1695929, _1695931, _1695933] : [-(c_List_Opartition(_1695929, _1695931, _1695933) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695929), tc_List_Olist(_1695929)), hAPP(c_List_Ofilter(_1695929, _1695931), _1695933)), hAPP(c_List_Ofilter(_1695929, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1695929, c_fNot), _1695931)), _1695933)))], (45621 ^ _779308) ^ [_1695993, _1695995, _1695997] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1695993), tc_List_Olist(_1695993)), c_List_Opartition(_1695993, _1695995, _1695997)) = hAPP(c_List_Ofilter(_1695993, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1695993, c_fNot), _1695995)), _1695997))], (45623 ^ _779308) ^ [_1696048, _1696050, _1696052] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1696048), tc_List_Olist(_1696048)), c_List_Opartition(_1696048, _1696050, _1696052)) = hAPP(c_List_Ofilter(_1696048, _1696050), _1696052))], (45625 ^ _779308) ^ [_1696095, _1696097, _1696099, _1696101] : [-(hAPP(c_List_Ofilter(_1696095, _1696097), hAPP(c_List_Ofilter(_1696095, _1696099), _1696101)) = hAPP(c_List_Ofilter(_1696095, hAPP(hAPP(c_COMBS(_1696095, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1696095), c_fconj), _1696099)), _1696097)), _1696101))], (45627 ^ _779308) ^ [_1696162, _1696164, _1696166, _1696168] : [-(hAPP(c_List_Ofilter(_1696162, _1696164), c_List_Oremove1(_1696162, _1696166, _1696168)) = c_List_Oremove1(_1696162, _1696166, hAPP(c_List_Ofilter(_1696162, _1696164), _1696168)))], (45629 ^ _779308) ^ [_1696207, _1696209, _1696211, _1696213] : [-(hBOOL(hAPP(_1696207, _1696209))), -(c_List_Oremove1(_1696211, _1696209, hAPP(c_List_Ofilter(_1696211, _1696207), _1696213)) = hAPP(c_List_Ofilter(_1696211, _1696207), _1696213))], (45635 ^ _779308) ^ [_1696265, _1696267, _1696269, _1696271, _1696273, _1696275] : [class_Orderings_Olinorder(_1696265), -(hBOOL(hAPP(_1696267, _1696269))), -(hAPP(c_List_Ofilter(_1696271, _1696267), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696271, _1696265, _1696273), _1696269), _1696275)) = hAPP(c_List_Ofilter(_1696271, _1696267), _1696275))], (45645 ^ _779308) ^ [_1696411, _1696413, _1696415, _1696417, _1696419] : [-(hAPP(c_List_Ofilter(_1696411, _1696413), hAPP(hAPP(c_List_Omap(_1696415, _1696411), _1696417), _1696419)) = hAPP(hAPP(c_List_Omap(_1696415, _1696411), _1696417), hAPP(c_List_Ofilter(_1696415, hAPP(c_Fun_Ocomp(_1696411, tc_HOL_Obool, _1696415, _1696413), _1696417)), _1696419)))], (45647 ^ _779308) ^ [_1696480, _1696482] : [-(hAPP(c_List_Ofilter(_1696480, _1696482), c_List_Olist_ONil(_1696480)) = c_List_Olist_ONil(_1696480))], (45649 ^ _779308) ^ [_1696515] : [-(c_List_Otranspose(_1696515, c_List_Olist_ONil(tc_List_Olist(_1696515))) = c_List_Olist_ONil(tc_List_Olist(_1696515)))], (45651 ^ _779308) ^ [_1696564, _1696566, _1696568, _1696570] : [hBOOL(hAPP(_1696564, _1696566)), -(hAPP(c_List_Ofilter(_1696568, _1696564), hAPP(hAPP(c_List_Olist_OCons(_1696568), _1696566), _1696570)) = hAPP(hAPP(c_List_Olist_OCons(_1696568), _1696566), hAPP(c_List_Ofilter(_1696568, _1696564), _1696570)))], (45657 ^ _779308) ^ [_1696699, _1696701, _1696703, _1696705] : [-(hBOOL(hAPP(_1696699, _1696701))), -(hAPP(c_List_Ofilter(_1696703, _1696699), hAPP(hAPP(c_List_Olist_OCons(_1696703), _1696701), _1696705)) = hAPP(c_List_Ofilter(_1696703, _1696699), _1696705))], (45663 ^ _779308) ^ [_1696763, _1696765, _1696767, _1696769] : [-(hAPP(c_List_Ofilter(_1696763, _1696765), hAPP(hAPP(c_List_Oappend(_1696763), _1696767), _1696769)) = hAPP(hAPP(c_List_Oappend(_1696763), hAPP(c_List_Ofilter(_1696763, _1696765), _1696767)), hAPP(c_List_Ofilter(_1696763, _1696765), _1696769)))], (45675 ^ _779308) ^ [_1697049, _1697051, _1697053] : [45677 ^ _779308 : [(45678 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1697049), 45676 ^ [_1697049, _1697051, _1697053]), hAPP(c_List_Oset(_1697049), _1697053))))], (45680 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1697051, 45676 ^ [_1697049, _1697051, _1697053])))]], -(hAPP(c_List_Ofilter(_1697049, _1697051), _1697053) = c_List_Olist_ONil(_1697049))], (45665 ^ _779308) ^ [_1696844, _1696846, _1696848] : [hAPP(c_List_Ofilter(_1696844, _1696846), _1696848) = c_List_Olist_ONil(_1696844), 45668 ^ _779308 : [(45669 ^ _779308) ^ [_1696941] : [hBOOL(hAPP(hAPP(c_member(_1696844), _1696941), hAPP(c_List_Oset(_1696844), _1696848))), hBOOL(hAPP(_1696846, _1696941))]]], (45684 ^ _779308) ^ [_1697166, _1697168, _1697170, _1697172, _1697174] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697166)), hAPP(c_List_Ofilter(_1697166, _1697168), hAPP(hAPP(c_List_Omap(_1697170, _1697166), _1697172), _1697174))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697170)), hAPP(c_List_Ofilter(_1697170, hAPP(c_Fun_Ocomp(_1697166, tc_HOL_Obool, _1697170, _1697168), _1697172)), _1697174)))], (45686 ^ _779308) ^ [_1697240, _1697242, _1697244] : [-(c_List_Oremdups(_1697240, hAPP(c_List_Ofilter(_1697240, _1697242), _1697244)) = hAPP(c_List_Ofilter(_1697240, _1697242), c_List_Oremdups(_1697240, _1697244)))], (45688 ^ _779308) ^ [_1697281, _1697283, _1697285, _1697287] : [-(hBOOL(hAPP(_1697281, _1697283))), -(hAPP(c_List_OremoveAll(_1697285, _1697283), hAPP(c_List_Ofilter(_1697285, _1697281), _1697287)) = hAPP(c_List_Ofilter(_1697285, _1697281), _1697287))], (45694 ^ _779308) ^ [_1697341, _1697343] : [-(c_List_OremoveAll(_1697341, _1697343) = c_List_Ofilter(_1697341, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1697341), c_fNot), hAPP(c_fequal, _1697343))))], (45696 ^ _779308) ^ [_1697385, _1697387] : [-(c_List_Otranspose(_1697385, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1697385)), c_List_Olist_ONil(_1697385)), _1697387)) = c_List_Otranspose(_1697385, _1697387))], (45698 ^ _779308) ^ [_1697428, _1697430, _1697432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697428), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1697430))), c_List_Otranspose(_1697430, _1697432)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1697430)), c_List_Otranspose(_1697430, _1697432)), _1697428) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1697430), _1697430), hAPP(hAPP(c_COMBC(tc_List_Olist(_1697430), tc_Nat_Onat, _1697430), c_List_Onth(_1697430)), _1697428)), hAPP(c_List_Ofilter(tc_List_Olist(_1697430), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1697430)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697428)), c_Nat_Osize__class_Osize(tc_List_Olist(_1697430)))), _1697432)))], (45704 ^ _779308) ^ [_1697671, _1697673, _1697675, _1697677] : [-(c_List_Otranspose(_1697671, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1697673), tc_List_Olist(_1697671)), hAPP(c_List_Omap(_1697673, _1697671), _1697675)), _1697677)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1697673), tc_List_Olist(_1697671)), hAPP(c_List_Omap(_1697673, _1697671), _1697675)), c_List_Otranspose(_1697673, _1697677)))], (45706 ^ _779308) ^ [_1697744, _1697746, _1697748] : [-(hAPP(c_List_Oset(_1697744), hAPP(c_List_Ofilter(_1697744, _1697746), _1697748)) = hAPP(c_Set_OCollect(_1697744), hAPP(hAPP(c_COMBS(_1697744, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1697744), c_fconj), hAPP(hAPP(c_COMBC(_1697744, tc_fun(_1697744, tc_HOL_Obool), tc_HOL_Obool), c_member(_1697744)), hAPP(c_List_Oset(_1697744), _1697748)))), _1697746)))], (45708 ^ _779308) ^ [_1697827, _1697829, _1697831, _1697833] : [hBOOL(hAPP(hAPP(c_member(_1697827), _1697829), hAPP(c_List_Oset(_1697827), _1697831))), -(hBOOL(hAPP(_1697833, _1697829))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697827)), hAPP(c_List_Ofilter(_1697827, _1697833), _1697831))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697827)), _1697831))))], (45718 ^ _779308) ^ [_1698001, _1698003, _1698005] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1698001, tc_HOL_Obool)), hAPP(c_List_Oset(_1698001), _1698003)), hAPP(hAPP(c_Set_Oinsert(_1698001), _1698005), c_Orderings_Obot__class_Obot(tc_fun(_1698001, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1698001), hAPP(c_List_Ofilter(_1698001, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698001), c_fNot), hAPP(hAPP(c_COMBC(_1698001, _1698001, tc_HOL_Obool), c_fequal), _1698005))), _1698003)))], (45720 ^ _779308) ^ [_1698088, _1698090, _1698092] : [hBOOL(hAPP(c_List_Odistinct(_1698088), _1698090)), -(hAPP(c_List_Ofilter(_1698088, hAPP(hAPP(c_COMBC(_1698088, tc_fun(_1698088, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698088)), hAPP(c_List_Oset(_1698088), c_List_Osublist(_1698088, _1698090, _1698092)))), _1698090) = c_List_Osublist(_1698088, _1698090, _1698092))], (45736 ^ _779308) ^ [_1698468, _1698470] : [45738 ^ _779308 : [(45739 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698468)), 45737 ^ [_1698468, _1698470]), hAPP(c_List_Oset(tc_List_Olist(_1698468)), _1698470))))], (45741 ^ _779308) ^ [] : [45737 ^ [_1698468, _1698470] = c_List_Olist_ONil(_1698468)]], -(c_List_Otranspose(_1698468, _1698470) = c_List_Olist_ONil(tc_List_Olist(_1698468)))], (45726 ^ _779308) ^ [_1698258, _1698260] : [c_List_Otranspose(_1698258, _1698260) = c_List_Olist_ONil(tc_List_Olist(_1698258)), 45729 ^ _779308 : [(45730 ^ _779308) ^ [_1698353] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1698258)), _1698353), hAPP(c_List_Oset(tc_List_Olist(_1698258)), _1698260))), -(_1698353 = c_List_Olist_ONil(_1698258))]]], (45745 ^ _779308) ^ [_1698663, _1698665, _1698667] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698663)), hAPP(c_List_Ofilter(_1698663, _1698665), _1698667)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698663)), _1698667)))), hAPP(hAPP(c_COMBB(_1698663, tc_HOL_Obool, tc_Nat_Onat), _1698665), hAPP(c_List_Onth(_1698663), _1698667))))))], (45747 ^ _779308) ^ [_1698743, _1698745] : [-(c_List_Oconcat(tc_List_Olist(_1698743), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698743), tc_List_Olist(tc_List_Olist(_1698743))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1698743)), _1698743, c_List_Olist_ONil(tc_List_Olist(_1698743)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1698743), tc_List_Olist(tc_List_Olist(_1698743))), _1698743), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698743), tc_List_Olist(tc_List_Olist(_1698743)), tc_List_Olist(tc_List_Olist(_1698743))), c_List_Olist_OCons(tc_List_Olist(_1698743))), c_List_Olist_ONil(tc_List_Olist(_1698743)))))), _1698745)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698743), tc_List_Olist(_1698743)), c_List_Otl(_1698743)), hAPP(c_List_Ofilter(tc_List_Olist(_1698743), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1698743)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698743), tc_List_Olist(_1698743), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1698743)))), _1698745)))], (45749 ^ _779308) ^ [_1698895, _1698897, _1698899, _1698901] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1698895)), c_List_Otranspose__rel(_1698895)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698895)), hAPP(hAPP(c_List_Olist_OCons(_1698895), _1698897), _1698899)), _1698901))), -(c_List_Otranspose(_1698895, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698895)), hAPP(hAPP(c_List_Olist_OCons(_1698895), _1698897), _1698899)), _1698901)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698895)), hAPP(hAPP(c_List_Olist_OCons(_1698895), _1698897), c_List_Oconcat(_1698895, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698895), tc_List_Olist(_1698895)), c_List_Olist_Olist__case(tc_List_Olist(_1698895), _1698895, c_List_Olist_ONil(_1698895), hAPP(hAPP(c_COMBB(tc_List_Olist(_1698895), tc_fun(tc_List_Olist(_1698895), tc_List_Olist(_1698895)), _1698895), c_COMBK(tc_List_Olist(_1698895), tc_List_Olist(_1698895))), hAPP(hAPP(c_COMBC(_1698895, tc_List_Olist(_1698895), tc_List_Olist(_1698895)), c_List_Olist_OCons(_1698895)), c_List_Olist_ONil(_1698895))))), _1698901)))), c_List_Otranspose(_1698895, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698895)), _1698899), c_List_Oconcat(tc_List_Olist(_1698895), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698895), tc_List_Olist(tc_List_Olist(_1698895))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1698895)), _1698895, c_List_Olist_ONil(tc_List_Olist(_1698895)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1698895), tc_List_Olist(tc_List_Olist(_1698895))), _1698895), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698895), tc_List_Olist(tc_List_Olist(_1698895)), tc_List_Olist(tc_List_Olist(_1698895))), c_List_Olist_OCons(tc_List_Olist(_1698895))), c_List_Olist_ONil(tc_List_Olist(_1698895)))))), _1698901))))))], (45755 ^ _779308) ^ [_1699428, _1699430] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1699428)), c_List_Otranspose__rel(_1699428)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699428)), c_List_Olist_ONil(_1699428)), _1699430))), -(c_List_Otranspose(_1699428, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699428)), c_List_Olist_ONil(_1699428)), _1699430)) = c_List_Otranspose(_1699428, _1699430))], (45761 ^ _779308) ^ [_1699587, _1699589, _1699591, _1699593] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1699587, tc_Nat_Onat), _1699587), c_Product__Type_Ofst(_1699587, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1699587, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1699587, tc_Nat_Onat)), _1699589), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1699587, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1699587, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1699587, tc_Nat_Onat), _1699591), _1699593))) = hAPP(hAPP(c_List_Omap(tc_prod(_1699587, tc_Nat_Onat), _1699587), c_Product__Type_Ofst(_1699587, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1699587, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1699587, tc_Nat_Onat)), _1699589), c_Product__Type_Osnd(_1699587, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1699587, tc_Nat_Onat), _1699591), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1699593)))))], (45763 ^ _779308) ^ [_1699730, _1699732] : [-(c_Random_Oselect__weight(_1699730, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1699730), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1699730, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1699730, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1699730)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1699732)) = c_Random_Oselect__weight(_1699730, _1699732))], (45765 ^ _779308) ^ [_1699793, _1699795] : [-(c_Random_Opick(_1699793, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1699793), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1699793, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1699793, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1699793)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1699795)) = c_Random_Opick(_1699793, _1699795))], (45767 ^ _779308) ^ [_1699856] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1699856)), c_List_Otranspose__rel(_1699856)), c_List_Olist_ONil(tc_List_Olist(_1699856)))), -(c_List_Otranspose(_1699856, c_List_Olist_ONil(tc_List_Olist(_1699856))) = c_List_Olist_ONil(tc_List_Olist(_1699856)))], (45773 ^ _779308) ^ [_1699983, _1699985] : [-(c_List_Ofoldr(tc_List_Olist(_1699983), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1699983)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1699983))), c_List_Otranspose(_1699983, _1699985), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699983))), hAPP(c_List_Ofilter(tc_List_Olist(_1699983), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1699983)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699983), tc_List_Olist(_1699983), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1699983)))), _1699985)))], (45775 ^ _779308) ^ [_1700080, _1700082, _1700084, _1700086] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700080)), _1700082))), c_List_Ofoldr(tc_List_Olist(_1700084), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700084)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700084))), _1700086, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700080)), _1700082)), c_List_Ofoldr(tc_List_Olist(_1700084), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700084)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700084), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700084)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700084)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1700084), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700084)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700084), tc_List_Olist(_1700084), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700084)))), _1700086), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (45777 ^ _779308) ^ [_1700249, _1700251, _1700253, _1700255] : [-(c_List_Ofoldr(_1700249, _1700251, _1700253, c_List_Olist_ONil(_1700249), _1700255) = _1700255)], (45779 ^ _779308) ^ [_1700286, _1700288, _1700290, _1700292, _1700294, _1700296] : [-(c_List_Ofoldr(_1700286, _1700288, _1700290, hAPP(hAPP(c_List_Olist_OCons(_1700286), _1700292), _1700294), _1700296) = hAPP(hAPP(_1700290, _1700292), c_List_Ofoldr(_1700286, _1700288, _1700290, _1700294, _1700296)))], (45781 ^ _779308) ^ [_1700345, _1700347, _1700349, _1700351, _1700353, _1700355] : [-(c_List_Ofoldr(_1700345, _1700347, _1700349, hAPP(hAPP(c_List_Oappend(_1700345), _1700351), _1700353), _1700355) = c_List_Ofoldr(_1700345, _1700347, _1700349, _1700351, c_List_Ofoldr(_1700345, _1700347, _1700349, _1700353, _1700355)))], (45783 ^ _779308) ^ [_1700404, _1700406, _1700408] : [class_Groups_Oab__semigroup__add(_1700404), -(c_List_Ofoldr(_1700404, _1700404, c_Groups_Oplus__class_Oplus(_1700404), _1700406, _1700408) = hAPP(c_List_Ofoldl(_1700404, _1700404, c_Groups_Oplus__class_Oplus(_1700404), _1700408), _1700406))], (45789 ^ _779308) ^ [_1700517, _1700519, _1700521, _1700523, _1700525, _1700527, _1700529] : [-(c_List_Ofoldr(_1700517, _1700519, _1700521, hAPP(hAPP(c_List_Omap(_1700523, _1700517), _1700525), _1700527), _1700529) = c_List_Ofoldr(_1700523, _1700519, hAPP(c_Fun_Ocomp(_1700517, tc_fun(_1700519, _1700519), _1700523, _1700521), _1700525), _1700527, _1700529))], (45791 ^ _779308) ^ [_1700584, _1700586] : [class_Groups_Omonoid__add(_1700584), -(hAPP(c_List_Ofoldl(_1700584, _1700584, c_Groups_Oplus__class_Oplus(_1700584), c_Groups_Ozero__class_Ozero(_1700584)), _1700586) = c_List_Ofoldr(_1700584, _1700584, c_Groups_Oplus__class_Oplus(_1700584), _1700586, c_Groups_Ozero__class_Ozero(_1700584)))], (45797 ^ _779308) ^ [_1700703, _1700705, _1700707] : [class_Groups_Omonoid__add(_1700703), -(hAPP(c_List_Ofoldl(_1700703, _1700703, c_Groups_Oplus__class_Oplus(_1700703), _1700705), _1700707) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1700703), _1700705), c_List_Ofoldr(_1700703, _1700703, c_Groups_Oplus__class_Oplus(_1700703), _1700707, c_Groups_Ozero__class_Ozero(_1700703))))], (45803 ^ _779308) ^ [_1700836, _1700838] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1700836))), c_List_Otranspose(_1700836, _1700838)) = c_List_Ofoldr(tc_List_Olist(_1700836), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700836)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700836))), _1700838, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45805 ^ _779308) ^ [_1700897, _1700899, _1700901] : [-(c_List_Osublist(_1700897, _1700899, _1700901) = hAPP(hAPP(c_List_Omap(tc_prod(_1700897, tc_Nat_Onat), _1700897), c_Product__Type_Ofst(_1700897, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1700897, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1700897, tc_Nat_Onat), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_prod(_1700897, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1700897, tc_Nat_Onat))), _1700901)), hAPP(hAPP(c_List_Ozip(_1700897, tc_Nat_Onat), _1700899), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700897)), _1700899))))))], (45807 ^ _779308) ^ [_1701000, _1701002, _1701004, _1701006] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1701000, tc_Nat_Onat), _1701000), c_Product__Type_Ofst(_1701000, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701000, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701000, tc_Nat_Onat), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_prod(_1701000, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1701000, tc_Nat_Onat))), _1701002)), hAPP(hAPP(c_List_Ozip(_1701000, tc_Nat_Onat), _1701004), c_List_Oupt(_1701006, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701006), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701000)), _1701004)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1701000, tc_Nat_Onat), _1701000), c_Product__Type_Ofst(_1701000, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701000, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701000, tc_Nat_Onat), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), tc_prod(_1701000, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1701000, tc_Nat_Onat), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_prod(_1701000, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1701000, tc_Nat_Onat))), _1701006))), _1701002)), hAPP(hAPP(c_List_Ozip(_1701000, tc_Nat_Onat), _1701004), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701000)), _1701004))))))], (45809 ^ _779308) ^ [_1701205, _1701207] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1701205), _1701207) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701205, _1701207)))], (45811 ^ _779308) ^ [_1701242, _1701244] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1701242, _1701244)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1701242), _1701244))], (45813 ^ _779308) ^ [_1701279, _1701281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701279), _1701281)), -(c_List_Oupt(_1701279, hAPP(c_Nat_OSuc, _1701281)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1701279, _1701281)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1701281), c_List_Olist_ONil(tc_Nat_Onat))))], (45819 ^ _779308) ^ [_1701417, _1701419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701417), _1701419)), -(c_List_Oupt(_1701417, hAPP(c_Nat_OSuc, _1701419)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1701417, _1701419)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1701419), c_List_Olist_ONil(tc_Nat_Onat))))], (45825 ^ _779308) ^ [_1701540, _1701542] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701540), _1701542))), -(c_List_Oupt(_1701540, hAPP(c_Nat_OSuc, _1701542)) = c_List_Olist_ONil(tc_Nat_Onat))], (45831 ^ _779308) ^ [_1701589, _1701591, _1701593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1701589), _1701591)), -(c_List_Oupt(_1701589, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701591), _1701593)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1701589, _1701591)), c_List_Oupt(_1701591, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701591), _1701593))))], (45837 ^ _779308) ^ [_1701741, _1701743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701741), _1701743)), -(c_List_Oupt(_1701741, _1701743) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1701741), c_List_Oupt(hAPP(c_Nat_OSuc, _1701741), _1701743)))], (45843 ^ _779308) ^ [_1701852, _1701854] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701852), _1701854))), -(c_List_Oupt(_1701852, _1701854) = c_List_Olist_ONil(tc_Nat_Onat))], (45849 ^ _779308) ^ [_1701898, _1701900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701898), _1701900)), -(c_List_Oupt(_1701898, _1701900) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1701898), c_List_Oupt(hAPP(c_Nat_OSuc, _1701898), _1701900)))], (45855 ^ _779308) ^ [_1702015, _1702017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702015), _1702017)), -(c_List_Oupt(_1702017, _1702015) = c_List_Olist_ONil(tc_Nat_Onat))], (45871 ^ _779308) ^ [_1702225, _1702227] : [45872 ^ _779308 : [(45873 ^ _779308) ^ [] : [_1702227 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (45875 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702227), _1702225))]], -(c_List_Oupt(_1702225, _1702227) = c_List_Olist_ONil(tc_Nat_Onat))], (45861 ^ _779308) ^ [_1702123, _1702125] : [c_List_Oupt(_1702123, _1702125) = c_List_Olist_ONil(tc_Nat_Onat), -(_1702125 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702125), _1702123)))], (45879 ^ _779308) ^ [_1702358] : [-(c_List_Oupt(_1702358, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (45881 ^ _779308) ^ [_1702384, _1702386, _1702388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702384), _1702386)), _1702388)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1702386), c_List_Oupt(_1702384, _1702388)) = c_List_Oupt(_1702384, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702384), _1702386)))], (45887 ^ _779308) ^ [_1702521, _1702523] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1702521), _1702523)) = c_List_Oupt(_1702521, _1702523))], (45889 ^ _779308) ^ [_1702558, _1702560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702558), _1702560)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1702558, _1702560)) = _1702558)], (45895 ^ _779308) ^ [_1702657, _1702659, _1702661] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1702657), c_List_Oupt(_1702659, _1702661)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702659), _1702657), _1702661))], (45897 ^ _779308) ^ [_1702702, _1702704] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1702702, _1702704))))], (45899 ^ _779308) ^ [_1702732, _1702734] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1702732, _1702734)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1702734), _1702732))], (45901 ^ _779308) ^ [_1702778, _1702780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702778)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702780))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702778), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702780)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702778)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702778)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702780))))], (45907 ^ _779308) ^ [_1702931, _1702933] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702931)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702933)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702931), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1702933)) = c_List_Olist_ONil(tc_Nat_Onat))], (45913 ^ _779308) ^ [_1703010, _1703012, _1703014, _1703016] : [c_List_Oupt(_1703010, _1703012) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1703014), _1703016), 45916 ^ _779308 : [(45917 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703010), _1703012)))], (45919 ^ _779308) ^ [] : [-(_1703010 = _1703014)], (45921 ^ _779308) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703010), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1703012) = _1703016)]]], (45923 ^ _779308) ^ [_1703183, _1703185, _1703187, _1703189] : [-(c_List_Oupt(_1703183, _1703185) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1703187), _1703189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703183), _1703185)), _1703183 = _1703187, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703183), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1703185) = _1703189], (45937 ^ _779308) ^ [_1703424, _1703426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703424), _1703426)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1703424, _1703426)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1703426), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45943 ^ _779308) ^ [_1703535, _1703537] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1703535, _1703537)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1703535), hAPP(c_Nat_OSuc, _1703537)))], (45945 ^ _779308) ^ [_1703575, _1703577] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1703575, _1703577) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1703575, hAPP(c_Nat_OSuc, _1703577))))], (45947 ^ _779308) ^ [_1703613] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1703613) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1703613)))], (45949 ^ _779308) ^ [_1703645, _1703647, _1703649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703645), _1703647)), _1703649)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1703645, _1703649)), _1703647) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703645), _1703647))], (45955 ^ _779308) ^ [_1703776, _1703778] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1703776, _1703778) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1703776), hAPP(c_Nat_OSuc, _1703778))))], (45957 ^ _779308) ^ [_1703817, _1703819] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1703817, _1703819) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1703817), _1703819)))], (45959 ^ _779308) ^ [_1703855] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1703855) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1703855))))], (45961 ^ _779308) ^ [_1703890, _1703892] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1703890), hAPP(c_List_Onth(_1703890), _1703892)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703890)), _1703892))) = _1703892)], (45963 ^ _779308) ^ [_1703939, _1703941, _1703943, _1703945] : [class_Groups_Ocomm__monoid__add(_1703939), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1703939), _1703941), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1703943, _1703945))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1703939), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1703939), _1703941), c_List_Oupt(_1703943, _1703945))))], (45969 ^ _779308) ^ [_1704082, _1704084, _1704086, _1704088] : [class_Groups_Ocomm__monoid__add(_1704082), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1704082), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704082), _1704084), c_List_Oupt(_1704086, _1704088))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1704082), _1704084), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704086, _1704088))))], (45975 ^ _779308) ^ [_1704225, _1704227, _1704229, _1704231, _1704233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1704225), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1704227), _1704229))), -(hAPP(hAPP(c_List_Onth(_1704231), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704231), _1704233), c_List_Oupt(_1704229, _1704227))), _1704225) = hAPP(_1704233, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704229), _1704225)))], (45981 ^ _779308) ^ [_1704388, _1704390, _1704392] : [45982 ^ _779308 : [(45983 ^ _779308) ^ [] : [-(_1704388 = c_List_Olist_ONil(tc_List_Olist(_1704390)))], (45985 ^ _779308) ^ [] : [_1704392 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 45989 ^ _779308 : [(45990 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45988 ^ [_1704388, _1704390, _1704392]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1704390))), _1704388))))], (45992 ^ _779308) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704390)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1704390)), _1704388), 45988 ^ [_1704388, _1704390, _1704392])) = _1704392]], -(c_List_Otranspose(_1704390, _1704388) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1704390)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1704390)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1704390), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1704390)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1704390)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1704390), hAPP(hAPP(c_COMBB(tc_List_Olist(_1704390), tc_fun(tc_Nat_Onat, _1704390), tc_Nat_Onat), c_List_Onth(_1704390)), hAPP(c_List_Onth(tc_List_Olist(_1704390)), _1704388))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1704390))), _1704388)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1704392)))], (45996 ^ _779308) ^ [_1704898, _1704900, _1704902, _1704904, _1704906] : [class_Orderings_Olinorder(_1704898), hBOOL(hAPP(hAPP(c_member(_1704900), _1704902), hAPP(c_List_Oset(_1704900), _1704904))), c_List_Olinorder__class_Osorted(_1704898, hAPP(hAPP(c_List_Omap(_1704900, _1704898), _1704906), _1704904)), hAPP(c_List_Ohd(_1704900), hAPP(c_List_Ofilter(_1704900, hAPP(hAPP(c_COMBB(_1704898, tc_HOL_Obool, _1704900), hAPP(c_fequal, hAPP(_1704906, _1704902))), _1704906)), _1704904)) = _1704902, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1704900, _1704898, _1704906), _1704902), c_List_Oremove1(_1704900, _1704902, _1704904)) = _1704904)], (46014 ^ _779308) ^ [_1705277] : [class_Orderings_Olinorder(_1705277), -(c_List_Olinorder__class_Osorted(_1705277, c_List_Olist_ONil(_1705277)))], (46020 ^ _779308) ^ [_1705354, _1705356] : [class_Orderings_Olinorder(_1705354), -(c_List_Olinorder__class_Osorted(_1705354, hAPP(hAPP(c_List_Olist_OCons(_1705354), _1705356), c_List_Olist_ONil(_1705354))))], (46026 ^ _779308) ^ [_1705449, _1705451] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1705449, _1705451)))], (46028 ^ _779308) ^ [_1705477, _1705479] : [class_Orderings_Olinorder(_1705477), -(c_List_Olinorder__class_Osorted(_1705477, c_List_Olinorder__class_Osort__key(_1705477, _1705477, c_COMBI(_1705477), _1705479)))], (46034 ^ _779308) ^ [_1705566, _1705568, _1705570] : [class_Orderings_Olinorder(_1705566), c_List_Olinorder__class_Osorted(_1705566, _1705568), -(c_List_Olinorder__class_Osorted(_1705566, c_List_Olinorder__class_Oinsort__insert__key(_1705566, _1705566, c_COMBI(_1705566), _1705570, _1705568)))], (46044 ^ _779308) ^ [_1705713, _1705715, _1705717] : [class_Orderings_Olinorder(_1705713), c_List_Olinorder__class_Osorted(_1705713, _1705715), -(c_List_Olinorder__class_Osorted(_1705713, hAPP(hAPP(c_List_Odrop(_1705713), _1705717), _1705715)))], (46054 ^ _779308) ^ [_1705860, _1705862] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1705860, _1705862)))], (46056 ^ _779308) ^ [_1705888, _1705890, _1705892] : [class_Orderings_Olinorder(_1705888), c_List_Olinorder__class_Osorted(_1705888, _1705890), -(c_List_Olinorder__class_Osorted(_1705888, hAPP(hAPP(c_List_Otake(_1705888), _1705892), _1705890)))], (46066 ^ _779308) ^ [_1706035, _1706037, _1706039] : [class_Orderings_Olinorder(_1706035), c_List_Olinorder__class_Osorted(_1706035, _1706037), -(c_List_Olinorder__class_Osorted(_1706035, c_List_Oremove1(_1706035, _1706039, _1706037)))], (46076 ^ _779308) ^ [_1706174, _1706176] : [class_Orderings_Olinorder(_1706174), c_List_Olinorder__class_Osorted(_1706174, _1706176), -(c_List_Olinorder__class_Osorted(_1706174, hAPP(c_List_Otl(_1706174), _1706176)))], (46086 ^ _779308) ^ [_1706311, _1706313, _1706315] : [class_Orderings_Olinorder(_1706311), 46089 ^ _779308 : [(46090 ^ _779308) ^ [] : [c_List_Olinorder__class_Osorted(_1706311, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1706311, _1706311, c_COMBI(_1706311)), _1706313), _1706315)), -(c_List_Olinorder__class_Osorted(_1706311, _1706315))], (46096 ^ _779308) ^ [] : [c_List_Olinorder__class_Osorted(_1706311, _1706315), -(c_List_Olinorder__class_Osorted(_1706311, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1706311, _1706311, c_COMBI(_1706311)), _1706313), _1706315)))]]], (46102 ^ _779308) ^ [_1706558, _1706560] : [class_Orderings_Olinorder(_1706558), -(_1706560 = c_List_Olist_ONil(_1706558)), c_List_Olinorder__class_Osorted(_1706558, _1706560), -(c_List_Olinorder__class_Osorted(_1706558, c_List_Obutlast(_1706558, _1706560)))], (46116 ^ _779308) ^ [_1706750] : [class_Orderings_Olinorder(_1706750), -(c_List_Olinorder__class_Osorted(_1706750, c_List_Olist_ONil(_1706750)))], (46122 ^ _779308) ^ [_1706827, _1706829, _1706831, _1706833] : [class_Orderings_Olinorder(_1706827), 46125 ^ _779308 : [(46126 ^ _779308) ^ [] : [c_List_Olinorder__class_Osorted(_1706827, hAPP(hAPP(c_List_Olist_OCons(_1706827), _1706829), hAPP(hAPP(c_List_Olist_OCons(_1706827), _1706831), _1706833))), 46129 ^ _779308 : [(46130 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1706827), _1706829), _1706831)))], (46132 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1706827, hAPP(hAPP(c_List_Olist_OCons(_1706827), _1706831), _1706833)))]]], (46134 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1706827, hAPP(hAPP(c_List_Olist_OCons(_1706827), _1706829), hAPP(hAPP(c_List_Olist_OCons(_1706827), _1706831), _1706833)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1706827), _1706829), _1706831)), c_List_Olinorder__class_Osorted(_1706827, hAPP(hAPP(c_List_Olist_OCons(_1706827), _1706831), _1706833))]]], (46144 ^ _779308) ^ [_1707213, _1707215, _1707217, _1707219] : [class_Orderings_Olinorder(_1707213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707213), _1707215), _1707217)), c_List_Olinorder__class_Osorted(_1707213, hAPP(hAPP(c_List_Olist_OCons(_1707213), _1707217), _1707219)), -(c_List_Olinorder__class_Osorted(_1707213, hAPP(hAPP(c_List_Olist_OCons(_1707213), _1707215), hAPP(hAPP(c_List_Olist_OCons(_1707213), _1707217), _1707219))))], (46158 ^ _779308) ^ [_1707466, _1707468] : [class_Orderings_Olinorder(_1707466), c_List_Olinorder__class_Osorted(_1707466, _1707468), -(c_List_Olinorder__class_Osorted(_1707466, c_List_Oremdups(_1707466, _1707468)))], (46168 ^ _779308) ^ [_1707599, _1707601, _1707603] : [class_Orderings_Olinorder(_1707599), c_List_Olinorder__class_Osorted(_1707599, _1707601), hBOOL(hAPP(c_List_Odistinct(_1707599), _1707601)), c_List_Olinorder__class_Osorted(_1707599, _1707603), hBOOL(hAPP(c_List_Odistinct(_1707599), _1707603)), hAPP(c_List_Oset(_1707599), _1707601) = hAPP(c_List_Oset(_1707599), _1707603), -(_1707601 = _1707603)], (46194 ^ _779308) ^ [_1707982, _1707984, _1707986, _1707988] : [class_Orderings_Olinorder(_1707982), -(c_List_Olinorder__class_Osorted(_1707982, hAPP(hAPP(c_List_Omap(_1707984, _1707982), _1707986), c_List_Olinorder__class_Osort__key(_1707984, _1707982, _1707986, _1707988))))], (46200 ^ _779308) ^ [_1708089, _1708091, _1708093, _1708095, _1708097] : [class_Orderings_Olinorder(_1708089), c_List_Olinorder__class_Osorted(_1708089, hAPP(hAPP(c_List_Omap(_1708091, _1708089), _1708093), _1708095)), -(c_List_Olinorder__class_Osorted(_1708089, hAPP(hAPP(c_List_Omap(_1708091, _1708089), _1708093), c_List_Olinorder__class_Oinsort__insert__key(_1708091, _1708089, _1708093, _1708097, _1708095))))], (46210 ^ _779308) ^ [_1708276, _1708278, _1708280, _1708282, _1708284] : [class_Orderings_Olinorder(_1708276), c_List_Olinorder__class_Osorted(_1708276, hAPP(hAPP(c_List_Omap(_1708278, _1708276), _1708280), _1708282)), -(c_List_Olinorder__class_Osorted(_1708276, hAPP(hAPP(c_List_Omap(_1708278, _1708276), _1708280), c_List_Oremove1(_1708278, _1708284, _1708282))))], (46220 ^ _779308) ^ [_1708459, _1708461, _1708463, _1708465, _1708467] : [class_Orderings_Olinorder(_1708459), 46223 ^ _779308 : [(46224 ^ _779308) ^ [] : [c_List_Olinorder__class_Osorted(_1708459, hAPP(hAPP(c_List_Omap(_1708461, _1708459), _1708463), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1708461, _1708459, _1708463), _1708465), _1708467))), -(c_List_Olinorder__class_Osorted(_1708459, hAPP(hAPP(c_List_Omap(_1708461, _1708459), _1708463), _1708467)))], (46230 ^ _779308) ^ [] : [c_List_Olinorder__class_Osorted(_1708459, hAPP(hAPP(c_List_Omap(_1708461, _1708459), _1708463), _1708467)), -(c_List_Olinorder__class_Osorted(_1708459, hAPP(hAPP(c_List_Omap(_1708461, _1708459), _1708463), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1708461, _1708459, _1708463), _1708465), _1708467))))]]], (46236 ^ _779308) ^ [_1708766, _1708768, _1708770, _1708772, _1708774] : [class_Orderings_Olinorder(_1708766), c_List_Olinorder__class_Osorted(_1708766, hAPP(hAPP(c_List_Omap(_1708768, _1708766), _1708770), _1708772)), -(c_List_Olinorder__class_Osorted(_1708766, hAPP(hAPP(c_List_Omap(_1708768, _1708766), _1708770), hAPP(c_List_Ofilter(_1708768, _1708774), _1708772))))], (46246 ^ _779308) ^ [_1708953, _1708955, _1708957, _1708959, _1708961] : [class_Orderings_Olinorder(_1708953), -(c_List_Olinorder__class_Osorted(_1708953, hAPP(hAPP(c_List_Omap(_1708955, _1708953), _1708957), hAPP(c_List_Ofilter(_1708955, hAPP(hAPP(c_COMBC(_1708955, _1708953, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1708953, tc_fun(_1708953, tc_HOL_Obool), _1708955), c_fequal), _1708957)), hAPP(_1708959, _1708961))), _1708961))))], (46252 ^ _779308) ^ [_1709116, _1709118, _1709120] : [class_Orderings_Olinorder(_1709116), -(c_List_Olinorder__class_Osorted(_1709116, hAPP(c_List_Ofilter(_1709116, hAPP(hAPP(c_COMBC(_1709116, _1709116, tc_HOL_Obool), c_fequal), hAPP(_1709118, _1709120))), _1709120)))], (46258 ^ _779308) ^ [_1709231, _1709233, _1709235] : [class_Orderings_Olinorder(_1709231), 46261 ^ _779308 : [(46262 ^ _779308) ^ [] : [c_List_Olinorder__class_Osorted(_1709231, hAPP(hAPP(c_List_Olist_OCons(_1709231), _1709233), _1709235)), 46265 ^ _779308 : [(46266 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709231, _1709235))], (46268 ^ _779308) ^ [_1709417] : [hBOOL(hAPP(hAPP(c_member(_1709231), _1709417), hAPP(c_List_Oset(_1709231), _1709235))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709231), _1709233), _1709417)))]]], (46274 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709231, hAPP(hAPP(c_List_Olist_OCons(_1709231), _1709233), _1709235))), c_List_Olinorder__class_Osorted(_1709231, _1709235), 46280 ^ _779308 : [(46281 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709231), 46279 ^ [_1709231, _1709233, _1709235]), hAPP(c_List_Oset(_1709231), _1709235))))], (46283 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709231), _1709233), 46279 ^ [_1709231, _1709233, _1709235]))]]]]], (46287 ^ _779308) ^ [_1709756, _1709758, _1709760] : [class_Orderings_Olinorder(_1709756), 46290 ^ _779308 : [(46291 ^ _779308) ^ [] : [c_List_Olinorder__class_Osorted(_1709756, hAPP(hAPP(c_List_Oappend(_1709756), _1709758), _1709760)), 46294 ^ _779308 : [(46295 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709756, _1709758))], (46297 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709756, _1709760))], (46299 ^ _779308) ^ [_1709992] : [hBOOL(hAPP(hAPP(c_member(_1709756), _1709992), hAPP(c_List_Oset(_1709756), _1709758))), 46302 ^ _779308 : [(46303 ^ _779308) ^ [_1710102] : [hBOOL(hAPP(hAPP(c_member(_1709756), _1710102), hAPP(c_List_Oset(_1709756), _1709760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709756), _1709992), _1710102)))]]]]], (46309 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1709756, hAPP(hAPP(c_List_Oappend(_1709756), _1709758), _1709760))), c_List_Olinorder__class_Osorted(_1709756, _1709758), c_List_Olinorder__class_Osorted(_1709756, _1709760), 46319 ^ _779308 : [(46320 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709756), 46318 ^ [_1709756, _1709758, _1709760]), hAPP(c_List_Oset(_1709756), _1709758))))], (46323 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1709756), 46321 ^ [_1709756, _1709758, _1709760]), hAPP(c_List_Oset(_1709756), _1709760))))], (46325 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1709756), 46318 ^ [_1709756, _1709758, _1709760]), 46321 ^ [_1709756, _1709758, _1709760]))]]]]], (46329 ^ _779308) ^ [_1710604, _1710606, _1710608, _1710610, _1710612, _1710614] : [class_Orderings_Olinorder(_1710604), c_List_Olinorder__class_Osorted(_1710604, hAPP(hAPP(c_List_Omap(_1710606, _1710604), _1710608), _1710610)), hBOOL(hAPP(_1710612, _1710614)), -(hAPP(c_List_Ofilter(_1710606, _1710612), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1710606, _1710604, _1710608), _1710614), _1710610)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1710606, _1710604, _1710608), _1710614), hAPP(c_List_Ofilter(_1710606, _1710612), _1710610)))], (46343 ^ _779308) ^ [_1710893, _1710895, _1710897] : [class_Orderings_Olinorder(_1710893), 46346 ^ _779308 : [(46347 ^ _779308) ^ [] : [c_List_Olinorder__class_Osorted(_1710893, hAPP(hAPP(c_List_Olist_OCons(_1710893), _1710895), _1710897)), 46350 ^ _779308 : [(46357 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710893, _1710897))], (46351 ^ _779308) ^ [_1711061] : [hBOOL(hAPP(hAPP(c_member(_1710893), _1711061), hAPP(c_List_Oset(_1710893), _1710897))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710893), _1710895), _1711061)))]]], (46359 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710893, hAPP(hAPP(c_List_Olist_OCons(_1710893), _1710895), _1710897))), 46363 ^ _779308 : [(46364 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1710893), 46362 ^ [_1710893, _1710895, _1710897]), hAPP(c_List_Oset(_1710893), _1710897))))], (46366 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710893), _1710895), 46362 ^ [_1710893, _1710895, _1710897]))]], c_List_Olinorder__class_Osorted(_1710893, _1710897)]]], (46372 ^ _779308) ^ [_1711419, _1711421] : [class_Orderings_Olinorder(_1711419), hBOOL(hAPP(c_Finite__Set_Ofinite(_1711419), _1711421)), 46379 ^ _779308 : [(46380 ^ _779308) ^ [] : [-(hAPP(c_List_Oset(_1711419), c_List_Olinorder__class_Osorted__list__of__set(_1711419, _1711421)) = _1711421)], (46382 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711419, c_List_Olinorder__class_Osorted__list__of__set(_1711419, _1711421)))], (46384 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1711419), c_List_Olinorder__class_Osorted__list__of__set(_1711419, _1711421))))]]], (46386 ^ _779308) ^ [_1711640, _1711642, _1711644] : [class_Orderings_Olinorder(_1711640), hBOOL(hAPP(hAPP(c_member(_1711640), _1711642), hAPP(c_List_Oset(_1711640), _1711644))), c_List_Olinorder__class_Osorted(_1711640, _1711644), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1711640, _1711640, c_COMBI(_1711640)), _1711642), c_List_Oremove1(_1711640, _1711642, _1711644)) = _1711644)], (46400 ^ _779308) ^ [_1711881, _1711883, _1711885, _1711887] : [class_Orderings_Olinorder(_1711881), c_List_Olinorder__class_Osorted(_1711881, _1711883), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1711885), _1711887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711887), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711881)), _1711883))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711881), hAPP(hAPP(c_List_Onth(_1711881), _1711883), _1711885)), hAPP(hAPP(c_List_Onth(_1711881), _1711883), _1711887))))], (46418 ^ _779308) ^ [_1712208, _1712210] : [class_Orderings_Olinorder(_1712208), 46421 ^ _779308 : [(46436 ^ _779308) ^ [] : [46438 ^ _779308 : [(46439 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46437 ^ [_1712208, _1712210]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712208)), _1712210))))], (46442 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46440 ^ [_1712208, _1712210]), 46437 ^ [_1712208, _1712210])))], (46444 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712208), hAPP(hAPP(c_List_Onth(_1712208), _1712210), 46440 ^ [_1712208, _1712210])), hAPP(hAPP(c_List_Onth(_1712208), _1712210), 46437 ^ [_1712208, _1712210])))]], -(c_List_Olinorder__class_Osorted(_1712208, _1712210))], (46422 ^ _779308) ^ [] : [c_List_Olinorder__class_Osorted(_1712208, _1712210), 46425 ^ _779308 : [(46426 ^ _779308) ^ [_1712379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712379), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712208)), _1712210))), 46429 ^ _779308 : [(46430 ^ _779308) ^ [_1712496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712496), _1712379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712208), hAPP(hAPP(c_List_Onth(_1712208), _1712210), _1712496)), hAPP(hAPP(c_List_Onth(_1712208), _1712210), _1712379))))]]]]]]], (46448 ^ _779308) ^ [_1712932, _1712934, _1712936, _1712938, _1712940] : [class_Orderings_Olinorder(_1712932), c_Fun_Oinj__on(_1712934, _1712932, _1712936, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1712934, tc_HOL_Obool)), hAPP(c_List_Oset(_1712934), _1712938)), hAPP(c_List_Oset(_1712934), _1712940))), c_List_Olinorder__class_Osorted(_1712932, hAPP(hAPP(c_List_Omap(_1712934, _1712932), _1712936), _1712938)), hBOOL(hAPP(c_List_Odistinct(_1712932), hAPP(hAPP(c_List_Omap(_1712934, _1712932), _1712936), _1712938))), c_List_Olinorder__class_Osorted(_1712932, hAPP(hAPP(c_List_Omap(_1712934, _1712932), _1712936), _1712940)), hBOOL(hAPP(c_List_Odistinct(_1712932), hAPP(hAPP(c_List_Omap(_1712934, _1712932), _1712936), _1712940))), hAPP(c_List_Oset(_1712934), _1712938) = hAPP(c_List_Oset(_1712934), _1712940), -(_1712938 = _1712940)], (46478 ^ _779308) ^ [_1713515, _1713517, _1713519] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1713515), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1713515))), _1713517))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713519), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1713515))), _1713517))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1713515), _1713515), hAPP(hAPP(c_COMBC(tc_List_Olist(_1713515), tc_Nat_Onat, _1713515), c_List_Onth(_1713515)), _1713519)), hAPP(c_List_Ofilter(tc_List_Olist(_1713515), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1713515)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713519)), c_Nat_Osize__class_Osize(tc_List_Olist(_1713515)))), c_List_Otranspose(_1713515, _1713517))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1713515)), _1713517), _1713519))], (46488 ^ _779308) ^ [_1713842, _1713844, _1713846, _1713848] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1713842), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1713842))), _1713844))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713846), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1713842))), c_List_Otranspose(_1713842, _1713844)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713848), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1713842))), hAPP(c_List_Ofilter(tc_List_Olist(_1713842), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1713842)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713846)), c_Nat_Osize__class_Osize(tc_List_Olist(_1713842)))), _1713844)))), -(hAPP(hAPP(c_List_Onth(_1713842), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1713842)), c_List_Otranspose(_1713842, _1713844)), _1713846)), _1713848) = hAPP(hAPP(c_List_Onth(_1713842), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1713842)), _1713844), _1713848)), _1713846))], (46502 ^ _779308) ^ [_1714265, _1714267] : [-(c_Fun_Oinj__on(tc_List_Olist(_1714265), tc_List_Olist(_1714265), c_List_Orev(_1714265), _1714267))], (46504 ^ _779308) ^ [_1714313, _1714315] : [hBOOL(hAPP(c_List_Odistinct(_1714313), hAPP(c_List_Orev(_1714313), _1714315))), -(hBOOL(hAPP(c_List_Odistinct(_1714313), _1714315)))], (46510 ^ _779308) ^ [_1714412, _1714414] : [hBOOL(hAPP(c_List_Odistinct(_1714412), _1714414)), -(hBOOL(hAPP(c_List_Odistinct(_1714412), hAPP(c_List_Orev(_1714412), _1714414))))], (46516 ^ _779308) ^ [_1714532, _1714534] : [hAPP(c_List_Orev(_1714532), _1714534) = c_List_Olist_ONil(_1714532), -(_1714534 = c_List_Olist_ONil(_1714532))], (46522 ^ _779308) ^ [_1714623, _1714625] : [_1714625 = c_List_Olist_ONil(_1714623), -(hAPP(c_List_Orev(_1714623), _1714625) = c_List_Olist_ONil(_1714623))], (46528 ^ _779308) ^ [_1714735, _1714737] : [c_List_Olist_ONil(_1714735) = hAPP(c_List_Orev(_1714735), _1714737), -(_1714737 = c_List_Olist_ONil(_1714735))], (46534 ^ _779308) ^ [_1714826, _1714828] : [_1714828 = c_List_Olist_ONil(_1714826), -(c_List_Olist_ONil(_1714826) = hAPP(c_List_Orev(_1714826), _1714828))], (46540 ^ _779308) ^ [_1714923] : [-(hAPP(c_List_Orev(_1714923), c_List_Olist_ONil(_1714923)) = c_List_Olist_ONil(_1714923))], (46542 ^ _779308) ^ [_1714973, _1714975, _1714977] : [hAPP(hAPP(c_List_Olist_OCons(_1714973), _1714975), c_List_Olist_ONil(_1714973)) = hAPP(c_List_Orev(_1714973), _1714977), -(_1714977 = hAPP(hAPP(c_List_Olist_OCons(_1714973), _1714975), c_List_Olist_ONil(_1714973)))], (46548 ^ _779308) ^ [_1715098, _1715100, _1715102] : [_1715102 = hAPP(hAPP(c_List_Olist_OCons(_1715098), _1715100), c_List_Olist_ONil(_1715098)), -(hAPP(hAPP(c_List_Olist_OCons(_1715098), _1715100), c_List_Olist_ONil(_1715098)) = hAPP(c_List_Orev(_1715098), _1715102))], (46554 ^ _779308) ^ [_1715247, _1715249, _1715251] : [hAPP(c_List_Orev(_1715247), _1715249) = hAPP(hAPP(c_List_Olist_OCons(_1715247), _1715251), c_List_Olist_ONil(_1715247)), -(_1715249 = hAPP(hAPP(c_List_Olist_OCons(_1715247), _1715251), c_List_Olist_ONil(_1715247)))], (46560 ^ _779308) ^ [_1715372, _1715374, _1715376] : [_1715374 = hAPP(hAPP(c_List_Olist_OCons(_1715372), _1715376), c_List_Olist_ONil(_1715372)), -(hAPP(c_List_Orev(_1715372), _1715374) = hAPP(hAPP(c_List_Olist_OCons(_1715372), _1715376), c_List_Olist_ONil(_1715372)))], (46566 ^ _779308) ^ [_1715503, _1715505, _1715507] : [-(hAPP(c_List_Orev(_1715503), hAPP(hAPP(c_List_Oappend(_1715503), _1715505), _1715507)) = hAPP(hAPP(c_List_Oappend(_1715503), hAPP(c_List_Orev(_1715503), _1715507)), hAPP(c_List_Orev(_1715503), _1715505)))], (46568 ^ _779308) ^ [_1715561, _1715563] : [-(hAPP(c_List_Orev(_1715561), c_List_Oconcat(_1715561, _1715563)) = c_List_Oconcat(_1715561, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1715561), tc_List_Olist(_1715561)), c_List_Orev(_1715561)), hAPP(c_List_Orev(tc_List_Olist(_1715561)), _1715563))))], (46570 ^ _779308) ^ [_1715619, _1715621, _1715623, _1715625] : [-(hAPP(c_List_Orev(_1715619), hAPP(hAPP(c_List_Omap(_1715621, _1715619), _1715623), _1715625)) = hAPP(hAPP(c_List_Omap(_1715621, _1715619), _1715623), hAPP(c_List_Orev(_1715621), _1715625)))], (46572 ^ _779308) ^ [_1715676, _1715678, _1715680] : [-(hAPP(c_List_Orev(_1715676), hAPP(c_List_Ofilter(_1715676, _1715678), _1715680)) = hAPP(c_List_Ofilter(_1715676, _1715678), hAPP(c_List_Orev(_1715676), _1715680)))], (46574 ^ _779308) ^ [_1715725, _1715727, _1715729, _1715731] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715725)), _1715727) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1715729)), _1715731), -(hAPP(hAPP(c_List_Ozip(_1715725, _1715729), hAPP(c_List_Orev(_1715725), _1715727)), hAPP(c_List_Orev(_1715729), _1715731)) = hAPP(c_List_Orev(tc_prod(_1715725, _1715729)), hAPP(hAPP(c_List_Ozip(_1715725, _1715729), _1715727), _1715731)))], (46580 ^ _779308) ^ [_1715906, _1715908] : [-(hAPP(c_List_Oset(_1715906), hAPP(c_List_Orev(_1715906), _1715908)) = hAPP(c_List_Oset(_1715906), _1715908))], (46582 ^ _779308) ^ [_1715970, _1715972, _1715974, _1715976, _1715978] : [c_List_Olist__all2(_1715970, _1715972, _1715974, hAPP(c_List_Orev(_1715970), _1715976), hAPP(c_List_Orev(_1715972), _1715978)), -(c_List_Olist__all2(_1715970, _1715972, _1715974, _1715976, _1715978))], (46588 ^ _779308) ^ [_1716081, _1716083, _1716085, _1716087, _1716089] : [c_List_Olist__all2(_1716081, _1716083, _1716085, _1716087, _1716089), -(c_List_Olist__all2(_1716081, _1716083, _1716085, hAPP(c_List_Orev(_1716081), _1716087), hAPP(c_List_Orev(_1716083), _1716089)))], (46594 ^ _779308) ^ [_1716222, _1716224, _1716226, _1716228, _1716230] : [c_List_Olist__all2(_1716222, _1716224, _1716226, hAPP(c_List_Orev(_1716222), _1716228), _1716230), -(c_List_Olist__all2(_1716222, _1716224, _1716226, _1716228, hAPP(c_List_Orev(_1716224), _1716230)))], (46600 ^ _779308) ^ [_1716333, _1716335, _1716337, _1716339, _1716341] : [c_List_Olist__all2(_1716333, _1716335, _1716337, _1716339, hAPP(c_List_Orev(_1716335), _1716341)), -(c_List_Olist__all2(_1716333, _1716335, _1716337, hAPP(c_List_Orev(_1716333), _1716339), _1716341))], (46606 ^ _779308) ^ [_1716450, _1716452] : [-(hAPP(c_List_Orev(_1716450), hAPP(c_List_Orev(_1716450), _1716452)) = _1716452)], (46608 ^ _779308) ^ [_1716503, _1716505, _1716507] : [hAPP(c_List_Orev(_1716503), _1716505) = _1716507, -(_1716505 = hAPP(c_List_Orev(_1716503), _1716507))], (46614 ^ _779308) ^ [_1716598, _1716600, _1716602] : [_1716600 = hAPP(c_List_Orev(_1716598), _1716602), -(hAPP(c_List_Orev(_1716598), _1716600) = _1716602)], (46620 ^ _779308) ^ [_1716717, _1716719, _1716721] : [hAPP(c_List_Orev(_1716717), _1716719) = hAPP(c_List_Orev(_1716717), _1716721), -(_1716719 = _1716721)], (46626 ^ _779308) ^ [_1716812, _1716814, _1716816] : [_1716814 = _1716816, -(hAPP(c_List_Orev(_1716812), _1716814) = hAPP(c_List_Orev(_1716812), _1716816))], (46632 ^ _779308) ^ [_1716913, _1716915] : [class_Groups_Ocomm__monoid__add(_1716913), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1716913), hAPP(c_List_Orev(_1716913), _1716915)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1716913), _1716915))], (46638 ^ _779308) ^ [_1717018, _1717020] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717018)), hAPP(c_List_Orev(_1717018), _1717020)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717018)), _1717020))], (46640 ^ _779308) ^ [_1717062, _1717064, _1717066, _1717068, _1717070] : [-(hAPP(c_List_Ofoldl(_1717062, _1717064, _1717066, _1717068), _1717070) = c_List_Ofoldr(_1717064, _1717062, hAPP(c_COMBC(_1717062, _1717064, _1717062), _1717066), hAPP(c_List_Orev(_1717064), _1717070), _1717068))], (46642 ^ _779308) ^ [_1717119, _1717121, _1717123, _1717125, _1717127] : [-(c_List_Ofoldr(_1717119, _1717121, _1717123, _1717125, _1717127) = hAPP(c_List_Ofoldl(_1717121, _1717119, hAPP(c_COMBC(_1717119, _1717121, _1717121), _1717123), _1717127), hAPP(c_List_Orev(_1717119), _1717125)))], (46644 ^ _779308) ^ [_1717197, _1717199, _1717201, _1717203] : [hAPP(c_List_Orev(_1717197), _1717199) = hAPP(hAPP(c_List_Olist_OCons(_1717197), _1717201), _1717203), -(_1717199 = hAPP(hAPP(c_List_Oappend(_1717197), hAPP(c_List_Orev(_1717197), _1717203)), hAPP(hAPP(c_List_Olist_OCons(_1717197), _1717201), c_List_Olist_ONil(_1717197))))], (46650 ^ _779308) ^ [_1717346, _1717348, _1717350, _1717352] : [_1717348 = hAPP(hAPP(c_List_Oappend(_1717346), hAPP(c_List_Orev(_1717346), _1717352)), hAPP(hAPP(c_List_Olist_OCons(_1717346), _1717350), c_List_Olist_ONil(_1717346))), -(hAPP(c_List_Orev(_1717346), _1717348) = hAPP(hAPP(c_List_Olist_OCons(_1717346), _1717350), _1717352))], (46656 ^ _779308) ^ [_1717501, _1717503, _1717505] : [-(hAPP(c_List_Orev(_1717501), hAPP(hAPP(c_List_Olist_OCons(_1717501), _1717503), _1717505)) = hAPP(hAPP(c_List_Oappend(_1717501), hAPP(c_List_Orev(_1717501), _1717505)), hAPP(hAPP(c_List_Olist_OCons(_1717501), _1717503), c_List_Olist_ONil(_1717501))))], (46658 ^ _779308) ^ [_1717560, _1717562] : [-(_1717560 = c_List_Olist_ONil(_1717562)), -(hAPP(c_List_Ohd(_1717562), hAPP(c_List_Orev(_1717562), _1717560)) = c_List_Olast(_1717562, _1717560))], (46664 ^ _779308) ^ [_1717607, _1717609] : [-(_1717607 = c_List_Olist_ONil(_1717609)), -(c_List_Olast(_1717609, hAPP(c_List_Orev(_1717609), _1717607)) = hAPP(c_List_Ohd(_1717609), _1717607))], (46670 ^ _779308) ^ [_1717658, _1717660] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1717658), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1717658))), c_List_Otranspose(_1717658, _1717660)))))], (46672 ^ _779308) ^ [_1717704, _1717706] : [-(hAPP(c_List_Orev(_1717704), _1717706) = hAPP(c_List_Ofoldl(tc_List_Olist(_1717704), _1717704, hAPP(c_COMBC(_1717704, tc_List_Olist(_1717704), tc_List_Olist(_1717704)), c_List_Olist_OCons(_1717704)), c_List_Olist_ONil(_1717704)), _1717706))], (46674 ^ _779308) ^ [_1717759, _1717761, _1717763] : [-(hAPP(c_List_Orev(_1717759), hAPP(hAPP(c_List_Odrop(_1717759), _1717761), _1717763)) = hAPP(hAPP(c_List_Otake(_1717759), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717759)), _1717763)), _1717761)), hAPP(c_List_Orev(_1717759), _1717763)))], (46676 ^ _779308) ^ [_1717825, _1717827, _1717829] : [-(hAPP(c_List_Orev(_1717825), hAPP(hAPP(c_List_Otake(_1717825), _1717827), _1717829)) = hAPP(hAPP(c_List_Odrop(_1717825), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717825)), _1717829)), _1717827)), hAPP(c_List_Orev(_1717825), _1717829)))], (46678 ^ _779308) ^ [_1717891, _1717893, _1717895] : [-(hAPP(c_List_Orotate(_1717891, _1717893), hAPP(c_List_Orev(_1717891), _1717895)) = hAPP(c_List_Orev(_1717891), hAPP(c_List_Orotate(_1717891, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717891)), _1717895)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1717893, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717891)), _1717895)))), _1717895)))], (46680 ^ _779308) ^ [_1717964, _1717966, _1717968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1717964), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717966)), _1717968))), -(hAPP(hAPP(c_List_Onth(_1717966), hAPP(c_List_Orev(_1717966), _1717968)), _1717964) = hAPP(hAPP(c_List_Onth(_1717966), _1717968), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717966)), _1717968)), hAPP(c_Nat_OSuc, _1717964))))], (46686 ^ _779308) ^ [_1718141, _1718143, _1718145, _1718147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718141), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718143)), _1718145))), -(hAPP(c_List_Orev(_1718143), hAPP(hAPP(c_List_Olist__update(_1718143, _1718145), _1718141), _1718147)) = hAPP(hAPP(c_List_Olist__update(_1718143, hAPP(c_List_Orev(_1718143), _1718145)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718143)), _1718145)), _1718141)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1718147))], (46692 ^ _779308) ^ [_1718340, _1718342, _1718344, _1718346] : [class_Orderings_Olinorder(_1718340), c_List_Olinorder__class_Osorted(_1718340, hAPP(c_List_Orev(_1718340), _1718342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1718344), _1718346)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718346), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718340)), _1718342))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1718340), hAPP(hAPP(c_List_Onth(_1718340), _1718342), _1718346)), hAPP(hAPP(c_List_Onth(_1718340), _1718342), _1718344))))], (46710 ^ _779308) ^ [_1718677, _1718679, _1718681] : [class_Orderings_Olinorder(_1718677), c_List_Olinorder__class_Osorted(_1718677, hAPP(c_List_Orev(_1718677), _1718679)), 46717 ^ _779308 : [(46718 ^ _779308) ^ [] : [_1718679 = c_List_Olist_ONil(_1718677), -(c_List_Ofoldr(_1718677, _1718677, c_Orderings_Oord__class_Omax(_1718677), _1718679, _1718681) = _1718681)], (46724 ^ _779308) ^ [] : [-(_1718679 = c_List_Olist_ONil(_1718677)), -(c_List_Ofoldr(_1718677, _1718677, c_Orderings_Oord__class_Omax(_1718677), _1718679, _1718681) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1718677), hAPP(hAPP(c_List_Onth(_1718677), _1718679), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1718681))]]], (46730 ^ _779308) ^ [_1718991, _1718993] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1718991), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1718991))), _1718993))), 46733 ^ _779308 : [(46734 ^ _779308) ^ [] : [_1718993 = c_List_Olist_ONil(tc_List_Olist(_1718991)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1718991))), c_List_Otranspose(_1718991, _1718993)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46740 ^ _779308) ^ [] : [-(_1718993 = c_List_Olist_ONil(tc_List_Olist(_1718991))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1718991))), c_List_Otranspose(_1718991, _1718993)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718991)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1718991)), _1718993), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (46746 ^ _779308) ^ [_1719301, _1719303, _1719305] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719301), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719301))), _1719303))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719305), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719301))), _1719303))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719301))), hAPP(c_List_Ofilter(tc_List_Olist(_1719301), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1719301)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719305)), c_Nat_Osize__class_Osize(tc_List_Olist(_1719301)))), c_List_Otranspose(_1719301, _1719303))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719301)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719301)), _1719303), _1719305)))], (46756 ^ _779308) ^ [_1719610, _1719612] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719610), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719610))), _1719612))), -(c_List_Otranspose(_1719610, c_List_Otranspose(_1719610, _1719612)) = c_List_OtakeWhile(tc_List_Olist(_1719610), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1719610)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1719610), tc_List_Olist(_1719610), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1719610))), _1719612))], (46762 ^ _779308) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (46764 ^ _779308) ^ [_1719821, _1719823, _1719825] : [class_Orderings_Olinorder(_1719821), c_List_Olinorder__class_Osorted(_1719821, _1719823), -(c_List_Olinorder__class_Osorted(_1719821, c_List_OtakeWhile(_1719821, _1719825, _1719823)))], (46774 ^ _779308) ^ [_1719960, _1719962, _1719964] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719960)), c_List_OtakeWhile(_1719960, _1719962, _1719964))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719960)), _1719964))))], (46786 ^ _779308) ^ [_1720224, _1720226, _1720228] : [46788 ^ _779308 : [(46789 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720224), 46787 ^ [_1720224, _1720226, _1720228]), hAPP(c_List_Oset(_1720224), _1720228))))], (46791 ^ _779308) ^ [] : [hBOOL(hAPP(_1720226, 46787 ^ [_1720224, _1720226, _1720228]))]], -(c_List_OtakeWhile(_1720224, _1720226, _1720228) = _1720228)], (46776 ^ _779308) ^ [_1720028, _1720030, _1720032] : [c_List_OtakeWhile(_1720028, _1720030, _1720032) = _1720032, 46779 ^ _779308 : [(46780 ^ _779308) ^ [_1720115] : [hBOOL(hAPP(hAPP(c_member(_1720028), _1720115), hAPP(c_List_Oset(_1720028), _1720032))), -(hBOOL(hAPP(_1720030, _1720115)))]]], (46795 ^ _779308) ^ [_1720412, _1720414, _1720416, _1720418] : [hBOOL(hAPP(hAPP(c_member(_1720412), _1720414), hAPP(c_List_Oset(_1720412), c_List_OtakeWhile(_1720412, _1720416, _1720418)))), 46798 ^ _779308 : [(46799 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720412), _1720414), hAPP(c_List_Oset(_1720412), _1720418))))], (46801 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1720416, _1720414)))]]], (46803 ^ _779308) ^ [_1720579, _1720581, _1720583, _1720585, _1720587] : [-(hAPP(hAPP(c_List_Ozip(_1720579, _1720581), _1720583), c_List_OtakeWhile(_1720581, _1720585, _1720587)) = c_List_OtakeWhile(tc_prod(_1720579, _1720581), hAPP(c_Fun_Ocomp(_1720581, tc_HOL_Obool, tc_prod(_1720579, _1720581), _1720585), c_Product__Type_Osnd(_1720579, _1720581)), hAPP(hAPP(c_List_Ozip(_1720579, _1720581), _1720583), _1720587)))], (46805 ^ _779308) ^ [_1720653, _1720655, _1720657, _1720659, _1720661] : [-(hAPP(hAPP(c_List_Ozip(_1720653, _1720655), c_List_OtakeWhile(_1720653, _1720657, _1720659)), _1720661) = c_List_OtakeWhile(tc_prod(_1720653, _1720655), hAPP(c_Fun_Ocomp(_1720653, tc_HOL_Obool, tc_prod(_1720653, _1720655), _1720657), c_Product__Type_Ofst(_1720653, _1720655)), hAPP(hAPP(c_List_Ozip(_1720653, _1720655), _1720659), _1720661)))], (46807 ^ _779308) ^ [_1720727, _1720729, _1720731, _1720733, _1720735] : [-(c_List_OtakeWhile(_1720727, _1720729, hAPP(hAPP(c_List_Omap(_1720731, _1720727), _1720733), _1720735)) = hAPP(hAPP(c_List_Omap(_1720731, _1720727), _1720733), c_List_OtakeWhile(_1720731, hAPP(c_Fun_Ocomp(_1720727, tc_HOL_Obool, _1720731, _1720729), _1720733), _1720735)))], (46809 ^ _779308) ^ [_1720788, _1720790, _1720792, _1720794, _1720796] : [-(hBOOL(hAPP(_1720788, _1720790))), -(c_List_OtakeWhile(_1720792, _1720788, hAPP(hAPP(c_List_Oappend(_1720792), _1720794), hAPP(hAPP(c_List_Olist_OCons(_1720792), _1720790), _1720796))) = c_List_OtakeWhile(_1720792, _1720788, _1720794))], (46815 ^ _779308) ^ [_1720871, _1720873, _1720875, _1720877] : [hBOOL(hAPP(_1720871, _1720873)), -(c_List_OtakeWhile(_1720875, _1720871, hAPP(hAPP(c_List_Olist_OCons(_1720875), _1720873), _1720877)) = hAPP(hAPP(c_List_Olist_OCons(_1720875), _1720873), c_List_OtakeWhile(_1720875, _1720871, _1720877)))], (46821 ^ _779308) ^ [_1720998, _1721000, _1721002, _1721004] : [-(hBOOL(hAPP(_1720998, _1721000))), -(c_List_OtakeWhile(_1721002, _1720998, hAPP(hAPP(c_List_Olist_OCons(_1721002), _1721000), _1721004)) = c_List_Olist_ONil(_1721002))], (46827 ^ _779308) ^ [_1721056, _1721058] : [-(c_List_OtakeWhile(_1721056, _1721058, c_List_Olist_ONil(_1721056)) = c_List_Olist_ONil(_1721056))], (46829 ^ _779308) ^ [_1721089, _1721091, _1721093] : [-(c_List_OtakeWhile(_1721089, _1721091, _1721093) = hAPP(hAPP(c_List_Otake(_1721089), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721089)), c_List_OtakeWhile(_1721089, _1721091, _1721093))), _1721093))], (46831 ^ _779308) ^ [_1721139, _1721141, _1721143] : [hBOOL(hAPP(c_List_Odistinct(_1721139), _1721141)), -(hBOOL(hAPP(c_List_Odistinct(_1721139), c_List_OtakeWhile(_1721139, _1721143, _1721141))))], (46837 ^ _779308) ^ [_1721242] : [-(c_List_Oreturn__list(_1721242) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1721242))], (46839 ^ _779308) ^ [_1721270, _1721272, _1721274, _1721276, _1721278] : [hBOOL(hAPP(hAPP(c_member(_1721270), _1721272), hAPP(c_List_Oset(_1721270), _1721274))), -(hBOOL(hAPP(_1721276, _1721272))), -(c_List_OtakeWhile(_1721270, _1721276, hAPP(hAPP(c_List_Oappend(_1721270), _1721274), _1721278)) = c_List_OtakeWhile(_1721270, _1721276, _1721274))], (46849 ^ _779308) ^ [_1721428, _1721430, _1721432, _1721434] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721428), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721430)), c_List_OtakeWhile(_1721430, _1721432, _1721434)))), -(hAPP(hAPP(c_List_Onth(_1721430), c_List_OtakeWhile(_1721430, _1721432, _1721434)), _1721428) = hAPP(hAPP(c_List_Onth(_1721430), _1721434), _1721428))], (46855 ^ _779308) ^ [_1721581, _1721583, _1721585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721581)), c_List_OtakeWhile(_1721581, _1721583, _1721585))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721581)), _1721585))), hBOOL(hAPP(_1721583, hAPP(hAPP(c_List_Onth(_1721581), _1721585), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721581)), c_List_OtakeWhile(_1721581, _1721583, _1721585)))))], (46861 ^ _779308) ^ [_1721748, _1721750] : [-(_1721748 = c_List_Olist_ONil(_1721750)), hBOOL(hAPP(c_List_Odistinct(_1721750), _1721748)), -(c_List_OtakeWhile(_1721750, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1721750), c_fNot), hAPP(hAPP(c_COMBC(_1721750, _1721750, tc_HOL_Obool), c_fequal), c_List_Olast(_1721750, _1721748))), _1721748) = c_List_Obutlast(_1721750, _1721748))], (46871 ^ _779308) ^ [_1721945, _1721947, _1721949, _1721951, _1721953] : [class_Orderings_Olinorder(_1721945), c_List_Olinorder__class_Osorted(_1721945, hAPP(c_List_Orev(_1721945), hAPP(hAPP(c_List_Omap(_1721947, _1721945), _1721949), _1721951))), -(hAPP(c_List_Ofilter(_1721947, hAPP(hAPP(c_COMBB(_1721945, tc_HOL_Obool, _1721947), hAPP(c_Orderings_Oord__class_Oless(_1721945), _1721953)), _1721949)), _1721951) = c_List_OtakeWhile(_1721947, hAPP(hAPP(c_COMBB(_1721945, tc_HOL_Obool, _1721947), hAPP(c_Orderings_Oord__class_Oless(_1721945), _1721953)), _1721949), _1721951))], (46881 ^ _779308) ^ [_1722192] : [c_List_Onat__list(_1722192), -(c_List_Oembed__list(c_List_Oreturn__list(_1722192)) = _1722192)], (46887 ^ _779308) ^ [_1722273, _1722275] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1722273), _1722275) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1722273)), c_List_Oembed__list(_1722275))))], (46889 ^ _779308) ^ [_1722316] : [-(c_List_Oembed__list(_1722316) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1722316))], (46891 ^ _779308) ^ [_1722344, _1722346, _1722348] : [hBOOL(hAPP(c_List_Odistinct(_1722344), _1722346)), hBOOL(hAPP(hAPP(c_member(_1722344), _1722348), hAPP(c_List_Oset(_1722344), _1722346))), -(c_List_OtakeWhile(_1722344, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722344), c_fNot), hAPP(hAPP(c_COMBC(_1722344, _1722344, tc_HOL_Obool), c_fequal), _1722348)), hAPP(c_List_Orev(_1722344), _1722346)) = hAPP(c_List_Orev(_1722344), hAPP(c_List_Otl(_1722344), c_List_OdropWhile(_1722344, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722344), c_fNot), hAPP(hAPP(c_COMBC(_1722344, _1722344, tc_HOL_Obool), c_fequal), _1722348)), _1722346))))], (46901 ^ _779308) ^ [_1722635, _1722637, _1722639] : [hBOOL(hAPP(c_List_Odistinct(_1722635), _1722637)), hBOOL(hAPP(hAPP(c_member(_1722635), _1722639), hAPP(c_List_Oset(_1722635), _1722637))), -(c_List_OdropWhile(_1722635, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722635), c_fNot), hAPP(hAPP(c_COMBC(_1722635, _1722635, tc_HOL_Obool), c_fequal), _1722639)), hAPP(c_List_Orev(_1722635), _1722637)) = hAPP(hAPP(c_List_Olist_OCons(_1722635), _1722639), hAPP(c_List_Orev(_1722635), c_List_OtakeWhile(_1722635, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722635), c_fNot), hAPP(hAPP(c_COMBC(_1722635, _1722635, tc_HOL_Obool), c_fequal), _1722639)), _1722637))))], (46911 ^ _779308) ^ [_1722932, _1722934, _1722936] : [-(hAPP(hAPP(c_List_Oappend(_1722932), c_List_OtakeWhile(_1722932, _1722934, _1722936)), c_List_OdropWhile(_1722932, _1722934, _1722936)) = _1722936)], (46913 ^ _779308) ^ [_1722975, _1722977, _1722979] : [class_Orderings_Olinorder(_1722975), c_List_Olinorder__class_Osorted(_1722975, _1722977), -(c_List_Olinorder__class_Osorted(_1722975, c_List_OdropWhile(_1722975, _1722979, _1722977)))], (46923 ^ _779308) ^ [_1723114, _1723116, _1723118] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723114)), c_List_OdropWhile(_1723114, _1723116, _1723118))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723114)), _1723118))))], (46935 ^ _779308) ^ [_1723382, _1723384, _1723386] : [46937 ^ _779308 : [(46938 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1723382), 46936 ^ [_1723382, _1723384, _1723386]), hAPP(c_List_Oset(_1723382), _1723386))))], (46940 ^ _779308) ^ [] : [hBOOL(hAPP(_1723384, 46936 ^ [_1723382, _1723384, _1723386]))]], -(c_List_OdropWhile(_1723382, _1723384, _1723386) = c_List_Olist_ONil(_1723382))], (46925 ^ _779308) ^ [_1723182, _1723184, _1723186] : [c_List_OdropWhile(_1723182, _1723184, _1723186) = c_List_Olist_ONil(_1723182), 46928 ^ _779308 : [(46929 ^ _779308) ^ [_1723273] : [hBOOL(hAPP(hAPP(c_member(_1723182), _1723273), hAPP(c_List_Oset(_1723182), _1723186))), -(hBOOL(hAPP(_1723184, _1723273)))]]], (46944 ^ _779308) ^ [_1723589, _1723591, _1723593, _1723595] : [hBOOL(hAPP(_1723589, _1723591)), -(c_List_OdropWhile(_1723593, _1723589, hAPP(hAPP(c_List_Olist_OCons(_1723593), _1723591), _1723595)) = c_List_OdropWhile(_1723593, _1723589, _1723595))], (46950 ^ _779308) ^ [_1723700, _1723702, _1723704, _1723706] : [-(hBOOL(hAPP(_1723700, _1723702))), -(c_List_OdropWhile(_1723704, _1723700, hAPP(hAPP(c_List_Olist_OCons(_1723704), _1723702), _1723706)) = hAPP(hAPP(c_List_Olist_OCons(_1723704), _1723702), _1723706))], (46956 ^ _779308) ^ [_1723764, _1723766] : [-(c_List_OdropWhile(_1723764, _1723766, c_List_Olist_ONil(_1723764)) = c_List_Olist_ONil(_1723764))], (46958 ^ _779308) ^ [_1723797, _1723799, _1723801] : [hBOOL(hAPP(c_List_Odistinct(_1723797), _1723799)), -(hBOOL(hAPP(c_List_Odistinct(_1723797), c_List_OdropWhile(_1723797, _1723801, _1723799))))], (46964 ^ _779308) ^ [_1723899, _1723901, _1723903] : [-(c_List_OdropWhile(_1723899, _1723901, _1723903) = c_List_Olist_ONil(_1723899)), hBOOL(hAPP(_1723901, hAPP(c_List_Ohd(_1723899), c_List_OdropWhile(_1723899, _1723901, _1723903))))], (46970 ^ _779308) ^ [_1724005, _1724007, _1724009, _1724011, _1724013] : [-(c_List_OdropWhile(_1724005, _1724007, hAPP(hAPP(c_List_Omap(_1724009, _1724005), _1724011), _1724013)) = hAPP(hAPP(c_List_Omap(_1724009, _1724005), _1724011), c_List_OdropWhile(_1724009, hAPP(c_Fun_Ocomp(_1724005, tc_HOL_Obool, _1724009, _1724007), _1724011), _1724013)))], (46972 ^ _779308) ^ [_1724070, _1724072, _1724074, _1724076, _1724078] : [hBOOL(hAPP(hAPP(c_member(_1724070), _1724072), hAPP(c_List_Oset(_1724070), _1724074))), -(hBOOL(hAPP(_1724076, _1724072))), -(c_List_OdropWhile(_1724070, _1724076, hAPP(hAPP(c_List_Oappend(_1724070), _1724074), _1724078)) = hAPP(hAPP(c_List_Oappend(_1724070), c_List_OdropWhile(_1724070, _1724076, _1724074)), _1724078))], (46982 ^ _779308) ^ [_1724268, _1724270, _1724272, _1724274, _1724276] : [c_List_OdropWhile(_1724268, _1724270, _1724272) = hAPP(hAPP(c_List_Olist_OCons(_1724268), _1724274), _1724276), 46985 ^ _779308 : [(46986 ^ _779308) ^ [] : [-(_1724272 = hAPP(hAPP(c_List_Oappend(_1724268), c_List_OtakeWhile(_1724268, _1724270, _1724272)), hAPP(hAPP(c_List_Olist_OCons(_1724268), _1724274), _1724276)))], (46988 ^ _779308) ^ [] : [hBOOL(hAPP(_1724270, _1724274))]]], (46990 ^ _779308) ^ [_1724449, _1724451, _1724453, _1724455, _1724457] : [-(c_List_OdropWhile(_1724449, _1724451, _1724453) = hAPP(hAPP(c_List_Olist_OCons(_1724449), _1724455), _1724457)), _1724453 = hAPP(hAPP(c_List_Oappend(_1724449), c_List_OtakeWhile(_1724449, _1724451, _1724453)), hAPP(hAPP(c_List_Olist_OCons(_1724449), _1724455), _1724457)), -(hBOOL(hAPP(_1724451, _1724455)))], (47000 ^ _779308) ^ [_1724663, _1724665, _1724667] : [-(c_List_OdropWhile(_1724663, _1724665, _1724667) = hAPP(hAPP(c_List_Odrop(_1724663), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724663)), c_List_OtakeWhile(_1724663, _1724665, _1724667))), _1724667))], (47002 ^ _779308) ^ [_1724713, _1724715, _1724717, _1724719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1724713), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724715)), c_List_OdropWhile(_1724715, _1724717, _1724719)))), -(hAPP(hAPP(c_List_Onth(_1724715), c_List_OdropWhile(_1724715, _1724717, _1724719)), _1724713) = hAPP(hAPP(c_List_Onth(_1724715), _1724719), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1724713), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724715)), c_List_OtakeWhile(_1724715, _1724717, _1724719)))))], (47008 ^ _779308) ^ [_1724900, _1724902, _1724904, _1724906, _1724908] : [class_Groups_Omonoid__add(_1724900), 47014 ^ _779308 : [(47015 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1724902), 47013 ^ [_1724900, _1724902, _1724904, _1724906, _1724908]), hAPP(c_List_Oset(_1724902), _1724904))))], (47017 ^ _779308) ^ [] : [hBOOL(hAPP(_1724906, 47013 ^ [_1724900, _1724902, _1724904, _1724906, _1724908]))], (47019 ^ _779308) ^ [] : [hAPP(_1724908, 47013 ^ [_1724900, _1724902, _1724904, _1724906, _1724908]) = c_Groups_Ozero__class_Ozero(_1724900)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1724900), hAPP(hAPP(c_List_Omap(_1724902, _1724900), _1724908), hAPP(c_List_Ofilter(_1724902, _1724906), _1724904))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1724900), hAPP(hAPP(c_List_Omap(_1724902, _1724900), _1724908), _1724904)))], (47023 ^ _779308) ^ [_1725291, _1725293] : [class_Orderings_Olinorder(_1725291), 47030 ^ _779308 : [(47031 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47028 ^ [_1725291, _1725293]), 47029 ^ [_1725291, _1725293])))], (47033 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47029 ^ [_1725291, _1725293]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725291)), _1725293))))], (47035 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1725291), hAPP(hAPP(c_List_Onth(_1725291), _1725293), 47028 ^ [_1725291, _1725293])), hAPP(hAPP(c_List_Onth(_1725291), _1725293), 47029 ^ [_1725291, _1725293])))]], -(c_List_Olinorder__class_Osorted(_1725291, _1725293))], (47039 ^ _779308) ^ [_1725662, _1725664, _1725666] : [47041 ^ _779308 : [(47042 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1725662), 47040 ^ [_1725662, _1725664, _1725666]), hAPP(c_List_Oset(_1725662), c_List_OdropWhile(_1725662, _1725664, _1725666)))))], (47044 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1725664, 47040 ^ [_1725662, _1725664, _1725666])))]], -(c_List_OtakeWhile(_1725662, _1725664, _1725666) = hAPP(c_List_Ofilter(_1725662, _1725664), _1725666))], (47048 ^ _779308) ^ [_1725783, _1725785, _1725787, _1725789] : [47050 ^ _779308 : [(47051 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47049 ^ [_1725783, _1725785, _1725787, _1725789]), _1725783)))], (47053 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47049 ^ [_1725783, _1725785, _1725787, _1725789]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725785)), _1725787))))], (47055 ^ _779308) ^ [] : [hBOOL(hAPP(_1725789, hAPP(hAPP(c_List_Onth(_1725785), _1725787), 47049 ^ [_1725783, _1725785, _1725787, _1725789])))]], 47058 ^ _779308 : [(47059 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725783), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725785)), _1725787))))], (47061 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1725789, hAPP(hAPP(c_List_Onth(_1725785), _1725787), _1725783))))]], -(c_List_OtakeWhile(_1725785, _1725789, _1725787) = hAPP(hAPP(c_List_Otake(_1725785), _1725783), _1725787))], (47065 ^ _779308) ^ [_1726187, _1726189, _1726191, _1726193] : [47067 ^ _779308 : [(47068 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47066 ^ [_1726187, _1726189, _1726191, _1726193]), _1726187)))], (47070 ^ _779308) ^ [] : [hBOOL(hAPP(_1726189, hAPP(hAPP(c_List_Onth(_1726191), _1726193), 47066 ^ [_1726187, _1726189, _1726191, _1726193])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1726187), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726191)), _1726193))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1726187), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726191)), c_List_OtakeWhile(_1726191, _1726189, _1726193)))))], (47078 ^ _779308) ^ [_1726495, _1726497] : [class_Orderings_Olinorder(_1726495), 47081 ^ _779308 : [(47082 ^ _779308) ^ [] : [c_List_Olinorder__class_Osorted(_1726495, _1726497), -(_1726497 = c_List_Olist_ONil(_1726495)), 47091 ^ _779308 : [(47092 ^ _779308) ^ [] : [-(_1726497 = hAPP(hAPP(c_List_Olist_OCons(_1726495), 47090 ^ [_1726495, _1726497]), 47089 ^ [_1726495, _1726497]))], (47100 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1726495, 47089 ^ [_1726495, _1726497]))], (47094 ^ _779308) ^ [_1726829] : [hBOOL(hAPP(hAPP(c_member(_1726495), _1726829), hAPP(c_List_Oset(_1726495), 47089 ^ [_1726495, _1726497]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726495), 47090 ^ [_1726495, _1726497]), _1726829)))]]], (47102 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1726495, _1726497)), 47103 ^ _779308 : [(47104 ^ _779308) ^ [] : [_1726497 = c_List_Olist_ONil(_1726495)], (47106 ^ _779308) ^ [_1727055, _1727057] : [_1726497 = hAPP(hAPP(c_List_Olist_OCons(_1726495), _1727055), _1727057), 47112 ^ _779308 : [(47113 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726495), 47111 ^ [_1726495, _1726497, _1727055, _1727057]), hAPP(c_List_Oset(_1726495), _1727057))))], (47115 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726495), _1727055), 47111 ^ [_1726495, _1726497, _1727055, _1727057]))]], c_List_Olinorder__class_Osorted(_1726495, _1727057)]]]]], (47121 ^ _779308) ^ [_1727376, _1727378, _1727380] : [hBOOL(hAPP(hAPP(c_member(_1727376), _1727378), hAPP(c_List_Oset(_1727376), _1727380))), -(c_List_Oinsert(_1727376, _1727378, _1727380) = _1727380)], (47127 ^ _779308) ^ [_1727481, _1727483, _1727485] : [-(hBOOL(hAPP(hAPP(c_member(_1727481), _1727483), hAPP(c_List_Oset(_1727481), _1727485)))), -(c_List_Oinsert(_1727481, _1727483, _1727485) = hAPP(hAPP(c_List_Olist_OCons(_1727481), _1727483), _1727485))], (47133 ^ _779308) ^ [_1727541, _1727543, _1727545] : [-(hBOOL(hAPP(hAPP(c_member(_1727541), _1727543), hAPP(c_List_Oset(_1727541), _1727545)))), -(c_List_Oinsert(_1727541, _1727543, _1727545) = hAPP(hAPP(c_List_Olist_OCons(_1727541), _1727543), _1727545))], (47139 ^ _779308) ^ [_1727603, _1727605, _1727607] : [-(c_List_Oinsert(_1727603, _1727605, c_List_Oremdups(_1727603, _1727607)) = c_List_Oremdups(_1727603, c_List_Oinsert(_1727603, _1727605, _1727607)))], (47141 ^ _779308) ^ [_1727644, _1727646, _1727648] : [hBOOL(hAPP(c_List_Odistinct(_1727644), _1727646)), -(hBOOL(hAPP(c_List_Odistinct(_1727644), c_List_Oinsert(_1727644, _1727648, _1727646))))], (47147 ^ _779308) ^ [_1727747, _1727749, _1727751] : [hBOOL(hAPP(hAPP(c_member(_1727747), _1727749), hAPP(c_List_Oset(_1727747), _1727751))), -(c_List_Oinsert(_1727747, _1727749, _1727751) = _1727751)], (47153 ^ _779308) ^ [_1727858, _1727860, _1727862] : [-(hAPP(c_List_Oset(_1727858), c_List_Oinsert(_1727858, _1727860, _1727862)) = hAPP(hAPP(c_Set_Oinsert(_1727858), _1727860), hAPP(c_List_Oset(_1727858), _1727862)))], (47155 ^ _779308) ^ [_1727907, _1727909] : [-(c_List_Oinsert(_1727907, _1727909, c_List_Olist_ONil(_1727907)) = hAPP(hAPP(c_List_Olist_OCons(_1727907), _1727909), c_List_Olist_ONil(_1727907)))], (47157 ^ _779308) ^ [_1727948, _1727950, _1727952, _1727954] : [-(c_List_Omaps(_1727948, _1727950, _1727952, _1727954) = c_List_Oconcat(_1727950, hAPP(hAPP(c_List_Omap(_1727948, tc_List_Olist(_1727950)), _1727952), _1727954)))], (47159 ^ _779308) ^ [_1727996, _1727998, _1728000, _1728002] : [-(c_List_Oconcat(_1727996, hAPP(hAPP(c_List_Omap(_1727998, tc_List_Olist(_1727996)), _1728000), _1728002)) = c_List_Omaps(_1727998, _1727996, _1728000, _1728002))], (47161 ^ _779308) ^ [_1728044, _1728046, _1728048] : [-(c_List_Omaps(_1728044, _1728046, _1728048, c_List_Olist_ONil(_1728044)) = c_List_Olist_ONil(_1728046))], (47163 ^ _779308) ^ [_1728080, _1728082, _1728084, _1728086, _1728088] : [-(c_List_Omaps(_1728080, _1728082, _1728084, hAPP(hAPP(c_List_Olist_OCons(_1728080), _1728086), _1728088)) = hAPP(hAPP(c_List_Oappend(_1728082), hAPP(_1728084, _1728086)), c_List_Omaps(_1728080, _1728082, _1728084, _1728088)))], (47165 ^ _779308) ^ [_1728140, _1728142] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1728140)), _1728142)), 47171 ^ _779308 : [(47172 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728140)), 47170 ^ [_1728140, _1728142]), hAPP(c_List_Oset(tc_List_Olist(_1728140)), _1728142))))], (47174 ^ _779308) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1728140), 47170 ^ [_1728140, _1728142]))]], 47178 ^ _779308 : [(47179 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728140)), 47177 ^ [_1728140, _1728142]), hAPP(c_List_Oset(tc_List_Olist(_1728140)), _1728142))))], (47182 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1728140)), 47180 ^ [_1728140, _1728142]), hAPP(c_List_Oset(tc_List_Olist(_1728140)), _1728142))))], (47184 ^ _779308) ^ [] : [47177 ^ [_1728140, _1728142] = 47180 ^ [_1728140, _1728142]], (47186 ^ _779308) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1728140, tc_HOL_Obool)), hAPP(c_List_Oset(_1728140), 47177 ^ [_1728140, _1728142])), hAPP(c_List_Oset(_1728140), 47180 ^ [_1728140, _1728142])) = c_Orderings_Obot__class_Obot(tc_fun(_1728140, tc_HOL_Obool))]], -(hBOOL(hAPP(c_List_Odistinct(_1728140), c_List_Oconcat(_1728140, _1728142))))], (47190 ^ _779308) ^ [_1728857, _1728859, _1728861, _1728863, _1728865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1728857, _1728859)), hAPP(_1728857, _1728861))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1728863, _1728863)), hAPP(hAPP(c_Product__Type_OPair(_1728863, _1728863), _1728859), _1728861)), c_List_Omeasures(_1728863, _1728865))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1728863, _1728863)), hAPP(hAPP(c_Product__Type_OPair(_1728863, _1728863), _1728859), _1728861)), c_List_Omeasures(_1728863, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1728863, tc_Nat_Onat)), _1728857), _1728865)))))], (47200 ^ _779308) ^ [_1729130, _1729132] : [-(c_Wellfounded_Owf(_1729130, c_List_Omeasures(_1729130, _1729132)))], (47202 ^ _779308) ^ [_1729173, _1729175, _1729177] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1729173, _1729173)), hAPP(hAPP(c_Product__Type_OPair(_1729173, _1729173), _1729175), _1729177)), c_List_Omeasures(_1729173, c_List_Olist_ONil(tc_fun(_1729173, tc_Nat_Onat)))))], (47204 ^ _779308) ^ [_1729227, _1729229] : [-(c_List_Omeasures(_1729227, _1729229) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1729227), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1729227, tc_List_Olist(tc_fun(_1729227, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1729227, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1729227, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1729227), c_List_Omap(tc_fun(_1729227, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1729227, tc_Nat_Onat), _1729227, tc_Nat_Onat), c_COMBI(tc_fun(_1729227, tc_Nat_Onat))))), _1729229)))], (47206 ^ _779308) ^ [_1729348, _1729350, _1729352, _1729354, _1729356] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1729348, _1729348)), hAPP(hAPP(c_Product__Type_OPair(_1729348, _1729348), _1729350), _1729352)), c_List_Omeasures(_1729348, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729348, tc_Nat_Onat)), _1729354), _1729356)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1729354, _1729350)), hAPP(_1729354, _1729352)))), 47213 ^ _779308 : [(47214 ^ _779308) ^ [] : [-(hAPP(_1729354, _1729350) = hAPP(_1729354, _1729352))], (47216 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729348, _1729348)), hAPP(hAPP(c_Product__Type_OPair(_1729348, _1729348), _1729350), _1729352)), c_List_Omeasures(_1729348, _1729356))))]]], (47218 ^ _779308) ^ [_1729627, _1729629, _1729631, _1729633, _1729635] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729627, _1729627)), hAPP(hAPP(c_Product__Type_OPair(_1729627, _1729627), _1729629), _1729631)), c_List_Omeasures(_1729627, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729627, tc_Nat_Onat)), _1729633), _1729635))))), 47219 ^ _779308 : [(47220 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1729633, _1729629)), hAPP(_1729633, _1729631)))], (47222 ^ _779308) ^ [] : [hAPP(_1729633, _1729629) = hAPP(_1729633, _1729631), hBOOL(hAPP(hAPP(c_member(tc_prod(_1729627, _1729627)), hAPP(hAPP(c_Product__Type_OPair(_1729627, _1729627), _1729629), _1729631)), c_List_Omeasures(_1729627, _1729635)))]]], (47230 ^ _779308) ^ [_1729950, _1729952, _1729954, _1729956, _1729958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1729950, _1729952)), hAPP(_1729950, _1729954))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729956, _1729956)), hAPP(hAPP(c_Product__Type_OPair(_1729956, _1729956), _1729952), _1729954)), c_List_Omeasures(_1729956, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729956, tc_Nat_Onat)), _1729950), _1729958)))))], (47236 ^ _779308) ^ [_1730121, _1730123, _1730125, _1730127, _1730129, _1730131, _1730133, _1730135] : [47238 ^ _779308 : [(47239 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730121), 47237 ^ [_1730121, _1730123, _1730125, _1730127, _1730129, _1730131, _1730133, _1730135]), hAPP(c_List_Oset(_1730121), _1730123))))], (47241 ^ _779308) ^ [] : [hAPP(c_Fun_Ocomp(_1730125, _1730125, _1730127, hAPP(_1730129, 47237 ^ [_1730121, _1730123, _1730125, _1730127, _1730129, _1730131, _1730133, _1730135])), _1730131) = hAPP(c_Fun_Ocomp(_1730127, _1730125, _1730127, _1730131), hAPP(_1730133, 47237 ^ [_1730121, _1730123, _1730125, _1730127, _1730129, _1730131, _1730133, _1730135]))]], -(hAPP(c_List_Ofoldl(_1730125, _1730121, hAPP(c_COMBC(_1730121, _1730125, _1730125), _1730129), hAPP(_1730131, _1730135)), _1730123) = hAPP(_1730131, hAPP(c_List_Ofoldl(_1730127, _1730121, hAPP(c_COMBC(_1730121, _1730127, _1730127), _1730133), _1730135), _1730123)))], (47245 ^ _779308) ^ [_1730490, _1730492, _1730494, _1730496] : [class_Orderings_Oorder(_1730490), class_Enum_Oenum(_1730492), 47252 ^ _779308 : [(47253 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1730492, _1730490)), _1730494), _1730496)), 47256 ^ _779308 : [(47257 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730492, _1730490)), _1730494), _1730496)))], (47259 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1730492), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1730492), c_fNot), hAPP(hAPP(c_COMBS(_1730492, _1730490, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1730490, tc_fun(_1730490, tc_HOL_Obool), _1730492), c_fequal), _1730494)), _1730496)))))]]], (47261 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1730492, _1730490)), _1730494), _1730496))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730492, _1730490)), _1730494), _1730496)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1730492), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1730492), c_fNot), hAPP(hAPP(c_COMBS(_1730492, _1730490, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1730490, tc_fun(_1730490, tc_HOL_Obool), _1730492), c_fequal), _1730494)), _1730496))))]]], (47271 ^ _779308) ^ [_1731010, _1731012, _1731014] : [class_Enum_Oenum(_1731010), class_Enum_Oenum(_1731012), 47278 ^ _779308 : [(47279 ^ _779308) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731012, _1731010)), _1731014)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731012), hAPP(hAPP(c_COMBB(tc_fun(_1731010, tc_HOL_Obool), tc_HOL_Obool, _1731012), c_Enum_Oenum__class_Oenum__ex(_1731010)), hAPP(hAPP(c_COMBB(tc_fun(_1731010, tc_prod(_1731012, _1731010)), tc_fun(_1731010, tc_HOL_Obool), _1731012), hAPP(c_COMBB(tc_prod(_1731012, _1731010), tc_HOL_Obool, _1731010), _1731014)), c_Product__Type_OPair(_1731012, _1731010))))))], (47285 ^ _779308) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731012), hAPP(hAPP(c_COMBB(tc_fun(_1731010, tc_HOL_Obool), tc_HOL_Obool, _1731012), c_Enum_Oenum__class_Oenum__ex(_1731010)), hAPP(hAPP(c_COMBB(tc_fun(_1731010, tc_prod(_1731012, _1731010)), tc_fun(_1731010, tc_HOL_Obool), _1731012), hAPP(c_COMBB(tc_prod(_1731012, _1731010), tc_HOL_Obool, _1731010), _1731014)), c_Product__Type_OPair(_1731012, _1731010))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731012, _1731010)), _1731014)))]]], (47291 ^ _779308) ^ [_1731449, _1731451] : [class_Enum_Oenum(_1731449), 47294 ^ _779308 : [(47295 ^ _779308) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731449), _1731451)), -(hBOOL(hAPP(_1731451, 47298 ^ [_1731449, _1731451])))], (47302 ^ _779308) ^ [] : [47303 ^ _779308 : [(47304 ^ _779308) ^ [_1731629] : [hBOOL(hAPP(_1731451, _1731629))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731449), _1731451)))]]], (47308 ^ _779308) ^ [_1731692, _1731694] : [class_Enum_Oenum(_1731692), 47311 ^ _779308 : [(47312 ^ _779308) ^ [] : [47313 ^ _779308 : [(47314 ^ _779308) ^ [_1731794] : [hBOOL(hAPP(_1731694, _1731794))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731692), _1731694)))], (47318 ^ _779308) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731692), _1731694)), -(hBOOL(hAPP(_1731694, 47321 ^ [_1731692, _1731694])))]]], (47325 ^ _779308) ^ [_1731935, _1731937, _1731939, _1731941, _1731943] : [47326 ^ _779308 : [(47327 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731935)), hAPP(hAPP(c_List_Otake(_1731935), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731935)), _1731937)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731939)), _1731941))), _1731937)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731939)), hAPP(hAPP(c_List_Otake(_1731939), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731935)), _1731937)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731939)), _1731941))), _1731941)))], (47329 ^ _779308) ^ [] : [hBOOL(hAPP(_1731943, hAPP(hAPP(c_List_Ozip(_1731935, _1731939), hAPP(hAPP(c_List_Otake(_1731935), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731935)), _1731937)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731939)), _1731941))), _1731937)), hAPP(hAPP(c_List_Otake(_1731939), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731935)), _1731937)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731939)), _1731941))), _1731941))))]], -(hBOOL(hAPP(_1731943, hAPP(hAPP(c_List_Ozip(_1731935, _1731939), _1731937), _1731941))))], (47333 ^ _779308) ^ [_1732347, _1732349, _1732351, _1732353] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1732347, _1732349, _1732351, _1732353) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1732347, _1732349), _1732351), _1732353)))], (47335 ^ _779308) ^ [_1732392, _1732394, _1732396, _1732398] : [47337 ^ _779308 : [(47338 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1732392), 47336 ^ [_1732392, _1732394, _1732396, _1732398]), hAPP(c_List_Oset(_1732392), _1732394))))], (47340 ^ _779308) ^ [] : [hBOOL(hAPP(_1732396, 47336 ^ [_1732392, _1732394, _1732396, _1732398]))]], -(c_List_OdropWhile(_1732392, _1732396, hAPP(hAPP(c_List_Oappend(_1732392), _1732394), _1732398)) = c_List_OdropWhile(_1732392, _1732396, _1732398))], (47344 ^ _779308) ^ [_1732610, _1732612, _1732614, _1732616, _1732618] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732610)), _1732612) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732614)), _1732616), 47350 ^ _779308 : [(47351 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47349 ^ [_1732610, _1732612, _1732614, _1732616, _1732618]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732610)), _1732612))))], (47353 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1732618, hAPP(hAPP(c_List_Onth(_1732610), _1732612), 47349 ^ [_1732610, _1732612, _1732614, _1732616, _1732618])), hAPP(hAPP(c_List_Onth(_1732614), _1732616), 47349 ^ [_1732610, _1732612, _1732614, _1732616, _1732618])))]], -(c_List_Olist__all2(_1732610, _1732614, _1732618, _1732612, _1732616))], (47357 ^ _779308) ^ [_1732968, _1732970] : [class_Orderings_Olinorder(_1732968), hBOOL(hAPP(c_Finite__Set_Ofinite(_1732968), _1732970)), 47365 ^ _779308 : [(47366 ^ _779308) ^ [] : [-(hAPP(c_List_Oset(_1732968), 47364 ^ [_1732968, _1732970]) = _1732970)], (47368 ^ _779308) ^ [] : [-(c_List_Olinorder__class_Osorted(_1732968, 47364 ^ [_1732968, _1732970]))], (47370 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1732968), 47364 ^ [_1732968, _1732970])))], (47372 ^ _779308) ^ [_1733294] : [-(_1733294 = 47364 ^ [_1732968, _1732970]), hAPP(c_List_Oset(_1732968), _1733294) = _1732970, c_List_Olinorder__class_Osorted(_1732968, _1733294), hBOOL(hAPP(c_List_Odistinct(_1732968), _1733294))]]], (47386 ^ _779308) ^ [_1733525, _1733527, _1733529, _1733531] : [47388 ^ _779308 : [(47389 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733525), 47387 ^ [_1733525, _1733527, _1733529, _1733531]), hAPP(c_List_Oset(_1733525), _1733527))))], (47391 ^ _779308) ^ [] : [hBOOL(hAPP(_1733529, 47387 ^ [_1733525, _1733527, _1733529, _1733531]))]], -(c_List_OtakeWhile(_1733525, _1733529, hAPP(hAPP(c_List_Oappend(_1733525), _1733527), _1733531)) = hAPP(hAPP(c_List_Oappend(_1733525), _1733527), c_List_OtakeWhile(_1733525, _1733529, _1733531)))], (47395 ^ _779308) ^ [_1733759, _1733761, _1733763, _1733765, _1733767] : [class_Orderings_Olinorder(_1733759), 47401 ^ _779308 : [(47402 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733761), 47400 ^ [_1733759, _1733761, _1733763, _1733765, _1733767]), hAPP(c_List_Oset(_1733761), _1733763))))], (47404 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1733759), hAPP(_1733765, _1733767)), hAPP(_1733765, 47400 ^ [_1733759, _1733761, _1733763, _1733765, _1733767])))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1733761, _1733759, _1733765), _1733767), _1733763) = hAPP(hAPP(c_List_Olist_OCons(_1733761), _1733767), _1733763))], (47408 ^ _779308) ^ [_1734102, _1734104, _1734106, _1734108, _1734110] : [hAPP(hAPP(c_List_Olist_OCons(_1734102), _1734104), _1734106) = hAPP(c_List_Ofilter(_1734102, _1734108), _1734110), 47413 ^ _779308 : [(47414 ^ _779308) ^ [] : [-(_1734110 = hAPP(hAPP(c_List_Oappend(_1734102), 47411 ^ [_1734102, _1734104, _1734106, _1734108, _1734110]), hAPP(hAPP(c_List_Olist_OCons(_1734102), _1734104), 47412 ^ [_1734102, _1734104, _1734106, _1734108, _1734110])))], (47422 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1734108, _1734104)))], (47424 ^ _779308) ^ [] : [-(_1734106 = hAPP(c_List_Ofilter(_1734102, _1734108), 47412 ^ [_1734102, _1734104, _1734106, _1734108, _1734110]))], (47416 ^ _779308) ^ [_1734416] : [hBOOL(hAPP(hAPP(c_member(_1734102), _1734416), hAPP(c_List_Oset(_1734102), 47411 ^ [_1734102, _1734104, _1734106, _1734108, _1734110]))), hBOOL(hAPP(_1734108, _1734416))]]], (47426 ^ _779308) ^ [_1734620, _1734622, _1734624, _1734626, _1734628] : [-(hAPP(hAPP(c_List_Olist_OCons(_1734620), _1734622), _1734624) = hAPP(c_List_Ofilter(_1734620, _1734626), _1734628)), 47427 ^ _779308 : [(47428 ^ _779308) ^ [_1734748, _1734750] : [_1734628 = hAPP(hAPP(c_List_Oappend(_1734620), _1734750), hAPP(hAPP(c_List_Olist_OCons(_1734620), _1734622), _1734748)), 47434 ^ _779308 : [(47435 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734620), 47433 ^ [_1734620, _1734622, _1734624, _1734626, _1734628, _1734748, _1734750]), hAPP(c_List_Oset(_1734620), _1734750))))], (47437 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1734626, 47433 ^ [_1734620, _1734622, _1734624, _1734626, _1734628, _1734748, _1734750])))]], hBOOL(hAPP(_1734626, _1734622)), _1734624 = hAPP(c_List_Ofilter(_1734620, _1734626), _1734748)]]], (47447 ^ _779308) ^ [_1735170, _1735172, _1735174, _1735176, _1735178] : [hAPP(c_List_Ofilter(_1735170, _1735172), _1735174) = hAPP(hAPP(c_List_Olist_OCons(_1735170), _1735176), _1735178), 47452 ^ _779308 : [(47453 ^ _779308) ^ [] : [-(_1735174 = hAPP(hAPP(c_List_Oappend(_1735170), 47450 ^ [_1735170, _1735172, _1735174, _1735176, _1735178]), hAPP(hAPP(c_List_Olist_OCons(_1735170), _1735176), 47451 ^ [_1735170, _1735172, _1735174, _1735176, _1735178])))], (47461 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1735172, _1735176)))], (47463 ^ _779308) ^ [] : [-(_1735178 = hAPP(c_List_Ofilter(_1735170, _1735172), 47451 ^ [_1735170, _1735172, _1735174, _1735176, _1735178]))], (47455 ^ _779308) ^ [_1735484] : [hBOOL(hAPP(hAPP(c_member(_1735170), _1735484), hAPP(c_List_Oset(_1735170), 47450 ^ [_1735170, _1735172, _1735174, _1735176, _1735178]))), hBOOL(hAPP(_1735172, _1735484))]]], (47465 ^ _779308) ^ [_1735688, _1735690, _1735692, _1735694, _1735696] : [-(hAPP(c_List_Ofilter(_1735688, _1735690), _1735692) = hAPP(hAPP(c_List_Olist_OCons(_1735688), _1735694), _1735696)), 47466 ^ _779308 : [(47467 ^ _779308) ^ [_1735816, _1735818] : [_1735692 = hAPP(hAPP(c_List_Oappend(_1735688), _1735818), hAPP(hAPP(c_List_Olist_OCons(_1735688), _1735694), _1735816)), 47473 ^ _779308 : [(47474 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735688), 47472 ^ [_1735688, _1735690, _1735692, _1735694, _1735696, _1735816, _1735818]), hAPP(c_List_Oset(_1735688), _1735818))))], (47476 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1735690, 47472 ^ [_1735688, _1735690, _1735692, _1735694, _1735696, _1735816, _1735818])))]], hBOOL(hAPP(_1735690, _1735694)), _1735696 = hAPP(c_List_Ofilter(_1735688, _1735690), _1735816)]]], (47486 ^ _779308) ^ [_1736214, _1736216, _1736218, _1736220] : [class_Orderings_Oorder(_1736214), class_Enum_Oenum(_1736216), 47493 ^ _779308 : [(47494 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736216, _1736214)), _1736218), _1736220)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736216), hAPP(hAPP(c_COMBS(_1736216, _1736214, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736214, tc_fun(_1736214, tc_HOL_Obool), _1736216), c_Orderings_Oord__class_Oless__eq(_1736214)), _1736218)), _1736220))))], (47500 ^ _779308) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736216), hAPP(hAPP(c_COMBS(_1736216, _1736214, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1736214, tc_fun(_1736214, tc_HOL_Obool), _1736216), c_Orderings_Oord__class_Oless__eq(_1736214)), _1736218)), _1736220))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1736216, _1736214)), _1736218), _1736220)))]]], (47506 ^ _779308) ^ [_1736604, _1736606] : [class_Enum_Oenum(_1736604), 47509 ^ _779308 : [(47510 ^ _779308) ^ [] : [hBOOL(hAPP(_1736606, 47511 ^ [_1736604, _1736606])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736604), _1736606)))], (47517 ^ _779308) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736604), _1736606)), 47520 ^ _779308 : [(47521 ^ _779308) ^ [_1736822] : [-(hBOOL(hAPP(_1736606, _1736822)))]]]]], (47523 ^ _779308) ^ [_1736857, _1736859] : [class_Enum_Oenum(_1736857), 47526 ^ _779308 : [(47527 ^ _779308) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736857), _1736859)), 47530 ^ _779308 : [(47531 ^ _779308) ^ [_1736983] : [-(hBOOL(hAPP(_1736859, _1736983)))]]], (47533 ^ _779308) ^ [] : [hBOOL(hAPP(_1736859, 47534 ^ [_1736857, _1736859])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1736857), _1736859)))]]], (47540 ^ _779308) ^ [_1737110, _1737112, _1737114] : [class_Enum_Oenum(_1737110), class_Enum_Oenum(_1737112), 47547 ^ _779308 : [(47548 ^ _779308) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1737112, _1737110)), _1737114)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737112), hAPP(hAPP(c_COMBB(tc_fun(_1737110, tc_HOL_Obool), tc_HOL_Obool, _1737112), c_Enum_Oenum__class_Oenum__all(_1737110)), hAPP(hAPP(c_COMBB(tc_fun(_1737110, tc_prod(_1737112, _1737110)), tc_fun(_1737110, tc_HOL_Obool), _1737112), hAPP(c_COMBB(tc_prod(_1737112, _1737110), tc_HOL_Obool, _1737110), _1737114)), c_Product__Type_OPair(_1737112, _1737110))))))], (47554 ^ _779308) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737112), hAPP(hAPP(c_COMBB(tc_fun(_1737110, tc_HOL_Obool), tc_HOL_Obool, _1737112), c_Enum_Oenum__class_Oenum__all(_1737110)), hAPP(hAPP(c_COMBB(tc_fun(_1737110, tc_prod(_1737112, _1737110)), tc_fun(_1737110, tc_HOL_Obool), _1737112), hAPP(c_COMBB(tc_prod(_1737112, _1737110), tc_HOL_Obool, _1737110), _1737114)), c_Product__Type_OPair(_1737112, _1737110))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1737112, _1737110)), _1737114)))]]], (47560 ^ _779308) ^ [_1737549, _1737551, _1737553, _1737555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737549), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737551)), _1737553))), 47566 ^ _779308 : [(47567 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737551), 47565 ^ [_1737549, _1737551, _1737553, _1737555]), hAPP(c_List_Oset(_1737551), _1737553))))], (47569 ^ _779308) ^ [] : [hBOOL(hAPP(_1737555, 47565 ^ [_1737549, _1737551, _1737553, _1737555]))]], -(hBOOL(hAPP(_1737555, hAPP(hAPP(c_List_Onth(_1737551), _1737553), _1737549))))], (47573 ^ _779308) ^ [_1737835, _1737837, _1737839] : [class_Orderings_Olinorder(_1737835), 47579 ^ _779308 : [(47580 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737835), 47578 ^ [_1737835, _1737837, _1737839]), hAPP(c_List_Oset(_1737835), _1737837))))], (47582 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1737835), _1737839), 47578 ^ [_1737835, _1737837, _1737839]))]], c_List_Olinorder__class_Osorted(_1737835, _1737837), -(c_List_Olinorder__class_Osorted(_1737835, hAPP(hAPP(c_List_Olist_OCons(_1737835), _1737839), _1737837)))], (47590 ^ _779308) ^ [_1738169, _1738171, _1738173] : [c_List_Olist__ex(_1738169, _1738171, _1738173), 47594 ^ _779308 : [(47595 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47593 ^ [_1738169, _1738171, _1738173]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738169)), _1738173))))], (47597 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1738171, hAPP(hAPP(c_List_Onth(_1738169), _1738173), 47593 ^ [_1738169, _1738171, _1738173]))))]]], (47599 ^ _779308) ^ [_1738339, _1738341, _1738343] : [-(c_List_Olist__ex(_1738339, _1738341, _1738343)), 47600 ^ _779308 : [(47601 ^ _779308) ^ [_1738404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738404), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738339)), _1738343))), hBOOL(hAPP(_1738341, hAPP(hAPP(c_List_Onth(_1738339), _1738343), _1738404)))]]], (47609 ^ _779308) ^ [_1738577, _1738579, _1738581] : [hBOOL(hAPP(hAPP(c_member(_1738577), _1738579), hAPP(c_List_Oset(_1738577), _1738581))), -(_1738581 = hAPP(hAPP(c_List_Oappend(_1738577), 47612 ^ [_1738577, _1738579, _1738581]), hAPP(hAPP(c_List_Olist_OCons(_1738577), _1738579), 47613 ^ [_1738577, _1738579, _1738581])))], (47617 ^ _779308) ^ [_1738736, _1738738, _1738740] : [47618 ^ _779308 : [(47619 ^ _779308) ^ [_1738813, _1738815] : [_1738740 = hAPP(hAPP(c_List_Oappend(_1738736), _1738815), hAPP(hAPP(c_List_Olist_OCons(_1738736), _1738738), _1738813))]], -(hBOOL(hAPP(hAPP(c_member(_1738736), _1738738), hAPP(c_List_Oset(_1738736), _1738740))))], (47623 ^ _779308) ^ [_1738908, _1738910] : [c_List_Olist__ex(_1738908, _1738910, c_List_Olist_ONil(_1738908))], (47635 ^ _779308) ^ [_1739069, _1739071, _1739073, _1739075] : [47636 ^ _779308 : [(47637 ^ _779308) ^ [] : [c_List_Olist__ex(_1739069, _1739071, _1739073)], (47639 ^ _779308) ^ [] : [c_List_Olist__ex(_1739069, _1739071, _1739075)]], -(c_List_Olist__ex(_1739069, _1739071, hAPP(hAPP(c_List_Oappend(_1739069), _1739073), _1739075)))], (47625 ^ _779308) ^ [_1738957, _1738959, _1738961, _1738963] : [c_List_Olist__ex(_1738957, _1738959, hAPP(hAPP(c_List_Oappend(_1738957), _1738961), _1738963)), -(c_List_Olist__ex(_1738957, _1738959, _1738961)), -(c_List_Olist__ex(_1738957, _1738959, _1738963))], (47643 ^ _779308) ^ [_1739230, _1739232, _1739234] : [c_List_Olist__ex(_1739230, _1739232, _1739234), 47647 ^ _779308 : [(47648 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739230), 47646 ^ [_1739230, _1739232, _1739234]), hAPP(c_List_Oset(_1739230), _1739234))))], (47650 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1739232, 47646 ^ [_1739230, _1739232, _1739234])))]]], (47652 ^ _779308) ^ [_1739384, _1739386, _1739388] : [-(c_List_Olist__ex(_1739384, _1739386, _1739388)), 47653 ^ _779308 : [(47654 ^ _779308) ^ [_1739441] : [hBOOL(hAPP(hAPP(c_member(_1739384), _1739441), hAPP(c_List_Oset(_1739384), _1739388))), hBOOL(hAPP(_1739386, _1739441))]]], (47662 ^ _779308) ^ [_1739598, _1739600, _1739602] : [c_List_Olist__ex(_1739598, _1739600, hAPP(c_List_Orev(_1739598), _1739602)), -(c_List_Olist__ex(_1739598, _1739600, _1739602))], (47668 ^ _779308) ^ [_1739687, _1739689, _1739691] : [c_List_Olist__ex(_1739687, _1739689, _1739691), -(c_List_Olist__ex(_1739687, _1739689, hAPP(c_List_Orev(_1739687), _1739691)))], (47684 ^ _779308) ^ [_1739917, _1739919, _1739921, _1739923] : [47685 ^ _779308 : [(47686 ^ _779308) ^ [] : [hBOOL(hAPP(_1739919, _1739921))], (47688 ^ _779308) ^ [] : [c_List_Olist__ex(_1739917, _1739919, _1739923)]], -(c_List_Olist__ex(_1739917, _1739919, hAPP(hAPP(c_List_Olist_OCons(_1739917), _1739921), _1739923)))], (47674 ^ _779308) ^ [_1739803, _1739805, _1739807, _1739809] : [c_List_Olist__ex(_1739803, _1739805, hAPP(hAPP(c_List_Olist_OCons(_1739803), _1739807), _1739809)), -(hBOOL(hAPP(_1739805, _1739807))), -(c_List_Olist__ex(_1739803, _1739805, _1739809))], (47692 ^ _779308) ^ [_1740080, _1740082, _1740084] : [hBOOL(hAPP(hAPP(c_member(_1740080), _1740082), hAPP(c_List_Oset(_1740080), _1740084))), 47697 ^ _779308 : [(47698 ^ _779308) ^ [] : [-(_1740084 = hAPP(hAPP(c_List_Oappend(_1740080), 47695 ^ [_1740080, _1740082, _1740084]), hAPP(hAPP(c_List_Olist_OCons(_1740080), _1740082), 47696 ^ [_1740080, _1740082, _1740084])))], (47700 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1740080), _1740082), hAPP(c_List_Oset(_1740080), 47695 ^ [_1740080, _1740082, _1740084])))]]], (47702 ^ _779308) ^ [_1740335, _1740337, _1740339] : [-(hBOOL(hAPP(hAPP(c_member(_1740335), _1740337), hAPP(c_List_Oset(_1740335), _1740339)))), 47703 ^ _779308 : [(47704 ^ _779308) ^ [_1740424] : [47705 ^ _779308 : [(47706 ^ _779308) ^ [_1740497] : [_1740339 = hAPP(hAPP(c_List_Oappend(_1740335), _1740424), hAPP(hAPP(c_List_Olist_OCons(_1740335), _1740337), _1740497))]], -(hBOOL(hAPP(hAPP(c_member(_1740335), _1740337), hAPP(c_List_Oset(_1740335), _1740424))))]]], (47712 ^ _779308) ^ [_1740636, _1740638, _1740640] : [hBOOL(hAPP(hAPP(c_member(_1740636), _1740638), hAPP(c_List_Oset(_1740636), _1740640))), 47717 ^ _779308 : [(47718 ^ _779308) ^ [] : [-(_1740640 = hAPP(hAPP(c_List_Oappend(_1740636), 47715 ^ [_1740636, _1740638, _1740640]), hAPP(hAPP(c_List_Olist_OCons(_1740636), _1740638), 47716 ^ [_1740636, _1740638, _1740640])))], (47720 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1740636), _1740638), hAPP(c_List_Oset(_1740636), 47716 ^ [_1740636, _1740638, _1740640])))]]], (47722 ^ _779308) ^ [_1740891, _1740893, _1740895] : [-(hBOOL(hAPP(hAPP(c_member(_1740891), _1740893), hAPP(c_List_Oset(_1740891), _1740895)))), 47723 ^ _779308 : [(47724 ^ _779308) ^ [_1740980, _1740982] : [_1740895 = hAPP(hAPP(c_List_Oappend(_1740891), _1740982), hAPP(hAPP(c_List_Olist_OCons(_1740891), _1740893), _1740980)), -(hBOOL(hAPP(hAPP(c_member(_1740891), _1740893), hAPP(c_List_Oset(_1740891), _1740980))))]]], (47742 ^ _779308) ^ [_1741395, _1741397, _1741399] : [47744 ^ _779308 : [(47745 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47743 ^ [_1741395, _1741397, _1741399]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741395)), _1741399))))], (47747 ^ _779308) ^ [] : [hBOOL(hAPP(_1741397, hAPP(hAPP(c_List_Onth(_1741395), _1741399), 47743 ^ [_1741395, _1741397, _1741399])))]], -(c_List_Olist__all(_1741395, _1741397, _1741399))], (47732 ^ _779308) ^ [_1741181, _1741183, _1741185] : [c_List_Olist__all(_1741181, _1741183, _1741185), 47735 ^ _779308 : [(47736 ^ _779308) ^ [_1741270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741270), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741181)), _1741185))), -(hBOOL(hAPP(_1741183, hAPP(hAPP(c_List_Onth(_1741181), _1741185), _1741270))))]]], (47751 ^ _779308) ^ [] : [-(c_FunDef_Ois__measure(tc_Int_Oint, hAPP(c_Fun_Ocomp(tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, c_Int_Onat), c_Groups_Oabs__class_Oabs(tc_Int_Oint))))], (47753 ^ _779308) ^ [_1741621, _1741623] : [-(c_List_Olist__all(_1741621, _1741623, c_List_Olist_ONil(_1741621)))], (47755 ^ _779308) ^ [_1741670, _1741672, _1741674, _1741676] : [c_List_Olist__all(_1741670, _1741672, hAPP(hAPP(c_List_Oappend(_1741670), _1741674), _1741676)), 47758 ^ _779308 : [(47759 ^ _779308) ^ [] : [-(c_List_Olist__all(_1741670, _1741672, _1741674))], (47761 ^ _779308) ^ [] : [-(c_List_Olist__all(_1741670, _1741672, _1741676))]]], (47763 ^ _779308) ^ [_1741795, _1741797, _1741799, _1741801] : [-(c_List_Olist__all(_1741795, _1741797, hAPP(hAPP(c_List_Oappend(_1741795), _1741799), _1741801))), c_List_Olist__all(_1741795, _1741797, _1741799), c_List_Olist__all(_1741795, _1741797, _1741801)], (47773 ^ _779308) ^ [_1741956] : [class_Nat_Osize(_1741956), -(c_FunDef_Ois__measure(_1741956, c_Nat_Osize__class_Osize(_1741956)))], (47779 ^ _779308) ^ [_1742033, _1742035] : [-(c_FunDef_Ois__measure(_1742033, _1742035))], (47781 ^ _779308) ^ [_1742058, _1742060] : [-(c_FunDef_Ois__measure(_1742058, _1742060))], (47783 ^ _779308) ^ [_1742083, _1742085] : [-(c_FunDef_Ois__measure(_1742083, _1742085))], (47795 ^ _779308) ^ [_1742316, _1742318, _1742320] : [47797 ^ _779308 : [(47798 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742316), 47796 ^ [_1742316, _1742318, _1742320]), hAPP(c_List_Oset(_1742316), _1742320))))], (47800 ^ _779308) ^ [] : [hBOOL(hAPP(_1742318, 47796 ^ [_1742316, _1742318, _1742320]))]], -(c_List_Olist__all(_1742316, _1742318, _1742320))], (47785 ^ _779308) ^ [_1742126, _1742128, _1742130] : [c_List_Olist__all(_1742126, _1742128, _1742130), 47788 ^ _779308 : [(47789 ^ _779308) ^ [_1742207] : [hBOOL(hAPP(hAPP(c_member(_1742126), _1742207), hAPP(c_List_Oset(_1742126), _1742130))), -(hBOOL(hAPP(_1742128, _1742207)))]]], (47804 ^ _779308) ^ [_1742498, _1742500, _1742502] : [c_FunDef_Ois__measure(_1742498, _1742500), -(c_FunDef_Ois__measure(tc_prod(_1742498, _1742502), hAPP(hAPP(c_COMBB(_1742498, tc_Nat_Onat, tc_prod(_1742498, _1742502)), _1742500), c_Product__Type_Ofst(_1742498, _1742502))))], (47810 ^ _779308) ^ [_1742615, _1742617, _1742619] : [c_FunDef_Ois__measure(_1742615, _1742617), -(c_FunDef_Ois__measure(tc_prod(_1742619, _1742615), hAPP(hAPP(c_COMBB(_1742615, tc_Nat_Onat, tc_prod(_1742619, _1742615)), _1742617), c_Product__Type_Osnd(_1742619, _1742615))))], (47816 ^ _779308) ^ [_1742750, _1742752, _1742754] : [c_List_Olist__all(_1742750, _1742752, hAPP(c_List_Orev(_1742750), _1742754)), -(c_List_Olist__all(_1742750, _1742752, _1742754))], (47822 ^ _779308) ^ [_1742839, _1742841, _1742843] : [c_List_Olist__all(_1742839, _1742841, _1742843), -(c_List_Olist__all(_1742839, _1742841, hAPP(c_List_Orev(_1742839), _1742843)))], (47828 ^ _779308) ^ [_1742955, _1742957, _1742959, _1742961] : [c_List_Olist__all(_1742955, _1742957, hAPP(hAPP(c_List_Olist_OCons(_1742955), _1742959), _1742961)), 47831 ^ _779308 : [(47832 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1742957, _1742959)))], (47834 ^ _779308) ^ [] : [-(c_List_Olist__all(_1742955, _1742957, _1742961))]]], (47836 ^ _779308) ^ [_1743082, _1743084, _1743086, _1743088] : [-(c_List_Olist__all(_1743082, _1743084, hAPP(hAPP(c_List_Olist_OCons(_1743082), _1743086), _1743088))), hBOOL(hAPP(_1743084, _1743086)), c_List_Olist__all(_1743082, _1743084, _1743088)], (47846 ^ _779308) ^ [_1743263, _1743265, _1743267] : [47848 ^ _779308 : [(47849 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743263), 47847 ^ [_1743263, _1743265, _1743267]), hAPP(c_List_Oset(_1743263), _1743265))))], (47851 ^ _779308) ^ [] : [hBOOL(hAPP(_1743267, 47847 ^ [_1743263, _1743265, _1743267]))]], -(c_List_Olist__all(_1743263, _1743267, _1743265))], (47855 ^ _779308) ^ [_1743439, _1743441, _1743443] : [c_List_Olist__all(_1743439, _1743443, _1743441), 47858 ^ _779308 : [(47859 ^ _779308) ^ [_1743520] : [hBOOL(hAPP(hAPP(c_member(_1743439), _1743520), hAPP(c_List_Oset(_1743439), _1743441))), -(hBOOL(hAPP(_1743443, _1743520)))]]], (47875 ^ _779308) ^ [_1743843, _1743845, _1743847] : [47877 ^ _779308 : [(47878 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743843), 47876 ^ [_1743843, _1743845, _1743847]), hAPP(c_List_Oset(_1743843), _1743847))))], (47880 ^ _779308) ^ [] : [hBOOL(hAPP(_1743845, 47876 ^ [_1743843, _1743845, _1743847]))]], -(c_List_Olist__all(_1743843, _1743845, _1743847))], (47865 ^ _779308) ^ [_1743653, _1743655, _1743657] : [c_List_Olist__all(_1743653, _1743655, _1743657), 47868 ^ _779308 : [(47869 ^ _779308) ^ [_1743734] : [hBOOL(hAPP(hAPP(c_member(_1743653), _1743734), hAPP(c_List_Oset(_1743653), _1743657))), -(hBOOL(hAPP(_1743655, _1743734)))]]], (47900 ^ _779308) ^ [_1744322, _1744324, _1744326, _1744328] : [-(c_List_Olist__ex1(_1744322, _1744324, hAPP(hAPP(c_List_Olist_OCons(_1744322), _1744326), _1744328))), 47903 ^ _779308 : [(47904 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1744324, _1744326)))], (47906 ^ _779308) ^ [] : [c_List_Olist__all(_1744322, hAPP(hAPP(c_COMBS(_1744322, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1744322), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1744322), c_fNot), _1744324))), hAPP(c_fequal, _1744326)), _1744328)]], 47907 ^ _779308 : [(47908 ^ _779308) ^ [] : [hBOOL(hAPP(_1744324, _1744326))], (47910 ^ _779308) ^ [] : [c_List_Olist__ex1(_1744322, _1744324, _1744328)]]], (47884 ^ _779308) ^ [_1744046, _1744048, _1744050, _1744052] : [c_List_Olist__ex1(_1744046, _1744048, hAPP(hAPP(c_List_Olist_OCons(_1744046), _1744050), _1744052)), 47887 ^ _779308 : [(47888 ^ _779308) ^ [] : [hBOOL(hAPP(_1744048, _1744050)), -(c_List_Olist__all(_1744046, hAPP(hAPP(c_COMBS(_1744046, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1744046), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1744046), c_fNot), _1744048))), hAPP(c_fequal, _1744050)), _1744052))], (47894 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1744048, _1744050))), -(c_List_Olist__ex1(_1744046, _1744048, _1744052))]]], (47914 ^ _779308) ^ [] : [-(c_Nat__Transfer_Otransfer__morphism(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_COMBK(tc_HOL_Obool, tc_Nat_Onat), c_fTrue)))], (47916 ^ _779308) ^ [_1744660, _1744662] : [c_List_Olist__ex1(_1744660, _1744662, c_List_Olist_ONil(_1744660))], (47918 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47920 ^ _779308) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47922 ^ _779308) ^ [_1744742, _1744744, _1744746] : [c_List_Olist__ex1(_1744742, _1744744, _1744746), 47926 ^ _779308 : [(47927 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744742), 47925 ^ [_1744742, _1744744, _1744746]), hAPP(c_List_Oset(_1744742), _1744746))))], (47929 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1744744, 47925 ^ [_1744742, _1744744, _1744746])))], (47931 ^ _779308) ^ [_1744988] : [-(_1744988 = 47925 ^ [_1744742, _1744744, _1744746]), hBOOL(hAPP(hAPP(c_member(_1744742), _1744988), hAPP(c_List_Oset(_1744742), _1744746))), hBOOL(hAPP(_1744744, _1744988))]]], (47941 ^ _779308) ^ [_1745175, _1745177, _1745179] : [-(c_List_Olist__ex1(_1745175, _1745177, _1745179)), 47942 ^ _779308 : [(47943 ^ _779308) ^ [_1745269] : [hBOOL(hAPP(hAPP(c_member(_1745175), _1745269), hAPP(c_List_Oset(_1745175), _1745179))), hBOOL(hAPP(_1745177, _1745269)), 47951 ^ _779308 : [(47952 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745175), 47950 ^ [_1745175, _1745177, _1745179, _1745269]), hAPP(c_List_Oset(_1745175), _1745179))))], (47954 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1745177, 47950 ^ [_1745175, _1745177, _1745179, _1745269])))], (47956 ^ _779308) ^ [] : [47950 ^ [_1745175, _1745177, _1745179, _1745269] = _1745269]]]]], (47960 ^ _779308) ^ [_1745622, _1745624, _1745626, _1745628, _1745630] : [_1745622 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1745624, _1745626, _1745628, _1745630), _1745622) = c_Lazy__Sequence_Ohit__bound(_1745626))], (47966 ^ _779308) ^ [_1745719, _1745721, _1745723, _1745725, _1745727] : [-(_1745719 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1745721, _1745723, _1745725, _1745727), _1745719) = c_Lazy__Sequence_Ohb__bind(_1745721, _1745723, hAPP(_1745725, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1745719), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1745721, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1745723))), _1745727), _1745719)))], (47972 ^ _779308) ^ [_1745817, _1745819, _1745821, _1745823, _1745825] : [_1745817 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1745819, _1745821, _1745823, _1745825), _1745817) = c_Lazy__Sequence_Oempty(_1745821))], (47978 ^ _779308) ^ [_1745914, _1745916, _1745918, _1745920, _1745922] : [-(_1745914 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1745916, _1745918, _1745920, _1745922), _1745914) = hAPP(c_Lazy__Sequence_Obind(_1745916, _1745918, hAPP(_1745920, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1745914), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1745916, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1745918)), _1745922), _1745914)))], (47984 ^ _779308) ^ [_1745994, _1745996, _1745998, _1746000, _1746002, _1746004, _1746006] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1745994, _1745996, _1745998, _1746000, _1746002, _1746004, _1746006) = c_New__DSequence_Oneg__decr__bind(_1745994, _1745996, hAPP(hAPP(hAPP(_1745998, _1746002), _1746004), _1746006), hAPP(hAPP(c_COMBC(_1745994, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1745996)))), hAPP(hAPP(c_COMBC(_1745994, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1745996))))), hAPP(hAPP(c_COMBC(_1745994, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1745996)))))), _1746000), _1746002)), _1746004)), _1746006)))], (47986 ^ _779308) ^ [_1746111, _1746113, _1746115, _1746117, _1746119, _1746121, _1746123] : [-(c_New__Random__Sequence_Opos__decr__bind(_1746111, _1746113, _1746115, _1746117, _1746119, _1746121, _1746123) = c_New__DSequence_Opos__decr__bind(_1746111, _1746113, hAPP(hAPP(hAPP(_1746115, _1746119), _1746121), _1746123), hAPP(hAPP(c_COMBC(_1746111, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746113))), hAPP(hAPP(c_COMBC(_1746111, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746113)))), hAPP(hAPP(c_COMBC(_1746111, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746113))))), _1746117), _1746119)), _1746121)), _1746123)))], (47988 ^ _779308) ^ [_1746222, _1746224, _1746226, _1746228, _1746230] : [-(hAPP(c_New__DSequence_Oneg__bind(_1746222, _1746224, _1746226, _1746228), _1746230) = c_Lazy__Sequence_Ohb__bind(_1746222, _1746224, hAPP(_1746226, _1746230), hAPP(hAPP(c_COMBC(_1746222, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746224))), _1746228), _1746230)))], (47990 ^ _779308) ^ [_1746283, _1746285] : [-(hAPP(c_New__DSequence_Opos__empty(_1746283), _1746285) = c_Lazy__Sequence_Oempty(_1746283))], (47992 ^ _779308) ^ [_1746315, _1746317, _1746319, _1746321] : [-(c_New__Random__Sequence_Opos__empty(_1746315, _1746317, _1746319, _1746321) = c_New__DSequence_Opos__empty(_1746315))], (47994 ^ _779308) ^ [_1746351, _1746353, _1746355, _1746357, _1746359, _1746361, _1746363] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1746351, _1746353, _1746355, _1746357), _1746359), _1746361), _1746363) = c_New__DSequence_Oneg__bind(_1746351, _1746353, hAPP(hAPP(hAPP(_1746355, _1746359), _1746361), _1746363), hAPP(hAPP(c_COMBC(_1746351, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746353)))), hAPP(hAPP(c_COMBC(_1746351, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746353))))), hAPP(hAPP(c_COMBC(_1746351, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746353)))))), _1746357), _1746359)), _1746361)), _1746363)))], (47996 ^ _779308) ^ [_1746474, _1746476, _1746478, _1746480, _1746482] : [-(hAPP(c_New__DSequence_Opos__bind(_1746474, _1746476, _1746478, _1746480), _1746482) = hAPP(c_Lazy__Sequence_Obind(_1746474, _1746476, hAPP(_1746478, _1746482)), hAPP(hAPP(c_COMBC(_1746474, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746476)), _1746480), _1746482)))], (47998 ^ _779308) ^ [_1746535, _1746537, _1746539, _1746541] : [-(c_New__Random__Sequence_Oneg__map(_1746535, _1746537, _1746539, _1746541) = c_New__Random__Sequence_Oneg__bind(_1746535, _1746537, _1746541, hAPP(c_Fun_Ocomp(_1746537, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746537)))))), _1746535, c_New__Random__Sequence_Oneg__single(_1746537)), _1746539)))], (48000 ^ _779308) ^ [_1746600, _1746602, _1746604, _1746606, _1746608] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1746600), _1746602), _1746604), _1746606), _1746608) = c_New__DSequence_Oneg__single(_1746600, _1746602))], (48002 ^ _779308) ^ [_1746648, _1746650, _1746652, _1746654, _1746656, _1746658, _1746660] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1746648, _1746650, _1746652, _1746654), _1746656), _1746658), _1746660) = c_New__DSequence_Opos__bind(_1746648, _1746650, hAPP(hAPP(hAPP(_1746652, _1746656), _1746658), _1746660), hAPP(hAPP(c_COMBC(_1746648, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746650))), hAPP(hAPP(c_COMBC(_1746648, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746650)))), hAPP(hAPP(c_COMBC(_1746648, tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746650))))), _1746654), _1746656)), _1746658)), _1746660)))], (48004 ^ _779308) ^ [_1746765, _1746767, _1746769] : [-(hAPP(c_New__DSequence_Oneg__single(_1746765, _1746767), _1746769) = c_Lazy__Sequence_Ohb__single(_1746765, _1746767))], (48006 ^ _779308) ^ [_1746801, _1746803, _1746805, _1746807] : [-(c_New__Random__Sequence_Opos__map(_1746801, _1746803, _1746805, _1746807) = c_New__Random__Sequence_Opos__bind(_1746801, _1746803, _1746807, hAPP(c_Fun_Ocomp(_1746803, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746803))))), _1746801, c_New__Random__Sequence_Opos__single(_1746803)), _1746805)))], (48008 ^ _779308) ^ [_1746864, _1746866, _1746868, _1746870, _1746872] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1746864), _1746866), _1746868), _1746870), _1746872) = c_New__DSequence_Opos__single(_1746864, _1746866))], (48010 ^ _779308) ^ [_1746912, _1746914, _1746916] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746912)), c_List_Osplice(_1746912, _1746914, _1746916)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746912)), _1746914)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746912)), _1746916)))], (48012 ^ _779308) ^ [_1746970, _1746972, _1746974, _1746976, _1746978] : [-(c_List_Osplice(_1746970, hAPP(hAPP(c_List_Olist_OCons(_1746970), _1746972), _1746974), hAPP(hAPP(c_List_Olist_OCons(_1746970), _1746976), _1746978)) = hAPP(hAPP(c_List_Olist_OCons(_1746970), _1746972), hAPP(hAPP(c_List_Olist_OCons(_1746970), _1746976), c_List_Osplice(_1746970, _1746974, _1746978))))], (48014 ^ _779308) ^ [_1747041, _1747043] : [-(c_List_Osplice(_1747041, c_List_Olist_ONil(_1747041), _1747043) = _1747043)], (48016 ^ _779308) ^ [_1747072, _1747074] : [-(c_List_Osplice(_1747072, _1747074, c_List_Olist_ONil(_1747072)) = _1747074)], (48018 ^ _779308) ^ [_1747103, _1747105, _1747107] : [-(c_List_Osplice(_1747103, hAPP(hAPP(c_List_Olist_OCons(_1747103), _1747105), _1747107), c_List_Olist_ONil(_1747103)) = hAPP(hAPP(c_List_Olist_OCons(_1747103), _1747105), _1747107))], (48020 ^ _779308) ^ [_1747152, _1747154, _1747156] : [-(hAPP(c_New__DSequence_Opos__single(_1747152, _1747154), _1747156) = hAPP(c_Lazy__Sequence_Osingle(_1747152), _1747154))], (48022 ^ _779308) ^ [_1747205, _1747207] : [c_Wellfounded_Oacyclic(_1747205, hAPP(c_Set_OCollect(tc_prod(_1747205, _1747205)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747205, _1747205, tc_HOL_Obool), c_Predicate_Oconversep(_1747205, _1747205, _1747207)))), -(c_Wellfounded_Oacyclic(_1747205, hAPP(c_Set_OCollect(tc_prod(_1747205, _1747205)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747205, _1747205, tc_HOL_Obool), _1747207))))], (48028 ^ _779308) ^ [_1747346, _1747348] : [c_Wellfounded_Oacyclic(_1747346, hAPP(c_Set_OCollect(tc_prod(_1747346, _1747346)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747346, _1747346, tc_HOL_Obool), _1747348))), -(c_Wellfounded_Oacyclic(_1747346, hAPP(c_Set_OCollect(tc_prod(_1747346, _1747346)), hAPP(c_Product__Type_Oprod_Oprod__case(_1747346, _1747346, tc_HOL_Obool), c_Predicate_Oconversep(_1747346, _1747346, _1747348)))))], (48034 ^ _779308) ^ [_1747493, _1747495, _1747497, _1747499] : [-(c_Predicate_Oconversep(_1747493, _1747495, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1747493, tc_fun(_1747495, tc_HOL_Obool))), _1747497), _1747499)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1747495, tc_fun(_1747493, tc_HOL_Obool))), c_Predicate_Oconversep(_1747493, _1747495, _1747497)), c_Predicate_Oconversep(_1747493, _1747495, _1747499)))], (48036 ^ _779308) ^ [_1747562, _1747564, _1747566, _1747568] : [-(c_Predicate_Oconversep(_1747562, _1747564, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1747562, tc_fun(_1747564, tc_HOL_Obool))), _1747566), _1747568)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1747564, tc_fun(_1747562, tc_HOL_Obool))), c_Predicate_Oconversep(_1747562, _1747564, _1747566)), c_Predicate_Oconversep(_1747562, _1747564, _1747568)))], (48038 ^ _779308) ^ [_1747631, _1747633, _1747635, _1747637, _1747639] : [-(c_Predicate_Oconversep(_1747631, _1747633, c_Predicate_Opred__comp(_1747631, _1747635, _1747633, _1747637, _1747639)) = c_Predicate_Opred__comp(_1747633, _1747635, _1747631, c_Predicate_Oconversep(_1747635, _1747633, _1747639), c_Predicate_Oconversep(_1747631, _1747635, _1747637)))], (48040 ^ _779308) ^ [_1747686, _1747688, _1747690, _1747692, _1747694] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1747686, _1747688, _1747690), _1747692), _1747694)), -(hBOOL(hAPP(hAPP(_1747690, _1747694), _1747692)))], (48046 ^ _779308) ^ [_1747797, _1747799, _1747801, _1747803, _1747805] : [hBOOL(hAPP(hAPP(_1747797, _1747799), _1747801)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1747803, _1747805, _1747797), _1747801), _1747799)))], (48052 ^ _779308) ^ [_1747932, _1747934, _1747936, _1747938, _1747940] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1747932, _1747934, _1747936), _1747938), _1747940)), -(hBOOL(hAPP(hAPP(_1747936, _1747940), _1747938)))], (48058 ^ _779308) ^ [_1748039, _1748041, _1748043, _1748045, _1748047] : [hBOOL(hAPP(hAPP(_1748043, _1748047), _1748045)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748039, _1748041, _1748043), _1748045), _1748047)))], (48064 ^ _779308) ^ [_1748176, _1748178, _1748180, _1748182, _1748184] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748176, _1748178, _1748180), _1748182), _1748184)), -(hBOOL(hAPP(hAPP(_1748180, _1748184), _1748182)))], (48070 ^ _779308) ^ [_1748283, _1748285, _1748287, _1748289, _1748291] : [hBOOL(hAPP(hAPP(_1748287, _1748291), _1748289)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748283, _1748285, _1748287), _1748289), _1748291)))], (48076 ^ _779308) ^ [_1748396, _1748398, _1748400] : [-(c_Predicate_Oconversep(_1748396, _1748398, c_Predicate_Oconversep(_1748398, _1748396, _1748400)) = _1748400)], (48078 ^ _779308) ^ [_1748431] : [-(c_Predicate_Oconversep(_1748431, _1748431, c_fequal) = c_fequal)], (48080 ^ _779308) ^ [_1748476, _1748478, _1748480] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748476, _1748476, hAPP(hAPP(c_COMBB(tc_fun(_1748476, tc_HOL_Obool), tc_fun(_1748476, tc_HOL_Obool), _1748476), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1748476), c_fNot)), c_fequal)), _1748478), _1748480)), _1748478 = _1748480], (48086 ^ _779308) ^ [_1748614, _1748616, _1748618] : [-(_1748616 = _1748618), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748614, _1748614, hAPP(hAPP(c_COMBB(tc_fun(_1748614, tc_HOL_Obool), tc_fun(_1748614, tc_HOL_Obool), _1748614), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1748614), c_fNot)), c_fequal)), _1748616), _1748618)))], (48092 ^ _779308) ^ [_1748710, _1748712, _1748714, _1748716, _1748718] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748710, _1748712, hAPP(hAPP(c_COMBC(_1748710, tc_fun(tc_prod(_1748710, _1748712), tc_HOL_Obool), tc_fun(_1748712, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1748712, tc_fun(tc_fun(tc_prod(_1748710, _1748712), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1748710, _1748712), tc_HOL_Obool), tc_fun(_1748712, tc_HOL_Obool)), _1748710), c_COMBC(_1748712, tc_fun(tc_prod(_1748710, _1748712), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1748712, tc_prod(_1748710, _1748712)), tc_fun(_1748712, tc_fun(tc_fun(tc_prod(_1748710, _1748712), tc_HOL_Obool), tc_HOL_Obool)), _1748710), hAPP(c_COMBB(tc_prod(_1748710, _1748712), tc_fun(tc_fun(tc_prod(_1748710, _1748712), tc_HOL_Obool), tc_HOL_Obool), _1748712), c_member(tc_prod(_1748710, _1748712)))), c_Product__Type_OPair(_1748710, _1748712)))), _1748714)), _1748716), _1748718)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1748712, _1748710)), hAPP(hAPP(c_Product__Type_OPair(_1748712, _1748710), _1748716), _1748718)), hAPP(c_Relation_Oconverse(_1748710, _1748712), _1748714))))], (48098 ^ _779308) ^ [_1749093, _1749095, _1749097, _1749099, _1749101] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1749095, _1749093)), hAPP(hAPP(c_Product__Type_OPair(_1749095, _1749093), _1749099), _1749101)), hAPP(c_Relation_Oconverse(_1749093, _1749095), _1749097))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749093, _1749095, hAPP(hAPP(c_COMBC(_1749093, tc_fun(tc_prod(_1749093, _1749095), tc_HOL_Obool), tc_fun(_1749095, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749095, tc_fun(tc_fun(tc_prod(_1749093, _1749095), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1749093, _1749095), tc_HOL_Obool), tc_fun(_1749095, tc_HOL_Obool)), _1749093), c_COMBC(_1749095, tc_fun(tc_prod(_1749093, _1749095), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749095, tc_prod(_1749093, _1749095)), tc_fun(_1749095, tc_fun(tc_fun(tc_prod(_1749093, _1749095), tc_HOL_Obool), tc_HOL_Obool)), _1749093), hAPP(c_COMBB(tc_prod(_1749093, _1749095), tc_fun(tc_fun(tc_prod(_1749093, _1749095), tc_HOL_Obool), tc_HOL_Obool), _1749095), c_member(tc_prod(_1749093, _1749095)))), c_Product__Type_OPair(_1749093, _1749095)))), _1749097)), _1749099), _1749101)))], (48104 ^ _779308) ^ [_1749482, _1749484, _1749486, _1749488] : [-(c_Lazy__Sequence_Oproduct(_1749482, _1749484, _1749486, _1749488) = hAPP(c_Lazy__Sequence_Obind(_1749482, tc_prod(_1749482, _1749484), _1749486), hAPP(hAPP(c_COMBB(tc_fun(_1749484, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749482, _1749484))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749482, _1749484)), _1749482), c_Lazy__Sequence_Obind(_1749484, tc_prod(_1749482, _1749484), _1749488)), hAPP(hAPP(c_COMBB(tc_fun(_1749484, tc_prod(_1749482, _1749484)), tc_fun(_1749484, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749482, _1749484))), _1749482), hAPP(c_COMBB(tc_prod(_1749482, _1749484), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1749482, _1749484)), _1749484), c_Lazy__Sequence_Osingle(tc_prod(_1749482, _1749484)))), c_Product__Type_OPair(_1749482, _1749484)))))], (48106 ^ _779308) ^ [_1749599, _1749601, _1749603] : [-(_1749599 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1749601), c_List_Oreplicate(_1749601, _1749599, _1749603)) = c_List_Oreplicate(_1749601, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1749599), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1749603))], (48112 ^ _779308) ^ [_1749656, _1749658, _1749660] : [-(c_List_Oreplicate(_1749656, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749656)), hAPP(c_List_Ofilter(_1749656, hAPP(c_fequal, _1749658)), _1749660)), _1749658) = hAPP(c_List_Ofilter(_1749656, hAPP(c_fequal, _1749658)), _1749660))], (48114 ^ _779308) ^ [_1749712, _1749714, _1749716] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749712)), c_List_Oreplicate(_1749712, _1749714, _1749716)) = _1749714)], (48116 ^ _779308) ^ [_1749750, _1749752, _1749754, _1749756] : [-(hAPP(hAPP(c_List_Omap(_1749750, _1749752), hAPP(c_COMBK(_1749752, _1749750), _1749754)), _1749756) = c_List_Oreplicate(_1749752, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749750)), _1749756), _1749754))], (48118 ^ _779308) ^ [_1749805, _1749807, _1749809, _1749811] : [-(hAPP(hAPP(c_List_Oappend(_1749805), c_List_Oreplicate(_1749805, _1749807, _1749809)), hAPP(hAPP(c_List_Olist_OCons(_1749805), _1749809), _1749811)) = hAPP(hAPP(c_List_Olist_OCons(_1749805), _1749809), hAPP(hAPP(c_List_Oappend(_1749805), c_List_Oreplicate(_1749805, _1749807, _1749809)), _1749811)))], (48120 ^ _779308) ^ [_1749874, _1749876, _1749878] : [-(c_List_Oreplicate(_1749874, hAPP(c_Nat_OSuc, _1749876), _1749878) = hAPP(hAPP(c_List_Olist_OCons(_1749874), _1749878), c_List_Oreplicate(_1749874, _1749876, _1749878)))], (48122 ^ _779308) ^ [_1749920, _1749922, _1749924] : [-(hAPP(c_List_Orev(_1749920), c_List_Oreplicate(_1749920, _1749922, _1749924)) = c_List_Oreplicate(_1749920, _1749922, _1749924))], (48124 ^ _779308) ^ [_1749960, _1749962, _1749964, _1749966] : [-(hAPP(hAPP(c_List_Odrop(_1749960), _1749962), c_List_Oreplicate(_1749960, _1749964, _1749966)) = c_List_Oreplicate(_1749960, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1749964), _1749962), _1749966))], (48126 ^ _779308) ^ [_1750007, _1750009, _1750011] : [-(_1750007 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1750009), c_List_Oreplicate(_1750009, _1750007, _1750011)) = _1750011)], (48132 ^ _779308) ^ [_1750050, _1750052, _1750054] : [-(_1750050 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1750052, c_List_Oreplicate(_1750052, _1750050, _1750054)) = _1750054)], (48138 ^ _779308) ^ [_1750095, _1750097, _1750099, _1750101] : [-(hAPP(hAPP(c_List_Otake(_1750095), _1750097), c_List_Oreplicate(_1750095, _1750099, _1750101)) = c_List_Oreplicate(_1750095, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1750097), _1750099), _1750101))], (48140 ^ _779308) ^ [_1750146, _1750148, _1750150, _1750152, _1750154, _1750156] : [-(hAPP(hAPP(c_List_Ozip(_1750146, _1750148), c_List_Oreplicate(_1750146, _1750150, _1750152)), c_List_Oreplicate(_1750148, _1750154, _1750156)) = c_List_Oreplicate(tc_prod(_1750146, _1750148), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1750150), _1750154), hAPP(hAPP(c_Product__Type_OPair(_1750146, _1750148), _1750152), _1750156)))], (48142 ^ _779308) ^ [_1750239, _1750241, _1750243, _1750245] : [48149 ^ _779308 : [(48150 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1750245, _1750243)))], (48152 ^ _779308) ^ [] : [_1750241 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 48143 ^ _779308 : [(48144 ^ _779308) ^ [_1750311] : [hBOOL(hAPP(hAPP(c_member(_1750239), _1750311), hAPP(c_List_Oset(_1750239), c_List_Oreplicate(_1750239, _1750241, _1750243)))), hBOOL(hAPP(_1750245, _1750311))]]], (48154 ^ _779308) ^ [_1750481, _1750483, _1750485, _1750487] : [48162 ^ _779308 : [(48163 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750481), 48161 ^ [_1750481, _1750483, _1750485, _1750487]), hAPP(c_List_Oset(_1750481), c_List_Oreplicate(_1750481, _1750483, _1750485)))))], (48165 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1750487, 48161 ^ [_1750481, _1750483, _1750485, _1750487])))]], hBOOL(hAPP(_1750487, _1750485)), -(_1750483 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48167 ^ _779308) ^ [_1750737, _1750739, _1750741, _1750743] : [48169 ^ _779308 : [(48170 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750737), 48168 ^ [_1750737, _1750739, _1750741, _1750743]), hAPP(c_List_Oset(_1750737), c_List_Oreplicate(_1750737, _1750739, _1750741)))))], (48172 ^ _779308) ^ [] : [hBOOL(hAPP(_1750743, 48168 ^ [_1750737, _1750739, _1750741, _1750743]))]], -(hBOOL(hAPP(_1750743, _1750741))), -(_1750739 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48180 ^ _779308) ^ [_1750944, _1750946, _1750948, _1750950] : [48181 ^ _779308 : [(48182 ^ _779308) ^ [] : [hBOOL(hAPP(_1750950, _1750948))], (48184 ^ _779308) ^ [] : [_1750946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 48185 ^ _779308 : [(48186 ^ _779308) ^ [_1751069] : [hBOOL(hAPP(hAPP(c_member(_1750944), _1751069), hAPP(c_List_Oset(_1750944), c_List_Oreplicate(_1750944, _1750946, _1750948)))), -(hBOOL(hAPP(_1750950, _1751069)))]]], (48192 ^ _779308) ^ [_1751220, _1751222, _1751224, _1751226, _1751228] : [c_List_Oreplicate(_1751220, _1751222, _1751224) = c_List_Oreplicate(_1751220, _1751226, _1751228), 48195 ^ _779308 : [(48196 ^ _779308) ^ [] : [-(_1751222 = _1751226)], (48198 ^ _779308) ^ [] : [-(_1751222 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1751224 = _1751228)]]], (48204 ^ _779308) ^ [_1751356, _1751358, _1751360, _1751362, _1751364] : [-(c_List_Oreplicate(_1751356, _1751358, _1751360) = c_List_Oreplicate(_1751356, _1751362, _1751364)), _1751358 = _1751362, 48209 ^ _779308 : [(48210 ^ _779308) ^ [] : [_1751358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48212 ^ _779308) ^ [] : [_1751360 = _1751364]]], (48216 ^ _779308) ^ [_1751555, _1751557, _1751559, _1751561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751555), _1751557)), -(hAPP(hAPP(c_List_Onth(_1751559), c_List_Oreplicate(_1751559, _1751557, _1751561)), _1751555) = _1751561)], (48222 ^ _779308) ^ [_1751670, _1751672, _1751674, _1751676] : [-(c_List_Oreplicate(_1751670, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1751672), _1751674), _1751676) = hAPP(hAPP(c_List_Oappend(_1751670), c_List_Oreplicate(_1751670, _1751672, _1751676)), c_List_Oreplicate(_1751670, _1751674, _1751676)))], (48224 ^ _779308) ^ [_1751725, _1751727, _1751729, _1751731] : [-(hAPP(hAPP(c_List_Oappend(_1751725), c_List_Oreplicate(_1751725, _1751727, _1751729)), c_List_Oreplicate(_1751725, _1751731, _1751729)) = hAPP(hAPP(c_List_Oappend(_1751725), c_List_Oreplicate(_1751725, _1751731, _1751729)), c_List_Oreplicate(_1751725, _1751727, _1751729)))], (48226 ^ _779308) ^ [_1751801, _1751803, _1751805, _1751807] : [hBOOL(hAPP(_1751801, _1751803)), -(hAPP(c_List_Ofilter(_1751805, _1751801), c_List_Oreplicate(_1751805, _1751807, _1751803)) = c_List_Oreplicate(_1751805, _1751807, _1751803))], (48232 ^ _779308) ^ [_1751908, _1751910, _1751912, _1751914] : [-(hBOOL(hAPP(_1751908, _1751910))), -(hAPP(c_List_Ofilter(_1751912, _1751908), c_List_Oreplicate(_1751912, _1751914, _1751910)) = c_List_Olist_ONil(_1751912))], (48238 ^ _779308) ^ [_1751964, _1751966] : [-(c_List_Oconcat(_1751964, c_List_Oreplicate(tc_List_Olist(_1751964), _1751966, c_List_Olist_ONil(_1751964))) = c_List_Olist_ONil(_1751964))], (48240 ^ _779308) ^ [_1752002, _1752004] : [-(c_List_Oreplicate(_1752002, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1752004) = c_List_Olist_ONil(_1752002))], (48242 ^ _779308) ^ [_1752051, _1752053, _1752055] : [c_List_Olist_ONil(_1752051) = c_List_Oreplicate(_1752051, _1752053, _1752055), -(_1752053 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48248 ^ _779308) ^ [_1752138, _1752140, _1752142] : [_1752140 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1752138) = c_List_Oreplicate(_1752138, _1752140, _1752142))], (48254 ^ _779308) ^ [_1752249, _1752251, _1752253] : [c_List_Oreplicate(_1752249, _1752251, _1752253) = c_List_Olist_ONil(_1752249), -(_1752251 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48260 ^ _779308) ^ [_1752336, _1752338, _1752340] : [_1752338 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1752336, _1752338, _1752340) = c_List_Olist_ONil(_1752336))], (48266 ^ _779308) ^ [_1752429, _1752431, _1752433, _1752435, _1752437] : [-(hAPP(hAPP(c_List_Omap(_1752429, _1752431), _1752433), c_List_Oreplicate(_1752429, _1752435, _1752437)) = c_List_Oreplicate(_1752431, _1752435, hAPP(_1752433, _1752437)))], (48268 ^ _779308) ^ [_1752501, _1752503, _1752505, _1752507] : [hBOOL(hAPP(hAPP(c_member(_1752501), _1752503), hAPP(c_List_Oset(_1752501), c_List_Oreplicate(_1752501, _1752505, _1752507)))), 48271 ^ _779308 : [(48272 ^ _779308) ^ [] : [-(_1752503 = _1752507)], (48274 ^ _779308) ^ [] : [_1752505 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (48276 ^ _779308) ^ [_1752644, _1752646, _1752648, _1752650] : [-(hBOOL(hAPP(hAPP(c_member(_1752644), _1752646), hAPP(c_List_Oset(_1752644), c_List_Oreplicate(_1752644, _1752648, _1752650))))), _1752646 = _1752650, -(_1752648 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48286 ^ _779308) ^ [_1752818, _1752820, _1752822] : [-(hAPP(hAPP(c_List_Oappend(_1752818), c_List_Oreplicate(_1752818, _1752820, _1752822)), hAPP(hAPP(c_List_Olist_OCons(_1752818), _1752822), c_List_Olist_ONil(_1752818))) = hAPP(hAPP(c_List_Olist_OCons(_1752818), _1752822), c_List_Oreplicate(_1752818, _1752820, _1752822)))], (48288 ^ _779308) ^ [_1752879, _1752881, _1752883] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1752879), hAPP(c_COMBK(_1752879, tc_Nat_Onat), _1752881)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1752883)) = c_List_Oreplicate(_1752879, _1752883, _1752881))], (48290 ^ _779308) ^ [_1752924, _1752926, _1752928] : [-(_1752924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1752926), c_List_Oreplicate(_1752926, _1752924, _1752928)) = hAPP(hAPP(c_Set_Oinsert(_1752926), _1752928), c_Orderings_Obot__class_Obot(tc_fun(_1752926, tc_HOL_Obool))))], (48296 ^ _779308) ^ [_1752996, _1752998, _1753000] : [_1752996 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1752998), c_List_Oreplicate(_1752998, _1752996, _1753000)) = c_Orderings_Obot__class_Obot(tc_fun(_1752998, tc_HOL_Obool)))], (48302 ^ _779308) ^ [_1753097, _1753099, _1753101] : [-(_1753097 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1753099), c_List_Oreplicate(_1753099, _1753097, _1753101)) = hAPP(hAPP(c_Set_Oinsert(_1753099), _1753101), c_Orderings_Obot__class_Obot(tc_fun(_1753099, tc_HOL_Obool))))], (48308 ^ _779308) ^ [_1753159, _1753161, _1753163] : [-(hAPP(c_List_Oset(_1753159), c_List_Oreplicate(_1753159, hAPP(c_Nat_OSuc, _1753161), _1753163)) = hAPP(hAPP(c_Set_Oinsert(_1753159), _1753163), c_Orderings_Obot__class_Obot(tc_fun(_1753159, tc_HOL_Obool))))], (48310 ^ _779308) ^ [_1753211, _1753213] : [class_Lazy__Sequence_Osmall__lazy(_1753211), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1753211), _1753213) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1753211), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1753211)), c_List_Olist_ONil(_1753211)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753211))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1753213)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1753211, tc_List_Olist(_1753211)), tc_List_Olist(_1753211), c_Lazy__Sequence_Oproduct(_1753211, tc_List_Olist(_1753211), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1753211, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1753213), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1753211), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1753213), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1753211, tc_List_Olist(_1753211), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753211))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1753211), tc_List_Olist(_1753211)), tc_fun(tc_List_Olist(_1753211), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753211))), _1753211), hAPP(c_COMBB(tc_List_Olist(_1753211), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1753211)), tc_List_Olist(_1753211)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1753211)))), c_List_Olist_OCons(_1753211))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1753211)))))], (48316 ^ _779308) ^ [_1753572, _1753574] : [-(c_Predicate_Opred__comp(_1753572, _1753572, _1753572, c_fequal, c_Predicate_Opred__comp(_1753572, _1753572, _1753572, _1753574, c_fequal)) = _1753574)], (48318 ^ _779308) ^ [_1753609, _1753611, _1753613] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1753609, _1753611), _1753613) = c_Lazy__Sequence_Oproduct(_1753609, _1753611, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1753609, _1753613), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1753611, _1753613))), class_Lazy__Sequence_Osmall__lazy(_1753609), class_Lazy__Sequence_Osmall__lazy(_1753611)], (48328 ^ _779308) ^ [_1753772, _1753774, _1753776, _1753778] : [-(hAPP(c_New__DSequence_Opos__union(_1753772, _1753774, _1753776), _1753778) = c_Lazy__Sequence_Oappend(_1753772, hAPP(_1753774, _1753778), hAPP(_1753776, _1753778)))], (48330 ^ _779308) ^ [_1753818, _1753820, _1753822] : [class_Fields_Olinordered__field(_1753818), 48336 ^ _779308 : [(48337 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1753818), c_Groups_Ozero__class_Ozero(_1753818)), 48335 ^ [_1753818, _1753820, _1753822])))], (48339 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1753818), _1753820), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1753818), _1753822), 48335 ^ [_1753818, _1753820, _1753822])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1753818), _1753820), _1753822)))], (48343 ^ _779308) ^ [_1754096, _1754098, _1754100, _1754102, _1754104, _1754106] : [-(c_New__Random__Sequence_Opos__union(_1754096, _1754098, _1754100, _1754102, _1754104, _1754106) = c_New__DSequence_Opos__union(_1754096, hAPP(hAPP(hAPP(_1754098, _1754102), _1754104), _1754106), hAPP(hAPP(hAPP(_1754100, _1754102), _1754104), _1754106)))], (48345 ^ _779308) ^ [_1754167, _1754169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754167), _1754169)), -(c_Lazy__Sequence_Osmall__lazy_H(_1754167, _1754169) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (48351 ^ _779308) ^ [_1754254, _1754256] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754254), _1754256))), -(c_Lazy__Sequence_Osmall__lazy_H(_1754254, _1754256) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1754256), c_Lazy__Sequence_Osmall__lazy_H(_1754254, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1754256), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48357 ^ _779308) ^ [_1754316] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1754316) = c_Lazy__Sequence_Osmall__lazy_H(_1754316, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1754316)))], (48359 ^ _779308) ^ [_1754348, _1754350] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1754348), _1754350))), 48362 ^ _779308 : [(48363 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754348), _1754350)), -(c_Lazy__Sequence_Osmall__lazy_H(_1754348, _1754350) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (48369 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1754348), _1754350))), -(c_Lazy__Sequence_Osmall__lazy_H(_1754348, _1754350) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1754350), c_Lazy__Sequence_Osmall__lazy_H(_1754348, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1754350), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (48375 ^ _779308) ^ [_1754604, _1754606, _1754608] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754604)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1754604, _1754606, _1754608)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754604)), _1754608)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48377 ^ _779308) ^ [_1754655, _1754657, _1754659, _1754661] : [-(c_Lazy__Sequence_Oappend(_1754655, c_Lazy__Sequence_Olazy__sequence_OInsert(_1754655, _1754657, _1754659), _1754661) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754655, _1754657, c_Lazy__Sequence_Oappend(_1754655, _1754659, _1754661)))], (48379 ^ _779308) ^ [_1754724, _1754726, _1754728, _1754730, _1754732] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1754724, _1754726, _1754728) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754724, _1754730, _1754732), 48382 ^ _779308 : [(48383 ^ _779308) ^ [] : [-(_1754726 = _1754730)], (48385 ^ _779308) ^ [] : [-(_1754728 = _1754732)]]], (48387 ^ _779308) ^ [_1754845, _1754847, _1754849, _1754851, _1754853] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1754845, _1754847, _1754849) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754845, _1754851, _1754853)), _1754847 = _1754851, _1754849 = _1754853], (48397 ^ _779308) ^ [_1755004, _1755006, _1755008, _1755010] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755004, _1755006), c_Lazy__Sequence_Olazy__sequence_OInsert(_1755004, _1755008, _1755010)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1755006, _1755008)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755004, _1755006), _1755010))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48399 ^ _779308) ^ [_1755064, _1755066, _1755068] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1755064), _1755066))), -(hBOOL(hAPP(hAPP(_1755068, _1755064), _1755066))), 48406 ^ _779308 : [(48407 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 48404 ^ [_1755064, _1755066, _1755068]), 48405 ^ [_1755064, _1755066, _1755068]))))], (48415 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1755068, 48404 ^ [_1755064, _1755066, _1755068]), 48405 ^ [_1755064, _1755066, _1755068]))], (48409 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 48404 ^ [_1755064, _1755066, _1755068]), 48405 ^ [_1755064, _1755066, _1755068]))), -(hBOOL(hAPP(hAPP(_1755068, 48404 ^ [_1755064, _1755066, _1755068]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48405 ^ [_1755064, _1755066, _1755068]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (48419 ^ _779308) ^ [_1755516, _1755518] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1755516)), _1755518) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1755516, tc_Lazy__Sequence_Olazy__sequence(_1755516)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1755516, tc_Lazy__Sequence_Olazy__sequence(_1755516), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755516), tc_Nat_Onat), _1755516), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1755516), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1755516)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1755516)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1755516), _1755518)))], (48421 ^ _779308) ^ [_1755612, _1755614, _1755616] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755612, _1755614), _1755616) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1755612, tc_Lazy__Sequence_Olazy__sequence(_1755612)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1755612, tc_Lazy__Sequence_Olazy__sequence(_1755612), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1755612, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755612), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755612), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755612), tc_Nat_Onat)), _1755612), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1755612), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755612), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755612), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1755612), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1755612)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1755612, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755612), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755612), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755612), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1755612), tc_Nat_Onat)), _1755612), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1755612))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1755612), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1755614))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755612, _1755614))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1755612), _1755616)))], (48423 ^ _779308) ^ [_1755805, _1755807, _1755809, _1755811, _1755813] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1755805, _1755807, _1755809, _1755811, _1755813) = c_Option_Ooption_Ooption__case(_1755805, tc_prod(_1755807, tc_Lazy__Sequence_Olazy__sequence(_1755807)), _1755809, hAPP(c_Product__Type_Oprod_Oprod__case(_1755807, tc_Lazy__Sequence_Olazy__sequence(_1755807), _1755805), _1755811), hAPP(c_Lazy__Sequence_Oyield(_1755807), _1755813)))], (48425 ^ _779308) ^ [_1755867] : [-(c_Lazy__Sequence_Oyieldn(_1755867) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1755867), _1755867, c_Lazy__Sequence_Oyield(_1755867)))], (48427 ^ _779308) ^ [_1755900, _1755902, _1755904, _1755906, _1755908, _1755910] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1755900, _1755902, _1755904, _1755906, c_Lazy__Sequence_Olazy__sequence_OInsert(_1755902, _1755908, _1755910)) = hAPP(hAPP(_1755906, _1755908), _1755910))], (48429 ^ _779308) ^ [_1755949, _1755951, _1755953, _1755955, _1755957] : [48431 ^ _779308 : [(48432 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1755949), 48430 ^ [_1755949, _1755951, _1755953, _1755955, _1755957]), _1755951)))], (48434 ^ _779308) ^ [] : [c_Relation_Orefl__on(_1755953, hAPP(_1755955, 48430 ^ [_1755949, _1755951, _1755953, _1755955, _1755957]), hAPP(_1755957, 48430 ^ [_1755949, _1755951, _1755953, _1755955, _1755957]))]], -(c_Relation_Orefl__on(_1755953, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1755949, tc_fun(_1755953, tc_HOL_Obool)), _1755951), _1755955), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1755949, tc_fun(tc_prod(_1755953, _1755953), tc_HOL_Obool)), _1755951), _1755957)))], (48438 ^ _779308) ^ [_1756235, _1756237, _1756239] : [hBOOL(hAPP(hAPP(c_member(_1756235), _1756237), hAPP(c_List_Oset(_1756235), _1756239))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1756235), _1756239), _1756237)))], (48444 ^ _779308) ^ [_1756348, _1756350, _1756352] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756348), _1756352), _1756350)), -(hBOOL(hAPP(hAPP(c_member(_1756348), _1756350), hAPP(c_List_Oset(_1756348), _1756352))))], (48460 ^ _779308) ^ [_1756622, _1756624, _1756626, _1756628] : [48461 ^ _779308 : [(48462 ^ _779308) ^ [] : [_1756624 = _1756628], (48464 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756622), _1756626), _1756628))]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1756622), hAPP(hAPP(c_List_Olist_OCons(_1756622), _1756624), _1756626)), _1756628)))], (48450 ^ _779308) ^ [_1756488, _1756490, _1756492, _1756494] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756488), hAPP(hAPP(c_List_Olist_OCons(_1756488), _1756490), _1756492)), _1756494)), -(_1756490 = _1756494), -(hBOOL(hAPP(hAPP(c_List_Omember(_1756488), _1756492), _1756494)))], (48468 ^ _779308) ^ [_1756787] : [-(c_List_Omember(_1756787) = c_List_Oset(_1756787))], (48470 ^ _779308) ^ [_1756826, _1756828] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756826), c_List_Olist_ONil(_1756826)), _1756828))], (48472 ^ _779308) ^ [_1756878, _1756880, _1756882] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756878), _1756880), _1756882)), -(hBOOL(hAPP(hAPP(c_member(_1756878), _1756882), hAPP(c_List_Oset(_1756878), _1756880))))], (48478 ^ _779308) ^ [_1756991, _1756993, _1756995] : [hBOOL(hAPP(hAPP(c_member(_1756991), _1756995), hAPP(c_List_Oset(_1756991), _1756993))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1756991), _1756993), _1756995)))], (48484 ^ _779308) ^ [_1757128, _1757130, _1757132] : [c_List_Olist__ex1(_1757128, _1757130, _1757132), 48488 ^ _779308 : [(48489 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757128), 48487 ^ [_1757128, _1757130, _1757132]), hAPP(c_List_Oset(_1757128), _1757132))))], (48491 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1757130, 48487 ^ [_1757128, _1757130, _1757132])))], (48493 ^ _779308) ^ [_1757374] : [-(_1757374 = 48487 ^ [_1757128, _1757130, _1757132]), hBOOL(hAPP(hAPP(c_member(_1757128), _1757374), hAPP(c_List_Oset(_1757128), _1757132))), hBOOL(hAPP(_1757130, _1757374))]]], (48503 ^ _779308) ^ [_1757561, _1757563, _1757565] : [-(c_List_Olist__ex1(_1757561, _1757563, _1757565)), 48504 ^ _779308 : [(48505 ^ _779308) ^ [_1757655] : [hBOOL(hAPP(hAPP(c_member(_1757561), _1757655), hAPP(c_List_Oset(_1757561), _1757565))), hBOOL(hAPP(_1757563, _1757655)), 48513 ^ _779308 : [(48514 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757561), 48512 ^ [_1757561, _1757563, _1757565, _1757655]), hAPP(c_List_Oset(_1757561), _1757565))))], (48516 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1757563, 48512 ^ [_1757561, _1757563, _1757565, _1757655])))], (48518 ^ _779308) ^ [] : [48512 ^ [_1757561, _1757563, _1757565, _1757655] = _1757655]]]]], (48522 ^ _779308) ^ [_1757990, _1757992, _1757994, _1757996] : [class_Groups_Ocomm__monoid__add(_1757990), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1757992, tc_HOL_Obool)), _1757994)), 48532 ^ _779308 : [(48533 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1757992, tc_HOL_Obool)), 48531 ^ [_1757990, _1757992, _1757994, _1757996]), _1757994)))], (48535 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1757992), 48531 ^ [_1757990, _1757992, _1757994, _1757996]))]], 48539 ^ _779308 : [(48540 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1757992, tc_HOL_Obool)), 48538 ^ [_1757990, _1757992, _1757994, _1757996]), _1757994)))], (48543 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1757992, tc_HOL_Obool)), 48541 ^ [_1757990, _1757992, _1757994, _1757996]), _1757994)))], (48545 ^ _779308) ^ [] : [48538 ^ [_1757990, _1757992, _1757994, _1757996] = 48541 ^ [_1757990, _1757992, _1757994, _1757996]], (48548 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757992), 48546 ^ [_1757990, _1757992, _1757994, _1757996]), 48538 ^ [_1757990, _1757992, _1757994, _1757996])))], (48550 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757992), 48546 ^ [_1757990, _1757992, _1757994, _1757996]), 48541 ^ [_1757990, _1757992, _1757994, _1757996])))], (48552 ^ _779308) ^ [] : [hAPP(_1757996, 48546 ^ [_1757990, _1757992, _1757994, _1757996]) = c_Groups_Ozero__class_Ozero(_1757990)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1757992, _1757990), _1757996), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1757992, tc_HOL_Obool), _1757994)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1757992, tc_HOL_Obool), _1757990), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1757992, _1757990), _1757996)), _1757994))], (48556 ^ _779308) ^ [_1758999, _1759001, _1759003] : [-(c_FunDef_OTHE__default(_1759001, _1759003, _1758999) = c_HOL_OThe(_1759001, _1758999)), 48557 ^ _779308 : [(48558 ^ _779308) ^ [_1759063] : [hBOOL(hAPP(_1758999, _1759063)), 48562 ^ _779308 : [(48563 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1758999, 48561 ^ [_1758999, _1759001, _1759003, _1759063])))], (48565 ^ _779308) ^ [] : [48561 ^ [_1758999, _1759001, _1759003, _1759063] = _1759063]]]]], (48569 ^ _779308) ^ [_1759257, _1759259, _1759261] : [-(c_FunDef_OTHE__default(_1759259, _1759261, _1759257) = _1759261), 48571 ^ _779308 : [(48572 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1759257, 48570 ^ [_1759257, _1759259, _1759261])))], (48574 ^ _779308) ^ [_1759379] : [hBOOL(hAPP(_1759257, _1759379)), -(_1759379 = 48570 ^ [_1759257, _1759259, _1759261])]]], (48582 ^ _779308) ^ [_1759518, _1759520, _1759522, _1759524, _1759526, _1759528, _1759530] : [48584 ^ _779308 : [(48585 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759518), 48583 ^ [_1759518, _1759520, _1759522, _1759524, _1759526, _1759528, _1759530]), _1759520)))], (48587 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1759522, 48583 ^ [_1759518, _1759520, _1759522, _1759524, _1759526, _1759528, _1759530]), _1759524), _1759526))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1759518, tc_fun(_1759528, tc_fun(_1759530, tc_HOL_Obool))), _1759520), _1759522), _1759524), _1759526)))], (48591 ^ _779308) ^ [_1759776, _1759778, _1759780, _1759782, _1759784, _1759786, _1759788] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1759776, tc_fun(_1759778, tc_fun(_1759780, tc_HOL_Obool))), _1759782), _1759784), _1759786), _1759788)), 48595 ^ _779308 : [(48596 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759776), 48594 ^ [_1759776, _1759778, _1759780, _1759782, _1759784, _1759786, _1759788]), _1759782)))], (48598 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1759784, 48594 ^ [_1759776, _1759778, _1759780, _1759782, _1759784, _1759786, _1759788]), _1759786), _1759788)))]]], (48600 ^ _779308) ^ [_1760002, _1760004] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1760002)), _1760004)), 48604 ^ _779308 : [(48605 ^ _779308) ^ [_1760103] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1760002)), _1760103), _1760004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760002)), _1760103)), 48603 ^ [_1760002, _1760004])))]]], (48611 ^ _779308) ^ [_1760242, _1760244] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1760242, _1760244), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760242)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48613 ^ _779308) ^ [_1760275] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1760275)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760275)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48615 ^ _779308) ^ [_1760307, _1760309] : [-(c_Lazy__Sequence_Oappend(_1760307, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760307), _1760309) = _1760309)], (48617 ^ _779308) ^ [_1760353, _1760355, _1760357] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1760353, _1760355, _1760357) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760353)], (48619 ^ _779308) ^ [_1760401, _1760403, _1760405] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760401) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1760401, _1760403, _1760405)], (48621 ^ _779308) ^ [_1760434, _1760436, _1760438, _1760440] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1760434, _1760436, _1760438, _1760440, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760436)) = _1760438)], (48623 ^ _779308) ^ [_1760489, _1760491, _1760493] : [c_List_Olist__ex(tc_Int_Oint, _1760489, c_List_Oupto(_1760491, _1760493)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1760489), _1760491, _1760493)], (48629 ^ _779308) ^ [_1760579, _1760581, _1760583] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1760579), _1760581, _1760583)), -(c_List_Olist__ex(tc_Int_Oint, _1760579, c_List_Oupto(_1760581, _1760583)))], (48635 ^ _779308) ^ [_1760645, _1760647, _1760649] : [c_List_Olist__all(tc_Int_Oint, _1760645, c_List_Oupto(_1760647, _1760649)), -(c_List_Oall__interval__int(_1760645, _1760647, _1760649))], (48641 ^ _779308) ^ [_1760730, _1760732, _1760734] : [c_List_Oall__interval__int(_1760730, _1760732, _1760734), -(c_List_Olist__all(tc_Int_Oint, _1760730, c_List_Oupto(_1760732, _1760734)))], (48657 ^ _779308) ^ [_1761020, _1761022, _1761024] : [48659 ^ _779308 : [(48660 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 48658 ^ [_1761020, _1761022, _1761024]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1761022, _1761024))))], (48662 ^ _779308) ^ [] : [hBOOL(hAPP(_1761020, 48658 ^ [_1761020, _1761022, _1761024]))]], -(c_List_Oall__interval__int(_1761020, _1761022, _1761024))], (48647 ^ _779308) ^ [_1760839, _1760841, _1760843] : [c_List_Oall__interval__int(_1760839, _1760841, _1760843), 48650 ^ _779308 : [(48651 ^ _779308) ^ [_1760917] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1760917), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1760841, _1760843))), -(hBOOL(hAPP(_1760839, _1760917)))]]], (48666 ^ _779308) ^ [_1761196, _1761198, _1761200, _1761202] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761196, _1761198, _1761200, c_Code__Numeral_OSuc__code__numeral(_1761202)) = hAPP(hAPP(_1761200, _1761202), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761196, _1761198, _1761200, _1761202)))], (48668 ^ _779308) ^ [_1761258, _1761260, _1761262, _1761264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761258), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1761260, _1761262, _1761258, _1761264) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761260)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1761260)))], (48674 ^ _779308) ^ [_1761389, _1761391, _1761393, _1761395] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761389), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1761391, _1761393, _1761389, _1761395) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1761391, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm)), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1761393, _1761395)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1761391, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1761391, _1761393, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1761389), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1761395))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1761391, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391))))), tc_prod(_1761391, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1761391)), hAPP(hAPP(c_COMBB(_1761391, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761391)))), tc_prod(_1761391, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1761391)), c_Product__Type_Ofst(_1761391, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (48680 ^ _779308) ^ [_1761768, _1761770, _1761772] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761768, _1761770, _1761772, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1761770)], (48682 ^ _779308) ^ [_1761800, _1761802, _1761804] : [-(c_Random__Sequence_Oempty(_1761800, _1761802, _1761804) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761800)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1761800)))], (48684 ^ _779308) ^ [_1761849, _1761851, _1761853, _1761855] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1761849), _1761851), _1761853), _1761855) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761849)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1761849), _1761851)))], (48686 ^ _779308) ^ [_1761910, _1761912, _1761914, _1761916] : [-(c_Random__Sequence_Omap(_1761910, _1761912, _1761914, _1761916) = c_Random__Sequence_Obind(_1761910, _1761912, _1761916, hAPP(c_Fun_Ocomp(_1761912, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1761912)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1761910, c_Random__Sequence_Osingle(_1761912)), _1761914)))], (48688 ^ _779308) ^ [_1761981, _1761983, _1761985, _1761987, _1761989, _1761991, _1761993] : [hBOOL(hAPP(hAPP(_1761981, hAPP(c_Product__Type_Osnd(_1761983, _1761985), _1761987)), hAPP(c_Product__Type_Ofst(_1761983, _1761985), _1761987))), 48695 ^ _779308 : [(48696 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1761981, 48694 ^ [_1761981, _1761983, _1761985, _1761987, _1761989, _1761991, _1761993]), 48693 ^ [_1761981, _1761983, _1761985, _1761987, _1761989, _1761991, _1761993])))], (48698 ^ _779308) ^ [] : [hBOOL(hAPP(_1761989, hAPP(hAPP(_1761991, 48693 ^ [_1761981, _1761983, _1761985, _1761987, _1761989, _1761991, _1761993]), 48694 ^ [_1761981, _1761983, _1761985, _1761987, _1761989, _1761991, _1761993])))]], -(hBOOL(hAPP(_1761989, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1761983, _1761985, _1761993), _1761991), _1761987))))], (48702 ^ _779308) ^ [_1762378, _1762380, _1762382, _1762384] : [-(hAPP(c_Relation_OImage(_1762378, _1762380, hAPP(c_Set_OCollect(tc_prod(_1762378, _1762380)), hAPP(c_Product__Type_Oprod_Oprod__case(_1762378, _1762380, tc_HOL_Obool), _1762382))), _1762384) = hAPP(c_Set_OCollect(_1762380), hAPP(hAPP(c_COMBB(tc_fun(_1762378, tc_HOL_Obool), tc_HOL_Obool, _1762380), c_HOL_OEx(_1762378)), hAPP(hAPP(c_COMBB(tc_fun(_1762378, tc_HOL_Obool), tc_fun(_1762378, tc_HOL_Obool), _1762380), hAPP(c_COMBS(_1762378, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1762378), c_fconj), hAPP(hAPP(c_COMBC(_1762378, tc_fun(_1762378, tc_HOL_Obool), tc_HOL_Obool), c_member(_1762378)), _1762384)))), hAPP(c_COMBC(_1762378, _1762380, tc_HOL_Obool), _1762382)))))], (48704 ^ _779308) ^ [_1762504, _1762506, _1762508, _1762510, _1762512] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762504), tc_List_Olist(_1762504))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762504), tc_List_Olist(_1762504)), _1762506), _1762508)), c_List_Olexord(_1762504, _1762510))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762504), tc_List_Olist(_1762504))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762504), tc_List_Olist(_1762504)), _1762508), _1762512)), c_List_Olexord(_1762504, _1762510))), c_Relation_Otrans(_1762504, _1762510), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1762504), tc_List_Olist(_1762504))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1762504), tc_List_Olist(_1762504)), _1762506), _1762512)), c_List_Olexord(_1762504, _1762510))))], (48718 ^ _779308) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (48720 ^ _779308) ^ [_1762901, _1762903, _1762905, _1762907] : [c_Relation_Otrans(_1762901, _1762903), c_Relation_Otrans(_1762905, _1762907), -(c_Relation_Otrans(tc_prod(_1762901, _1762905), c_Wellfounded_Olex__prod(_1762901, _1762905, _1762903, _1762907)))], (48744 ^ _779308) ^ [_1763511, _1763513] : [48747 ^ _779308 : [(48748 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763511, _1763511)), hAPP(hAPP(c_Product__Type_OPair(_1763511, _1763511), 48745 ^ [_1763511, _1763513]), 48746 ^ [_1763511, _1763513])), _1763513)))], (48751 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763511, _1763511)), hAPP(hAPP(c_Product__Type_OPair(_1763511, _1763511), 48746 ^ [_1763511, _1763513]), 48749 ^ [_1763511, _1763513])), _1763513)))], (48753 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763511, _1763511)), hAPP(hAPP(c_Product__Type_OPair(_1763511, _1763511), 48745 ^ [_1763511, _1763513]), 48749 ^ [_1763511, _1763513])), _1763513))]], -(c_Relation_Otrans(_1763511, _1763513))], (48730 ^ _779308) ^ [_1763069, _1763071] : [c_Relation_Otrans(_1763069, _1763071), 48733 ^ _779308 : [(48734 ^ _779308) ^ [_1763205, _1763207] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763069, _1763069)), hAPP(hAPP(c_Product__Type_OPair(_1763069, _1763069), _1763207), _1763205)), _1763071)), 48737 ^ _779308 : [(48738 ^ _779308) ^ [_1763348] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763069, _1763069)), hAPP(hAPP(c_Product__Type_OPair(_1763069, _1763069), _1763205), _1763348)), _1763071)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763069, _1763069)), hAPP(hAPP(c_Product__Type_OPair(_1763069, _1763069), _1763207), _1763348)), _1763071)))]]]]], (48757 ^ _779308) ^ [_1763931, _1763933, _1763935, _1763937, _1763939] : [c_Relation_Otrans(_1763931, _1763933), hBOOL(hAPP(hAPP(c_member(tc_prod(_1763931, _1763931)), hAPP(hAPP(c_Product__Type_OPair(_1763931, _1763931), _1763935), _1763937)), _1763933)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1763931, _1763931)), hAPP(hAPP(c_Product__Type_OPair(_1763931, _1763931), _1763937), _1763939)), _1763933)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763931, _1763931)), hAPP(hAPP(c_Product__Type_OPair(_1763931, _1763931), _1763935), _1763939)), _1763933)))], (48771 ^ _779308) ^ [_1764244, _1764246] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1764244, tc_HOL_Obool), _1764246) = hAPP(c_Set_OCollect(_1764244), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1764244, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1764244), c_HOL_OEx(tc_fun(_1764244, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1764244, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1764244, tc_HOL_Obool), tc_HOL_Obool), _1764244), hAPP(c_COMBS(tc_fun(_1764244, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1764244, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1764244, tc_HOL_Obool), tc_fun(tc_fun(_1764244, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1764244, tc_HOL_Obool))), _1764246)))), c_member(_1764244)))))], (48773 ^ _779308) ^ [_1764372, _1764374] : [c_Relation_Otrans(_1764372, _1764374), -(c_Relation_Otrans(_1764372, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1764372, _1764372), tc_HOL_Obool)), _1764374), c_Relation_OId(_1764372))))], (48779 ^ _779308) ^ [_1764481, _1764483, _1764485, _1764487] : [c_Relation_Otrans(_1764481, _1764483), -(c_Relation_Otrans(_1764485, hAPP(hAPP(c_Relation_Oinv__image(_1764481, _1764485), _1764483), _1764487)))], (48785 ^ _779308) ^ [_1764580, _1764582] : [c_Relation_Otrans(_1764580, _1764582), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1764580, _1764580), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1764580, _1764580, _1764580), _1764582), _1764582)), _1764582)))], (48791 ^ _779308) ^ [_1764703] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1764703, tc_HOL_Obool) = c_Set_OBex(_1764703))], (48793 ^ _779308) ^ [_1764731, _1764733, _1764735] : [c_Relation_Otrans(_1764731, _1764733), c_Relation_Otrans(_1764731, _1764735), -(c_Relation_Otrans(_1764731, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1764731, _1764731), tc_HOL_Obool)), _1764733), _1764735)))], (48814 ^ _779308) ^ [_1765107, _1765109] : [48815 ^ _779308 : [(48816 ^ _779308) ^ [_1765173] : [hBOOL(hAPP(_1765109, _1765173))]], 48818 ^ _779308 : [(48819 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765107), 48817 ^ [_1765107, _1765109]), c_Orderings_Otop__class_Otop(tc_fun(_1765107, tc_HOL_Obool)))))], (48821 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1765109, 48817 ^ [_1765107, _1765109])))]]], (48803 ^ _779308) ^ [_1764907, _1764909] : [-(hBOOL(hAPP(_1764909, 48810 ^ [_1764907, _1764909]))), 48804 ^ _779308 : [(48805 ^ _779308) ^ [_1764968] : [hBOOL(hAPP(hAPP(c_member(_1764907), _1764968), c_Orderings_Otop__class_Otop(tc_fun(_1764907, tc_HOL_Obool)))), hBOOL(hAPP(_1764909, _1764968))]]], (48823 ^ _779308) ^ [_1765276, _1765278, _1765280, _1765282] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765276), _1765278)), 48826 ^ _779308 : [(48837 ^ _779308) ^ [] : [48839 ^ _779308 : [(48840 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765276), 48838 ^ [_1765276, _1765278, _1765280, _1765282]), _1765278)))], (48842 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765280), hAPP(c_Set_OCollect(_1765280), hAPP(hAPP(c_COMBC(_1765280, _1765276, tc_HOL_Obool), _1765282), 48838 ^ [_1765276, _1765278, _1765280, _1765282]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1765280), hAPP(c_Set_OCollect(_1765280), hAPP(hAPP(c_COMBB(tc_fun(_1765276, tc_HOL_Obool), tc_HOL_Obool, _1765280), c_HOL_OEx(_1765276)), hAPP(hAPP(c_COMBB(tc_fun(_1765276, tc_HOL_Obool), tc_fun(_1765276, tc_HOL_Obool), _1765280), hAPP(c_COMBS(_1765276, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765276), c_fconj), hAPP(hAPP(c_COMBC(_1765276, tc_fun(_1765276, tc_HOL_Obool), tc_HOL_Obool), c_member(_1765276)), _1765278)))), _1765282))))))], (48827 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765280), hAPP(c_Set_OCollect(_1765280), hAPP(hAPP(c_COMBB(tc_fun(_1765276, tc_HOL_Obool), tc_HOL_Obool, _1765280), c_HOL_OEx(_1765276)), hAPP(hAPP(c_COMBB(tc_fun(_1765276, tc_HOL_Obool), tc_fun(_1765276, tc_HOL_Obool), _1765280), hAPP(c_COMBS(_1765276, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765276), c_fconj), hAPP(hAPP(c_COMBC(_1765276, tc_fun(_1765276, tc_HOL_Obool), tc_HOL_Obool), c_member(_1765276)), _1765278)))), _1765282))))), 48830 ^ _779308 : [(48831 ^ _779308) ^ [_1765584] : [hBOOL(hAPP(hAPP(c_member(_1765276), _1765584), _1765278)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1765280), hAPP(c_Set_OCollect(_1765280), hAPP(hAPP(c_COMBC(_1765280, _1765276, tc_HOL_Obool), _1765282), _1765584)))))]]]]], (48846 ^ _779308) ^ [_1765980, _1765982] : [c_Relation_Otrans(_1765980, _1765982), -(c_Relation_Otrans(tc_List_Olist(_1765980), c_List_Olistrel(_1765980, _1765982)))], (48852 ^ _779308) ^ [_1766067, _1766069, _1766071] : [hBOOL(hAPP(hAPP(c_member(_1766069), _1766067), c_Orderings_Obot__class_Obot(tc_fun(_1766069, tc_HOL_Obool)))), hBOOL(hAPP(_1766071, _1766067))], (48858 ^ _779308) ^ [_1766188, _1766190] : [c_Relation_Otrans(_1766188, hAPP(c_Relation_Oconverse(_1766188, _1766188), _1766190)), -(c_Relation_Otrans(_1766188, _1766190))], (48864 ^ _779308) ^ [_1766273, _1766275] : [c_Relation_Otrans(_1766273, _1766275), -(c_Relation_Otrans(_1766273, hAPP(c_Relation_Oconverse(_1766273, _1766273), _1766275)))], (48870 ^ _779308) ^ [_1766364, _1766366] : [c_Relation_Otrans(_1766364, _1766366), -(c_Relation_Otrans(tc_List_Olist(_1766364), c_List_Olexord(_1766364, _1766366)))], (48876 ^ _779308) ^ [_1766451] : [-(c_Relation_Otrans(tc_fun(_1766451, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1766451)))], (48878 ^ _779308) ^ [_1766479] : [-(c_Relation_Otrans(_1766479, c_Relation_OId(_1766479)))], (48880 ^ _779308) ^ [_1766504, _1766506] : [-(c_Relation_Otrans(_1766504, c_Relation_OId__on(_1766504, _1766506)))], (48882 ^ _779308) ^ [_1766532, _1766534] : [-(c_Relation_Otrans(_1766532, c_Transitive__Closure_Otrancl(_1766532, _1766534)))], (48884 ^ _779308) ^ [_1766560, _1766562] : [c_Relation_Otrans(_1766560, _1766562), -(c_Transitive__Closure_Otrancl(_1766560, _1766562) = _1766562)], (48890 ^ _779308) ^ [_1766643, _1766645] : [-(c_Relation_Otrans(_1766643, c_Transitive__Closure_Ortrancl(_1766643, _1766645)))], (48892 ^ _779308) ^ [_1766689, _1766691, _1766693] : [c_List_Olist__ex(_1766689, _1766691, _1766693), 48896 ^ _779308 : [(48897 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766689), 48895 ^ [_1766689, _1766691, _1766693]), hAPP(c_List_Oset(_1766689), _1766693))))], (48899 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1766691, 48895 ^ [_1766689, _1766691, _1766693])))]]], (48901 ^ _779308) ^ [_1766843, _1766845, _1766847] : [-(c_List_Olist__ex(_1766843, _1766845, _1766847)), 48902 ^ _779308 : [(48903 ^ _779308) ^ [_1766900] : [hBOOL(hAPP(hAPP(c_member(_1766843), _1766900), hAPP(c_List_Oset(_1766843), _1766847))), hBOOL(hAPP(_1766845, _1766900))]]], (48921 ^ _779308) ^ [_1767247, _1767249, _1767251] : [c_List_Olist__ex(_1767247, _1767251, _1767249), 48925 ^ _779308 : [(48926 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767247), 48924 ^ [_1767247, _1767249, _1767251]), hAPP(c_List_Oset(_1767247), _1767249))))], (48928 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1767251, 48924 ^ [_1767247, _1767249, _1767251])))]]], (48911 ^ _779308) ^ [_1767057, _1767059, _1767061] : [-(c_List_Olist__ex(_1767057, _1767061, _1767059)), 48912 ^ _779308 : [(48913 ^ _779308) ^ [_1767114] : [hBOOL(hAPP(hAPP(c_member(_1767057), _1767114), hAPP(c_List_Oset(_1767057), _1767059))), hBOOL(hAPP(_1767061, _1767114))]]], (48930 ^ _779308) ^ [_1767407, _1767409, _1767411, _1767413] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1767407, tc_fun(_1767409, tc_HOL_Obool)), _1767411), _1767413) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1767409, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1767409, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1767407, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1767409, tc_HOL_Obool)), c_HOL_OEx(_1767407)), hAPP(hAPP(c_COMBB(tc_fun(_1767407, tc_HOL_Obool), tc_fun(_1767407, tc_HOL_Obool), tc_fun(_1767409, tc_HOL_Obool)), hAPP(c_COMBS(_1767407, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1767407), c_fconj), hAPP(hAPP(c_COMBC(_1767407, tc_fun(_1767407, tc_HOL_Obool), tc_HOL_Obool), c_member(_1767407)), _1767411)))), hAPP(hAPP(c_COMBC(tc_fun(_1767409, tc_HOL_Obool), tc_fun(_1767407, tc_fun(_1767409, tc_HOL_Obool)), tc_fun(_1767407, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767409, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1767407, tc_fun(_1767409, tc_HOL_Obool)), tc_fun(_1767407, tc_HOL_Obool)), tc_fun(_1767409, tc_HOL_Obool)), c_COMBB(tc_fun(_1767409, tc_HOL_Obool), tc_HOL_Obool, _1767407)), c_fequal)), _1767413))))))], (48932 ^ _779308) ^ [_1767591, _1767593, _1767595, _1767597] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1767591, tc_fun(_1767593, tc_HOL_Obool)), _1767595), _1767597) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1767593, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1767593, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1767591, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1767593, tc_HOL_Obool)), c_HOL_OEx(_1767591)), hAPP(hAPP(c_COMBB(tc_fun(_1767591, tc_HOL_Obool), tc_fun(_1767591, tc_HOL_Obool), tc_fun(_1767593, tc_HOL_Obool)), hAPP(c_COMBS(_1767591, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1767591), c_fconj), hAPP(hAPP(c_COMBC(_1767591, tc_fun(_1767591, tc_HOL_Obool), tc_HOL_Obool), c_member(_1767591)), _1767595)))), hAPP(hAPP(c_COMBC(tc_fun(_1767593, tc_HOL_Obool), tc_fun(_1767591, tc_fun(_1767593, tc_HOL_Obool)), tc_fun(_1767591, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767593, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1767591, tc_fun(_1767593, tc_HOL_Obool)), tc_fun(_1767591, tc_HOL_Obool)), tc_fun(_1767593, tc_HOL_Obool)), c_COMBB(tc_fun(_1767593, tc_HOL_Obool), tc_HOL_Obool, _1767591)), c_fequal)), _1767597))))))], (48934 ^ _779308) ^ [_1767775, _1767777, _1767779, _1767781] : [class_Complete__Lattice_Ocomplete__lattice(_1767775), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1767777, _1767775), _1767779), _1767781) = c_Complete__Lattice_OSup__class_OSup(_1767775, hAPP(c_Set_OCollect(_1767775), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767777, _1767775), tc_HOL_Obool), tc_HOL_Obool, _1767775), c_HOL_OEx(tc_fun(_1767777, _1767775))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767777, _1767775), tc_HOL_Obool), tc_fun(tc_fun(_1767777, _1767775), tc_HOL_Obool), _1767775), hAPP(c_COMBS(tc_fun(_1767777, _1767775), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1767777, _1767775)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1767777, _1767775), tc_fun(tc_fun(_1767777, _1767775), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1767777, _1767775))), _1767779)))), hAPP(hAPP(c_COMBC(_1767775, tc_fun(tc_fun(_1767777, _1767775), _1767775), tc_fun(tc_fun(_1767777, _1767775), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1767775, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1767777, _1767775), _1767775), tc_fun(tc_fun(_1767777, _1767775), tc_HOL_Obool)), _1767775), c_COMBB(_1767775, tc_HOL_Obool, tc_fun(_1767777, _1767775))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1767777, _1767775), _1767777, _1767775), c_COMBI(tc_fun(_1767777, _1767775))), _1767781)))))))], (48940 ^ _779308) ^ [_1768218, _1768220, _1768222, _1768224] : [class_Complete__Lattice_Ocomplete__lattice(_1768218), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1768220, _1768218), _1768222), _1768224) = c_Complete__Lattice_OSup__class_OSup(_1768218, hAPP(c_Set_OCollect(_1768218), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768220, _1768218), tc_HOL_Obool), tc_HOL_Obool, _1768218), c_HOL_OEx(tc_fun(_1768220, _1768218))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768220, _1768218), tc_HOL_Obool), tc_fun(tc_fun(_1768220, _1768218), tc_HOL_Obool), _1768218), hAPP(c_COMBS(tc_fun(_1768220, _1768218), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768220, _1768218)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768220, _1768218), tc_fun(tc_fun(_1768220, _1768218), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768220, _1768218))), _1768222)))), hAPP(hAPP(c_COMBC(_1768218, tc_fun(tc_fun(_1768220, _1768218), _1768218), tc_fun(tc_fun(_1768220, _1768218), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768218, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768220, _1768218), _1768218), tc_fun(tc_fun(_1768220, _1768218), tc_HOL_Obool)), _1768218), c_COMBB(_1768218, tc_HOL_Obool, tc_fun(_1768220, _1768218))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768220, _1768218), _1768220, _1768218), c_COMBI(tc_fun(_1768220, _1768218))), _1768224)))))))], (48946 ^ _779308) ^ [_1768661, _1768663, _1768665, _1768667] : [class_Complete__Lattice_Ocomplete__lattice(_1768661), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1768663, _1768661), _1768665), _1768667) = c_Complete__Lattice_OInf__class_OInf(_1768661, hAPP(c_Set_OCollect(_1768661), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768663, _1768661), tc_HOL_Obool), tc_HOL_Obool, _1768661), c_HOL_OEx(tc_fun(_1768663, _1768661))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768663, _1768661), tc_HOL_Obool), tc_fun(tc_fun(_1768663, _1768661), tc_HOL_Obool), _1768661), hAPP(c_COMBS(tc_fun(_1768663, _1768661), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768663, _1768661)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768663, _1768661), tc_fun(tc_fun(_1768663, _1768661), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768663, _1768661))), _1768665)))), hAPP(hAPP(c_COMBC(_1768661, tc_fun(tc_fun(_1768663, _1768661), _1768661), tc_fun(tc_fun(_1768663, _1768661), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768661, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768663, _1768661), _1768661), tc_fun(tc_fun(_1768663, _1768661), tc_HOL_Obool)), _1768661), c_COMBB(_1768661, tc_HOL_Obool, tc_fun(_1768663, _1768661))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768663, _1768661), _1768663, _1768661), c_COMBI(tc_fun(_1768663, _1768661))), _1768667)))))))], (48952 ^ _779308) ^ [_1769104, _1769106, _1769108, _1769110] : [class_Complete__Lattice_Ocomplete__lattice(_1769104), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1769106, _1769104), _1769108), _1769110) = c_Complete__Lattice_OInf__class_OInf(_1769104, hAPP(c_Set_OCollect(_1769104), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769106, _1769104), tc_HOL_Obool), tc_HOL_Obool, _1769104), c_HOL_OEx(tc_fun(_1769106, _1769104))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769106, _1769104), tc_HOL_Obool), tc_fun(tc_fun(_1769106, _1769104), tc_HOL_Obool), _1769104), hAPP(c_COMBS(tc_fun(_1769106, _1769104), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1769106, _1769104)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1769106, _1769104), tc_fun(tc_fun(_1769106, _1769104), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1769106, _1769104))), _1769108)))), hAPP(hAPP(c_COMBC(_1769104, tc_fun(tc_fun(_1769106, _1769104), _1769104), tc_fun(tc_fun(_1769106, _1769104), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1769104, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1769106, _1769104), _1769104), tc_fun(tc_fun(_1769106, _1769104), tc_HOL_Obool)), _1769104), c_COMBB(_1769104, tc_HOL_Obool, tc_fun(_1769106, _1769104))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1769106, _1769104), _1769106, _1769104), c_COMBI(tc_fun(_1769106, _1769104))), _1769110)))))))], (48958 ^ _779308) ^ [_1769547, _1769549, _1769551, _1769553] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1769547), _1769549)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1769547), _1769551)), -(_1769551 = c_Orderings_Obot__class_Obot(tc_fun(_1769547, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1769547, _1769553, _1769549, _1769551)), 48972 ^ _779308 : [(48973 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769547), 48971 ^ [_1769547, _1769549, _1769551, _1769553]), _1769549)))], (48975 ^ _779308) ^ [_1769892] : [hBOOL(hAPP(hAPP(c_member(_1769547), _1769892), _1769551)), hBOOL(hAPP(hAPP(_1769553, 48971 ^ [_1769547, _1769549, _1769551, _1769553]), _1769892))]]], (48983 ^ _779308) ^ [_1770073, _1770075] : [c_Predicate_Otransp(_1770073, _1770075), -(c_Relation_Otrans(_1770073, hAPP(c_Set_OCollect(tc_prod(_1770073, _1770073)), hAPP(c_Product__Type_Oprod_Oprod__case(_1770073, _1770073, tc_HOL_Obool), _1770075))))], (48989 ^ _779308) ^ [_1770176, _1770178] : [c_Relation_Otrans(_1770176, hAPP(c_Set_OCollect(tc_prod(_1770176, _1770176)), hAPP(c_Product__Type_Oprod_Oprod__case(_1770176, _1770176, tc_HOL_Obool), _1770178))), -(c_Predicate_Otransp(_1770176, _1770178))], (48995 ^ _779308) ^ [_1770285, _1770287, _1770289, _1770291, _1770293] : [c_Predicate_Otransp(_1770285, _1770287), hBOOL(hAPP(hAPP(_1770287, _1770289), _1770291)), hBOOL(hAPP(hAPP(_1770287, _1770291), _1770293)), -(hBOOL(hAPP(hAPP(_1770287, _1770289), _1770293)))], (49009 ^ _779308) ^ [_1770529, _1770531] : [c_Equiv__Relations_Oequivp(_1770529, _1770531), 49012 ^ _779308 : [(49013 ^ _779308) ^ [] : [-(c_Predicate_Oreflp(_1770529, _1770531))], (49015 ^ _779308) ^ [] : [-(c_Predicate_Osymp(_1770529, _1770531))], (49017 ^ _779308) ^ [] : [-(c_Predicate_Otransp(_1770529, _1770531))]]], (49019 ^ _779308) ^ [_1770652, _1770654] : [-(c_Equiv__Relations_Oequivp(_1770652, _1770654)), c_Predicate_Oreflp(_1770652, _1770654), c_Predicate_Osymp(_1770652, _1770654), c_Predicate_Otransp(_1770652, _1770654)], (49033 ^ _779308) ^ [_1770835, _1770837] : [c_Predicate_Oreflp(_1770835, _1770837), c_Predicate_Osymp(_1770835, _1770837), c_Predicate_Otransp(_1770835, _1770837), -(c_Equiv__Relations_Oequivp(_1770835, _1770837))], (49047 ^ _779308) ^ [_1771016, _1771018, _1771020, _1771022] : [c_Predicate_Osymp(_1771016, _1771018), hBOOL(hAPP(hAPP(_1771018, _1771020), _1771022)), -(hBOOL(hAPP(hAPP(_1771018, _1771022), _1771020)))], (49057 ^ _779308) ^ [_1771173, _1771175] : [c_Equiv__Relations_Oequivp(_1771173, _1771175), 49060 ^ _779308 : [(49061 ^ _779308) ^ [] : [-(c_Predicate_Oreflp(_1771173, _1771175))], (49063 ^ _779308) ^ [] : [-(c_Predicate_Osymp(_1771173, _1771175))], (49065 ^ _779308) ^ [] : [-(c_Predicate_Otransp(_1771173, _1771175))]]], (49067 ^ _779308) ^ [_1771325, _1771327, _1771329, _1771331] : [c_Wellfounded_Omax__extp(_1771325, _1771327, _1771329, _1771331), 49070 ^ _779308 : [(49071 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1771325), _1771329)))], (49073 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1771325), _1771331)))], (49075 ^ _779308) ^ [] : [_1771331 = c_Orderings_Obot__class_Obot(tc_fun(_1771325, tc_HOL_Obool))], (49077 ^ _779308) ^ [_1771541] : [hBOOL(hAPP(hAPP(c_member(_1771325), _1771541), _1771329)), 49081 ^ _779308 : [(49082 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771325), 49080 ^ [_1771325, _1771327, _1771329, _1771331, _1771541]), _1771331)))], (49084 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1771327, _1771541), 49080 ^ [_1771325, _1771327, _1771329, _1771331, _1771541])))]]]]], (49086 ^ _779308) ^ [_1771725, _1771727, _1771729, _1771731] : [-(c_Wellfounded_Omax__extp(_1771725, _1771727, _1771729, _1771731)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1771725), _1771729)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1771725), _1771731)), -(_1771731 = c_Orderings_Obot__class_Obot(tc_fun(_1771725, tc_HOL_Obool))), 49100 ^ _779308 : [(49101 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771725), 49099 ^ [_1771725, _1771727, _1771729, _1771731]), _1771729)))], (49103 ^ _779308) ^ [_1772070] : [hBOOL(hAPP(hAPP(c_member(_1771725), _1772070), _1771731)), hBOOL(hAPP(hAPP(_1771727, 49099 ^ [_1771725, _1771727, _1771729, _1771731]), _1772070))]]], (49111 ^ _779308) ^ [_1772238, _1772240] : [c_Relation_Otrans(_1772238, _1772240), c_Relation_Oantisym(_1772238, _1772240), -(c_Relation_Otrans(_1772238, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1772238, _1772238), tc_HOL_Obool)), _1772240), c_Relation_OId(_1772238))))], (49121 ^ _779308) ^ [_1772399, _1772401] : [-(c_Relation_Oantisym(_1772399, c_Relation_OId__on(_1772399, _1772401)))], (49123 ^ _779308) ^ [_1772427, _1772429, _1772431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1772427, _1772427), tc_HOL_Obool)), _1772429), _1772431)), c_Relation_Oantisym(_1772427, _1772431), -(c_Relation_Oantisym(_1772427, _1772429))], (49133 ^ _779308) ^ [_1772586] : [-(c_Relation_Oantisym(_1772586, c_Relation_OId(_1772586)))], (49135 ^ _779308) ^ [_1772611] : [-(c_Relation_Oantisym(_1772611, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1772611, _1772611), tc_HOL_Obool))))], (49137 ^ _779308) ^ [_1772657, _1772659] : [c_Relation_Oantisym(_1772657, hAPP(c_Relation_Oconverse(_1772657, _1772657), _1772659)), -(c_Relation_Oantisym(_1772657, _1772659))], (49143 ^ _779308) ^ [_1772742, _1772744] : [c_Relation_Oantisym(_1772742, _1772744), -(c_Relation_Oantisym(_1772742, hAPP(c_Relation_Oconverse(_1772742, _1772742), _1772744)))], (49163 ^ _779308) ^ [_1773173, _1773175] : [49166 ^ _779308 : [(49167 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773173, _1773173)), hAPP(hAPP(c_Product__Type_OPair(_1773173, _1773173), 49164 ^ [_1773173, _1773175]), 49165 ^ [_1773173, _1773175])), _1773175)))], (49169 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773173, _1773173)), hAPP(hAPP(c_Product__Type_OPair(_1773173, _1773173), 49165 ^ [_1773173, _1773175]), 49164 ^ [_1773173, _1773175])), _1773175)))], (49171 ^ _779308) ^ [] : [49164 ^ [_1773173, _1773175] = 49165 ^ [_1773173, _1773175]]], -(c_Relation_Oantisym(_1773173, _1773175))], (49149 ^ _779308) ^ [_1772848, _1772850] : [c_Relation_Oantisym(_1772848, _1772850), 49152 ^ _779308 : [(49153 ^ _779308) ^ [_1772960, _1772962] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1772848, _1772848)), hAPP(hAPP(c_Product__Type_OPair(_1772848, _1772848), _1772962), _1772960)), _1772850)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1772848, _1772848)), hAPP(hAPP(c_Product__Type_OPair(_1772848, _1772848), _1772960), _1772962)), _1772850)), -(_1772962 = _1772960)]]], (49175 ^ _779308) ^ [_1773494, _1773496, _1773498, _1773500] : [c_Relation_Oantisym(_1773494, _1773496), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773494, _1773494)), hAPP(hAPP(c_Product__Type_OPair(_1773494, _1773494), _1773498), _1773500)), _1773496)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773494, _1773494)), hAPP(hAPP(c_Product__Type_OPair(_1773494, _1773494), _1773500), _1773498)), _1773496)), -(_1773498 = _1773500)], (49189 ^ _779308) ^ [_1773778, _1773780] : [c_Relation_Oantisym(_1773778, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1773778, _1773778), tc_HOL_Obool)), _1773780), c_Relation_OId(_1773778))), -(c_Relation_Oantisym(_1773778, _1773780))], (49195 ^ _779308) ^ [_1773883, _1773885] : [c_Relation_Oantisym(_1773883, _1773885), -(c_Relation_Oantisym(_1773883, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1773883, _1773883), tc_HOL_Obool)), _1773885), c_Relation_OId(_1773883))))], (49201 ^ _779308) ^ [_1773994, _1773996] : [c_Wellfounded_Oacyclic(_1773994, _1773996), -(c_Relation_Oantisym(_1773994, c_Transitive__Closure_Ortrancl(_1773994, _1773996)))], (49207 ^ _779308) ^ [_1774077, _1774079, _1774081, _1774083, _1774085, _1774087] : [-(c_Partial__Function_Ofun__lub(_1774077, _1774079, _1774081, _1774083, _1774085, _1774087) = hAPP(_1774083, hAPP(c_Set_OCollect(_1774077), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774081, _1774077), tc_HOL_Obool), tc_HOL_Obool, _1774077), c_HOL_OEx(tc_fun(_1774081, _1774077))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774081, _1774077), tc_HOL_Obool), tc_fun(tc_fun(_1774081, _1774077), tc_HOL_Obool), _1774077), hAPP(c_COMBS(tc_fun(_1774081, _1774077), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1774081, _1774077)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1774081, _1774077), tc_fun(tc_fun(_1774081, _1774077), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1774081, _1774077))), _1774085)))), hAPP(hAPP(c_COMBC(_1774077, tc_fun(tc_fun(_1774081, _1774077), _1774077), tc_fun(tc_fun(_1774081, _1774077), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774077, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1774081, _1774077), _1774077), tc_fun(tc_fun(_1774081, _1774077), tc_HOL_Obool)), _1774077), c_COMBB(_1774077, tc_HOL_Obool, tc_fun(_1774081, _1774077))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1774081, _1774077), _1774081, _1774077), c_COMBI(tc_fun(_1774081, _1774077))), _1774087)))))))], (49209 ^ _779308) ^ [_1774290, _1774292] : [c_Relation_Osym(_1774290, _1774292), c_Relation_Otrans(_1774290, _1774292), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1774290, _1774290), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1774290, _1774290, _1774290), hAPP(c_Relation_Oconverse(_1774290, _1774290), _1774292)), _1774292)), _1774292)))], (49229 ^ _779308) ^ [_1774755, _1774757] : [49232 ^ _779308 : [(49233 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774755, _1774755)), hAPP(hAPP(c_Product__Type_OPair(_1774755, _1774755), 49230 ^ [_1774755, _1774757]), 49231 ^ [_1774755, _1774757])), _1774757)))], (49235 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774755, _1774755)), hAPP(hAPP(c_Product__Type_OPair(_1774755, _1774755), 49231 ^ [_1774755, _1774757]), 49230 ^ [_1774755, _1774757])), _1774757))]], -(c_Relation_Osym(_1774755, _1774757))], (49219 ^ _779308) ^ [_1774492, _1774494] : [c_Relation_Osym(_1774492, _1774494), 49222 ^ _779308 : [(49223 ^ _779308) ^ [_1774598, _1774600] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774492, _1774492)), hAPP(hAPP(c_Product__Type_OPair(_1774492, _1774492), _1774600), _1774598)), _1774494)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774492, _1774492)), hAPP(hAPP(c_Product__Type_OPair(_1774492, _1774492), _1774598), _1774600)), _1774494)))]]], (49239 ^ _779308) ^ [_1775020, _1775022, _1775024, _1775026] : [c_Relation_Osym(_1775020, _1775022), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775020, _1775020)), hAPP(hAPP(c_Product__Type_OPair(_1775020, _1775020), _1775024), _1775026)), _1775022)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775020, _1775020)), hAPP(hAPP(c_Product__Type_OPair(_1775020, _1775020), _1775026), _1775024)), _1775022)))], (49249 ^ _779308) ^ [_1775233, _1775235, _1775237, _1775239] : [c_Relation_Osym(_1775233, _1775235), -(c_Relation_Osym(_1775237, hAPP(hAPP(c_Relation_Oinv__image(_1775233, _1775237), _1775235), _1775239)))], (49255 ^ _779308) ^ [_1775332, _1775334] : [-(c_Relation_Osym(_1775332, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1775332, _1775332), tc_HOL_Obool)), _1775334), hAPP(c_Relation_Oconverse(_1775332, _1775332), _1775334))))], (49257 ^ _779308) ^ [_1775377, _1775379, _1775381] : [c_Relation_Osym(_1775377, _1775379), c_Relation_Osym(_1775377, _1775381), -(c_Relation_Osym(_1775377, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1775377, _1775377), tc_HOL_Obool)), _1775379), _1775381)))], (49267 ^ _779308) ^ [_1775538, _1775540] : [c_Relation_Osym(_1775538, _1775540), -(c_Relation_Osym(tc_List_Olist(_1775538), c_List_Olistrel(_1775538, _1775540)))], (49273 ^ _779308) ^ [_1775640, _1775642] : [c_Relation_Osym(_1775640, hAPP(c_Relation_Oconverse(_1775640, _1775640), _1775642)), -(c_Relation_Osym(_1775640, _1775642))], (49279 ^ _779308) ^ [_1775725, _1775727] : [c_Relation_Osym(_1775725, _1775727), -(c_Relation_Osym(_1775725, hAPP(c_Relation_Oconverse(_1775725, _1775725), _1775727)))], (49285 ^ _779308) ^ [_1775831, _1775833] : [c_Relation_Osym(_1775831, _1775833), -(hAPP(c_Relation_Oconverse(_1775831, _1775831), _1775833) = _1775833)], (49291 ^ _779308) ^ [_1775916, _1775918] : [hAPP(c_Relation_Oconverse(_1775916, _1775916), _1775918) = _1775918, -(c_Relation_Osym(_1775916, _1775918))], (49297 ^ _779308) ^ [_1776007] : [-(c_Relation_Osym(_1776007, c_Relation_OId(_1776007)))], (49299 ^ _779308) ^ [_1776032, _1776034, _1776036] : [c_Relation_Osym(_1776032, _1776034), c_Relation_Osym(_1776032, _1776036), -(c_Relation_Osym(_1776032, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1776032, _1776032), tc_HOL_Obool)), _1776034), _1776036)))], (49309 ^ _779308) ^ [_1776193, _1776195] : [-(c_Relation_Osym(_1776193, c_Relation_OId__on(_1776193, _1776195)))], (49311 ^ _779308) ^ [_1776221, _1776223] : [c_Relation_Osym(_1776221, _1776223), -(c_Relation_Osym(_1776221, c_Transitive__Closure_Otrancl(_1776221, _1776223)))], (49317 ^ _779308) ^ [_1776304, _1776306] : [c_Relation_Osym(_1776304, _1776306), -(c_Relation_Osym(_1776304, c_Transitive__Closure_Ortrancl(_1776304, _1776306)))], (49323 ^ _779308) ^ [_1776387, _1776389] : [-(c_Relation_Osym(_1776387, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1776387, _1776387), tc_HOL_Obool)), _1776389), hAPP(c_Relation_Oconverse(_1776387, _1776387), _1776389))))], (49325 ^ _779308) ^ [_1776450, _1776452, _1776454] : [c_Equiv__Relations_Oequiv(_1776450, _1776452, _1776454), 49328 ^ _779308 : [(49329 ^ _779308) ^ [] : [-(c_Relation_Orefl__on(_1776450, _1776452, _1776454))], (49331 ^ _779308) ^ [] : [-(c_Relation_Osym(_1776450, _1776454))], (49333 ^ _779308) ^ [] : [-(c_Relation_Otrans(_1776450, _1776454))]]], (49335 ^ _779308) ^ [_1776579, _1776581, _1776583] : [-(c_Equiv__Relations_Oequiv(_1776579, _1776581, _1776583)), c_Relation_Orefl__on(_1776579, _1776581, _1776583), c_Relation_Osym(_1776579, _1776583), c_Relation_Otrans(_1776579, _1776583)], (49349 ^ _779308) ^ [_1776772, _1776774, _1776776] : [c_Relation_Orefl__on(_1776772, _1776774, _1776776), c_Relation_Osym(_1776772, _1776776), c_Relation_Otrans(_1776772, _1776776), -(c_Equiv__Relations_Oequiv(_1776772, _1776774, _1776776))], (49363 ^ _779308) ^ [_1776963, _1776965, _1776967] : [c_Equiv__Relations_Oequiv(_1776963, _1776965, _1776967), 49366 ^ _779308 : [(49367 ^ _779308) ^ [] : [-(c_Relation_Orefl__on(_1776963, _1776965, _1776967))], (49369 ^ _779308) ^ [] : [-(c_Relation_Osym(_1776963, _1776967))], (49371 ^ _779308) ^ [] : [-(c_Relation_Otrans(_1776963, _1776967))]]], (49373 ^ _779308) ^ [_1777115, _1777117] : [c_Predicate_Osymp(_1777115, _1777117), -(c_Relation_Osym(_1777115, hAPP(c_Set_OCollect(tc_prod(_1777115, _1777115)), hAPP(c_Product__Type_Oprod_Oprod__case(_1777115, _1777115, tc_HOL_Obool), _1777117))))], (49379 ^ _779308) ^ [_1777218, _1777220] : [c_Relation_Osym(_1777218, hAPP(c_Set_OCollect(tc_prod(_1777218, _1777218)), hAPP(c_Product__Type_Oprod_Oprod__case(_1777218, _1777218, tc_HOL_Obool), _1777220))), -(c_Predicate_Osymp(_1777218, _1777220))], (49385 ^ _779308) ^ [_1777342, _1777344] : [c_Equiv__Relations_Opart__equivp(_1777342, _1777344), 49389 ^ _779308 : [(49390 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1777344, 49388 ^ [_1777342, _1777344]), 49388 ^ [_1777342, _1777344])))], (49392 ^ _779308) ^ [] : [-(c_Predicate_Osymp(_1777342, _1777344))], (49394 ^ _779308) ^ [] : [-(c_Predicate_Otransp(_1777342, _1777344))]]], (49396 ^ _779308) ^ [_1777494, _1777496] : [-(c_Equiv__Relations_Opart__equivp(_1777494, _1777496)), 49399 ^ _779308 : [(49400 ^ _779308) ^ [_1777571] : [hBOOL(hAPP(hAPP(_1777496, _1777571), _1777571))]], c_Predicate_Osymp(_1777494, _1777496), c_Predicate_Otransp(_1777494, _1777496)], (49410 ^ _779308) ^ [_1777700, _1777702] : [49411 ^ _779308 : [(49412 ^ _779308) ^ [_1777756] : [hBOOL(hAPP(hAPP(_1777700, _1777756), _1777756))]], c_Predicate_Osymp(_1777702, _1777700), c_Predicate_Otransp(_1777702, _1777700), -(c_Equiv__Relations_Opart__equivp(_1777702, _1777700))], (49424 ^ _779308) ^ [_1777904, _1777906] : [c_Equiv__Relations_Oequivp(_1777904, _1777906), -(c_Equiv__Relations_Opart__equivp(_1777904, _1777906))], (49461 ^ _779308) ^ [_1778577, _1778579] : [-(c_Equiv__Relations_Opart__equivp(_1778577, _1778579)), 49464 ^ _779308 : [(49465 ^ _779308) ^ [_1778697] : [hBOOL(hAPP(hAPP(_1778579, _1778697), _1778697))]], 49482 ^ _779308 : [(49483 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1778579, 49466 ^ [_1778577, _1778579]), 49466 ^ [_1778577, _1778579])))], (49485 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1778579, 49467 ^ [_1778577, _1778579]), 49467 ^ [_1778577, _1778579])))], (49487 ^ _779308) ^ [] : [-(hAPP(_1778579, 49466 ^ [_1778577, _1778579]) = hAPP(_1778579, 49467 ^ [_1778577, _1778579]))], (49489 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1778579, 49466 ^ [_1778577, _1778579]), 49467 ^ [_1778577, _1778579]))]], 49470 ^ _779308 : [(49471 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1778579, 49466 ^ [_1778577, _1778579]), 49467 ^ [_1778577, _1778579])))], (49473 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1778579, 49466 ^ [_1778577, _1778579]), 49466 ^ [_1778577, _1778579])), hBOOL(hAPP(hAPP(_1778579, 49467 ^ [_1778577, _1778579]), 49467 ^ [_1778577, _1778579])), hAPP(_1778579, 49466 ^ [_1778577, _1778579]) = hAPP(_1778579, 49467 ^ [_1778577, _1778579])]]], (49430 ^ _779308) ^ [_1777996, _1777998] : [c_Equiv__Relations_Opart__equivp(_1777996, _1777998), 49434 ^ _779308 : [(49435 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1777998, 49433 ^ [_1777996, _1777998]), 49433 ^ [_1777996, _1777998])))], (49437 ^ _779308) ^ [_1778169, _1778171] : [hBOOL(hAPP(hAPP(_1777998, _1778171), _1778169)), 49440 ^ _779308 : [(49441 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1777998, _1778171), _1778171)))], (49443 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1777998, _1778169), _1778169)))], (49445 ^ _779308) ^ [] : [-(hAPP(_1777998, _1778171) = hAPP(_1777998, _1778169))]]], (49447 ^ _779308) ^ [_1778338, _1778340] : [-(hBOOL(hAPP(hAPP(_1777998, _1778340), _1778338))), hBOOL(hAPP(hAPP(_1777998, _1778340), _1778340)), hBOOL(hAPP(hAPP(_1777998, _1778338), _1778338)), hAPP(_1777998, _1778340) = hAPP(_1777998, _1778338)]]], (49493 ^ _779308) ^ [_1779245, _1779247, _1779249, _1779251] : [c_Equiv__Relations_Opart__equivp(_1779245, _1779247), hBOOL(hAPP(hAPP(_1779247, _1779249), _1779251)), -(hBOOL(hAPP(hAPP(_1779247, _1779251), _1779249)))], (49503 ^ _779308) ^ [_1779402, _1779404, _1779406, _1779408, _1779410] : [c_Equiv__Relations_Opart__equivp(_1779402, _1779404), hBOOL(hAPP(hAPP(_1779404, _1779406), _1779408)), hBOOL(hAPP(hAPP(_1779404, _1779408), _1779410)), -(hBOOL(hAPP(hAPP(_1779404, _1779406), _1779410)))], (49517 ^ _779308) ^ [_1779631, _1779633] : [c_Equiv__Relations_Opart__equivp(_1779631, _1779633), 49521 ^ _779308 : [(49522 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1779633, 49520 ^ [_1779631, _1779633]), 49520 ^ [_1779631, _1779633])))], (49524 ^ _779308) ^ [] : [-(c_Predicate_Osymp(_1779631, _1779633))], (49526 ^ _779308) ^ [] : [-(c_Predicate_Otransp(_1779631, _1779633))]]], (49528 ^ _779308) ^ [_1779791, _1779793] : [c_Equiv__Relations_Opart__equivp(_1779791, _1779793), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1779791, tc_HOL_Obool)), 49531 ^ [_1779791, _1779793]), hAPP(hAPP(c_COMBB(tc_fun(_1779791, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1779791, tc_HOL_Obool)), c_HOL_OEx(_1779791)), hAPP(hAPP(c_COMBB(tc_fun(_1779791, tc_HOL_Obool), tc_fun(_1779791, tc_HOL_Obool), tc_fun(_1779791, tc_HOL_Obool)), hAPP(c_COMBS(_1779791, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1779791), c_fconj), hAPP(hAPP(c_COMBS(_1779791, _1779791, tc_HOL_Obool), _1779793), c_COMBI(_1779791))))), hAPP(hAPP(c_COMBC(tc_fun(_1779791, tc_HOL_Obool), tc_fun(_1779791, tc_fun(_1779791, tc_HOL_Obool)), tc_fun(_1779791, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779791, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1779791, tc_fun(_1779791, tc_HOL_Obool)), tc_fun(_1779791, tc_HOL_Obool)), tc_fun(_1779791, tc_HOL_Obool)), c_COMBB(tc_fun(_1779791, tc_HOL_Obool), tc_HOL_Obool, _1779791)), c_fequal)), _1779793))))))], (49535 ^ _779308) ^ [_1780170, _1780172, _1780174] : [c_Fun_Oinj__on(_1780170, _1780172, _1780174, c_Orderings_Otop__class_Otop(tc_fun(_1780170, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780172, _1780170, _1780170, c_Hilbert__Choice_Oinv__into(_1780170, _1780172, c_Orderings_Otop__class_Otop(tc_fun(_1780170, tc_HOL_Obool)), _1780174)), _1780174) = c_Fun_Oid(_1780170))], (49541 ^ _779308) ^ [_1780299, _1780301, _1780303] : [hAPP(c_Fun_Ocomp(_1780301, _1780299, _1780299, c_Hilbert__Choice_Oinv__into(_1780299, _1780301, c_Orderings_Otop__class_Otop(tc_fun(_1780299, tc_HOL_Obool)), _1780303)), _1780303) = c_Fun_Oid(_1780299), -(c_Fun_Oinj__on(_1780299, _1780301, _1780303, c_Orderings_Otop__class_Otop(tc_fun(_1780299, tc_HOL_Obool))))], (49547 ^ _779308) ^ [_1780434, _1780436, _1780438] : [c_Fun_Oinj__on(_1780434, _1780436, _1780438, c_Orderings_Otop__class_Otop(tc_fun(_1780434, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780436, _1780434, _1780434, c_Hilbert__Choice_Oinv__into(_1780434, _1780436, c_Orderings_Otop__class_Otop(tc_fun(_1780434, tc_HOL_Obool)), _1780438)), _1780438) = c_Fun_Oid(_1780434))], (49553 ^ _779308) ^ [_1780567, _1780569, _1780571, _1780573, _1780575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1780567, tc_HOL_Obool)), _1780569), hAPP(c_Set_Oimage(_1780571, _1780567, _1780573), _1780575))), -(c_Fun_Oinj__on(_1780567, _1780571, c_Hilbert__Choice_Oinv__into(_1780571, _1780567, _1780575, _1780573), _1780569))], (49559 ^ _779308) ^ [_1780698, _1780700, _1780702, _1780704, _1780706] : [c_Fun_Oinj__on(_1780698, _1780700, _1780702, _1780704), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1780698, tc_HOL_Obool)), _1780706), _1780704)), -(hAPP(c_Set_Oimage(_1780700, _1780698, c_Hilbert__Choice_Oinv__into(_1780698, _1780700, _1780704, _1780702)), hAPP(c_Set_Oimage(_1780698, _1780700, _1780702), _1780706)) = _1780706)], (49569 ^ _779308) ^ [_1780901, _1780903, _1780905] : [hAPP(c_Set_Oimage(_1780901, _1780903, _1780905), c_Orderings_Otop__class_Otop(tc_fun(_1780901, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1780903, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1780903, _1780901, c_Hilbert__Choice_Oinv__into(_1780901, _1780903, c_Orderings_Otop__class_Otop(tc_fun(_1780901, tc_HOL_Obool)), _1780905), c_Orderings_Otop__class_Otop(tc_fun(_1780903, tc_HOL_Obool))))], (49575 ^ _779308) ^ [_1781048, _1781050, _1781052, _1781054] : [c_Fun_Oinj__on(_1781048, _1781050, _1781052, c_Orderings_Otop__class_Otop(tc_fun(_1781048, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781050, _1781048, c_Hilbert__Choice_Oinv__into(_1781048, _1781050, c_Orderings_Otop__class_Otop(tc_fun(_1781048, tc_HOL_Obool)), _1781052)), hAPP(c_Set_Oimage(_1781048, _1781050, _1781052), _1781054)) = _1781054)], (49581 ^ _779308) ^ [_1781191, _1781193, _1781195, _1781197] : [c_Fun_Oinj__on(_1781191, _1781193, _1781195, c_Orderings_Otop__class_Otop(tc_fun(_1781191, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781193, _1781191, c_Hilbert__Choice_Oinv__into(_1781191, _1781193, c_Orderings_Otop__class_Otop(tc_fun(_1781191, tc_HOL_Obool)), _1781195)), hAPP(c_Set_Oimage(_1781191, _1781193, _1781195), _1781197)) = _1781197)], (49587 ^ _779308) ^ [_1781334, _1781336, _1781338] : [c_Fun_Oinj__on(_1781334, _1781336, _1781338, c_Orderings_Otop__class_Otop(tc_fun(_1781334, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781336, _1781334, c_Hilbert__Choice_Oinv__into(_1781334, _1781336, c_Orderings_Otop__class_Otop(tc_fun(_1781334, tc_HOL_Obool)), _1781338)), c_Orderings_Otop__class_Otop(tc_fun(_1781336, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781334, tc_HOL_Obool)))], (49593 ^ _779308) ^ [_1781481, _1781483, _1781485, _1781487, _1781489, _1781491] : [hAPP(c_Set_Oimage(_1781481, _1781483, _1781485), _1781487) = _1781489, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1781483, tc_HOL_Obool)), _1781491), _1781489)), -(hAPP(c_Set_Oimage(_1781481, _1781483, _1781485), hAPP(c_Set_Oimage(_1781483, _1781481, c_Hilbert__Choice_Oinv__into(_1781481, _1781483, _1781487, _1781485)), _1781491)) = _1781491)], (49603 ^ _779308) ^ [_1781716, _1781718, _1781720] : [hAPP(c_Set_Oimage(_1781716, _1781718, _1781720), c_Orderings_Otop__class_Otop(tc_fun(_1781716, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781718, tc_HOL_Obool)), 49606 ^ _779308 : [(49607 ^ _779308) ^ [_1781827] : [-(hAPP(_1781720, hAPP(c_Hilbert__Choice_Oinv__into(_1781716, _1781718, c_Orderings_Otop__class_Otop(tc_fun(_1781716, tc_HOL_Obool)), _1781720), _1781827)) = _1781827)]]], (49609 ^ _779308) ^ [_1781866, _1781868, _1781870] : [hAPP(_1781870, hAPP(c_Hilbert__Choice_Oinv__into(_1781866, _1781868, c_Orderings_Otop__class_Otop(tc_fun(_1781866, tc_HOL_Obool)), _1781870), 49610 ^ [_1781866, _1781868, _1781870])) = 49610 ^ [_1781866, _1781868, _1781870], -(hAPP(c_Set_Oimage(_1781866, _1781868, _1781870), c_Orderings_Otop__class_Otop(tc_fun(_1781866, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781868, tc_HOL_Obool)))], (49616 ^ _779308) ^ [_1782066, _1782068, _1782070, _1782072] : [hAPP(c_Set_Oimage(_1782066, _1782068, _1782070), c_Orderings_Otop__class_Otop(tc_fun(_1782066, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782068, tc_HOL_Obool)), -(hAPP(_1782070, hAPP(c_Hilbert__Choice_Oinv__into(_1782066, _1782068, c_Orderings_Otop__class_Otop(tc_fun(_1782066, tc_HOL_Obool)), _1782070), _1782072)) = _1782072)], (49622 ^ _779308) ^ [_1782213, _1782215, _1782217, _1782219] : [hAPP(c_Set_Oimage(_1782213, _1782215, _1782217), c_Orderings_Otop__class_Otop(tc_fun(_1782213, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782215, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1782213, _1782215, _1782217), hAPP(c_Set_Oimage(_1782215, _1782213, c_Hilbert__Choice_Oinv__into(_1782213, _1782215, c_Orderings_Otop__class_Otop(tc_fun(_1782213, tc_HOL_Obool)), _1782217)), _1782219)) = _1782219)], (49628 ^ _779308) ^ [_1782376, _1782378, _1782380, _1782382, _1782384] : [hBOOL(hAPP(hAPP(c_member(_1782376), _1782378), hAPP(c_Set_Oimage(_1782380, _1782376, _1782382), _1782384))), -(hAPP(_1782382, hAPP(c_Hilbert__Choice_Oinv__into(_1782380, _1782376, _1782384, _1782382), _1782378)) = _1782378)], (49634 ^ _779308) ^ [_1782509, _1782511, _1782513, _1782515, _1782517] : [hBOOL(hAPP(hAPP(c_member(_1782509), _1782511), hAPP(c_Set_Oimage(_1782513, _1782509, _1782515), _1782517))), -(hBOOL(hAPP(hAPP(c_member(_1782513), hAPP(c_Hilbert__Choice_Oinv__into(_1782513, _1782509, _1782517, _1782515), _1782511)), _1782517)))], (49640 ^ _779308) ^ [_1782650, _1782652, _1782654, _1782656, _1782658, _1782660] : [hAPP(c_Hilbert__Choice_Oinv__into(_1782650, _1782652, _1782654, _1782656), _1782658) = hAPP(c_Hilbert__Choice_Oinv__into(_1782650, _1782652, _1782654, _1782656), _1782660), hBOOL(hAPP(hAPP(c_member(_1782652), _1782658), hAPP(c_Set_Oimage(_1782650, _1782652, _1782656), _1782654))), hBOOL(hAPP(hAPP(c_member(_1782652), _1782660), hAPP(c_Set_Oimage(_1782650, _1782652, _1782656), _1782654))), -(_1782658 = _1782660)], (49654 ^ _779308) ^ [_1782943, _1782945, _1782947, _1782949, _1782951] : [c_Fun_Oinj__on(_1782943, _1782945, _1782947, _1782949), hBOOL(hAPP(hAPP(c_member(_1782943), _1782951), _1782949)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1782943, _1782945, _1782949, _1782947), hAPP(_1782947, _1782951)) = _1782951)], (49664 ^ _779308) ^ [_1783124, _1783126, _1783128, _1783130, _1783132, _1783134] : [c_Fun_Oinj__on(_1783124, _1783126, _1783128, _1783130), hBOOL(hAPP(hAPP(c_member(_1783124), _1783132), _1783130)), hAPP(_1783128, _1783132) = _1783134, -(hAPP(c_Hilbert__Choice_Oinv__into(_1783124, _1783126, _1783130, _1783128), _1783134) = _1783132)], (49678 ^ _779308) ^ [_1783369, _1783371, _1783373, _1783375, _1783377] : [c_Fun_Oinj__on(_1783369, _1783371, _1783373, c_Orderings_Otop__class_Otop(tc_fun(_1783369, tc_HOL_Obool))), hAPP(_1783373, _1783375) = _1783377, -(hAPP(c_Hilbert__Choice_Oinv__into(_1783369, _1783371, c_Orderings_Otop__class_Otop(tc_fun(_1783369, tc_HOL_Obool)), _1783373), _1783377) = _1783375)], (49688 ^ _779308) ^ [_1783556, _1783558, _1783560, _1783562] : [c_Fun_Oinj__on(_1783556, _1783558, _1783560, c_Orderings_Otop__class_Otop(tc_fun(_1783556, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1783556, _1783558, c_Orderings_Otop__class_Otop(tc_fun(_1783556, tc_HOL_Obool)), _1783560), hAPP(_1783560, _1783562)) = _1783562)], (49694 ^ _779308) ^ [_1783683] : [-(c_Hilbert__Choice_Oinv__into(_1783683, _1783683, c_Orderings_Otop__class_Otop(tc_fun(_1783683, tc_HOL_Obool)), c_Fun_Oid(_1783683)) = c_Fun_Oid(_1783683))], (49696 ^ _779308) ^ [_1783720, _1783722, _1783724, _1783726, _1783728] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1783720, _1783722, _1783724, _1783726), _1783728) = c_Hilbert__Choice_OEps(_1783720, hAPP(hAPP(c_COMBS(_1783720, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1783720), c_fconj), hAPP(hAPP(c_COMBC(_1783720, tc_fun(_1783720, tc_HOL_Obool), tc_HOL_Obool), c_member(_1783720)), _1783724))), hAPP(hAPP(c_COMBC(_1783720, _1783722, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1783722, tc_fun(_1783722, tc_HOL_Obool), _1783720), c_fequal), _1783726)), _1783728))))], (49698 ^ _779308) ^ [_1783820, _1783822, _1783824, _1783826] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1783820, _1783822, c_Orderings_Otop__class_Otop(tc_fun(_1783820, tc_HOL_Obool)), _1783824), _1783826) = c_Hilbert__Choice_OEps(_1783820, hAPP(hAPP(c_COMBC(_1783820, _1783822, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1783822, tc_fun(_1783822, tc_HOL_Obool), _1783820), c_fequal), _1783824)), _1783826)))], (49700 ^ _779308) ^ [_1783888, _1783890, _1783892, _1783894, _1783896] : [c_Fun_Oinj__on(_1783888, _1783890, _1783892, c_Orderings_Otop__class_Otop(tc_fun(_1783888, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1783890, _1783894, _1783888, hAPP(c_Fun_Ocomp(_1783888, _1783894, _1783890, _1783896), c_Hilbert__Choice_Oinv__into(_1783888, _1783890, c_Orderings_Otop__class_Otop(tc_fun(_1783888, tc_HOL_Obool)), _1783892))), _1783892) = _1783896)], (49706 ^ _779308) ^ [_1784037, _1784039, _1784041, _1784043, _1784045, _1784047, _1784049] : [c_Fun_Oinj__on(_1784037, _1784039, _1784041, hAPP(c_Set_Oimage(_1784043, _1784037, _1784045), _1784047)), c_Fun_Oinj__on(_1784043, _1784037, _1784045, _1784047), hBOOL(hAPP(hAPP(c_member(_1784039), _1784049), hAPP(c_Set_Oimage(_1784037, _1784039, _1784041), hAPP(c_Set_Oimage(_1784043, _1784037, _1784045), _1784047)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1784043, _1784039, _1784047, hAPP(c_Fun_Ocomp(_1784037, _1784039, _1784043, _1784041), _1784045)), _1784049) = hAPP(hAPP(c_Fun_Ocomp(_1784037, _1784043, _1784039, c_Hilbert__Choice_Oinv__into(_1784043, _1784037, _1784047, _1784045)), c_Hilbert__Choice_Oinv__into(_1784037, _1784039, hAPP(c_Set_Oimage(_1784043, _1784037, _1784045), _1784047), _1784041)), _1784049))], (49720 ^ _779308) ^ [_1784418, _1784420, _1784422] : [hAPP(c_Set_Oimage(_1784418, _1784420, _1784422), c_Orderings_Otop__class_Otop(tc_fun(_1784418, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784420, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1784418, _1784420, _1784420, _1784422), c_Hilbert__Choice_Oinv__into(_1784418, _1784420, c_Orderings_Otop__class_Otop(tc_fun(_1784418, tc_HOL_Obool)), _1784422)) = c_Fun_Oid(_1784420))], (49726 ^ _779308) ^ [_1784567, _1784569, _1784571] : [hAPP(c_Fun_Ocomp(_1784567, _1784569, _1784569, _1784571), c_Hilbert__Choice_Oinv__into(_1784567, _1784569, c_Orderings_Otop__class_Otop(tc_fun(_1784567, tc_HOL_Obool)), _1784571)) = c_Fun_Oid(_1784569), -(hAPP(c_Set_Oimage(_1784567, _1784569, _1784571), c_Orderings_Otop__class_Otop(tc_fun(_1784567, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784569, tc_HOL_Obool)))], (49732 ^ _779308) ^ [_1784722, _1784724, _1784726, _1784728, _1784730] : [c_Fun_Oinj__on(_1784722, _1784724, _1784726, c_Orderings_Otop__class_Otop(tc_fun(_1784722, tc_HOL_Obool))), 49738 ^ _779308 : [(49739 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1784724), 49737 ^ [_1784722, _1784724, _1784726, _1784728, _1784730]), hAPP(c_Set_Oimage(_1784722, _1784724, _1784726), c_Orderings_Otop__class_Otop(tc_fun(_1784722, tc_HOL_Obool))))))], (49741 ^ _779308) ^ [] : [hBOOL(hAPP(_1784728, hAPP(c_Hilbert__Choice_Oinv__into(_1784722, _1784724, c_Orderings_Otop__class_Otop(tc_fun(_1784722, tc_HOL_Obool)), _1784726), 49737 ^ [_1784722, _1784724, _1784726, _1784728, _1784730])))]], -(hBOOL(hAPP(_1784728, _1784730)))], (49745 ^ _779308) ^ [_1785048, _1785050, _1785052, _1785054, _1785056, _1785058] : [class_Groups_Ocomm__monoid__mult(_1785048), hBOOL(hAPP(c_Finite__Set_Ofinite(_1785050), _1785052)), 49755 ^ _779308 : [(49756 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785050), 49754 ^ [_1785048, _1785050, _1785052, _1785054, _1785056, _1785058]), _1785052)))], (49758 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785054), hAPP(_1785056, 49754 ^ [_1785048, _1785050, _1785052, _1785054, _1785056, _1785058])))]], 49762 ^ _779308 : [(49763 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785050), 49761 ^ [_1785048, _1785050, _1785052, _1785054, _1785056, _1785058]), _1785052)))], (49766 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785050), 49764 ^ [_1785048, _1785050, _1785052, _1785054, _1785056, _1785058]), _1785052)))], (49768 ^ _779308) ^ [] : [49761 ^ [_1785048, _1785050, _1785052, _1785054, _1785056, _1785058] = 49764 ^ [_1785048, _1785050, _1785052, _1785054, _1785056, _1785058]], (49770 ^ _779308) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785054, tc_HOL_Obool)), hAPP(_1785056, 49761 ^ [_1785048, _1785050, _1785052, _1785054, _1785056, _1785058])), hAPP(_1785056, 49764 ^ [_1785048, _1785050, _1785052, _1785054, _1785056, _1785058])) = c_Orderings_Obot__class_Obot(tc_fun(_1785054, tc_HOL_Obool))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785048, _1785054, c_Groups_Otimes__class_Otimes(_1785048)), _1785058), c_Groups_Oone__class_Oone(_1785048)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1785050, tc_fun(_1785054, tc_HOL_Obool)), _1785052), _1785056)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785048, _1785050, c_Groups_Otimes__class_Otimes(_1785048)), hAPP(hAPP(c_COMBB(tc_fun(_1785054, tc_HOL_Obool), _1785048, _1785050), hAPP(hAPP(c_Finite__Set_Ofold__image(_1785048, _1785054, c_Groups_Otimes__class_Otimes(_1785048)), _1785058), c_Groups_Oone__class_Oone(_1785048))), _1785056)), c_Groups_Oone__class_Oone(_1785048)), _1785052))], (49774 ^ _779308) ^ [_1786008, _1786010] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786008), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1786010, hAPP(c_Code__Numeral_Onat__of, 49779 ^ [_1786008, _1786010]))), -(hBOOL(hAPP(_1786010, _1786008)))], (49785 ^ _779308) ^ [_1786190] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786190), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1786190 = hAPP(c_Code__Numeral_Onat__of, 49788 ^ [_1786190]))], (49792 ^ _779308) ^ [_1786295, _1786297] : [49794 ^ _779308 : [(49795 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49793 ^ [_1786295, _1786297]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (49797 ^ _779308) ^ [] : [hBOOL(hAPP(_1786295, hAPP(c_Code__Numeral_Oof__nat, 49793 ^ [_1786295, _1786297])))]], -(hBOOL(hAPP(_1786295, _1786297)))], (49802 ^ _779308) ^ [_1786462] : [-(_1786462 = hAPP(c_Code__Numeral_Oof__nat, 49800 ^ [_1786462]))], (49804 ^ _779308) ^ [_1786490] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49800 ^ [_1786490]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (49806 ^ _779308) ^ [_1786525, _1786527, _1786529, _1786531] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1786525, _1786527, _1786529, _1786531, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1786527)) = _1786529)], (49808 ^ _779308) ^ [_1786571, _1786573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1786571), _1786573)), -(c_Quickcheck_Obeyond(_1786571, _1786573) = _1786573)], (49814 ^ _779308) ^ [_1786658, _1786660] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1786658), _1786660))), -(c_Quickcheck_Obeyond(_1786658, _1786660) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (49820 ^ _779308) ^ [_1786704] : [-(c_Quickcheck_Obeyond(_1786704, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (49822 ^ _779308) ^ [_1786730, _1786732, _1786734, _1786736, _1786738, _1786740] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1786730, _1786732, _1786734, _1786736, c_Lazy__Sequence_Olazy__sequence_OInsert(_1786732, _1786738, _1786740)) = hAPP(hAPP(hAPP(_1786736, _1786738), _1786740), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1786730, _1786732, _1786734, _1786736, _1786740)))], (49824 ^ _779308) ^ [_1786788, _1786790, _1786792, _1786794] : [c_Fun_Obij__betw(_1786788, _1786790, _1786792, c_Orderings_Otop__class_Otop(tc_fun(_1786788, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1786790, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1786788, _1786790, _1786792), hAPP(c_Set_OCollect(_1786788), _1786794)) = hAPP(c_Set_OCollect(_1786790), hAPP(hAPP(c_COMBB(_1786788, tc_HOL_Obool, _1786790), _1786794), c_Hilbert__Choice_Oinv__into(_1786788, _1786790, c_Orderings_Otop__class_Otop(tc_fun(_1786788, tc_HOL_Obool)), _1786792))))], (49830 ^ _779308) ^ [_1786969, _1786971, _1786973, _1786975, _1786977, _1786979] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1786969, _1786971, _1786973, _1786975), _1786977), _1786979) = hAPP(_1786975, hAPP(hAPP(c_Product__Type_OPair(_1786969, _1786971), _1786977), _1786979)))], (49832 ^ _779308) ^ [_1787025, _1787027, _1787029, _1787031, _1787033] : [hBOOL(hAPP(_1787025, hAPP(hAPP(c_Product__Type_OPair(_1787027, _1787029), _1787031), _1787033))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1787027, _1787029, tc_HOL_Obool, _1787025), _1787031), _1787033)))], (49838 ^ _779308) ^ [_1787190, _1787192] : [-(c_Fun_Obij__betw(_1787190, _1787190, c_Fun_Oid(_1787190), _1787192, _1787192))], (49840 ^ _779308) ^ [_1787318, _1787320, _1787322] : [c_Fun_Obij__betw(_1787318, _1787320, _1787322, c_Orderings_Otop__class_Otop(tc_fun(_1787318, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787320, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1787320, _1787318, c_Hilbert__Choice_Oinv__into(_1787318, _1787320, c_Orderings_Otop__class_Otop(tc_fun(_1787318, tc_HOL_Obool)), _1787322), c_Orderings_Otop__class_Otop(tc_fun(_1787320, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787318, tc_HOL_Obool))))], (49846 ^ _779308) ^ [_1787620, _1787622, _1787624] : [c_Fun_Obij__betw(_1787620, _1787622, _1787624, c_Orderings_Otop__class_Otop(tc_fun(_1787620, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787622, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1787622, _1787620, c_Orderings_Otop__class_Otop(tc_fun(_1787622, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1787620, _1787622, c_Orderings_Otop__class_Otop(tc_fun(_1787620, tc_HOL_Obool)), _1787624)) = _1787624)], (49852 ^ _779308) ^ [_1787958, _1787960, _1787962, _1787964, _1787966, _1787968] : [c_Fun_Obij__betw(_1787958, _1787960, _1787962, _1787964, _1787966), hBOOL(hAPP(hAPP(c_member(_1787958), _1787968), _1787964)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1787960, _1787958, _1787966, c_Hilbert__Choice_Oinv__into(_1787958, _1787960, _1787964, _1787962)), _1787968) = hAPP(_1787962, _1787968))], (49862 ^ _779308) ^ [_1788391, _1788393, _1788395, _1788397, _1788399] : [c_Fun_Obij__betw(_1788391, _1788393, _1788395, _1788397, _1788399), -(c_Fun_Obij__betw(_1788393, _1788391, c_Hilbert__Choice_Oinv__into(_1788391, _1788393, _1788397, _1788395), _1788399, _1788397))], (49868 ^ _779308) ^ [_1788683, _1788685, _1788687, _1788689, _1788691] : [c_Fun_Obij__betw(_1788683, _1788685, _1788687, c_Orderings_Otop__class_Otop(tc_fun(_1788683, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788685, tc_HOL_Obool))), c_Fun_Obij__betw(_1788689, _1788683, _1788691, c_Orderings_Otop__class_Otop(tc_fun(_1788689, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788683, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1788689, _1788685, c_Orderings_Otop__class_Otop(tc_fun(_1788689, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1788683, _1788685, _1788689, _1788687), _1788691)) = hAPP(c_Fun_Ocomp(_1788683, _1788689, _1788685, c_Hilbert__Choice_Oinv__into(_1788689, _1788683, c_Orderings_Otop__class_Otop(tc_fun(_1788689, tc_HOL_Obool)), _1788691)), c_Hilbert__Choice_Oinv__into(_1788683, _1788685, c_Orderings_Otop__class_Otop(tc_fun(_1788683, tc_HOL_Obool)), _1788687)))], (49878 ^ _779308) ^ [_1789240, _1789242, _1789244, _1789246, _1789248, _1789250, _1789252, _1789254] : [c_Fun_Obij__betw(_1789240, _1789242, _1789244, _1789246, _1789248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1789240, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1789250, _1789240, _1789252), _1789254)), _1789246)), 49885 ^ _779308 : [(49886 ^ _779308) ^ [] : [c_Fun_Obij__betw(_1789250, _1789240, _1789252, _1789254, _1789246), -(c_Fun_Obij__betw(_1789250, _1789242, hAPP(c_Fun_Ocomp(_1789240, _1789242, _1789250, _1789244), _1789252), _1789254, _1789248))], (49892 ^ _779308) ^ [] : [c_Fun_Obij__betw(_1789250, _1789242, hAPP(c_Fun_Ocomp(_1789240, _1789242, _1789250, _1789244), _1789252), _1789254, _1789248), -(c_Fun_Obij__betw(_1789250, _1789240, _1789252, _1789254, _1789246))]]], (49898 ^ _779308) ^ [_1790033, _1790035, _1790037, _1790039, _1790041] : [c_Fun_Obij__betw(_1790033, _1790035, _1790037, c_Orderings_Otop__class_Otop(tc_fun(_1790033, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790035, tc_HOL_Obool))), c_Fun_Obij__betw(_1790035, _1790039, _1790041, c_Orderings_Otop__class_Otop(tc_fun(_1790035, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790039, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1790033, _1790039, hAPP(c_Fun_Ocomp(_1790035, _1790039, _1790033, _1790041), _1790037), c_Orderings_Otop__class_Otop(tc_fun(_1790033, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790039, tc_HOL_Obool))))], (49908 ^ _779308) ^ [_1790540, _1790542, _1790544, _1790546, _1790548, _1790550, _1790552, _1790554] : [c_Fun_Obij__betw(_1790540, _1790542, _1790544, _1790546, _1790548), 49911 ^ _779308 : [(49912 ^ _779308) ^ [] : [c_Fun_Obij__betw(_1790542, _1790550, _1790552, _1790548, _1790554), -(c_Fun_Obij__betw(_1790540, _1790550, hAPP(c_Fun_Ocomp(_1790542, _1790550, _1790540, _1790552), _1790544), _1790546, _1790554))], (49918 ^ _779308) ^ [] : [c_Fun_Obij__betw(_1790540, _1790550, hAPP(c_Fun_Ocomp(_1790542, _1790550, _1790540, _1790552), _1790544), _1790546, _1790554), -(c_Fun_Obij__betw(_1790542, _1790550, _1790552, _1790548, _1790554))]]], (49924 ^ _779308) ^ [_1791228, _1791230, _1791232, _1791234, _1791236, _1791238, _1791240, _1791242] : [c_Fun_Obij__betw(_1791228, _1791230, _1791232, _1791234, _1791236), c_Fun_Obij__betw(_1791230, _1791238, _1791240, _1791236, _1791242), -(c_Fun_Obij__betw(_1791228, _1791238, hAPP(c_Fun_Ocomp(_1791230, _1791238, _1791228, _1791240), _1791232), _1791234, _1791242))], (49934 ^ _779308) ^ [_1791663, _1791665, _1791667, _1791669, _1791671] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1791663, _1791665, tc_HOL_Obool, _1791667), _1791669), _1791671)), -(hBOOL(hAPP(_1791667, hAPP(hAPP(c_Product__Type_OPair(_1791663, _1791665), _1791669), _1791671))))], (49940 ^ _779308) ^ [_1791975, _1791977, _1791979, _1791981, _1791983] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1791975, _1791977, tc_HOL_Obool, _1791979), _1791981), _1791983)), -(hBOOL(hAPP(_1791979, hAPP(hAPP(c_Product__Type_OPair(_1791975, _1791977), _1791981), _1791983))))], (49946 ^ _779308) ^ [_1792286, _1792288, _1792290, _1792292, _1792294, _1792296] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1792286, _1792288, _1792290, _1792292), _1792294), _1792296) = hAPP(_1792292, hAPP(hAPP(c_Product__Type_OPair(_1792286, _1792288), _1792294), _1792296)))], (49948 ^ _779308) ^ [_1792454, _1792456, _1792458, _1792460] : [c_Fun_Obij__betw(_1792454, _1792456, _1792458, c_Orderings_Otop__class_Otop(tc_fun(_1792454, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792456, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1792454, _1792456, _1792458), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1792454, tc_HOL_Obool)), _1792460)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1792456, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1792454, _1792456, _1792458), _1792460)))], (49954 ^ _779308) ^ [_1792790, _1792792, _1792794, _1792796] : [c_Fun_Obij__betw(_1792790, _1792792, _1792794, c_Orderings_Otop__class_Otop(tc_fun(_1792790, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1792792, tc_HOL_Obool))), 49957 ^ _779308 : [(49958 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792790), hAPP(c_Set_Ovimage(_1792790, _1792792, _1792794), _1792796))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1792792), _1792796)))], (49964 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792792), _1792796)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1792790), hAPP(c_Set_Ovimage(_1792790, _1792792, _1792794), _1792796))))]]], (49970 ^ _779308) ^ [_1793423, _1793425, _1793427, _1793429, _1793431, _1793433, _1793435] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1793423, tc_HOL_Obool)), _1793425), _1793427) = c_Orderings_Obot__class_Obot(tc_fun(_1793423, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1793429, tc_HOL_Obool)), _1793431), _1793433) = c_Orderings_Obot__class_Obot(tc_fun(_1793429, tc_HOL_Obool)), c_Fun_Obij__betw(_1793423, _1793429, _1793435, _1793425, _1793431), c_Fun_Obij__betw(_1793423, _1793429, _1793435, _1793427, _1793433), -(c_Fun_Obij__betw(_1793423, _1793429, _1793435, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793423, tc_HOL_Obool)), _1793425), _1793427), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793429, tc_HOL_Obool)), _1793431), _1793433)))], (49988 ^ _779308) ^ [_1794186, _1794188, _1794190, _1794192, _1794194, _1794196, _1794198] : [c_Fun_Obij__betw(_1794186, _1794188, _1794190, _1794192, _1794194), c_Fun_Obij__betw(_1794186, _1794188, _1794190, _1794196, _1794198), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1794188, tc_HOL_Obool)), _1794194), _1794198) = c_Orderings_Obot__class_Obot(tc_fun(_1794188, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1794186, _1794188, _1794190, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1794186, tc_HOL_Obool)), _1794192), _1794196), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1794188, tc_HOL_Obool)), _1794194), _1794198)))], (50002 ^ _779308) ^ [_1794709] : [-(c_Fun_Obij__betw(_1794709, _1794709, c_Fun_Oid(_1794709), c_Orderings_Otop__class_Otop(tc_fun(_1794709, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794709, tc_HOL_Obool))))], (50004 ^ _779308) ^ [_1794874, _1794876, _1794878] : [c_Fun_Obij__betw(_1794874, _1794874, c_Fun_Oid(_1794874), _1794876, _1794878), -(_1794876 = _1794878)], (50010 ^ _779308) ^ [_1795052, _1795054, _1795056] : [_1795054 = _1795056, -(c_Fun_Obij__betw(_1795052, _1795052, c_Fun_Oid(_1795052), _1795054, _1795056))], (50016 ^ _779308) ^ [_1795322, _1795324, _1795326, _1795328, _1795330] : [c_Fun_Obij__betw(_1795322, _1795324, _1795326, _1795328, _1795330), 50019 ^ _779308 : [(50020 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795322), _1795328)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1795324), _1795330)))], (50026 ^ _779308) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795324), _1795330)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1795322), _1795328)))]]], (50032 ^ _779308) ^ [_1795888, _1795890, _1795892, _1795894] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795888), _1795890)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1795892), _1795894)), 50039 ^ _779308 : [(50040 ^ _779308) ^ [] : [50041 ^ _779308 : [(50042 ^ _779308) ^ [_1796206] : [c_Fun_Obij__betw(_1795888, _1795892, _1796206, _1795890, _1795894)]], -(hAPP(c_Finite__Set_Ocard(_1795888), _1795890) = hAPP(c_Finite__Set_Ocard(_1795892), _1795894))], (50046 ^ _779308) ^ [] : [hAPP(c_Finite__Set_Ocard(_1795888), _1795890) = hAPP(c_Finite__Set_Ocard(_1795892), _1795894), -(c_Fun_Obij__betw(_1795888, _1795892, 50049 ^ [_1795888, _1795890, _1795892, _1795894], _1795890, _1795894))]]], (50053 ^ _779308) ^ [_1796649, _1796651, _1796653, _1796655] : [c_Fun_Obij__betw(_1796649, _1796651, _1796653, _1796655, c_Orderings_Obot__class_Obot(tc_fun(_1796651, tc_HOL_Obool))), -(_1796655 = c_Orderings_Obot__class_Obot(tc_fun(_1796649, tc_HOL_Obool)))], (50059 ^ _779308) ^ [_1796925, _1796927, _1796929, _1796931] : [c_Fun_Obij__betw(_1796925, _1796927, _1796929, c_Orderings_Obot__class_Obot(tc_fun(_1796925, tc_HOL_Obool)), _1796931), -(_1796931 = c_Orderings_Obot__class_Obot(tc_fun(_1796927, tc_HOL_Obool)))], (50065 ^ _779308) ^ [_1797215, _1797217, _1797219, _1797221, _1797223] : [c_Fun_Obij__betw(_1797215, _1797217, _1797219, _1797221, _1797223), -(hAPP(c_Finite__Set_Ocard(_1797215), _1797221) = hAPP(c_Finite__Set_Ocard(_1797217), _1797223))], (50071 ^ _779308) ^ [_1797511, _1797513, _1797515, _1797517, _1797519] : [c_Fun_Obij__betw(_1797511, _1797513, _1797515, _1797517, _1797519), -(c_Fun_Obij__betw(_1797513, _1797511, c_Fun_Othe__inv__into(_1797511, _1797513, _1797517, _1797515), _1797519, _1797517))], (50077 ^ _779308) ^ [_1797775, _1797777, _1797779] : [c_Fun_Obij__betw(_1797775, _1797777, _1797779, c_Orderings_Otop__class_Otop(tc_fun(_1797775, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1797777, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1797775, _1797777, _1797779, c_Orderings_Otop__class_Otop(tc_fun(_1797775, tc_HOL_Obool))))], (50083 ^ _779308) ^ [_1798073, _1798075, _1798077, _1798079, _1798081] : [c_Fun_Obij__betw(_1798073, _1798075, _1798077, _1798079, _1798081), -(c_Fun_Oinj__on(_1798073, _1798075, _1798077, _1798079))], (50089 ^ _779308) ^ [_1798382, _1798384, _1798386, _1798388, _1798390] : [c_Fun_Obij__betw(_1798382, _1798384, _1798386, _1798388, _1798390), 50092 ^ _779308 : [(50093 ^ _779308) ^ [] : [-(c_Fun_Oinj__on(_1798382, _1798384, _1798386, _1798388))], (50095 ^ _779308) ^ [] : [-(hAPP(c_Set_Oimage(_1798382, _1798384, _1798386), _1798388) = _1798390)]]], (50097 ^ _779308) ^ [_1798667, _1798669, _1798671, _1798673, _1798675] : [-(c_Fun_Obij__betw(_1798667, _1798669, _1798671, _1798673, _1798675)), c_Fun_Oinj__on(_1798667, _1798669, _1798671, _1798673), hAPP(c_Set_Oimage(_1798667, _1798669, _1798671), _1798673) = _1798675], (50107 ^ _779308) ^ [_1799050, _1799052, _1799054, _1799056] : [c_Fun_Oinj__on(_1799050, _1799052, _1799054, _1799056), -(c_Fun_Obij__betw(_1799050, _1799052, _1799054, _1799056, hAPP(c_Set_Oimage(_1799050, _1799052, _1799054), _1799056)))], (50113 ^ _779308) ^ [_1799310, _1799312, _1799314] : [c_Fun_Obij__betw(_1799310, _1799312, _1799314, c_Orderings_Otop__class_Otop(tc_fun(_1799310, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799312, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1799310, _1799312, _1799314), c_Orderings_Otop__class_Otop(tc_fun(_1799310, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1799312, tc_HOL_Obool)))], (50119 ^ _779308) ^ [_1799614, _1799616, _1799618, _1799620] : [c_Fun_Obij__betw(_1799614, _1799616, _1799618, _1799620, c_Orderings_Otop__class_Otop(tc_fun(_1799616, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1799614, _1799616, _1799618), c_Orderings_Otop__class_Otop(tc_fun(_1799614, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1799616, tc_HOL_Obool)))], (50125 ^ _779308) ^ [_1799956, _1799958, _1799960, _1799962, _1799964, _1799966, _1799968] : [c_Fun_Obij__betw(_1799956, _1799958, _1799960, _1799962, _1799964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1799956, tc_HOL_Obool)), _1799966), _1799962)), hAPP(c_Set_Oimage(_1799956, _1799958, _1799960), _1799966) = _1799968, -(c_Fun_Obij__betw(_1799956, _1799958, _1799960, _1799966, _1799968))], (50139 ^ _779308) ^ [_1800503, _1800505, _1800507] : [c_Fun_Obij__betw(_1800503, _1800505, _1800507, c_Orderings_Otop__class_Otop(tc_fun(_1800503, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1800505, tc_HOL_Obool))), 50142 ^ _779308 : [(50143 ^ _779308) ^ [] : [-(c_Fun_Oinj__on(_1800503, _1800505, _1800507, c_Orderings_Otop__class_Otop(tc_fun(_1800503, tc_HOL_Obool))))], (50145 ^ _779308) ^ [] : [-(hAPP(c_Set_Oimage(_1800503, _1800505, _1800507), c_Orderings_Otop__class_Otop(tc_fun(_1800503, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1800505, tc_HOL_Obool)))]]], (50147 ^ _779308) ^ [_1800822, _1800824, _1800826] : [-(c_Fun_Obij__betw(_1800822, _1800824, _1800826, c_Orderings_Otop__class_Otop(tc_fun(_1800822, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1800824, tc_HOL_Obool)))), c_Fun_Oinj__on(_1800822, _1800824, _1800826, c_Orderings_Otop__class_Otop(tc_fun(_1800822, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1800822, _1800824, _1800826), c_Orderings_Otop__class_Otop(tc_fun(_1800822, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1800824, tc_HOL_Obool))], (50157 ^ _779308) ^ [_1801221, _1801223, _1801225] : [c_Fun_Oinj__on(_1801221, _1801223, _1801225, c_Orderings_Otop__class_Otop(tc_fun(_1801221, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1801221, _1801223, _1801225), c_Orderings_Otop__class_Otop(tc_fun(_1801221, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1801223, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1801221, _1801223, _1801225, c_Orderings_Otop__class_Otop(tc_fun(_1801221, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1801223, tc_HOL_Obool))))], (50167 ^ _779308) ^ [_1801617, _1801619, _1801621, _1801623] : [-(c_Product__Type_Ocurry(_1801617, _1801619, _1801621, hAPP(c_Product__Type_Oprod_Oprod__case(_1801617, _1801619, _1801621), _1801623)) = _1801623)], (50169 ^ _779308) ^ [_1801755, _1801757, _1801759, _1801761] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1801755, _1801757, _1801759), c_Product__Type_Ocurry(_1801755, _1801757, _1801759, _1801761)) = _1801761)], (50171 ^ _779308) ^ [_1801936, _1801938, _1801940, _1801942, _1801944, _1801946] : [c_Fun_Obij__betw(_1801936, _1801938, _1801940, c_Orderings_Otop__class_Otop(tc_fun(_1801936, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1801938, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1801936, _1801938, _1801940), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1801942, tc_fun(_1801936, tc_HOL_Obool)), _1801944), _1801946)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1801942, tc_fun(_1801938, tc_HOL_Obool)), _1801944), hAPP(hAPP(c_COMBB(tc_fun(_1801936, tc_HOL_Obool), tc_fun(_1801938, tc_HOL_Obool), _1801942), c_Set_Oimage(_1801936, _1801938, _1801940)), _1801946)))], (50177 ^ _779308) ^ [_1802340, _1802342, _1802344, _1802346, _1802348] : [c_Fun_Obij__betw(_1802340, _1802342, _1802344, c_Orderings_Otop__class_Otop(tc_fun(_1802340, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1802342, tc_HOL_Obool))), 50180 ^ _779308 : [(50181 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802340, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1802340, _1802342, _1802344), _1802346)), _1802348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802342, tc_HOL_Obool)), _1802346), hAPP(c_Set_Oimage(_1802340, _1802342, _1802344), _1802348))))], (50187 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802342, tc_HOL_Obool)), _1802346), hAPP(c_Set_Oimage(_1802340, _1802342, _1802344), _1802348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1802340, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1802340, _1802342, _1802344), _1802346)), _1802348)))]]], (50193 ^ _779308) ^ [_1803004, _1803006, _1803008, _1803010] : [c_Fun_Obij__betw(_1803004, _1803006, _1803008, c_Orderings_Otop__class_Otop(tc_fun(_1803004, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1803006, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1803004, _1803006, _1803008), _1803010) = hAPP(c_Set_Oimage(_1803006, _1803004, c_Hilbert__Choice_Oinv__into(_1803004, _1803006, c_Orderings_Otop__class_Otop(tc_fun(_1803004, tc_HOL_Obool)), _1803008)), _1803010))], (50199 ^ _779308) ^ [_1803300, _1803302] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1803300), _1803302)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1803300, 50202 ^ [_1803300, _1803302], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1803300), _1803302)), _1803302))], (50206 ^ _779308) ^ [_1803667, _1803669, _1803671, _1803673, _1803675, _1803677] : [c_Fun_Oinj__on(_1803667, _1803669, _1803671, _1803673), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1803669, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1803667, _1803669, _1803671), _1803673)), _1803675)), c_Fun_Oinj__on(_1803669, _1803667, _1803677, _1803675), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1803667, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1803669, _1803667, _1803677), _1803675)), _1803673)), -(c_Fun_Obij__betw(_1803667, _1803669, 50221 ^ [_1803667, _1803669, _1803671, _1803673, _1803675, _1803677], _1803673, _1803675))], (50225 ^ _779308) ^ [_1804382, _1804384] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1804382), _1804384)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1804382, 50228 ^ [_1804382, _1804384], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1804382), _1804384)), _1804384))], (50232 ^ _779308) ^ [_1804690, _1804692] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1804690), _1804692)), -(c_Fun_Obij__betw(_1804690, tc_Nat_Onat, 50235 ^ [_1804690, _1804692], _1804692, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1804690), _1804692))))], (50239 ^ _779308) ^ [_1805040, _1805042, _1805044, _1805046, _1805048] : [50241 ^ _779308 : [(50242 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805040), 50240 ^ [_1805040, _1805042, _1805044, _1805046, _1805048]), _1805042)))], (50244 ^ _779308) ^ [] : [c_Relation_Orefl__on(_1805044, hAPP(_1805046, 50240 ^ [_1805040, _1805042, _1805044, _1805046, _1805048]), hAPP(_1805048, 50240 ^ [_1805040, _1805042, _1805044, _1805046, _1805048]))]], -(c_Relation_Orefl__on(_1805044, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1805040, tc_fun(_1805044, tc_HOL_Obool)), _1805042), _1805046), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1805040, tc_fun(tc_prod(_1805044, _1805044), tc_HOL_Obool)), _1805042), _1805048)))], (50248 ^ _779308) ^ [_1805568, _1805570, _1805572] : [c_Equiv__Relations_Oequivp(_1805568, _1805570), 50251 ^ _779308 : [(50263 ^ _779308) ^ [] : [50264 ^ _779308 : [(50265 ^ _779308) ^ [_1806151] : [hBOOL(hAPP(_1805572, _1806151))]], 50267 ^ _779308 : [(50268 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805568), 50266 ^ [_1805568, _1805570, _1805572]), c_Quotient_ORespects(_1805568, _1805570))))], (50270 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1805572, 50266 ^ [_1805568, _1805570, _1805572])))]]], (50252 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1805572, 50259 ^ [_1805568, _1805570, _1805572]))), 50253 ^ _779308 : [(50254 ^ _779308) ^ [_1805799] : [hBOOL(hAPP(hAPP(c_member(_1805568), _1805799), c_Quotient_ORespects(_1805568, _1805570))), hBOOL(hAPP(_1805572, _1805799))]]]]], (50272 ^ _779308) ^ [_1806537, _1806539, _1806541] : [hBOOL(hAPP(c_Quotient_ORespects(_1806537, _1806539), _1806541)), -(hBOOL(hAPP(hAPP(_1806539, _1806541), _1806541)))], (50278 ^ _779308) ^ [_1806725, _1806727, _1806729] : [hBOOL(hAPP(hAPP(_1806727, _1806729), _1806729)), -(hBOOL(hAPP(c_Quotient_ORespects(_1806725, _1806727), _1806729)))], (50284 ^ _779308) ^ [_1807006, _1807008, _1807010] : [hBOOL(hAPP(hAPP(c_member(_1807006), _1807008), c_Quotient_ORespects(_1807006, _1807010))), -(hBOOL(hAPP(hAPP(_1807010, _1807008), _1807008)))], (50290 ^ _779308) ^ [_1807204, _1807206, _1807208] : [hBOOL(hAPP(hAPP(_1807208, _1807206), _1807206)), -(hBOOL(hAPP(hAPP(c_member(_1807204), _1807206), c_Quotient_ORespects(_1807204, _1807208))))], (50296 ^ _779308) ^ [_1807480, _1807482, _1807484, _1807486] : [c_Equiv__Relations_Oequivp(_1807480, _1807482), 50302 ^ _779308 : [(50303 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1807484, 50301 ^ [_1807480, _1807482, _1807484, _1807486])))], (50305 ^ _779308) ^ [] : [hBOOL(hAPP(_1807486, 50301 ^ [_1807480, _1807482, _1807484, _1807486]))]], 50308 ^ _779308 : [(50309 ^ _779308) ^ [_1807941] : [hBOOL(hAPP(_1807484, _1807941))]], 50311 ^ _779308 : [(50312 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1807480), 50310 ^ [_1807480, _1807482, _1807484, _1807486]), c_Quotient_ORespects(_1807480, _1807482))))], (50314 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1807486, 50310 ^ [_1807480, _1807482, _1807484, _1807486])))]]], (50316 ^ _779308) ^ [_1808328, _1808330, _1808332, _1808334] : [c_Equiv__Relations_Oequivp(_1808328, _1808330), -(c_Quotient_OBabs(_1808328, _1808332, c_Quotient_ORespects(_1808328, _1808330), _1808334) = _1808334)], (50322 ^ _779308) ^ [_1808608, _1808610, _1808612, _1808614, _1808616] : [hBOOL(hAPP(hAPP(c_member(_1808608), _1808610), _1808612)), -(hAPP(c_Quotient_OBabs(_1808608, _1808614, _1808612, _1808616), _1808610) = hAPP(_1808616, _1808610))], (50328 ^ _779308) ^ [_1808886, _1808888, _1808890] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1808886, _1808886)), hAPP(hAPP(c_Product__Type_OPair(_1808886, _1808886), hAPP(_1808888, hAPP(c_Nat_OSuc, 50329 ^ [_1808886, _1808888, _1808890]))), hAPP(_1808888, 50329 ^ [_1808886, _1808888, _1808890]))), c_Transitive__Closure_Ortrancl(_1808886, _1808890))), c_Wellfounded_Owf(_1808886, c_Transitive__Closure_Otrancl(_1808886, _1808890)), 50337 ^ _779308 : [(50338 ^ _779308) ^ [_1809349] : [-(hAPP(_1808888, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50336 ^ [_1808886, _1808888, _1808890]), _1809349)) = hAPP(_1808888, 50336 ^ [_1808886, _1808888, _1808890]))]]], (50340 ^ _779308) ^ [_1809557, _1809559, _1809561, _1809563, _1809565, _1809567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1809557, tc_HOL_Obool)), _1809559), _1809561)), 50346 ^ _779308 : [(50347 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1809557), 50345 ^ [_1809557, _1809559, _1809561, _1809563, _1809565, _1809567]), _1809561)))], (50349 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1809563, tc_HOL_Obool)), hAPP(_1809565, 50345 ^ [_1809557, _1809559, _1809561, _1809563, _1809565, _1809567])), hAPP(_1809567, 50345 ^ [_1809557, _1809559, _1809561, _1809563, _1809565, _1809567])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1809563, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1809557, tc_fun(_1809563, tc_HOL_Obool)), _1809561), _1809565)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1809557, tc_fun(_1809563, tc_HOL_Obool)), _1809561), _1809567))))], (50353 ^ _779308) ^ [_1810295, _1810297, _1810299, _1810301, _1810303] : [50355 ^ _779308 : [(50356 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1810295), 50354 ^ [_1810295, _1810297, _1810299, _1810301, _1810303]), _1810297)))], (50358 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1810299, tc_HOL_Obool)), _1810301), hAPP(_1810303, 50354 ^ [_1810295, _1810297, _1810299, _1810301, _1810303])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1810299, tc_HOL_Obool)), _1810301), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1810295, tc_fun(_1810299, tc_HOL_Obool)), _1810297), _1810303))))], (50362 ^ _779308) ^ [_1810886, _1810888, _1810890, _1810892, _1810894, _1810896, _1810898, _1810900] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1810886, _1810888), tc_prod(_1810886, _1810888))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1810886, _1810888), tc_prod(_1810886, _1810888)), hAPP(hAPP(c_Product__Type_OPair(_1810886, _1810888), _1810890), _1810892)), hAPP(hAPP(c_Product__Type_OPair(_1810886, _1810888), _1810894), _1810896))), c_Transitive__Closure_Ortrancl(tc_prod(_1810886, _1810888), _1810898))), hBOOL(hAPP(hAPP(_1810900, _1810890), _1810892)), 50373 ^ _779308 : [(50374 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1810886, _1810888), tc_prod(_1810886, _1810888))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1810886, _1810888), tc_prod(_1810886, _1810888)), hAPP(hAPP(c_Product__Type_OPair(_1810886, _1810888), _1810890), _1810892)), hAPP(hAPP(c_Product__Type_OPair(_1810886, _1810888), 50371 ^ [_1810886, _1810888, _1810890, _1810892, _1810894, _1810896, _1810898, _1810900]), 50372 ^ [_1810886, _1810888, _1810890, _1810892, _1810894, _1810896, _1810898, _1810900]))), c_Transitive__Closure_Ortrancl(tc_prod(_1810886, _1810888), _1810898))))], (50378 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1810886, _1810888), tc_prod(_1810886, _1810888))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1810886, _1810888), tc_prod(_1810886, _1810888)), hAPP(hAPP(c_Product__Type_OPair(_1810886, _1810888), 50371 ^ [_1810886, _1810888, _1810890, _1810892, _1810894, _1810896, _1810898, _1810900]), 50372 ^ [_1810886, _1810888, _1810890, _1810892, _1810894, _1810896, _1810898, _1810900])), hAPP(hAPP(c_Product__Type_OPair(_1810886, _1810888), 50375 ^ [_1810886, _1810888, _1810890, _1810892, _1810894, _1810896, _1810898, _1810900]), 50376 ^ [_1810886, _1810888, _1810890, _1810892, _1810894, _1810896, _1810898, _1810900]))), _1810898)))], (50380 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1810900, 50371 ^ [_1810886, _1810888, _1810890, _1810892, _1810894, _1810896, _1810898, _1810900]), 50372 ^ [_1810886, _1810888, _1810890, _1810892, _1810894, _1810896, _1810898, _1810900])))], (50382 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1810900, 50375 ^ [_1810886, _1810888, _1810890, _1810892, _1810894, _1810896, _1810898, _1810900]), 50376 ^ [_1810886, _1810888, _1810890, _1810892, _1810894, _1810896, _1810898, _1810900]))]], -(hBOOL(hAPP(hAPP(_1810900, _1810894), _1810896)))], (50386 ^ _779308) ^ [_1813214, _1813216, _1813218, _1813220, _1813222, _1813224, _1813226] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1813214, _1813216), tc_prod(_1813214, _1813216))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1813214, _1813216), tc_prod(_1813214, _1813216)), hAPP(hAPP(c_Product__Type_OPair(_1813214, _1813216), _1813218), _1813220)), hAPP(hAPP(c_Product__Type_OPair(_1813214, _1813216), _1813222), _1813224))), c_Transitive__Closure_Ortrancl(tc_prod(_1813214, _1813216), _1813226))), -(hAPP(hAPP(c_Product__Type_OPair(_1813214, _1813216), _1813218), _1813220) = hAPP(hAPP(c_Product__Type_OPair(_1813214, _1813216), _1813222), _1813224)), 50395 ^ _779308 : [(50396 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1813214, _1813216), tc_prod(_1813214, _1813216))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1813214, _1813216), tc_prod(_1813214, _1813216)), hAPP(hAPP(c_Product__Type_OPair(_1813214, _1813216), _1813218), _1813220)), hAPP(hAPP(c_Product__Type_OPair(_1813214, _1813216), 50393 ^ [_1813214, _1813216, _1813218, _1813220, _1813222, _1813224, _1813226]), 50394 ^ [_1813214, _1813216, _1813218, _1813220, _1813222, _1813224, _1813226]))), _1813226)))], (50398 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1813214, _1813216), tc_prod(_1813214, _1813216))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1813214, _1813216), tc_prod(_1813214, _1813216)), hAPP(hAPP(c_Product__Type_OPair(_1813214, _1813216), 50393 ^ [_1813214, _1813216, _1813218, _1813220, _1813222, _1813224, _1813226]), 50394 ^ [_1813214, _1813216, _1813218, _1813220, _1813222, _1813224, _1813226])), hAPP(hAPP(c_Product__Type_OPair(_1813214, _1813216), _1813222), _1813224))), c_Transitive__Closure_Ortrancl(tc_prod(_1813214, _1813216), _1813226))))]]], (50400 ^ _779308) ^ [_1814564, _1814566, _1814568, _1814570, _1814572, _1814574, _1814576, _1814578] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1814564, _1814566), tc_prod(_1814564, _1814566))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1814564, _1814566), tc_prod(_1814564, _1814566)), hAPP(hAPP(c_Product__Type_OPair(_1814564, _1814566), _1814568), _1814570)), hAPP(hAPP(c_Product__Type_OPair(_1814564, _1814566), _1814572), _1814574))), c_Transitive__Closure_Ortrancl(tc_prod(_1814564, _1814566), _1814576))), hBOOL(hAPP(hAPP(_1814578, _1814572), _1814574)), 50413 ^ _779308 : [(50414 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1814564, _1814566), tc_prod(_1814564, _1814566))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1814564, _1814566), tc_prod(_1814564, _1814566)), hAPP(hAPP(c_Product__Type_OPair(_1814564, _1814566), 50409 ^ [_1814564, _1814566, _1814568, _1814570, _1814572, _1814574, _1814576, _1814578]), 50410 ^ [_1814564, _1814566, _1814568, _1814570, _1814572, _1814574, _1814576, _1814578])), hAPP(hAPP(c_Product__Type_OPair(_1814564, _1814566), 50411 ^ [_1814564, _1814566, _1814568, _1814570, _1814572, _1814574, _1814576, _1814578]), 50412 ^ [_1814564, _1814566, _1814568, _1814570, _1814572, _1814574, _1814576, _1814578]))), _1814576)))], (50416 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1814564, _1814566), tc_prod(_1814564, _1814566))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1814564, _1814566), tc_prod(_1814564, _1814566)), hAPP(hAPP(c_Product__Type_OPair(_1814564, _1814566), 50411 ^ [_1814564, _1814566, _1814568, _1814570, _1814572, _1814574, _1814576, _1814578]), 50412 ^ [_1814564, _1814566, _1814568, _1814570, _1814572, _1814574, _1814576, _1814578])), hAPP(hAPP(c_Product__Type_OPair(_1814564, _1814566), _1814572), _1814574))), c_Transitive__Closure_Ortrancl(tc_prod(_1814564, _1814566), _1814576))))], (50418 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(_1814578, 50411 ^ [_1814564, _1814566, _1814568, _1814570, _1814572, _1814574, _1814576, _1814578]), 50412 ^ [_1814564, _1814566, _1814568, _1814570, _1814572, _1814574, _1814576, _1814578])))], (50420 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(_1814578, 50409 ^ [_1814564, _1814566, _1814568, _1814570, _1814572, _1814574, _1814576, _1814578]), 50410 ^ [_1814564, _1814566, _1814568, _1814570, _1814572, _1814574, _1814576, _1814578]))]], -(hBOOL(hAPP(hAPP(_1814578, _1814568), _1814570)))], (50424 ^ _779308) ^ [_1817000, _1817002, _1817004, _1817006, _1817008, _1817010] : [50427 ^ _779308 : [(50428 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1817000, _1817000)), hAPP(hAPP(c_Product__Type_OPair(_1817000, _1817000), 50425 ^ [_1817000, _1817002, _1817004, _1817006, _1817008, _1817010]), 50426 ^ [_1817000, _1817002, _1817004, _1817006, _1817008, _1817010])), _1817002)))], (50432 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1817004, _1817004)), hAPP(hAPP(c_Product__Type_OPair(_1817004, _1817004), 50429 ^ [_1817000, _1817002, _1817004, _1817006, _1817008, _1817010]), 50430 ^ [_1817000, _1817002, _1817004, _1817006, _1817008, _1817010])), _1817006)))], (50434 ^ _779308) ^ [] : [hAPP(hAPP(_1817008, 50425 ^ [_1817000, _1817002, _1817004, _1817006, _1817008, _1817010]), 50429 ^ [_1817000, _1817002, _1817004, _1817006, _1817008, _1817010]) = hAPP(hAPP(_1817008, 50426 ^ [_1817000, _1817002, _1817004, _1817006, _1817008, _1817010]), 50430 ^ [_1817000, _1817002, _1817004, _1817006, _1817008, _1817010])]], -(c_Equiv__Relations_Ocongruent2(_1817000, _1817004, _1817010, _1817002, _1817006, _1817008))], (50438 ^ _779308) ^ [_1818267, _1818269, _1818271, _1818273] : [50441 ^ _779308 : [(50442 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1818267, _1818267)), hAPP(hAPP(c_Product__Type_OPair(_1818267, _1818267), 50439 ^ [_1818267, _1818269, _1818271, _1818273]), 50440 ^ [_1818267, _1818269, _1818271, _1818273])), _1818269)))], (50444 ^ _779308) ^ [] : [hAPP(_1818271, 50439 ^ [_1818267, _1818269, _1818271, _1818273]) = hAPP(_1818271, 50440 ^ [_1818267, _1818269, _1818271, _1818273])]], -(c_Equiv__Relations_Ocongruent(_1818267, _1818273, _1818269, _1818271))], (50448 ^ _779308) ^ [_1818870, _1818872, _1818874] : [-(c_Lazy__Sequence_Oflat(_1818870, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1818870), _1818872, _1818874)) = c_Lazy__Sequence_Oappend(_1818870, _1818872, c_Lazy__Sequence_Oflat(_1818870, _1818874)))], (50450 ^ _779308) ^ [_1819040, _1819042, _1819044] : [c_List_Olist__all(tc_Nat_Onat, _1819040, c_List_Oupt(_1819042, _1819044)), -(c_List_Oall__interval__nat(_1819040, _1819042, _1819044))], (50456 ^ _779308) ^ [_1819218, _1819220, _1819222] : [c_List_Oall__interval__nat(_1819218, _1819220, _1819222), -(c_List_Olist__all(tc_Nat_Onat, _1819218, c_List_Oupt(_1819220, _1819222)))], (50462 ^ _779308) ^ [_1819417] : [-(c_Lazy__Sequence_Oflat(_1819417, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1819417))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1819417))], (50474 ^ _779308) ^ [_1819943, _1819945, _1819947] : [50476 ^ _779308 : [(50477 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50475 ^ [_1819943, _1819945, _1819947]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1819945), _1819947))))], (50479 ^ _779308) ^ [] : [hBOOL(hAPP(_1819943, 50475 ^ [_1819943, _1819945, _1819947]))]], -(c_List_Oall__interval__nat(_1819943, _1819945, _1819947))], (50464 ^ _779308) ^ [_1819576, _1819578, _1819580] : [c_List_Oall__interval__nat(_1819576, _1819578, _1819580), 50467 ^ _779308 : [(50468 ^ _779308) ^ [_1819732] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1819732), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1819578), _1819580))), -(hBOOL(hAPP(_1819576, _1819732)))]]], (50483 ^ _779308) ^ [_1820400, _1820402, _1820404] : [c_List_Olist__ex(tc_Nat_Onat, _1820400, c_List_Oupt(_1820402, _1820404)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1820400), _1820402, _1820404)], (50489 ^ _779308) ^ [_1820585, _1820587, _1820589] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1820585), _1820587, _1820589)), -(c_List_Olist__ex(tc_Nat_Onat, _1820585, c_List_Oupt(_1820587, _1820589)))], (50495 ^ _779308) ^ [_1820835, _1820837, _1820839, _1820841] : [-(hAPP(c_Lazy__Sequence_Obind(_1820835, _1820837, _1820839), _1820841) = c_Lazy__Sequence_Oflat(_1820837, c_Lazy__Sequence_Omap(_1820835, tc_Lazy__Sequence_Olazy__sequence(_1820837), _1820841, _1820839)))], (50497 ^ _779308) ^ [_1821049, _1821051, _1821053, _1821055, _1821057, _1821059, _1821061, _1821063] : [c_Finite__Set_Ofolding__image(_1821049, _1821051, _1821053, _1821055, _1821057), hBOOL(hAPP(c_Finite__Set_Ofinite(_1821051), _1821059)), 50507 ^ _779308 : [(50508 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1821051), 50506 ^ [_1821049, _1821051, _1821053, _1821055, _1821057, _1821059, _1821061, _1821063]), _1821059)))], (50510 ^ _779308) ^ [] : [hAPP(_1821061, 50506 ^ [_1821049, _1821051, _1821053, _1821055, _1821057, _1821059, _1821061, _1821063]) = hAPP(_1821063, 50506 ^ [_1821049, _1821051, _1821053, _1821055, _1821057, _1821059, _1821061, _1821063])]], -(hAPP(hAPP(_1821057, _1821061), _1821059) = hAPP(hAPP(_1821057, _1821063), _1821059))], (50514 ^ _779308) ^ [_1821849, _1821851, _1821853, _1821855, _1821857] : [-(c_Lazy__Sequence_Omap(_1821849, _1821851, _1821853, c_Lazy__Sequence_Olazy__sequence_OInsert(_1821849, _1821855, _1821857)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1821851, hAPP(_1821853, _1821855), c_Lazy__Sequence_Omap(_1821849, _1821851, _1821853, _1821857)))], (50516 ^ _779308) ^ [_1821984, _1821986, _1821988] : [-(c_Lazy__Sequence_Omap(_1821984, _1821986, _1821988, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1821984)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1821986))], (50518 ^ _779308) ^ [_1822131, _1822133, _1822135, _1822137, _1822139] : [-(c_New__DSequence_Opos__map(_1822131, _1822133, _1822135, _1822137, _1822139) = c_Lazy__Sequence_Omap(_1822131, _1822133, _1822135, hAPP(_1822137, _1822139)))], (50520 ^ _779308) ^ [_1822274, _1822276, _1822278] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1822274), _1822276)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1822274), _1822278))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1822274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1822276), _1822278)))], (50530 ^ _779308) ^ [_1822602] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822602), _1822602)))], (50532 ^ _779308) ^ [_1822714, _1822716] : [class_Rings_Ocomm__semiring__1(_1822714), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1822714), _1822716), c_Groups_Ozero__class_Ozero(_1822714))))], (50538 ^ _779308) ^ [_1822911] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1822911)))], (50540 ^ _779308) ^ [_1823020, _1823022] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823020), _1823022)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1823022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1823020), _1823022)))], (50550 ^ _779308) ^ [_1823357, _1823359, _1823361] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823357), _1823359)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823357), _1823361))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1823357)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823359), _1823361)))], (50560 ^ _779308) ^ [_1823728, _1823730, _1823732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1823728)), 50563 ^ _779308 : [(50564 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823728), _1823730)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823728), _1823732))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823730), _1823732)))], (50570 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823730), _1823732)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823728), _1823730)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1823728), _1823732))))]]], (50576 ^ _779308) ^ [_1824316, _1824318, _1824320, _1824322, _1824324] : [class_Groups_Ocomm__monoid__mult(_1824316), class_Rings_Odvd(_1824316), hBOOL(hAPP(c_Finite__Set_Ofinite(_1824318), _1824320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1824318, tc_HOL_Obool)), _1824322), _1824320)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824316), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1824318, _1824316), _1824324), _1824322)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1824318, _1824316), _1824324), _1824320))))], (50594 ^ _779308) ^ [_1824937, _1824939, _1824941] : [class_Divides_Osemiring__div(_1824937), class_Int_Onumber(_1824937), 50601 ^ _779308 : [(50602 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824937), hAPP(c_Int_Onumber__class_Onumber__of(_1824937), _1824939)), hAPP(c_Int_Onumber__class_Onumber__of(_1824937), _1824941))), -(c_Divides_Odiv__class_Omod(_1824937, hAPP(c_Int_Onumber__class_Onumber__of(_1824937), _1824941), hAPP(c_Int_Onumber__class_Onumber__of(_1824937), _1824939)) = c_Groups_Ozero__class_Ozero(_1824937))], (50608 ^ _779308) ^ [] : [c_Divides_Odiv__class_Omod(_1824937, hAPP(c_Int_Onumber__class_Onumber__of(_1824937), _1824941), hAPP(c_Int_Onumber__class_Onumber__of(_1824937), _1824939)) = c_Groups_Ozero__class_Ozero(_1824937), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824937), hAPP(c_Int_Onumber__class_Onumber__of(_1824937), _1824939)), hAPP(c_Int_Onumber__class_Onumber__of(_1824937), _1824941))))]]], (50614 ^ _779308) ^ [_1825645, _1825647, _1825649, _1825651, _1825653] : [class_Divides_Osemiring__div(_1825645), -(_1825647 = c_Groups_Ozero__class_Ozero(_1825645)), -(_1825649 = c_Groups_Ozero__class_Ozero(_1825645)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825645), _1825647), _1825651)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825645), _1825649), _1825653)), 50633 ^ _779308 : [(50634 ^ _779308) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825645), _1825651), _1825647) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825645), _1825653), _1825649), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825645), _1825651), _1825649) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825645), _1825647), _1825653))], (50640 ^ _779308) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825645), _1825651), _1825649) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1825645), _1825647), _1825653), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825645), _1825651), _1825647) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1825645), _1825653), _1825649))]]], (50646 ^ _779308) ^ [_1826721, _1826723, _1826725, _1826727] : [class_Divides_Osemiring__div(_1826721), -(_1826723 = c_Groups_Ozero__class_Ozero(_1826721)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826721), _1826723), _1826725)), 50657 ^ _779308 : [(50658 ^ _779308) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826721), _1826725), _1826723) = _1826727, -(_1826725 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826721), _1826727), _1826723))], (50664 ^ _779308) ^ [] : [_1826725 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1826721), _1826727), _1826723), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1826721), _1826725), _1826723) = _1826727)]]], (50670 ^ _779308) ^ [_1827488, _1827490, _1827492] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827488), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1827490), _1827492))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827488), _1827492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1827492), _1827490)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827488), _1827490)))], (50684 ^ _779308) ^ [_1827956, _1827958, _1827960] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827956), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1827958), _1827960))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827956), _1827958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1827960), _1827958)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827956), _1827960)))], (50698 ^ _779308) ^ [_1828438, _1828440, _1828442, _1828444] : [class_Rings_Ocomm__semiring__1(_1828438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1828440), _1828442)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828438), hAPP(hAPP(c_Power_Opower__class_Opower(_1828438), _1828444), _1828440)), hAPP(hAPP(c_Power_Opower__class_Opower(_1828438), _1828444), _1828442))))], (50708 ^ _779308) ^ [_1828853, _1828855, _1828857, _1828859, _1828861] : [class_Rings_Ocomm__semiring__1(_1828853), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828853), _1828855), _1828857)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1828859), _1828861)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828853), hAPP(hAPP(c_Power_Opower__class_Opower(_1828853), _1828855), _1828859)), hAPP(hAPP(c_Power_Opower__class_Opower(_1828853), _1828857), _1828861))))], (50722 ^ _779308) ^ [_1829393, _1829395, _1829397, _1829399, _1829401] : [class_Rings_Ocomm__semiring__1(_1829393), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829393), hAPP(hAPP(c_Power_Opower__class_Opower(_1829393), _1829395), _1829397)), _1829399)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1829401), _1829397)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829393), hAPP(hAPP(c_Power_Opower__class_Opower(_1829393), _1829395), _1829401)), _1829399)))], (50736 ^ _779308) ^ [_1829948, _1829950, _1829952, _1829954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829948, _1829950)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829952, _1829954))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829948), _1829950)), 50743 ^ _779308 : [(50744 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829952), _1829948)))], (50746 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829950), _1829954)))]]], (50748 ^ _779308) ^ [_1830360, _1830362, _1830364, _1830366] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830360, _1830362)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830364, _1830366)))), 50749 ^ _779308 : [(50750 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830360), _1830362)))], (50752 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830364), _1830360)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830362), _1830366))]]], (50760 ^ _779308) ^ [_1830851, _1830853] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1830851), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830853))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830853), _1830851)))], (50766 ^ _779308) ^ [_1831041, _1831043] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831043), _1831041)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1831041), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831043))))], (50772 ^ _779308) ^ [_1831310, _1831312] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1831310), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831312))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831310), _1831312)))], (50778 ^ _779308) ^ [_1831500, _1831502] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831500), _1831502)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1831500), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831502))))], (50784 ^ _779308) ^ [_1831769, _1831771] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1831769), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1831771))), 50787 ^ _779308 : [(50788 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831769), _1831771)))], (50790 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1831771), _1831769))]]], (50792 ^ _779308) ^ [_1832045, _1832047] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1832045), c_SetInterval_Oord_OlessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1832047)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832045), _1832047)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832047), _1832045)))], (50802 ^ _779308) ^ [_1832416, _1832418] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1832416), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1832418))), 50805 ^ _779308 : [(50806 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832418), _1832416)))], (50808 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832416), _1832418))]]], (50810 ^ _779308) ^ [_1832692, _1832694] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1832692), c_SetInterval_Oord_OgreaterThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1832694)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832694), _1832692)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1832692), _1832694)))], (50820 ^ _779308) ^ [_1833062, _1833064, _1833066, _1833068] : [class_Divides_Osemiring__div(_1833062), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833062), _1833064), _1833066)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1833062), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1833062), _1833066), _1833064)), _1833068) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1833062), hAPP(hAPP(c_Power_Opower__class_Opower(_1833062), _1833066), _1833068)), hAPP(hAPP(c_Power_Opower__class_Opower(_1833062), _1833064), _1833068)))], (50830 ^ _779308) ^ [_1833487, _1833489, _1833491] : [class_Rings_Olinordered__idom(_1833487), 50833 ^ _779308 : [(50834 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833487), _1833489), hAPP(c_Groups_Oabs__class_Oabs(_1833487), _1833491))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833487), _1833489), _1833491)))], (50840 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833487), _1833489), _1833491)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833487), _1833489), hAPP(c_Groups_Oabs__class_Oabs(_1833487), _1833491))))]]], (50846 ^ _779308) ^ [_1834032, _1834034, _1834036] : [class_Rings_Olinordered__idom(_1834032), 50849 ^ _779308 : [(50850 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834032), hAPP(c_Groups_Oabs__class_Oabs(_1834032), _1834034)), _1834036)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834032), _1834034), _1834036)))], (50856 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834032), _1834034), _1834036)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834032), hAPP(c_Groups_Oabs__class_Oabs(_1834032), _1834034)), _1834036)))]]], (50862 ^ _779308) ^ [_1834577, _1834579, _1834581] : [class_Rings_Olinordered__idom(_1834577), hAPP(c_Groups_Oabs__class_Oabs(_1834577), _1834579) = hAPP(c_Groups_Oabs__class_Oabs(_1834577), _1834581), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834577), _1834579), _1834581)))], (50872 ^ _779308) ^ [_1834933] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1834933), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1834933 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (50878 ^ _779308) ^ [_1835099] : [_1835099 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835099), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (50884 ^ _779308) ^ [_1835315, _1835317] : [class_Rings_Ocomm__semiring__1(_1835315), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835315), c_Groups_Oone__class_Oone(_1835315)), _1835317)))], (50890 ^ _779308) ^ [_1835541, _1835543] : [class_Rings_Ocomm__semiring__1(_1835541), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835541), c_Groups_Ozero__class_Ozero(_1835541)), _1835543)), -(_1835543 = c_Groups_Ozero__class_Ozero(_1835541))], (50900 ^ _779308) ^ [_1835860, _1835862] : [class_Rings_Ocomm__semiring__1(_1835860), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835860), _1835862), _1835862)))], (50906 ^ _779308) ^ [_1836110, _1836112, _1836114, _1836116] : [class_Rings_Ocomm__semiring__1(_1836110), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1836110), _1836112), _1836114)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1836110), _1836114), _1836116)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1836110), _1836112), _1836116)))], (50920 ^ _779308) ^ [_1836595, _1836597] : [_1836595 = _1836597, 50923 ^ _779308 : [(50924 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836595), _1836597)))], (50926 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836597), _1836595)))]]], (50928 ^ _779308) ^ [_1836852, _1836854] : [-(_1836852 = _1836854), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836852), _1836854)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836854), _1836852))], (50938 ^ _779308) ^ [_1837202, _1837204] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837202), _1837204)), 50943 ^ _779308 : [(50944 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837202), _1837204)))], (50946 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837204), _1837202))]], -(_1837202 = _1837204)], (50950 ^ _779308) ^ [_1837560, _1837562] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837560), _1837562))), 50951 ^ _779308 : [(50958 ^ _779308) ^ [] : [_1837560 = _1837562], (50952 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837560), _1837562)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837562), _1837560)))]]], (50962 ^ _779308) ^ [_1837997, _1837999] : [50969 ^ _779308 : [(50970 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837997), _1837999)))], (50972 ^ _779308) ^ [] : [_1837997 = _1837999]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837997), _1837999)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837999), _1837997)))], (50974 ^ _779308) ^ [_1838357, _1838359] : [50981 ^ _779308 : [(50982 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838357), _1838359)))], (50984 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838359), _1838357))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838357), _1838359)), -(_1838357 = _1838359)], (50986 ^ _779308) ^ [_1838767, _1838769] : [-(_1838767 = _1838769), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838767), _1838769)), 50993 ^ _779308 : [(50994 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838767), _1838769)))], (50996 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1838769), _1838767))]]], (50998 ^ _779308) ^ [_1839175, _1839177] : [_1839175 = _1839177, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839175), _1839177)))], (51004 ^ _779308) ^ [_1839395, _1839397] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839395), _1839397)), 51007 ^ _779308 : [(51008 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839397), _1839395)), -(_1839397 = _1839395)], (51014 ^ _779308) ^ [] : [_1839397 = _1839395, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839397), _1839395)))]]], (51020 ^ _779308) ^ [_1839880, _1839882] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839880), _1839882)), 51025 ^ _779308 : [(51026 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839880), _1839882)))], (51028 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1839882), _1839880))]], -(_1839880 = _1839882)], (51032 ^ _779308) ^ [_1840286, _1840288] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840286), _1840288)), -(_1840286 = _1840288), 51039 ^ _779308 : [(51040 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840286), _1840288)))], (51042 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840288), _1840286))]]], (51044 ^ _779308) ^ [_1840708, _1840710, _1840712] : [_1840708 = _1840710, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840710), _1840712)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1840708), _1840712)))], (51054 ^ _779308) ^ [_1841051, _1841053, _1841055] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841051), _1841053)), _1841053 = _1841055, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841051), _1841055)))], (51064 ^ _779308) ^ [_1841380, _1841382] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841380), _1841382)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841382), _1841380)), -(_1841380 = _1841382)], (51074 ^ _779308) ^ [_1841699, _1841701] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841699), _1841701)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1841701), _1841699)), -(_1841699 = _1841701)], (51084 ^ _779308) ^ [_1842032, _1842034, _1842036] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842032), _1842034)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842034), _1842036)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842032), _1842036)))], (51094 ^ _779308) ^ [_1842385, _1842387, _1842389] : [_1842385 = _1842387, 51105 ^ _779308 : [(51106 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842385), _1842389)))], (51108 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842389), _1842385))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842387), _1842389)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842389), _1842387)))], (51110 ^ _779308) ^ [_1842922, _1842924, _1842926] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842922), _1842924)), 51121 ^ _779308 : [(51122 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842922), _1842926)))], (51124 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842926), _1842922))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842924), _1842926)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1842926), _1842924)))], (51126 ^ _779308) ^ [_1843455, _1843457] : [_1843455 = _1843457, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843455), _1843457)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843457), _1843455)))], (51136 ^ _779308) ^ [_1843778, _1843780] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843778), _1843780)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843780), _1843778))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843780), _1843778)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1843778), _1843780)))], (51150 ^ _779308) ^ [_1844215, _1844217] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844215), _1844217))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844215), _1844217)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844217), _1844215)))], (51160 ^ _779308) ^ [_1844547, _1844549] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844547), _1844549)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844549), _1844547))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844549), _1844547)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844547), _1844549)))], (51174 ^ _779308) ^ [_1844984, _1844986] : [_1844984 = _1844986, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844984), _1844986)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1844986), _1844984)))], (51184 ^ _779308) ^ [_1845307, _1845309] : [_1845309 = _1845307, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845307), _1845309)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845309), _1845307)))], (51194 ^ _779308) ^ [_1845644, _1845646, _1845648] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845644), _1845646)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845646), _1845644))), _1845646 = _1845648, 51205 ^ _779308 : [(51206 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845644), _1845648)))], (51208 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1845648), _1845644))]]], (51210 ^ _779308) ^ [_1846183, _1846185, _1846187] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1846183), _1846185)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1846185), _1846183))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1846185), _1846187)), 51221 ^ _779308 : [(51222 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1846183), _1846187)))], (51224 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1846187), _1846183))]]], (51226 ^ _779308) ^ [_1846718, _1846720] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1846718), _1846720)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1846720), _1846718))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1846720), _1846718)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1846718), _1846720)))], (51240 ^ _779308) ^ [_1847169, _1847171, _1847173] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1847169), _1847171)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1847171), _1847169))), 51255 ^ _779308 : [(51256 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1847169), _1847173)))], (51258 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1847173), _1847169))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1847171), _1847173)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1847173), _1847171)))], (51260 ^ _779308) ^ [_1847810, _1847812] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1847810), _1847812)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1847812), _1847810))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1847812), _1847810)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1847810), _1847812)))], (51274 ^ _779308) ^ [_1848275, _1848277, _1848279, _1848281] : [class_Divides_Osemiring__div(_1848275), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848275), _1848277), _1848279)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848275), _1848277), _1848281)), 51285 ^ _779308 : [(51286 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848275), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1848275), _1848279), _1848277)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1848275), _1848281), _1848277))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848275), _1848279), _1848281)))], (51292 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848275), _1848279), _1848281)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1848275), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1848275), _1848279), _1848277)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1848275), _1848281), _1848277))))]]], (51298 ^ _779308) ^ [_1849105, _1849107, _1849109, _1849111] : [class_Rings_Ocomm__semiring__1(_1849105), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849105), _1849107), _1849109)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849105), hAPP(hAPP(c_Power_Opower__class_Opower(_1849105), _1849107), _1849111)), hAPP(hAPP(c_Power_Opower__class_Opower(_1849105), _1849109), _1849111))))], (51308 ^ _779308) ^ [_1849510, _1849512, _1849514, _1849516] : [class_Divides_Osemiring__div(_1849510), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849510), _1849512), c_Divides_Odiv__class_Omod(_1849510, _1849514, _1849516))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849510), _1849512), _1849516)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1849510), _1849512), _1849514)))], (51322 ^ _779308) ^ [_1850002, _1850004, _1850006, _1850008] : [class_Divides_Osemiring__div(_1850002), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850002), _1850004), _1850006)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850002), _1850004), _1850008)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850002), _1850004), c_Divides_Odiv__class_Omod(_1850002, _1850006, _1850008))))], (51336 ^ _779308) ^ [_1850494, _1850496, _1850498, _1850500] : [class_Divides_Osemiring__div(_1850494), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850494), _1850496), _1850498)), -(c_Divides_Odiv__class_Omod(_1850494, c_Divides_Odiv__class_Omod(_1850494, _1850500, _1850498), _1850496) = c_Divides_Odiv__class_Omod(_1850494, _1850500, _1850496))], (51346 ^ _779308) ^ [_1850877, _1850879, _1850881, _1850883] : [class_Divides_Osemiring__div(_1850877), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850877), _1850879), _1850881)), 51353 ^ _779308 : [(51354 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850877), _1850879), c_Divides_Odiv__class_Omod(_1850877, _1850883, _1850881))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850877), _1850879), _1850883)))], (51360 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850877), _1850879), _1850883)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1850877), _1850879), c_Divides_Odiv__class_Omod(_1850877, _1850883, _1850881))))]]], (51366 ^ _779308) ^ [_1851546, _1851548, _1851550] : [class_Rings_Ocomm__ring__1(_1851546), 51369 ^ _779308 : [(51370 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851546), _1851548), hAPP(c_Groups_Ouminus__class_Ouminus(_1851546), _1851550))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851546), _1851548), _1851550)))], (51376 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851546), _1851548), _1851550)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1851546), _1851548), hAPP(c_Groups_Ouminus__class_Ouminus(_1851546), _1851550))))]]], (51382 ^ _779308) ^ [_1852091, _1852093, _1852095] : [class_Rings_Ocomm__ring__1(_1852091), 51385 ^ _779308 : [(51386 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1852091), hAPP(c_Groups_Ouminus__class_Ouminus(_1852091), _1852093)), _1852095)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1852091), _1852093), _1852095)))], (51392 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1852091), _1852093), _1852095)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1852091), hAPP(c_Groups_Ouminus__class_Ouminus(_1852091), _1852093)), _1852095)))]]], (51398 ^ _779308) ^ [_1852636, _1852638, _1852640] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1852636), _1852638)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1852636), _1852640)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1852636), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1852638), _1852640))))], (51408 ^ _779308) ^ [_1853015, _1853017, _1853019, _1853021] : [class_Rings_Ocomm__ring__1(_1853015), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1853015), _1853017), _1853019)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1853015), _1853017), _1853021)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1853015), _1853017), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1853015), _1853019), _1853021))))], (51422 ^ _779308) ^ [_1853501, _1853503, _1853505] : [class_Divides_Osemiring__div(_1853501), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1853501), _1853503), _1853505)), -(c_Divides_Odiv__class_Omod(_1853501, _1853505, _1853503) = c_Groups_Ozero__class_Ozero(_1853501))], (51432 ^ _779308) ^ [_1853848, _1853850, _1853852] : [class_Divides_Osemiring__div(_1853848), 51435 ^ _779308 : [(51436 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1853848), _1853850), _1853852)), -(c_Divides_Odiv__class_Omod(_1853848, _1853852, _1853850) = c_Groups_Ozero__class_Ozero(_1853848))], (51442 ^ _779308) ^ [] : [c_Divides_Odiv__class_Omod(_1853848, _1853852, _1853850) = c_Groups_Ozero__class_Ozero(_1853848), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1853848), _1853850), _1853852)))]]], (51448 ^ _779308) ^ [_1854375, _1854377, _1854379] : [class_Divides_Oring__div(_1854375), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1854375), _1854377), _1854379)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1854375), _1854379), hAPP(c_Groups_Ouminus__class_Ouminus(_1854375), _1854377)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1854375), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1854375), _1854379), _1854377)))], (51458 ^ _779308) ^ [_1854762, _1854764, _1854766] : [class_Divides_Oring__div(_1854762), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1854762), _1854764), _1854766)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1854762), hAPP(c_Groups_Ouminus__class_Ouminus(_1854762), _1854766)), _1854764) = hAPP(c_Groups_Ouminus__class_Ouminus(_1854762), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1854762), _1854766), _1854764)))], (51468 ^ _779308) ^ [_1855135, _1855137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1855135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1855135), _1855137)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855137), _1855135))], (51478 ^ _779308) ^ [_1855474] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855474), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1855474 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (51484 ^ _779308) ^ [_1855640] : [_1855640 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855640), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (51490 ^ _779308) ^ [_1855913, _1855915, _1855917, _1855919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855913, _1855915)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855917, _1855919))), 51493 ^ _779308 : [(51512 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855917), _1855919)))], (51494 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855913), _1855915)), 51497 ^ _779308 : [(51498 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855917), _1855913)))], (51500 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855915), _1855919)))], (51502 ^ _779308) ^ [] : [51503 ^ _779308 : [(51504 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855917), _1855913)))], (51506 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855913), _1855917))]], 51507 ^ _779308 : [(51508 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855915), _1855919)))], (51510 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1855919), _1855915))]]]]]]], (51514 ^ _779308) ^ [_1856790, _1856792, _1856794, _1856796] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856790, _1856792)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856794, _1856796)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856794), _1856796)), 51517 ^ _779308 : [(51518 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856790), _1856792)))], (51520 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856794), _1856790)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856792), _1856796)), 51527 ^ _779308 : [(51528 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856794), _1856790)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856790), _1856794)))], (51534 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856792), _1856796)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856796), _1856792)))]]]]], (51544 ^ _779308) ^ [_1857802, _1857804, _1857806, _1857808] : [class_Divides_Osemiring__div(_1857802), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1857802), _1857804), _1857806)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1857802), _1857804), _1857808)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1857802), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1857802), _1857806), _1857808)), _1857804) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1857802), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1857802), _1857806), _1857804)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1857802), _1857808), _1857804)))], (51558 ^ _779308) ^ [_1858353, _1858355] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1858353), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1858355), _1858353))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1858353), _1858355)))], (51564 ^ _779308) ^ [_1858547, _1858549] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1858547), _1858549)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1858547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1858549), _1858547))))], (51570 ^ _779308) ^ [_1858819, _1858821, _1858823, _1858825] : [class_Rings_Ocomm__semiring__1(_1858819), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1858819), _1858821), _1858823)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1858819), _1858821), _1858825)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1858819), _1858821), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1858819), _1858823), _1858825))))], (51594 ^ _779308) ^ [_1859607, _1859609] : [51595 ^ _779308 : [(51596 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859607), _1859609)))], (51598 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859609), _1859607))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1859607, _1859609))], (51584 ^ _779308) ^ [_1859320, _1859322] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1859320, _1859322), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859320), _1859322)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859322), _1859320)))], (51612 ^ _779308) ^ [_1860246, _1860248] : [51613 ^ _779308 : [(51614 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860246), _1860248)))], (51616 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860248), _1860246))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1860246, _1860248))], (51602 ^ _779308) ^ [_1859959, _1859961] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1859959, _1859961), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859959), _1859961)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1859961), _1859959)))], (51630 ^ _779308) ^ [_1860885, _1860887] : [51631 ^ _779308 : [(51632 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860885), _1860887)))], (51634 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860887), _1860885))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1860885, _1860887) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51620 ^ _779308) ^ [_1860598, _1860600] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1860598, _1860600) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860598), _1860600)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1860600), _1860598)))], (51648 ^ _779308) ^ [_1861524, _1861526] : [51649 ^ _779308 : [(51650 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1861524), _1861526)))], (51652 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1861526), _1861524))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1861524, _1861526) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51638 ^ _779308) ^ [_1861237, _1861239] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1861237, _1861239) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1861237), _1861239)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1861239), _1861237)))], (51656 ^ _779308) ^ [_1861847, _1861849] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1861847), _1861849)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1861849, _1861847) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51662 ^ _779308) ^ [_1862077, _1862079] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1862077), _1862079)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1862079, _1862077) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51668 ^ _779308) ^ [_1862309, _1862311] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1862309), _1862311)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1862311, _1862309) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51674 ^ _779308) ^ [_1862570, _1862572] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1862570, _1862572), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1862570), _1862572))], (51680 ^ _779308) ^ [_1862753, _1862755] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1862753), _1862755))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1862753, _1862755))], (51686 ^ _779308) ^ [_1863017, _1863019] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1863017, _1863019) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1863017), _1863019))], (51692 ^ _779308) ^ [_1863200, _1863202] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1863200), _1863202))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1863200, _1863202) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (51698 ^ _779308) ^ [_1863435, _1863437] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1863437, _1863435) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1863435), _1863437)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1863437), _1863435)))], (51708 ^ _779308) ^ [_1863810, _1863812, _1863814] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1863810, _1863812) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1863814), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 51711 ^ _779308 : [(51712 ^ _779308) ^ [] : [-(_1863810 = _1863812)], (51714 ^ _779308) ^ [] : [-(_1863812 = _1863814)]]], (51716 ^ _779308) ^ [_1864077, _1864079, _1864081] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1864077, _1864079) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1864081), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1864077 = _1864079, _1864079 = _1864081], (51726 ^ _779308) ^ [_1864381] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1864381, _1864381) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1864381), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51728 ^ _779308) ^ [_1864499, _1864501] : [_1864499 = _1864501, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1864499, _1864501) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1864499), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (51734 ^ _779308) ^ [_1864759, _1864761, _1864763, _1864765] : [class_Rings_Ocomm__ring(_1864759), class_Rings_Odvd(_1864759), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864759), _1864761), _1864763)), 51745 ^ _779308 : [(51746 ^ _779308) ^ [_1865198, _1865200] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864759), _1864761), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1864759), _1865200), _1864765))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864759), _1864761), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1864759), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1864759), _1865200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1864759), _1865198), _1864763))), _1864765))))], (51752 ^ _779308) ^ [_1865484, _1865486] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864759), _1864761), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1864759), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1864759), _1865486), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1864759), _1865484), _1864763))), _1864765))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864759), _1864761), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1864759), _1865486), _1864765))))]]], (51758 ^ _779308) ^ [_1865859, _1865861, _1865863, _1865865] : [class_Rings_Ocomm__ring(_1865859), class_Rings_Odvd(_1865859), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865859), _1865861), _1865863)), 51769 ^ _779308 : [(51770 ^ _779308) ^ [_1866298, _1866300] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865859), _1865861), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1865859), _1866300), _1865865))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865859), _1865861), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1865859), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1865859), _1866300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1865859), _1866298), _1865863))), _1865865))))], (51776 ^ _779308) ^ [_1866584, _1866586] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865859), _1865861), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1865859), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1865859), _1866586), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1865859), _1866584), _1865863))), _1865865))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865859), _1865861), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1865859), _1866586), _1865865))))]]], (51792 ^ _779308) ^ [_1867280, _1867282, _1867284] : [51793 ^ _779308 : [(51794 ^ _779308) ^ [] : [_1867280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51796 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1867282), _1867284))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1867280), _1867282)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1867280), _1867284))))], (51782 ^ _779308) ^ [_1866974, _1866976, _1866978] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1866974), _1866976)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1866974), _1866978))), -(_1866974 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1866976), _1866978)))], (51800 ^ _779308) ^ [_1867632, _1867634, _1867636] : [class_Divides_Osemiring__div(_1867632), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1867632), _1867634), _1867636)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1867632), _1867634), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1867632), _1867636), _1867634)) = _1867636)], (51810 ^ _779308) ^ [_1868013, _1868015, _1868017, _1868019] : [class_Divides_Osemiring__div(_1868013), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1868013), _1868015), _1868017)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1868013), _1868019), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1868013), _1868017), _1868015)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1868013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1868013), _1868019), _1868017)), _1868015))], (51820 ^ _779308) ^ [_1868422, _1868424, _1868426] : [class_Divides_Osemiring__div(_1868422), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1868422), _1868424), _1868426)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1868422), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1868422), _1868426), _1868424)), _1868424) = _1868426)], (51830 ^ _779308) ^ [_1868803, _1868805, _1868807, _1868809] : [class_Divides_Osemiring__div(_1868803), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1868803), _1868805), _1868807)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1868803), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1868803), _1868807), _1868805)), _1868809) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1868803), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1868803), _1868807), _1868809)), _1868805))], (51840 ^ _779308) ^ [_1869240, _1869242, _1869244, _1869246, _1869248] : [class_Divides_Osemiring__div(_1869240), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1869240), _1869242), _1869244)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1869240), _1869246), _1869248)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1869240), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1869240), _1869244), _1869242)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1869240), _1869248), _1869246)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1869240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1869240), _1869244), _1869248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1869240), _1869242), _1869246)))], (51854 ^ _779308) ^ [_1869806, _1869808, _1869810] : [class_Rings_Ocomm__semiring__1(_1869806), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1869806), _1869808), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1869806), _1869808), _1869810))))], (51860 ^ _779308) ^ [_1870064, _1870066, _1870068] : [class_Rings_Ocomm__semiring__1(_1870064), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870064), _1870066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1870064), _1870068), _1870066))))], (51866 ^ _779308) ^ [_1870336, _1870338, _1870340, _1870342] : [class_Rings_Ocomm__semiring__1(_1870336), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870336), _1870338), _1870340)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870336), _1870338), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1870336), _1870340), _1870342))))], (51876 ^ _779308) ^ [_1870725, _1870727, _1870729, _1870731] : [class_Rings_Ocomm__semiring__1(_1870725), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870725), _1870727), _1870729)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1870725), _1870727), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1870725), _1870731), _1870729))))], (51886 ^ _779308) ^ [_1871128, _1871130, _1871132, _1871134, _1871136] : [class_Rings_Ocomm__semiring__1(_1871128), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1871128), _1871130), _1871132)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1871128), _1871134), _1871136)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1871128), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1871128), _1871130), _1871134)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1871128), _1871132), _1871136))))], (51900 ^ _779308) ^ [_1871658, _1871660, _1871662, _1871664] : [class_Rings_Odvd(_1871658), _1871660 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1871658), _1871662), _1871664), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1871658), _1871662), _1871660)))], (51910 ^ _779308) ^ [_1872033, _1872035, _1872037, _1872039] : [class_Rings_Ocomm__semiring__1(_1872033), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1872033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1872033), _1872035), _1872037)), _1872039)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1872033), _1872035), _1872039)))], (51920 ^ _779308) ^ [_1872422, _1872424, _1872426, _1872428] : [class_Rings_Ocomm__semiring__1(_1872422), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1872422), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1872422), _1872424), _1872426)), _1872428)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1872422), _1872426), _1872428)))], (51930 ^ _779308) ^ [_1872811, _1872813, _1872815, _1872817] : [class_Rings_Oidom(_1872811), 51933 ^ _779308 : [(51944 ^ _779308) ^ [] : [51945 ^ _779308 : [(51946 ^ _779308) ^ [] : [_1872813 = c_Groups_Ozero__class_Ozero(_1872811)], (51948 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1872811), _1872815), _1872817))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1872811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1872811), _1872813), _1872815)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1872811), _1872813), _1872817))))], (51934 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1872811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1872811), _1872813), _1872815)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1872811), _1872813), _1872817))), -(_1872813 = c_Groups_Ozero__class_Ozero(_1872811)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1872811), _1872815), _1872817)))]]], (51952 ^ _779308) ^ [_1873595, _1873597, _1873599, _1873601] : [class_Rings_Oidom(_1873595), 51955 ^ _779308 : [(51966 ^ _779308) ^ [] : [51967 ^ _779308 : [(51968 ^ _779308) ^ [] : [_1873599 = c_Groups_Ozero__class_Ozero(_1873595)], (51970 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1873595), _1873597), _1873601))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1873595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1873595), _1873597), _1873599)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1873595), _1873601), _1873599))))], (51956 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1873595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1873595), _1873597), _1873599)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1873595), _1873601), _1873599))), -(_1873599 = c_Groups_Ozero__class_Ozero(_1873595)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1873595), _1873597), _1873601)))]]], (51974 ^ _779308) ^ [_1874365, _1874367, _1874369] : [class_Rings_Odvd(_1874365), class_Rings_Osemiring__0(_1874365), 51981 ^ _779308 : [(51982 ^ _779308) ^ [] : [51983 ^ _779308 : [(51984 ^ _779308) ^ [_1874684] : [hBOOL(hAPP(_1874367, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1874365), _1874369), _1874684)))]], 51986 ^ _779308 : [(51987 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1874365), _1874369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1874365), 51985 ^ [_1874365, _1874367, _1874369]), c_Groups_Ozero__class_Ozero(_1874365)))))], (51989 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1874367, 51985 ^ [_1874365, _1874367, _1874369])))]]], (51991 ^ _779308) ^ [] : [-(hBOOL(hAPP(_1874367, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1874365), _1874369), 51998 ^ [_1874365, _1874367, _1874369])))), 51992 ^ _779308 : [(51993 ^ _779308) ^ [_1875044] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1874365), _1874369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1874365), _1875044), c_Groups_Ozero__class_Ozero(_1874365)))), hBOOL(hAPP(_1874367, _1875044))]]]]], (52002 ^ _779308) ^ [_1875491, _1875493, _1875495, _1875497, _1875499] : [class_Rings_Ocomm__semiring__1(_1875491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1875493), _1875495)), hBOOL(hAPP(hAPP(c_member(_1875493), _1875497), _1875495)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1875491), hAPP(_1875499, _1875497)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1875493, _1875491), _1875499), _1875495))))], (52016 ^ _779308) ^ [_1875993, _1875995, _1875997] : [class_Rings_Ocomm__semiring__1(_1875993), 52021 ^ _779308 : [(52022 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1875995))], (52024 ^ _779308) ^ [] : [_1875997 = c_Groups_Oone__class_Oone(_1875993)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1875993), _1875997), hAPP(hAPP(c_Power_Opower__class_Opower(_1875993), _1875997), _1875995))))], (52028 ^ _779308) ^ [_1876414, _1876416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1876414)), 52031 ^ _779308 : [(52032 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1876414), _1876416)), _1876414)), -(_1876416 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (52038 ^ _779308) ^ [] : [_1876416 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1876414), _1876416)), _1876414)))]]], (52044 ^ _779308) ^ [_1876911, _1876913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1876911)), 52047 ^ _779308 : [(52048 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1876913), _1876911)), _1876911)), -(_1876913 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (52054 ^ _779308) ^ [] : [_1876913 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1876913), _1876911)), _1876911)))]]], (52060 ^ _779308) ^ [_1877436, _1877438, _1877440, _1877442] : [class_Orderings_Oorder(_1877436), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1877436, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1877438), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1877436), hAPP(_1877438, _1877440)), hAPP(_1877438, _1877442)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1877440), _1877442)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1877442), _1877440)))], (52078 ^ _779308) ^ [_1878028, _1878030, _1878032, _1878034] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1878028), _1878030)), c_Equiv__Relations_Oequiv(_1878028, _1878030, _1878032), 52088 ^ _779308 : [(52089 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1878028, tc_HOL_Obool)), 52087 ^ [_1878028, _1878030, _1878032, _1878034]), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1878028), _1878030), _1878032))))], (52091 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1878034), hAPP(c_Finite__Set_Ocard(_1878028), 52087 ^ [_1878028, _1878030, _1878032, _1878034])))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1878034), hAPP(c_Finite__Set_Ocard(_1878028), _1878030))))], (52095 ^ _779308) ^ [_1878723, _1878725] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1878723), _1878725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1878725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1878723), _1878725)))], (52105 ^ _779308) ^ [_1879046, _1879048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1879046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1879048)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1879046), _1879048)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _1879048), _1879046)), -(_1879046 = _1879048)], (52123 ^ _779308) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (52125 ^ _779308) ^ [_1879604, _1879606] : [class_Lattices_Obounded__lattice(_1879604), -(class_Lattices_Obounded__lattice(tc_fun(_1879606, _1879604)))], (52131 ^ _779308) ^ [_1879816, _1879818] : [class_Complete__Lattice_Ocomplete__lattice(_1879816), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1879818, _1879816)))], (52137 ^ _779308) ^ [_1880028, _1880030] : [class_Lattices_Obounded__lattice(_1880028), -(class_Lattices_Obounded__lattice__top(tc_fun(_1880030, _1880028)))], (52143 ^ _779308) ^ [_1880240, _1880242] : [class_Lattices_Obounded__lattice(_1880240), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1880242, _1880240)))], (52149 ^ _779308) ^ [_1880452, _1880454] : [class_Lattices_Olattice(_1880452), -(class_Lattices_Osemilattice__sup(tc_fun(_1880454, _1880452)))], (52155 ^ _779308) ^ [_1880664, _1880666] : [class_Lattices_Olattice(_1880664), -(class_Lattices_Osemilattice__inf(tc_fun(_1880666, _1880664)))], (52161 ^ _779308) ^ [_1880876, _1880878] : [class_Lattices_Odistrib__lattice(_1880876), -(class_Lattices_Odistrib__lattice(tc_fun(_1880878, _1880876)))], (52167 ^ _779308) ^ [_1881088, _1881090] : [class_Lattices_Oboolean__algebra(_1881088), -(class_Lattices_Oboolean__algebra(tc_fun(_1881090, _1881088)))], (52173 ^ _779308) ^ [_1881300, _1881302] : [class_Orderings_Opreorder(_1881300), -(class_Orderings_Opreorder(tc_fun(_1881302, _1881300)))], (52179 ^ _779308) ^ [_1881512, _1881514] : [-(class_Finite__Set_Ofinite(tc_fun(_1881512, _1881514))), class_Finite__Set_Ofinite(_1881512), class_Finite__Set_Ofinite(_1881514)], (52189 ^ _779308) ^ [_1881811, _1881813] : [class_Lattices_Olattice(_1881811), -(class_Lattices_Olattice(tc_fun(_1881813, _1881811)))], (52195 ^ _779308) ^ [_1882023, _1882025] : [class_Orderings_Oorder(_1882023), -(class_Orderings_Oorder(tc_fun(_1882025, _1882023)))], (52201 ^ _779308) ^ [_1882235, _1882237] : [class_Orderings_Otop(_1882235), -(class_Orderings_Otop(tc_fun(_1882237, _1882235)))], (52207 ^ _779308) ^ [_1882447, _1882449] : [class_Orderings_Oord(_1882447), -(class_Orderings_Oord(tc_fun(_1882449, _1882447)))], (52213 ^ _779308) ^ [_1882659, _1882661] : [class_Orderings_Obot(_1882659), -(class_Orderings_Obot(tc_fun(_1882661, _1882659)))], (52219 ^ _779308) ^ [_1882871, _1882873] : [class_Groups_Ouminus(_1882871), -(class_Groups_Ouminus(tc_fun(_1882873, _1882871)))], (52225 ^ _779308) ^ [_1883083, _1883085] : [class_Groups_Ominus(_1883083), -(class_Groups_Ominus(tc_fun(_1883085, _1883083)))], (52231 ^ _779308) ^ [_1883295, _1883297] : [-(class_Enum_Oenum(tc_fun(_1883295, _1883297))), class_Enum_Oenum(_1883295), class_Enum_Oenum(_1883297)], (52241 ^ _779308) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (52243 ^ _779308) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (52245 ^ _779308) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (52247 ^ _779308) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (52249 ^ _779308) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (52251 ^ _779308) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (52253 ^ _779308) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (52255 ^ _779308) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (52257 ^ _779308) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (52259 ^ _779308) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (52261 ^ _779308) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (52263 ^ _779308) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (52265 ^ _779308) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (52267 ^ _779308) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (52269 ^ _779308) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (52271 ^ _779308) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (52273 ^ _779308) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (52275 ^ _779308) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (52277 ^ _779308) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (52279 ^ _779308) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (52281 ^ _779308) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (52283 ^ _779308) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (52285 ^ _779308) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (52287 ^ _779308) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (52289 ^ _779308) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (52291 ^ _779308) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (52293 ^ _779308) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (52295 ^ _779308) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (52297 ^ _779308) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (52299 ^ _779308) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (52301 ^ _779308) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (52303 ^ _779308) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (52305 ^ _779308) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (52307 ^ _779308) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (52309 ^ _779308) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (52311 ^ _779308) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (52313 ^ _779308) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (52315 ^ _779308) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (52317 ^ _779308) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (52319 ^ _779308) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (52321 ^ _779308) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (52323 ^ _779308) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (52325 ^ _779308) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (52327 ^ _779308) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (52329 ^ _779308) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (52331 ^ _779308) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (52333 ^ _779308) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (52335 ^ _779308) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (52337 ^ _779308) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (52339 ^ _779308) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (52341 ^ _779308) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (52343 ^ _779308) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (52345 ^ _779308) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (52347 ^ _779308) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (52349 ^ _779308) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (52351 ^ _779308) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (52353 ^ _779308) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (52355 ^ _779308) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (52357 ^ _779308) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (52359 ^ _779308) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (52361 ^ _779308) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (52363 ^ _779308) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (52365 ^ _779308) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (52367 ^ _779308) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (52369 ^ _779308) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (52371 ^ _779308) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (52373 ^ _779308) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (52375 ^ _779308) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (52377 ^ _779308) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (52379 ^ _779308) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (52381 ^ _779308) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (52383 ^ _779308) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (52385 ^ _779308) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (52387 ^ _779308) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (52389 ^ _779308) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (52391 ^ _779308) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (52393 ^ _779308) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (52395 ^ _779308) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (52397 ^ _779308) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (52399 ^ _779308) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (52401 ^ _779308) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (52403 ^ _779308) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (52405 ^ _779308) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (52407 ^ _779308) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (52409 ^ _779308) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (52411 ^ _779308) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (52413 ^ _779308) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (52415 ^ _779308) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (52417 ^ _779308) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (52419 ^ _779308) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (52421 ^ _779308) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (52423 ^ _779308) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (52425 ^ _779308) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (52427 ^ _779308) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (52429 ^ _779308) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (52431 ^ _779308) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (52433 ^ _779308) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (52435 ^ _779308) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (52437 ^ _779308) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (52439 ^ _779308) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (52441 ^ _779308) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (52443 ^ _779308) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (52445 ^ _779308) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (52447 ^ _779308) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (52449 ^ _779308) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (52451 ^ _779308) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (52453 ^ _779308) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (52455 ^ _779308) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (52457 ^ _779308) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (52459 ^ _779308) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (52461 ^ _779308) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (52463 ^ _779308) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (52465 ^ _779308) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (52467 ^ _779308) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (52469 ^ _779308) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (52471 ^ _779308) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (52473 ^ _779308) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (52475 ^ _779308) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (52477 ^ _779308) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (52479 ^ _779308) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (52481 ^ _779308) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (52483 ^ _779308) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (52485 ^ _779308) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (52487 ^ _779308) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (52489 ^ _779308) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (52491 ^ _779308) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (52493 ^ _779308) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (52495 ^ _779308) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (52497 ^ _779308) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (52499 ^ _779308) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (52501 ^ _779308) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (52503 ^ _779308) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (52505 ^ _779308) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (52507 ^ _779308) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (52509 ^ _779308) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (52511 ^ _779308) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (52513 ^ _779308) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (52515 ^ _779308) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (52517 ^ _779308) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (52519 ^ _779308) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (52521 ^ _779308) ^ [_1891000] : [class_Lazy__Sequence_Osmall__lazy(_1891000), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1891000)))], (52527 ^ _779308) ^ [_1891175] : [-(class_Nat_Osize(tc_List_Olist(_1891175)))], (52529 ^ _779308) ^ [_1891283, _1891285] : [-(class_Finite__Set_Ofinite(tc_sum(_1891283, _1891285))), class_Finite__Set_Ofinite(_1891283), class_Finite__Set_Ofinite(_1891285)], (52539 ^ _779308) ^ [_1891582, _1891584] : [-(class_Enum_Oenum(tc_sum(_1891582, _1891584))), class_Enum_Oenum(_1891582), class_Enum_Oenum(_1891584)], (52549 ^ _779308) ^ [_1891866, _1891868] : [-(class_Nat_Osize(tc_sum(_1891866, _1891868)))], (52551 ^ _779308) ^ [_1891963] : [class_Finite__Set_Ofinite(_1891963), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1891963)))], (52557 ^ _779308) ^ [_1892153] : [class_Enum_Oenum(_1892153), -(class_Enum_Oenum(tc_Option_Ooption(_1892153)))], (52563 ^ _779308) ^ [_1892328] : [-(class_Nat_Osize(tc_Option_Ooption(_1892328)))], (52565 ^ _779308) ^ [_1892421, _1892423] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1892421, _1892423)))], (52567 ^ _779308) ^ [_1892532, _1892534] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1892532, _1892534))), class_Lazy__Sequence_Osmall__lazy(_1892532), class_Lazy__Sequence_Osmall__lazy(_1892534)], (52577 ^ _779308) ^ [_1892831, _1892833] : [-(class_Finite__Set_Ofinite(tc_prod(_1892831, _1892833))), class_Finite__Set_Ofinite(_1892831), class_Finite__Set_Ofinite(_1892833)], (52587 ^ _779308) ^ [_1893130, _1893132] : [-(class_Enum_Oenum(tc_prod(_1893130, _1893132))), class_Enum_Oenum(_1893130), class_Enum_Oenum(_1893132)], (52597 ^ _779308) ^ [_1893414, _1893416] : [-(class_Nat_Osize(tc_prod(_1893414, _1893416)))], (52599 ^ _779308) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (52601 ^ _779308) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (52603 ^ _779308) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (52605 ^ _779308) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (52607 ^ _779308) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (52609 ^ _779308) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52611 ^ _779308) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (52613 ^ _779308) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52615 ^ _779308) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52617 ^ _779308) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52619 ^ _779308) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52621 ^ _779308) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52623 ^ _779308) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52625 ^ _779308) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (52627 ^ _779308) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (52629 ^ _779308) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52631 ^ _779308) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52633 ^ _779308) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (52635 ^ _779308) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (52637 ^ _779308) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (52639 ^ _779308) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52641 ^ _779308) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52643 ^ _779308) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (52645 ^ _779308) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52647 ^ _779308) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (52649 ^ _779308) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (52651 ^ _779308) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (52653 ^ _779308) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (52655 ^ _779308) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (52657 ^ _779308) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (52659 ^ _779308) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (52661 ^ _779308) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (52663 ^ _779308) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (52665 ^ _779308) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (52667 ^ _779308) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (52669 ^ _779308) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (52671 ^ _779308) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (52673 ^ _779308) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (52675 ^ _779308) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (52677 ^ _779308) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (52679 ^ _779308) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (52681 ^ _779308) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (52683 ^ _779308) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (52685 ^ _779308) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (52687 ^ _779308) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (52689 ^ _779308) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (52691 ^ _779308) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (52693 ^ _779308) ^ [_1895987] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1895987)))], (52695 ^ _779308) ^ [_1896080, _1896082] : [-(hAPP(c_COMBI(_1896080), _1896082) = _1896082)], (52697 ^ _779308) ^ [_1896207, _1896209, _1896211, _1896213] : [-(hAPP(hAPP(c_COMBK(_1896207, _1896209), _1896211), _1896213) = _1896211)], (52699 ^ _779308) ^ [_1896370, _1896372, _1896374, _1896376, _1896378, _1896380] : [-(hAPP(hAPP(hAPP(c_COMBB(_1896370, _1896372, _1896374), _1896376), _1896378), _1896380) = hAPP(_1896376, hAPP(_1896378, _1896380)))], (52701 ^ _779308) ^ [_1896547, _1896549, _1896551, _1896553, _1896555, _1896557] : [-(hAPP(hAPP(hAPP(c_COMBC(_1896547, _1896549, _1896551), _1896553), _1896555), _1896557) = hAPP(hAPP(_1896553, _1896557), _1896555))], (52703 ^ _779308) ^ [_1896724, _1896726, _1896728, _1896730, _1896732, _1896734] : [-(hAPP(hAPP(hAPP(c_COMBS(_1896724, _1896726, _1896728), _1896730), _1896732), _1896734) = hAPP(hAPP(_1896730, _1896734), hAPP(_1896732, _1896734)))], (52705 ^ _779308) ^ [_1896863, _1896865] : [hBOOL(hAPP(hAPP(c_fequal, _1896863), _1896865)), -(_1896863 = _1896865)], (52711 ^ _779308) ^ [_1897085, _1897087] : [_1897085 = _1897087, -(hBOOL(hAPP(hAPP(c_fequal, _1897085), _1897087)))], (52717 ^ _779308) ^ [] : [hBOOL(c_fFalse)], (52719 ^ _779308) ^ [] : [-(hBOOL(c_fTrue))], (52721 ^ _779308) ^ [_1897398] : [hBOOL(hAPP(c_fNot, _1897398)), hBOOL(_1897398)], (52727 ^ _779308) ^ [_1897593] : [-(hBOOL(_1897593)), -(hBOOL(hAPP(c_fNot, _1897593)))], (52733 ^ _779308) ^ [_1897804, _1897806] : [hBOOL(_1897804), hBOOL(_1897806), -(hBOOL(hAPP(hAPP(c_fconj, _1897804), _1897806)))], (52743 ^ _779308) ^ [_1898113, _1898115] : [hBOOL(hAPP(hAPP(c_fconj, _1898113), _1898115)), -(hBOOL(_1898113))], (52749 ^ _779308) ^ [_1898333, _1898335] : [hBOOL(hAPP(hAPP(c_fconj, _1898333), _1898335)), -(hBOOL(_1898335))], (52755 ^ _779308) ^ [_1898553, _1898555] : [hBOOL(_1898553), -(hBOOL(hAPP(hAPP(c_fdisj, _1898553), _1898555)))], (52761 ^ _779308) ^ [_1898773, _1898775] : [hBOOL(_1898773), -(hBOOL(hAPP(hAPP(c_fdisj, _1898775), _1898773)))], (52767 ^ _779308) ^ [_1898993, _1898995] : [hBOOL(hAPP(hAPP(c_fdisj, _1898993), _1898995)), -(hBOOL(_1898993)), -(hBOOL(_1898995))], (52777 ^ _779308) ^ [_1899301, _1899303] : [-(hBOOL(_1899301)), -(hBOOL(hAPP(hAPP(c_fimplies, _1899301), _1899303)))], (52783 ^ _779308) ^ [_1899520, _1899522] : [hBOOL(_1899520), -(hBOOL(hAPP(hAPP(c_fimplies, _1899522), _1899520)))], (52799 ^ _779308) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), v_U)))], (52801 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), v_G), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))))], (52803 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, v_n)), hAPP(c_Finite__Set_Ocard(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))))], (52805 ^ _779308) ^ [] : [-(hAPP(c_Finite__Set_Ocard(t_a), v_G) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(t_a), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))), hAPP(c_Nat_OSuc, v_n)))], (52807 ^ _779308) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pn), v_U)))], (52809 ^ _779308) ^ [] : [hBOOL(hAPP(hAPP(c_member(t_a), hAPP(v_mgt__call, v_pn)), v_G))], (52789 ^ _779308) ^ [_1899740, _1899742] : [hBOOL(hAPP(hAPP(c_fimplies, _1899740), _1899742)), hBOOL(_1899740), -(hBOOL(_1899742))]], input).
% 143.38/138.37  ncf('1',plain,[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), v_G)), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))],start(52811 ^ 0)).
% 143.38/138.37  ncf('1.1',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), v_G)), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))), hBOOL(hAPP(hAPP(c_member(t_a), hAPP(v_mgt__call, v_pn)), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), v_G), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))],extension(6145 ^ 1,bind([[_877738, _877740, _877742, _877744], [t_a, hAPP(v_mgt__call, v_pn), v_G, hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)]]))).
% 143.38/138.37  ncf('1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(t_a), hAPP(v_mgt__call, v_pn)), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pn), v_U))],extension(6023 ^ 2,bind([[_875081, _875083, _875085, _875087, _875089], [tc_Com_Opname, v_pn, v_U, t_a, v_mgt__call]]))).
% 143.38/138.37  ncf('1.1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pn), v_U)))],extension(52807 ^ 3)).
% 143.38/138.37  ncf('1.1.2',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), v_G), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))))],extension(52801 ^ 2)).
% 143.38/138.37  %-----------------------------------------------------
% 143.38/138.37  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------