%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW375+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n011.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 12:26:04 EDT 2023

% Result   : Theorem 1.64s 2.47s
% Output   : Proof 1.64s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWW375+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n011.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 22:21:03 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 1.64/2.47  
% 1.64/2.47  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.64/2.47  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.64/2.47  %-----------------------------------------------------
% 1.64/2.47  ncf(matrix, plain, [(50897 ^ _777081) ^ [] : [hBOOL(hAPP(c_Com_OWT, v_y))], (2 ^ _777081) ^ [_777111] : [-(_777111 = _777111)], (4 ^ _777081) ^ [_777134, _777136] : [_777136 = _777134, -(_777134 = _777136)], (10 ^ _777081) ^ [_777207, _777209, _777211] : [-(_777211 = _777207), _777211 = _777209, _777209 = _777207], (20 ^ _777081) ^ [_777344, _777346, _777348, _777350] : [-(c_Option_Ois__none(_777348, _777344)), c_Option_Ois__none(_777350, _777346), _777350 = _777348, _777346 = _777344], (34 ^ _777081) ^ [_777537, _777539, _777541, _777543, _777545, _777547, _777549, _777551, _777553, _777555, _777557, _777559] : [-(c_Nitpick_Ofold__graph_H(_777557, _777553, _777549, _777545, _777541, _777537)), c_Nitpick_Ofold__graph_H(_777559, _777555, _777551, _777547, _777543, _777539), _777559 = _777557, _777555 = _777553, _777551 = _777549, _777547 = _777545, _777543 = _777541, _777539 = _777537], (64 ^ _777081) ^ [_778082, _778084, _778086, _778088, _778090, _778092, _778094, _778096] : [-(c_Nat__Transfer_Otransfer__morphism(_778094, _778090, _778086, _778082)), c_Nat__Transfer_Otransfer__morphism(_778096, _778092, _778088, _778084), _778096 = _778094, _778092 = _778090, _778088 = _778086, _778084 = _778082], (86 ^ _777081) ^ [_778435, _778437, _778439, _778441] : [-(c_Int_Oiszero(_778439, _778435)), c_Int_Oiszero(_778441, _778437), _778441 = _778439, _778437 = _778435], (100 ^ _777081) ^ [_778628, _778630, _778632, _778634] : [-(c_Nitpick_Orefl_H(_778632, _778628)), c_Nitpick_Orefl_H(_778634, _778630), _778634 = _778632, _778630 = _778628], (114 ^ _777081) ^ [_778821, _778823, _778825, _778827, _778829, _778831, _778833, _778835, _778837, _778839] : [-(c_Big__Operators_Ocomm__monoid__big(_778837, _778833, _778829, _778825, _778821)), c_Big__Operators_Ocomm__monoid__big(_778839, _778835, _778831, _778827, _778823), _778839 = _778837, _778835 = _778833, _778831 = _778829, _778827 = _778825, _778823 = _778821], (140 ^ _777081) ^ [_779266, _779268] : [-(class_Rings_Odivision__ring__inverse__zero(_779266)), _779268 = _779266, class_Rings_Odivision__ring__inverse__zero(_779268)], (150 ^ _777081) ^ [_779391, _779393] : [-(class_Rings_Odivision__ring(_779391)), _779393 = _779391, class_Rings_Odivision__ring(_779393)], (160 ^ _777081) ^ [_779516, _779518] : [-(class_Fields_Ofield__inverse__zero(_779516)), _779518 = _779516, class_Fields_Ofield__inverse__zero(_779518)], (170 ^ _777081) ^ [_779641, _779643] : [-(class_Fields_Olinordered__field(_779641)), _779643 = _779641, class_Fields_Olinordered__field(_779643)], (180 ^ _777081) ^ [_779766, _779768] : [-(class_Fields_Ofield(_779766)), _779768 = _779766, class_Fields_Ofield(_779768)], (190 ^ _777081) ^ [_779891, _779893] : [-(c_Nat__Transfer_Ois__nat(_779891)), _779893 = _779891, c_Nat__Transfer_Ois__nat(_779893)], (200 ^ _777081) ^ [_780016, _780018] : [-(class_Fields_Olinordered__field__inverse__zero(_780016)), _780018 = _780016, class_Fields_Olinordered__field__inverse__zero(_780018)], (210 ^ _777081) ^ [_780141, _780143, _780145, _780147, _780149, _780151, _780153, _780155, _780157, _780159] : [-(c_Finite__Set_Ofolding__image(_780157, _780153, _780149, _780145, _780141)), c_Finite__Set_Ofolding__image(_780159, _780155, _780151, _780147, _780143), _780159 = _780157, _780155 = _780153, _780151 = _780149, _780147 = _780145, _780143 = _780141], (236 ^ _777081) ^ [_780586, _780588, _780590, _780592, _780594, _780596] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_780594, _780590, _780586)), c_Hoare__Mirabelle_Ohoare__derivs(_780596, _780592, _780588), _780596 = _780594, _780592 = _780590, _780588 = _780586], (254 ^ _777081) ^ [_780855, _780857, _780859, _780861, _780863, _780865, _780867, _780869] : [-(c_Finite__Set_Ofolding__idem(_780867, _780863, _780859, _780855)), c_Finite__Set_Ofolding__idem(_780869, _780865, _780861, _780857), _780869 = _780867, _780865 = _780863, _780861 = _780859, _780857 = _780855], (276 ^ _777081) ^ [_781208, _781210, _781212, _781214] : [-(c_Equiv__Relations_Oequivp(_781212, _781208)), c_Equiv__Relations_Oequivp(_781214, _781210), _781214 = _781212, _781210 = _781208], (290 ^ _777081) ^ [_781401, _781403, _781405, _781407, _781409, _781411, _781413, _781415, _781417, _781419, _781421, _781423] : [-(c_Equiv__Relations_Ocongruent2(_781421, _781417, _781413, _781409, _781405, _781401)), c_Equiv__Relations_Ocongruent2(_781423, _781419, _781415, _781411, _781407, _781403), _781423 = _781421, _781419 = _781417, _781415 = _781413, _781411 = _781409, _781407 = _781405, _781403 = _781401], (320 ^ _777081) ^ [_781946, _781948, _781950, _781952, _781954, _781956, _781958, _781960] : [-(c_Wellfounded_Omax__extp(_781958, _781954, _781950, _781946)), c_Wellfounded_Omax__extp(_781960, _781956, _781952, _781948), _781960 = _781958, _781956 = _781954, _781952 = _781950, _781948 = _781946], (342 ^ _777081) ^ [_782299, _782301, _782303, _782305, _782307, _782309] : [-(c_Big__Operators_Osemilattice__big(_782307, _782303, _782299)), c_Big__Operators_Osemilattice__big(_782309, _782305, _782301), _782309 = _782307, _782305 = _782303, _782301 = _782299], (360 ^ _777081) ^ [_782568, _782570, _782572, _782574, _782576, _782578, _782580, _782582, _782584, _782586, _782588, _782590] : [-(c_Finite__Set_Ofolding__image__simple(_782588, _782584, _782580, _782576, _782572, _782568)), c_Finite__Set_Ofolding__image__simple(_782590, _782586, _782582, _782578, _782574, _782570), _782590 = _782588, _782586 = _782584, _782582 = _782580, _782578 = _782576, _782574 = _782572, _782570 = _782568], (390 ^ _777081) ^ [_783113, _783115, _783117, _783119] : [-(c_Predicate_Oreflp(_783117, _783113)), c_Predicate_Oreflp(_783119, _783115), _783119 = _783117, _783115 = _783113], (404 ^ _777081) ^ [_783306, _783308, _783310, _783312, _783314, _783316, _783318, _783320, _783322, _783324, _783326, _783328, _783330, _783332] : [-(c_Predicate_Opred__comp(_783330, _783326, _783322, _783318, _783314, _783310, _783306)), c_Predicate_Opred__comp(_783332, _783328, _783324, _783320, _783316, _783312, _783308), _783332 = _783330, _783328 = _783326, _783324 = _783322, _783320 = _783318, _783316 = _783314, _783312 = _783310, _783308 = _783306], (438 ^ _777081) ^ [_783959, _783961, _783963, _783965] : [-(c_FunDef_Oreduction__pair(_783963, _783959)), c_FunDef_Oreduction__pair(_783965, _783961), _783965 = _783963, _783961 = _783959], (452 ^ _777081) ^ [_784152, _784154, _784156, _784158] : [-(c_Nitpick_Owf_H(_784156, _784152)), c_Nitpick_Owf_H(_784158, _784154), _784158 = _784156, _784154 = _784152], (466 ^ _777081) ^ [_784345, _784347] : [-(c_Nitpick_Ounknown(_784345)), _784347 = _784345, c_Nitpick_Ounknown(_784347)], (476 ^ _777081) ^ [_784470, _784472, _784474, _784476, _784478, _784480, _784482, _784484] : [-(c_Equiv__Relations_Ocongruent(_784482, _784478, _784474, _784470)), c_Equiv__Relations_Ocongruent(_784484, _784480, _784476, _784472), _784484 = _784482, _784480 = _784478, _784476 = _784474, _784472 = _784470], (498 ^ _777081) ^ [_784823, _784825, _784827, _784829, _784831, _784833] : [-(c_Hoare__Mirabelle_Ohoare__valids(_784831, _784827, _784823)), c_Hoare__Mirabelle_Ohoare__valids(_784833, _784829, _784825), _784833 = _784831, _784829 = _784827, _784825 = _784823], (516 ^ _777081) ^ [_785092, _785094, _785096, _785098, _785100, _785102] : [-(c_Hoare__Mirabelle_Otriple__valid(_785100, _785096, _785092)), c_Hoare__Mirabelle_Otriple__valid(_785102, _785098, _785094), _785102 = _785100, _785098 = _785096, _785094 = _785092], (534 ^ _777081) ^ [_785361, _785363] : [-(c_Nat__Transfer_Onat__set(_785361)), _785363 = _785361, c_Nat__Transfer_Onat__set(_785363)], (544 ^ _777081) ^ [_785486, _785488, _785490, _785492, _785494, _785496, _785498, _785500] : [-(c_Map_Omap__le(_785498, _785494, _785490, _785486)), c_Map_Omap__le(_785500, _785496, _785492, _785488), _785500 = _785498, _785496 = _785494, _785492 = _785490, _785488 = _785486], (566 ^ _777081) ^ [_785839, _785841, _785843, _785845, _785847, _785849, _785851, _785853] : [-(c_List_Olistrelp(_785851, _785847, _785843, _785839)), c_List_Olistrelp(_785853, _785849, _785845, _785841), _785853 = _785851, _785849 = _785847, _785845 = _785843, _785841 = _785839], (588 ^ _777081) ^ [_786192, _786194] : [-(c_List_Onat__list(_786192)), _786194 = _786192, c_List_Onat__list(_786194)], (598 ^ _777081) ^ [_786317, _786319, _786321, _786323, _786325, _786327] : [-(c_Enum_Oex__n__lists(_786325, _786321, _786317)), c_Enum_Oex__n__lists(_786327, _786323, _786319), _786327 = _786325, _786323 = _786321, _786319 = _786317], (616 ^ _777081) ^ [_786586, _786588, _786590, _786592, _786594, _786596] : [-(c_Enum_Oall__n__lists(_786594, _786590, _786586)), c_Enum_Oall__n__lists(_786596, _786592, _786588), _786596 = _786594, _786592 = _786590, _786588 = _786586], (634 ^ _777081) ^ [_786855, _786857, _786859, _786861] : [-(c_Wellfounded_OwfP(_786859, _786855)), c_Wellfounded_OwfP(_786861, _786857), _786861 = _786859, _786857 = _786855], (648 ^ _777081) ^ [_787048, _787050, _787052, _787054, _787056, _787058, _787060, _787062, _787064, _787066] : [-(c_List_Olist__all2(_787064, _787060, _787056, _787052, _787048)), c_List_Olist__all2(_787066, _787062, _787058, _787054, _787050), _787066 = _787064, _787062 = _787060, _787058 = _787056, _787054 = _787052, _787050 = _787048], (674 ^ _777081) ^ [_787493, _787495, _787497, _787499] : [-(c_List_Olinorder__class_Osorted(_787497, _787493)), c_List_Olinorder__class_Osorted(_787499, _787495), _787499 = _787497, _787495 = _787493], (688 ^ _777081) ^ [_787686, _787688, _787690, _787692, _787694, _787696, _787698, _787700] : [-(c_Fun_Oinj__on(_787698, _787694, _787690, _787686)), c_Fun_Oinj__on(_787700, _787696, _787692, _787688), _787700 = _787698, _787696 = _787694, _787692 = _787690, _787688 = _787686], (710 ^ _777081) ^ [_788039, _788041, _788043, _788045, _788047, _788049] : [-(c_List_Olist__ex(_788047, _788043, _788039)), c_List_Olist__ex(_788049, _788045, _788041), _788049 = _788047, _788045 = _788043, _788041 = _788039], (728 ^ _777081) ^ [_788308, _788310, _788312, _788314, _788316, _788318, _788320, _788322, _788324, _788326] : [-(c_Typedef_Otype__definition(_788324, _788320, _788316, _788312, _788308)), c_Typedef_Otype__definition(_788326, _788322, _788318, _788314, _788310), _788326 = _788324, _788322 = _788320, _788318 = _788316, _788314 = _788312, _788310 = _788308], (754 ^ _777081) ^ [_788753, _788755, _788757, _788759, _788761, _788763] : [-(c_Equiv__Relations_Oequiv(_788761, _788757, _788753)), c_Equiv__Relations_Oequiv(_788763, _788759, _788755), _788763 = _788761, _788759 = _788757, _788755 = _788753], (772 ^ _777081) ^ [_789022, _789024, _789026, _789028, _789030, _789032] : [-(c_Relation_Orefl__on(_789030, _789026, _789022)), c_Relation_Orefl__on(_789032, _789028, _789024), _789032 = _789030, _789028 = _789026, _789024 = _789022], (790 ^ _777081) ^ [_789291, _789293, _789295, _789297] : [-(c_Relation_Oirrefl(_789295, _789291)), c_Relation_Oirrefl(_789297, _789293), _789297 = _789295, _789293 = _789291], (804 ^ _777081) ^ [_789484, _789486, _789488, _789490, _789492, _789494] : [-(c_Relation_Osingle__valued(_789492, _789488, _789484)), c_Relation_Osingle__valued(_789494, _789490, _789486), _789494 = _789492, _789490 = _789488, _789486 = _789484], (822 ^ _777081) ^ [_789753, _789755, _789757, _789759] : [-(c_Wellfounded_Owf(_789757, _789753)), c_Wellfounded_Owf(_789759, _789755), _789759 = _789757, _789755 = _789753], (836 ^ _777081) ^ [_789946, _789948, _789950, _789952, _789954, _789956] : [-(c_Relation_Ototal__on(_789954, _789950, _789946)), c_Relation_Ototal__on(_789956, _789952, _789948), _789956 = _789954, _789952 = _789950, _789948 = _789946], (854 ^ _777081) ^ [_790215, _790217, _790219, _790221] : [-(c_Wellfounded_Oacyclic(_790219, _790215)), c_Wellfounded_Oacyclic(_790221, _790217), _790221 = _790219, _790217 = _790215], (868 ^ _777081) ^ [_790408, _790410, _790412, _790414, _790416, _790418, _790420, _790422] : [-(c_Finite__Set_Ofolding(_790420, _790416, _790412, _790408)), c_Finite__Set_Ofolding(_790422, _790418, _790414, _790410), _790422 = _790420, _790418 = _790416, _790414 = _790412, _790410 = _790408], (890 ^ _777081) ^ [_790761, _790763, _790765, _790767, _790769, _790771] : [-(c_Finite__Set_Ofolding__one__idem(_790769, _790765, _790761)), c_Finite__Set_Ofolding__one__idem(_790771, _790767, _790763), _790771 = _790769, _790767 = _790765, _790763 = _790761], (908 ^ _777081) ^ [_791030, _791032, _791034, _791036, _791038, _791040] : [-(c_Finite__Set_Ofun__left__comm__idem(_791038, _791034, _791030)), c_Finite__Set_Ofun__left__comm__idem(_791040, _791036, _791032), _791040 = _791038, _791036 = _791034, _791032 = _791030], (926 ^ _777081) ^ [_791299, _791301] : [-(class_Lattices_Oab__semigroup__idem__mult(_791299)), _791301 = _791299, class_Lattices_Oab__semigroup__idem__mult(_791301)], (936 ^ _777081) ^ [_791424, _791426, _791428, _791430, _791432, _791434] : [-(c_Finite__Set_Ofolding__one(_791432, _791428, _791424)), c_Finite__Set_Ofolding__one(_791434, _791430, _791426), _791434 = _791432, _791430 = _791428, _791426 = _791424], (954 ^ _777081) ^ [_791693, _791695] : [-(class_Lattices_Obounded__lattice(_791693)), _791695 = _791693, class_Lattices_Obounded__lattice(_791695)], (964 ^ _777081) ^ [_791818, _791820] : [-(class_Rings_Olinordered__semiring__1__strict(_791818)), _791820 = _791818, class_Rings_Olinordered__semiring__1__strict(_791820)], (974 ^ _777081) ^ [_791943, _791945] : [-(class_Groups_Oordered__ab__group__add__abs(_791943)), _791945 = _791943, class_Groups_Oordered__ab__group__add__abs(_791945)], (984 ^ _777081) ^ [_792068, _792070] : [-(class_Groups_Olinordered__ab__group__add(_792068)), _792070 = _792068, class_Groups_Olinordered__ab__group__add(_792070)], (994 ^ _777081) ^ [_792193, _792195] : [-(class_Rings_Oring__1__no__zero__divisors(_792193)), _792195 = _792193, class_Rings_Oring__1__no__zero__divisors(_792195)], (1004 ^ _777081) ^ [_792318, _792320] : [-(class_Rings_Olinordered__ring__strict(_792318)), _792320 = _792318, class_Rings_Olinordered__ring__strict(_792320)], (1014 ^ _777081) ^ [_792443, _792445] : [-(class_Rings_Oring__no__zero__divisors(_792443)), _792445 = _792443, class_Rings_Oring__no__zero__divisors(_792445)], (1024 ^ _777081) ^ [_792568, _792570] : [-(class_Rings_Olinordered__semiring__1(_792568)), _792570 = _792568, class_Rings_Olinordered__semiring__1(_792570)], (1034 ^ _777081) ^ [_792693, _792695] : [-(class_Groups_Oordered__ab__group__add(_792693)), _792695 = _792693, class_Groups_Oordered__ab__group__add(_792695)], (1044 ^ _777081) ^ [_792818, _792820] : [-(class_Rings_Oordered__ring__abs(_792818)), _792820 = _792818, class_Rings_Oordered__ring__abs(_792820)], (1054 ^ _777081) ^ [_792943, _792945] : [-(class_Rings_Olinordered__ring(_792943)), _792945 = _792943, class_Rings_Olinordered__ring(_792945)], (1064 ^ _777081) ^ [_793068, _793070] : [-(class_Rings_Olinordered__idom(_793068)), _793070 = _793068, class_Rings_Olinordered__idom(_793070)], (1074 ^ _777081) ^ [_793193, _793195] : [-(class_Groups_Oab__group__add(_793193)), _793195 = _793193, class_Groups_Oab__group__add(_793195)], (1084 ^ _777081) ^ [_793318, _793320] : [-(class_Rings_Oordered__ring(_793318)), _793320 = _793318, class_Rings_Oordered__ring(_793320)], (1094 ^ _777081) ^ [_793443, _793445] : [-(class_Rings_Ocomm__ring__1(_793443)), _793445 = _793443, class_Rings_Ocomm__ring__1(_793445)], (1104 ^ _777081) ^ [_793568, _793570] : [-(class_Groups_Ogroup__add(_793568)), _793570 = _793568, class_Groups_Ogroup__add(_793570)], (1114 ^ _777081) ^ [_793693, _793695] : [-(class_Divides_Oring__div(_793693)), _793695 = _793693, class_Divides_Oring__div(_793695)], (1124 ^ _777081) ^ [_793818, _793820] : [-(class_Int_Oring__char__0(_793818)), _793820 = _793818, class_Int_Oring__char__0(_793820)], (1134 ^ _777081) ^ [_793943, _793945] : [-(class_Int_Onumber__ring(_793943)), _793945 = _793943, class_Int_Onumber__ring(_793945)], (1144 ^ _777081) ^ [_794068, _794070] : [-(class_Groups_Osgn__if(_794068)), _794070 = _794068, class_Groups_Osgn__if(_794070)], (1154 ^ _777081) ^ [_794193, _794195] : [-(class_Groups_Oabs__if(_794193)), _794195 = _794193, class_Groups_Oabs__if(_794195)], (1164 ^ _777081) ^ [_794318, _794320] : [-(class_Rings_Oring__1(_794318)), _794320 = _794318, class_Rings_Oring__1(_794320)], (1174 ^ _777081) ^ [_794443, _794445] : [-(class_Rings_Oring(_794443)), _794445 = _794443, class_Rings_Oring(_794445)], (1184 ^ _777081) ^ [_794568, _794570] : [-(class_Rings_Oidom(_794568)), _794570 = _794568, class_Rings_Oidom(_794570)], (1194 ^ _777081) ^ [_794693, _794695] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_794693)), _794695 = _794693, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_794695)], (1204 ^ _777081) ^ [_794818, _794820] : [-(class_Orderings_Owellorder(_794818)), _794820 = _794818, class_Orderings_Owellorder(_794820)], (1214 ^ _777081) ^ [_794943, _794945] : [-(class_Complete__Lattice_Ocomplete__lattice(_794943)), _794945 = _794943, class_Complete__Lattice_Ocomplete__lattice(_794945)], (1224 ^ _777081) ^ [_795068, _795070] : [-(class_Lattices_Obounded__lattice__top(_795068)), _795070 = _795068, class_Lattices_Obounded__lattice__top(_795070)], (1234 ^ _777081) ^ [_795193, _795195] : [-(class_Lattices_Obounded__lattice__bot(_795193)), _795195 = _795193, class_Lattices_Obounded__lattice__bot(_795195)], (1244 ^ _777081) ^ [_795318, _795320] : [-(class_Lattices_Osemilattice__sup(_795318)), _795320 = _795318, class_Lattices_Osemilattice__sup(_795320)], (1254 ^ _777081) ^ [_795443, _795445] : [-(class_Lattices_Osemilattice__inf(_795443)), _795445 = _795443, class_Lattices_Osemilattice__inf(_795445)], (1264 ^ _777081) ^ [_795568, _795570] : [-(class_Lattices_Odistrib__lattice(_795568)), _795570 = _795568, class_Lattices_Odistrib__lattice(_795570)], (1274 ^ _777081) ^ [_795693, _795695] : [-(class_Lattices_Oboolean__algebra(_795693)), _795695 = _795693, class_Lattices_Oboolean__algebra(_795695)], (1284 ^ _777081) ^ [_795818, _795820] : [-(class_Lattices_Olattice(_795818)), _795820 = _795818, class_Lattices_Olattice(_795820)], (1294 ^ _777081) ^ [_795943, _795945] : [-(class_Orderings_Otop(_795943)), _795945 = _795943, class_Orderings_Otop(_795945)], (1304 ^ _777081) ^ [_796068, _796070] : [-(class_Orderings_Obot(_796068)), _796070 = _796068, class_Orderings_Obot(_796070)], (1314 ^ _777081) ^ [_796193, _796195] : [-(class_Groups_Ouminus(_796193)), _796195 = _796193, class_Groups_Ouminus(_796195)], (1324 ^ _777081) ^ [_796318, _796320] : [-(class_Finite__Set_Ofinite(_796318)), _796320 = _796318, class_Finite__Set_Ofinite(_796320)], (1334 ^ _777081) ^ [_796443, _796445] : [-(class_Smallcheck_Osmall(_796443)), _796445 = _796443, class_Smallcheck_Osmall(_796445)], (1344 ^ _777081) ^ [_796568, _796570] : [-(class_Enum_Oenum(_796568)), _796570 = _796568, class_Enum_Oenum(_796570)], (1354 ^ _777081) ^ [_796693, _796695] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_796693)), _796695 = _796693, class_Groups_Oordered__cancel__ab__semigroup__add(_796695)], (1364 ^ _777081) ^ [_796818, _796820] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_796818)), _796820 = _796818, class_Groups_Oordered__ab__semigroup__add__imp__le(_796820)], (1374 ^ _777081) ^ [_796943, _796945] : [-(class_Rings_Olinordered__comm__semiring__strict(_796943)), _796945 = _796943, class_Rings_Olinordered__comm__semiring__strict(_796945)], (1384 ^ _777081) ^ [_797068, _797070] : [-(class_Groups_Olinordered__ab__semigroup__add(_797068)), _797070 = _797068, class_Groups_Olinordered__ab__semigroup__add(_797070)], (1394 ^ _777081) ^ [_797193, _797195] : [-(class_Rings_Olinordered__semiring__strict(_797193)), _797195 = _797193, class_Rings_Olinordered__semiring__strict(_797195)], (1404 ^ _777081) ^ [_797318, _797320] : [-(class_Groups_Oordered__ab__semigroup__add(_797318)), _797320 = _797318, class_Groups_Oordered__ab__semigroup__add(_797320)], (1414 ^ _777081) ^ [_797443, _797445] : [-(class_Groups_Oordered__comm__monoid__add(_797443)), _797445 = _797443, class_Groups_Oordered__comm__monoid__add(_797445)], (1424 ^ _777081) ^ [_797568, _797570] : [-(class_Groups_Ocancel__ab__semigroup__add(_797568)), _797570 = _797568, class_Groups_Ocancel__ab__semigroup__add(_797570)], (1434 ^ _777081) ^ [_797693, _797695] : [-(class_Rings_Oordered__cancel__semiring(_797693)), _797695 = _797693, class_Rings_Oordered__cancel__semiring(_797695)], (1444 ^ _777081) ^ [_797818, _797820] : [-(class_Rings_Oordered__comm__semiring(_797818)), _797820 = _797818, class_Rings_Oordered__comm__semiring(_797820)], (1454 ^ _777081) ^ [_797943, _797945] : [-(class_Groups_Ocancel__semigroup__add(_797943)), _797945 = _797943, class_Groups_Ocancel__semigroup__add(_797945)], (1464 ^ _777081) ^ [_798068, _798070] : [-(class_Rings_Olinordered__semiring(_798068)), _798070 = _798068, class_Rings_Olinordered__semiring(_798070)], (1474 ^ _777081) ^ [_798193, _798195] : [-(class_Rings_Olinordered__semidom(_798193)), _798195 = _798193, class_Rings_Olinordered__semidom(_798195)], (1484 ^ _777081) ^ [_798318, _798320] : [-(class_Groups_Oab__semigroup__mult(_798318)), _798320 = _798318, class_Groups_Oab__semigroup__mult(_798320)], (1494 ^ _777081) ^ [_798443, _798445] : [-(class_Groups_Ocomm__monoid__mult(_798443)), _798445 = _798443, class_Groups_Ocomm__monoid__mult(_798445)], (1504 ^ _777081) ^ [_798568, _798570] : [-(class_Groups_Oab__semigroup__add(_798568)), _798570 = _798568, class_Groups_Oab__semigroup__add(_798570)], (1514 ^ _777081) ^ [_798693, _798695] : [-(class_Rings_Oordered__semiring(_798693)), _798695 = _798693, class_Rings_Oordered__semiring(_798695)], (1524 ^ _777081) ^ [_798818, _798820] : [-(class_Rings_Ono__zero__divisors(_798818)), _798820 = _798818, class_Rings_Ono__zero__divisors(_798820)], (1534 ^ _777081) ^ [_798943, _798945] : [-(class_Groups_Ocomm__monoid__add(_798943)), _798945 = _798943, class_Groups_Ocomm__monoid__add(_798945)], (1544 ^ _777081) ^ [_799068, _799070] : [-(class_Rings_Ocomm__semiring__1(_799068)), _799070 = _799068, class_Rings_Ocomm__semiring__1(_799070)], (1554 ^ _777081) ^ [_799193, _799195] : [-(class_Groups_Osemigroup__add(_799193)), _799195 = _799193, class_Groups_Osemigroup__add(_799195)], (1564 ^ _777081) ^ [_799318, _799320] : [-(class_Divides_Osemiring__div(_799318)), _799320 = _799318, class_Divides_Osemiring__div(_799320)], (1574 ^ _777081) ^ [_799443, _799445] : [-(class_Rings_Ocomm__semiring(_799443)), _799445 = _799443, class_Rings_Ocomm__semiring(_799445)], (1584 ^ _777081) ^ [_799568, _799570] : [-(class_Nat_Osemiring__char__0(_799568)), _799570 = _799568, class_Nat_Osemiring__char__0(_799570)], (1594 ^ _777081) ^ [_799693, _799695] : [-(class_Rings_Ozero__neq__one(_799693)), _799695 = _799693, class_Rings_Ozero__neq__one(_799695)], (1604 ^ _777081) ^ [_799818, _799820] : [-(class_Orderings_Opreorder(_799818)), _799820 = _799818, class_Orderings_Opreorder(_799820)], (1614 ^ _777081) ^ [_799943, _799945] : [-(class_Orderings_Olinorder(_799943)), _799945 = _799943, class_Orderings_Olinorder(_799945)], (1624 ^ _777081) ^ [_800068, _800070] : [-(class_Groups_Omonoid__mult(_800068)), _800070 = _800068, class_Groups_Omonoid__mult(_800070)], (1634 ^ _777081) ^ [_800193, _800195] : [-(class_Groups_Omonoid__add(_800193)), _800195 = _800193, class_Groups_Omonoid__add(_800195)], (1644 ^ _777081) ^ [_800318, _800320] : [-(class_Rings_Osemiring__1(_800318)), _800320 = _800318, class_Rings_Osemiring__1(_800320)], (1654 ^ _777081) ^ [_800443, _800445] : [-(class_Rings_Osemiring__0(_800443)), _800445 = _800443, class_Rings_Osemiring__0(_800445)], (1664 ^ _777081) ^ [_800568, _800570] : [-(class_Rings_Omult__zero(_800568)), _800570 = _800568, class_Rings_Omult__zero(_800570)], (1674 ^ _777081) ^ [_800693, _800695] : [-(class_Orderings_Oorder(_800693)), _800695 = _800693, class_Orderings_Oorder(_800695)], (1684 ^ _777081) ^ [_800818, _800820] : [-(class_Rings_Osemiring(_800818)), _800820 = _800818, class_Rings_Osemiring(_800820)], (1694 ^ _777081) ^ [_800943, _800945] : [-(class_Orderings_Oord(_800943)), _800945 = _800943, class_Orderings_Oord(_800945)], (1704 ^ _777081) ^ [_801068, _801070] : [-(class_Groups_Ominus(_801068)), _801070 = _801068, class_Groups_Ominus(_801070)], (1714 ^ _777081) ^ [_801193, _801195] : [-(class_Power_Opower(_801193)), _801195 = _801193, class_Power_Opower(_801195)], (1724 ^ _777081) ^ [_801318, _801320] : [-(class_Groups_Ozero(_801318)), _801320 = _801318, class_Groups_Ozero(_801320)], (1734 ^ _777081) ^ [_801443, _801445] : [-(class_Int_Onumber(_801443)), _801445 = _801443, class_Int_Onumber(_801445)], (1744 ^ _777081) ^ [_801568, _801570] : [-(class_Groups_Oone(_801568)), _801570 = _801568, class_Groups_Oone(_801570)], (1754 ^ _777081) ^ [_801693, _801695] : [-(class_HOL_Oequal(_801693)), _801695 = _801693, class_HOL_Oequal(_801695)], (1764 ^ _777081) ^ [_801814, _801816] : [-(hBOOL(_801814)), _801816 = _801814, hBOOL(_801816)], (1774 ^ _777081) ^ [_802628, _802630, _802632, _802634, _802636, _802638, _802640, _802642, _802644, _802646] : [-(c_Option_Ooption_Ooption__rec(_802646, _802642, _802638, _802634, _802630) = c_Option_Ooption_Ooption__rec(_802644, _802640, _802636, _802632, _802628)), _802646 = _802644, _802642 = _802640, _802638 = _802636, _802634 = _802632, _802630 = _802628], (1796 ^ _777081) ^ [_803017, _803019, _803021, _803023, _803025, _803027, _803029, _803031, _803033, _803035, _803037, _803039, _803041, _803043, _803045, _803047, _803049, _803051, _803053, _803055] : [-(c_Com_Ocom_Ocom__case(_803055, _803051, _803047, _803043, _803039, _803035, _803031, _803027, _803023, _803019) = c_Com_Ocom_Ocom__case(_803053, _803049, _803045, _803041, _803037, _803033, _803029, _803025, _803021, _803017)), _803055 = _803053, _803051 = _803049, _803047 = _803045, _803043 = _803041, _803039 = _803037, _803035 = _803033, _803031 = _803029, _803027 = _803025, _803023 = _803021, _803019 = _803017], (1838 ^ _777081) ^ [_803966, _803968, _803970, _803972, _803974, _803976, _803978, _803980, _803982, _803984, _803986, _803988, _803990, _803992, _803994, _803996, _803998, _804000, _804002, _804004] : [-(c_Com_Ocom_Ocom__rec(_804004, _804000, _803996, _803992, _803988, _803984, _803980, _803976, _803972, _803968) = c_Com_Ocom_Ocom__rec(_804002, _803998, _803994, _803990, _803986, _803982, _803978, _803974, _803970, _803966)), _804004 = _804002, _804000 = _803998, _803996 = _803994, _803992 = _803990, _803988 = _803986, _803984 = _803982, _803980 = _803978, _803976 = _803974, _803972 = _803970, _803968 = _803966], (1880 ^ _777081) ^ [_804915, _804917, _804919, _804921, _804923, _804925, _804927, _804929] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_804929, _804925, _804921, _804917) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_804927, _804923, _804919, _804915)), _804929 = _804927, _804925 = _804923, _804921 = _804919, _804917 = _804915], (1898 ^ _777081) ^ [_805216, _805218, _805220, _805222, _805224, _805226] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_805226, _805222, _805218) = c_Hoare__Mirabelle_Otriple_Otriple__size(_805224, _805220, _805216)), _805226 = _805224, _805222 = _805220, _805218 = _805216], (1912 ^ _777081) ^ [_805437, _805439, _805441, _805443, _805445, _805447, _805449, _805451] : [-(c_Com_Ovname_Ovname__case(_805451, _805447, _805443, _805439) = c_Com_Ovname_Ovname__case(_805449, _805445, _805441, _805437)), _805451 = _805449, _805447 = _805445, _805443 = _805441, _805439 = _805437], (1930 ^ _777081) ^ [_805738, _805740, _805742, _805744, _805746, _805748, _805750, _805752] : [-(c_Com_Ovname_Ovname__rec(_805752, _805748, _805744, _805740) = c_Com_Ovname_Ovname__rec(_805750, _805746, _805742, _805738)), _805752 = _805750, _805748 = _805746, _805744 = _805742, _805740 = _805738], (1948 ^ _777081) ^ [_806039, _806041] : [_806041 = _806039, -(c_Com_Ovname_Ovname__size(_806041) = c_Com_Ovname_Ovname__size(_806039))], (1954 ^ _777081) ^ [_806124, _806126] : [_806126 = _806124, -(c_Com_Ovname_OGlb(_806126) = c_Com_Ovname_OGlb(_806124))], (1960 ^ _777081) ^ [_806209, _806211] : [_806211 = _806209, -(c_Com_Ocom_Ocom__size(_806211) = c_Com_Ocom_Ocom__size(_806209))], (1966 ^ _777081) ^ [_806294, _806296, _806298, _806300, _806302, _806304] : [-(c_Option_Ooption_Ooption__size(_806304, _806300, _806296) = c_Option_Ooption_Ooption__size(_806302, _806298, _806294)), _806304 = _806302, _806300 = _806298, _806296 = _806294], (1980 ^ _777081) ^ [_806515, _806517] : [_806517 = _806515, -(c_HOL_Obool_Obool__size(_806517) = c_HOL_Obool_Obool__size(_806515))], (1986 ^ _777081) ^ [_806600, _806602] : [_806602 = _806600, -(c_Nat_Onat_Onat__size(_806602) = c_Nat_Onat_Onat__size(_806600))], (1992 ^ _777081) ^ [_806685, _806687, _806689, _806691, _806693, _806695, _806697, _806699, _806701, _806703] : [-(c_Nitpick_Opair__box_Opair__box__size(_806703, _806699, _806695, _806691, _806687) = c_Nitpick_Opair__box_Opair__box__size(_806701, _806697, _806693, _806689, _806685)), _806703 = _806701, _806699 = _806697, _806695 = _806693, _806691 = _806689, _806687 = _806685], (2014 ^ _777081) ^ [_807074, _807076, _807078, _807080, _807082, _807084] : [-(c_Com_Ocom_OCall(_807084, _807080, _807076) = c_Com_Ocom_OCall(_807082, _807078, _807074)), _807084 = _807082, _807080 = _807078, _807076 = _807074], (2028 ^ _777081) ^ [_807295, _807297, _807299, _807301, _807303, _807305, _807307, _807309, _807311, _807313] : [-(c_Sum__Type_Osum_Osum__size(_807313, _807309, _807305, _807301, _807297) = c_Sum__Type_Osum_Osum__size(_807311, _807307, _807303, _807299, _807295)), _807313 = _807311, _807309 = _807307, _807305 = _807303, _807301 = _807299, _807297 = _807295], (2050 ^ _777081) ^ [_807684, _807686, _807688, _807690] : [-(c_Com_Ocom_OAss(_807690, _807686) = c_Com_Ocom_OAss(_807688, _807684)), _807690 = _807688, _807686 = _807684], (2060 ^ _777081) ^ [_807833, _807835, _807837, _807839] : [-(c_Option_Obind(_807839, _807835) = c_Option_Obind(_807837, _807833)), _807839 = _807837, _807835 = _807833], (2070 ^ _777081) ^ [_807982, _807984, _807986, _807988, _807990, _807992, _807994, _807996, _807998, _808000, _808002, _808004] : [-(c_Map_Omap__comp(_808004, _808000, _807996, _807992, _807988, _807984) = c_Map_Omap__comp(_808002, _807998, _807994, _807990, _807986, _807982)), _808004 = _808002, _808000 = _807998, _807996 = _807994, _807992 = _807990, _807988 = _807986, _807984 = _807982], (2096 ^ _777081) ^ [_808467, _808469, _808471, _808473] : [-(c_Com_Ocom_OSemi(_808473, _808469) = c_Com_Ocom_OSemi(_808471, _808467)), _808473 = _808471, _808469 = _808467], (2106 ^ _777081) ^ [_808616, _808618] : [_808618 = _808616, -(c_Com_Ovname_OLoc(_808618) = c_Com_Ovname_OLoc(_808616))], (2112 ^ _777081) ^ [_808701, _808703, _808705, _808707, _808709, _808711] : [-(c_Com_Ocom_OLocal(_808711, _808707, _808703) = c_Com_Ocom_OLocal(_808709, _808705, _808701)), _808711 = _808709, _808707 = _808705, _808703 = _808701], (2126 ^ _777081) ^ [_808922, _808924, _808926, _808928, _808930, _808932, _808934, _808936, _808938, _808940] : [-(c_Nitpick_Opair__box_Opair__box__rec(_808940, _808936, _808932, _808928, _808924) = c_Nitpick_Opair__box_Opair__box__rec(_808938, _808934, _808930, _808926, _808922)), _808940 = _808938, _808936 = _808934, _808932 = _808930, _808928 = _808926, _808924 = _808922], (2148 ^ _777081) ^ [_809311, _809313, _809315, _809317, _809319, _809321, _809323, _809325, _809327, _809329] : [-(c_Nitpick_Opair__box_Opair__box__case(_809329, _809325, _809321, _809317, _809313) = c_Nitpick_Opair__box_Opair__box__case(_809327, _809323, _809319, _809315, _809311)), _809329 = _809327, _809325 = _809323, _809321 = _809319, _809317 = _809315, _809313 = _809311], (2170 ^ _777081) ^ [_809700, _809702, _809704, _809706, _809708, _809710, _809712, _809714] : [-(c_Nitpick_Opair__box_OPairBox(_809714, _809710, _809706, _809702) = c_Nitpick_Opair__box_OPairBox(_809712, _809708, _809704, _809700)), _809714 = _809712, _809710 = _809708, _809706 = _809704, _809702 = _809700], (2188 ^ _777081) ^ [_810001, _810003, _810005, _810007, _810009, _810011] : [-(c_Sum__Type_OProjl(_810011, _810007, _810003) = c_Sum__Type_OProjl(_810009, _810005, _810001)), _810011 = _810009, _810007 = _810005, _810003 = _810001], (2202 ^ _777081) ^ [_810222, _810224, _810226, _810228, _810230, _810232] : [-(c_Sum__Type_OProjr(_810232, _810228, _810224) = c_Sum__Type_OProjr(_810230, _810226, _810222)), _810232 = _810230, _810228 = _810226, _810224 = _810222], (2216 ^ _777081) ^ [_810443, _810445, _810447, _810449, _810451, _810453] : [-(c_Smallcheck_Oorelse(_810453, _810449, _810445) = c_Smallcheck_Oorelse(_810451, _810447, _810443)), _810453 = _810451, _810449 = _810447, _810445 = _810443], (2230 ^ _777081) ^ [_810664, _810666, _810668, _810670] : [-(c_Option_Oset(_810670, _810666) = c_Option_Oset(_810668, _810664)), _810670 = _810668, _810666 = _810664], (2240 ^ _777081) ^ [_810813, _810815] : [_810815 = _810813, -(c_Hoare__Mirabelle_OMGT(_810815) = c_Hoare__Mirabelle_OMGT(_810813))], (2246 ^ _777081) ^ [_810898, _810900] : [_810900 = _810898, -(c_Natural_Oevalc(_810900) = c_Natural_Oevalc(_810898))], (2252 ^ _777081) ^ [_810983, _810985, _810987, _810989, _810991, _810993, _810995, _810997] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_810997, _810993, _810989, _810985) = c_Hoare__Mirabelle_Otriple_Otriple__case(_810995, _810991, _810987, _810983)), _810997 = _810995, _810993 = _810991, _810989 = _810987, _810985 = _810983], (2270 ^ _777081) ^ [_811284, _811286, _811288, _811290, _811292, _811294, _811296, _811298, _811300, _811302, _811304, _811306] : [-(c_Sum__Type_Osum_Osum__rec(_811306, _811302, _811298, _811294, _811290, _811286) = c_Sum__Type_Osum_Osum__rec(_811304, _811300, _811296, _811292, _811288, _811284)), _811306 = _811304, _811302 = _811300, _811298 = _811296, _811294 = _811292, _811290 = _811288, _811286 = _811284], (2296 ^ _777081) ^ [_811769, _811771, _811773, _811775, _811777, _811779, _811781, _811783] : [-(c_Sum__Type_OSumr(_811783, _811779, _811775, _811771) = c_Sum__Type_OSumr(_811781, _811777, _811773, _811769)), _811783 = _811781, _811779 = _811777, _811775 = _811773, _811771 = _811769], (2314 ^ _777081) ^ [_812070, _812072, _812074, _812076, _812078, _812080, _812082, _812084] : [-(c_Sum__Type_OSuml(_812084, _812080, _812076, _812072) = c_Sum__Type_OSuml(_812082, _812078, _812074, _812070)), _812084 = _812082, _812080 = _812078, _812076 = _812074, _812072 = _812070], (2332 ^ _777081) ^ [_812371, _812373, _812375, _812377, _812379, _812381] : [-(c_Partial__Function_Oflat__lub(_812381, _812377, _812373) = c_Partial__Function_Oflat__lub(_812379, _812375, _812371)), _812381 = _812379, _812377 = _812375, _812373 = _812371], (2346 ^ _777081) ^ [_812592, _812594, _812596, _812598, _812600, _812602, _812604, _812606] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_812606, _812602, _812598, _812594) = c_Nat_Osemiring__1__class_Oof__nat__aux(_812604, _812600, _812596, _812592)), _812606 = _812604, _812602 = _812600, _812598 = _812596, _812594 = _812592], (2364 ^ _777081) ^ [_812893, _812895, _812897, _812899] : [-(c_Int_Onat__aux(_812899, _812895) = c_Int_Onat__aux(_812897, _812893)), _812899 = _812897, _812895 = _812893], (2374 ^ _777081) ^ [_813042, _813044, _813046, _813048] : [-(c_Nitpick_Oint__lcm(_813048, _813044) = c_Nitpick_Oint__lcm(_813046, _813042)), _813048 = _813046, _813044 = _813042], (2384 ^ _777081) ^ [_813191, _813193, _813195, _813197] : [-(c_Nat__Transfer_Otsub(_813197, _813193) = c_Nat__Transfer_Otsub(_813195, _813191)), _813197 = _813195, _813193 = _813191], (2394 ^ _777081) ^ [_813340, _813342, _813344, _813346, _813348, _813350] : [-(c_Nat_Onat_Onat__rec(_813350, _813346, _813342) = c_Nat_Onat_Onat__rec(_813348, _813344, _813340)), _813350 = _813348, _813346 = _813344, _813342 = _813340], (2408 ^ _777081) ^ [_813561, _813563] : [_813563 = _813561, -(c_Nat_Osemiring__1__class_ONats(_813563) = c_Nat_Osemiring__1__class_ONats(_813561))], (2414 ^ _777081) ^ [_813646, _813648, _813650, _813652] : [-(c_Orderings_Oord_Omin(_813652, _813648) = c_Orderings_Oord_Omin(_813650, _813646)), _813652 = _813650, _813648 = _813646], (2424 ^ _777081) ^ [_813795, _813797] : [_813797 = _813795, -(c_Int_Oring__1__class_OInts(_813797) = c_Int_Oring__1__class_OInts(_813795))], (2430 ^ _777081) ^ [_813880, _813882, _813884, _813886] : [-(c_Orderings_Oord_Omax(_813886, _813882) = c_Orderings_Oord_Omax(_813884, _813880)), _813886 = _813884, _813882 = _813880], (2440 ^ _777081) ^ [_814029, _814031, _814033, _814035] : [-(c_SMT_Oz3div(_814035, _814031) = c_SMT_Oz3div(_814033, _814029)), _814035 = _814033, _814031 = _814029], (2450 ^ _777081) ^ [_814178, _814180, _814182, _814184] : [-(c_SMT_Oz3mod(_814184, _814180) = c_SMT_Oz3mod(_814182, _814178)), _814184 = _814182, _814180 = _814178], (2460 ^ _777081) ^ [_814327, _814329] : [_814329 = _814327, -(c_Int_Opred(_814329) = c_Int_Opred(_814327))], (2466 ^ _777081) ^ [_814412, _814414] : [_814414 = _814412, -(c_Int_Osucc(_814414) = c_Int_Osucc(_814412))], (2472 ^ _777081) ^ [_814497, _814499, _814501, _814503, _814505, _814507] : [-(c_Power_Opower_Opower(_814507, _814503, _814499) = c_Power_Opower_Opower(_814505, _814501, _814497)), _814507 = _814505, _814503 = _814501, _814499 = _814497], (2486 ^ _777081) ^ [_814718, _814720, _814722, _814724] : [-(c_Nitpick_Onat__lcm(_814724, _814720) = c_Nitpick_Onat__lcm(_814722, _814718)), _814724 = _814722, _814720 = _814718], (2496 ^ _777081) ^ [_814867, _814869, _814871, _814873, _814875, _814877] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_814877, _814873, _814869) = c_Smallcheck_Ofull__small__class_Ofull__small(_814875, _814871, _814867)), _814877 = _814875, _814873 = _814871, _814869 = _814867], (2510 ^ _777081) ^ [_815088, _815090, _815092, _815094, _815096, _815098] : [-(c_Smallcheck_Ofull__small_H(_815098, _815094, _815090) = c_Smallcheck_Ofull__small_H(_815096, _815092, _815088)), _815098 = _815096, _815094 = _815092, _815090 = _815088], (2524 ^ _777081) ^ [_815309, _815311] : [_815311 = _815309, -(c_Smallcheck_Osmall__class_Osmall(_815311) = c_Smallcheck_Osmall__class_Osmall(_815309))], (2530 ^ _777081) ^ [_815394, _815396, _815398, _815400] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_815400, _815396) = c_Code__Numeral_Odiv__mod__code__numeral(_815398, _815394)), _815400 = _815398, _815396 = _815394], (2540 ^ _777081) ^ [_815543, _815545, _815547, _815549] : [-(c_Groups_Osgn__class_Osgn(_815549, _815545) = c_Groups_Osgn__class_Osgn(_815547, _815543)), _815549 = _815547, _815545 = _815543], (2550 ^ _777081) ^ [_815692, _815694, _815696, _815698] : [-(c_Divides_Odivmod__int__rel(_815698, _815694) = c_Divides_Odivmod__int__rel(_815696, _815692)), _815698 = _815696, _815694 = _815692], (2560 ^ _777081) ^ [_815841, _815843, _815845, _815847] : [-(c_Divides_Opdivmod(_815847, _815843) = c_Divides_Opdivmod(_815845, _815841)), _815847 = _815845, _815843 = _815841], (2570 ^ _777081) ^ [_815990, _815992, _815994, _815996, _815998, _816000] : [-(c_Smallcheck_Osmall_H(_816000, _815996, _815992) = c_Smallcheck_Osmall_H(_815998, _815994, _815990)), _816000 = _815998, _815996 = _815994, _815992 = _815990], (2584 ^ _777081) ^ [_816211, _816213] : [_816213 = _816211, -(c_Divides_Oadjust(_816213) = c_Divides_Oadjust(_816211))], (2590 ^ _777081) ^ [_816296, _816298, _816300, _816302] : [-(c_Nitpick_Onat__gcd(_816302, _816298) = c_Nitpick_Onat__gcd(_816300, _816296)), _816302 = _816300, _816298 = _816296], (2600 ^ _777081) ^ [_816445, _816447, _816449, _816451] : [-(c_Divides_Odivmod__int(_816451, _816447) = c_Divides_Odivmod__int(_816449, _816445)), _816451 = _816449, _816447 = _816445], (2610 ^ _777081) ^ [_816594, _816596, _816598, _816600] : [-(c_Divides_OnegDivAlg(_816600, _816596) = c_Divides_OnegDivAlg(_816598, _816594)), _816600 = _816598, _816596 = _816594], (2620 ^ _777081) ^ [_816743, _816745, _816747, _816749] : [-(c_Divides_OposDivAlg(_816749, _816745) = c_Divides_OposDivAlg(_816747, _816743)), _816749 = _816747, _816745 = _816743], (2630 ^ _777081) ^ [_816892, _816894, _816896, _816898, _816900, _816902, _816904, _816906, _816908, _816910] : [-(c_Product__Type_Oprod_Oprod__size(_816910, _816906, _816902, _816898, _816894) = c_Product__Type_Oprod_Oprod__size(_816908, _816904, _816900, _816896, _816892)), _816910 = _816908, _816906 = _816904, _816902 = _816900, _816898 = _816896, _816894 = _816892], (2652 ^ _777081) ^ [_817281, _817283] : [_817283 = _817281, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_817283) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_817281))], (2658 ^ _777081) ^ [_817366, _817368, _817370, _817372] : [-(c_Divides_Odivmod__nat(_817372, _817368) = c_Divides_Odivmod__nat(_817370, _817366)), _817372 = _817370, _817368 = _817366], (2668 ^ _777081) ^ [_817515, _817517, _817519, _817521] : [-(c_Divides_Odivmod__nat__rel(_817521, _817517) = c_Divides_Odivmod__nat__rel(_817519, _817515)), _817521 = _817519, _817517 = _817515], (2678 ^ _777081) ^ [_817664, _817666, _817668, _817670, _817672, _817674, _817676, _817678, _817680, _817682] : [-(c_Product__Type_Oprod_Oprod__rec(_817682, _817678, _817674, _817670, _817666) = c_Product__Type_Oprod_Oprod__rec(_817680, _817676, _817672, _817668, _817664)), _817682 = _817680, _817678 = _817676, _817674 = _817672, _817670 = _817668, _817666 = _817664], (2700 ^ _777081) ^ [_818053, _818055, _818057, _818059, _818061, _818063, _818065, _818067] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_818067, _818063, _818059, _818055) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_818065, _818061, _818057, _818053)), _818067 = _818065, _818063 = _818061, _818059 = _818057, _818055 = _818053], (2718 ^ _777081) ^ [_818354, _818356, _818358, _818360] : [-(c_FunDef_Orp__inv__image(_818360, _818356) = c_FunDef_Orp__inv__image(_818358, _818354)), _818360 = _818358, _818356 = _818354], (2728 ^ _777081) ^ [_818503, _818505, _818507, _818509, _818511, _818513] : [-(c_SetInterval_Oord_OatMost(_818513, _818509, _818505) = c_SetInterval_Oord_OatMost(_818511, _818507, _818503)), _818513 = _818511, _818509 = _818507, _818505 = _818503], (2742 ^ _777081) ^ [_818724, _818726, _818728, _818730, _818732, _818734] : [-(c_SetInterval_Oord_OatLeast(_818734, _818730, _818726) = c_SetInterval_Oord_OatLeast(_818732, _818728, _818724)), _818734 = _818732, _818730 = _818728, _818726 = _818724], (2756 ^ _777081) ^ [_818945, _818947, _818949, _818951, _818953, _818955] : [-(c_SetInterval_Oord_OlessThan(_818955, _818951, _818947) = c_SetInterval_Oord_OlessThan(_818953, _818949, _818945)), _818955 = _818953, _818951 = _818949, _818947 = _818945], (2770 ^ _777081) ^ [_819166, _819168, _819170, _819172, _819174, _819176] : [-(c_SetInterval_Oord_OgreaterThan(_819176, _819172, _819168) = c_SetInterval_Oord_OgreaterThan(_819174, _819170, _819166)), _819176 = _819174, _819172 = _819170, _819168 = _819166], (2784 ^ _777081) ^ [_819387, _819389, _819391, _819393, _819395, _819397, _819399, _819401, _819403, _819405] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_819405, _819401, _819397, _819393, _819389) = c_SetInterval_Oord_OgreaterThanAtMost(_819403, _819399, _819395, _819391, _819387)), _819405 = _819403, _819401 = _819399, _819397 = _819395, _819393 = _819391, _819389 = _819387], (2806 ^ _777081) ^ [_819776, _819778, _819780, _819782, _819784, _819786, _819788, _819790, _819792, _819794] : [-(c_SetInterval_Oord_OatLeastLessThan(_819794, _819790, _819786, _819782, _819778) = c_SetInterval_Oord_OatLeastLessThan(_819792, _819788, _819784, _819780, _819776)), _819794 = _819792, _819790 = _819788, _819786 = _819784, _819782 = _819780, _819778 = _819776], (2828 ^ _777081) ^ [_820165, _820167, _820169, _820171, _820173, _820175, _820177, _820179] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_820179, _820175, _820171, _820167) = c_SetInterval_Oord_OgreaterThanLessThan(_820177, _820173, _820169, _820165)), _820179 = _820177, _820175 = _820173, _820171 = _820169, _820167 = _820165], (2846 ^ _777081) ^ [_820466, _820468, _820470, _820472, _820474, _820476, _820478, _820480] : [-(c_SetInterval_Oord_OatLeastAtMost(_820480, _820476, _820472, _820468) = c_SetInterval_Oord_OatLeastAtMost(_820478, _820474, _820470, _820466)), _820480 = _820478, _820476 = _820474, _820472 = _820470, _820468 = _820466], (2864 ^ _777081) ^ [_820767, _820769] : [_820769 = _820767, -(c_Int_OBit0(_820769) = c_Int_OBit0(_820767))], (2870 ^ _777081) ^ [_820852, _820854] : [_820854 = _820852, -(c_Rings_Oinverse__class_Odivide(_820854) = c_Rings_Oinverse__class_Odivide(_820852))], (2876 ^ _777081) ^ [_820937, _820939, _820941, _820943, _820945, _820947, _820949, _820951] : [-(c_Sum__Type_OPlus(_820951, _820947, _820943, _820939) = c_Sum__Type_OPlus(_820949, _820945, _820941, _820937)), _820951 = _820949, _820947 = _820945, _820943 = _820941, _820939 = _820937], (2894 ^ _777081) ^ [_821238, _821240, _821242, _821244, _821246, _821248, _821250, _821252] : [-(c_Fun_Othe__inv__into(_821252, _821248, _821244, _821240) = c_Fun_Othe__inv__into(_821250, _821246, _821242, _821238)), _821252 = _821250, _821248 = _821246, _821244 = _821242, _821240 = _821238], (2912 ^ _777081) ^ [_821539, _821541, _821543, _821545, _821547, _821549, _821551, _821553, _821555, _821557] : [-(c_Sum__Type_Osum_Osum__case(_821557, _821553, _821549, _821545, _821541) = c_Sum__Type_Osum_Osum__case(_821555, _821551, _821547, _821543, _821539)), _821557 = _821555, _821553 = _821551, _821549 = _821547, _821545 = _821543, _821541 = _821539], (2934 ^ _777081) ^ [_821928, _821930, _821932, _821934, _821936, _821938] : [-(c_Com_Ocom_OCond(_821938, _821934, _821930) = c_Com_Ocom_OCond(_821936, _821932, _821928)), _821938 = _821936, _821934 = _821932, _821930 = _821928], (2948 ^ _777081) ^ [_822149, _822151] : [_822151 = _822149, -(c_Hoare__Mirabelle_Otriple_Otriple(_822151) = c_Hoare__Mirabelle_Otriple_Otriple(_822149))], (2954 ^ _777081) ^ [_822234, _822236, _822238, _822240] : [-(c_Com_Ocom_OWhile(_822240, _822236) = c_Com_Ocom_OWhile(_822238, _822234)), _822240 = _822238, _822236 = _822234], (2964 ^ _777081) ^ [_822383, _822385, _822387, _822389, _822391, _822393] : [-(c_Hoare__Mirabelle_Opeek__and(_822393, _822389, _822385) = c_Hoare__Mirabelle_Opeek__and(_822391, _822387, _822383)), _822393 = _822391, _822389 = _822387, _822385 = _822383], (2978 ^ _777081) ^ [_822604, _822606] : [_822606 = _822604, -(c_SetInterval_Oord__class_OatLeast(_822606) = c_SetInterval_Oord__class_OatLeast(_822604))], (2984 ^ _777081) ^ [_822689, _822691, _822693, _822695] : [-(c_Set_Othe__elem(_822695, _822691) = c_Set_Othe__elem(_822693, _822689)), _822695 = _822693, _822691 = _822689], (2994 ^ _777081) ^ [_822838, _822840] : [_822840 = _822838, -(c_Nitpick_Ozero__frac(_822840) = c_Nitpick_Ozero__frac(_822838))], (3000 ^ _777081) ^ [_822923, _822925] : [_822925 = _822923, -(c_Nitpick_Oone__frac(_822925) = c_Nitpick_Oone__frac(_822923))], (3006 ^ _777081) ^ [_823008, _823010, _823012, _823014] : [-(c_Nitpick_Onumber__of__frac(_823014, _823010) = c_Nitpick_Onumber__of__frac(_823012, _823008)), _823014 = _823012, _823010 = _823008], (3016 ^ _777081) ^ [_823157, _823159, _823161, _823163, _823165, _823167] : [-(c_Nitpick_Ofrac(_823167, _823163, _823159) = c_Nitpick_Ofrac(_823165, _823161, _823157)), _823167 = _823165, _823163 = _823161, _823159 = _823157], (3030 ^ _777081) ^ [_823378, _823380, _823382, _823384] : [-(c_Nitpick_OAbs__Frac(_823384, _823380) = c_Nitpick_OAbs__Frac(_823382, _823378)), _823384 = _823382, _823380 = _823378], (3040 ^ _777081) ^ [_823527, _823529, _823531, _823533] : [-(c_Nitpick_Onorm__frac(_823533, _823529) = c_Nitpick_Onorm__frac(_823531, _823527)), _823533 = _823531, _823529 = _823527], (3050 ^ _777081) ^ [_823676, _823678, _823680, _823682, _823684, _823686] : [-(c_Finite__Set_Ofold1Set(_823686, _823682, _823678) = c_Finite__Set_Ofold1Set(_823684, _823680, _823676)), _823686 = _823684, _823682 = _823680, _823678 = _823676], (3064 ^ _777081) ^ [_823897, _823899, _823901, _823903, _823905, _823907, _823909, _823911, _823913, _823915] : [-(c_Fun_Ooverride__on(_823915, _823911, _823907, _823903, _823899) = c_Fun_Ooverride__on(_823913, _823909, _823905, _823901, _823897)), _823915 = _823913, _823911 = _823909, _823907 = _823905, _823903 = _823901, _823899 = _823897], (3086 ^ _777081) ^ [_824286, _824288, _824290, _824292, _824294, _824296, _824298, _824300] : [-(c_Nitpick_Oprod(_824300, _824296, _824292, _824288) = c_Nitpick_Oprod(_824298, _824294, _824290, _824286)), _824300 = _824298, _824296 = _824294, _824292 = _824290, _824288 = _824286], (3104 ^ _777081) ^ [_824587, _824589] : [_824589 = _824587, -(c_Int_Oring__1__class_Oof__int(_824589) = c_Int_Oring__1__class_Oof__int(_824587))], (3110 ^ _777081) ^ [_824672, _824674, _824676, _824678, _824680, _824682, _824684, _824686] : [-(c_Product__Type_Oapfst(_824686, _824682, _824678, _824674) = c_Product__Type_Oapfst(_824684, _824680, _824676, _824672)), _824686 = _824684, _824682 = _824680, _824678 = _824676, _824674 = _824672], (3128 ^ _777081) ^ [_824973, _824975, _824977, _824979, _824981, _824983, _824985, _824987] : [-(c_Product__Type_Oapsnd(_824987, _824983, _824979, _824975) = c_Product__Type_Oapsnd(_824985, _824981, _824977, _824973)), _824987 = _824985, _824983 = _824981, _824979 = _824977, _824975 = _824973], (3146 ^ _777081) ^ [_825274, _825276, _825278, _825280] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_825280, _825276) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_825278, _825274)), _825280 = _825278, _825276 = _825274], (3156 ^ _777081) ^ [_825423, _825425] : [_825425 = _825423, -(c_Wellfounded_Omeasure(_825425) = c_Wellfounded_Omeasure(_825423))], (3162 ^ _777081) ^ [_825508, _825510, _825512, _825514] : [-(c_Wellfounded_Omin__ext(_825514, _825510) = c_Wellfounded_Omin__ext(_825512, _825508)), _825514 = _825512, _825510 = _825508], (3172 ^ _777081) ^ [_825657, _825659] : [_825659 = _825657, -(c_Wellfounded_Ofinite__psubset(_825659) = c_Wellfounded_Ofinite__psubset(_825657))], (3178 ^ _777081) ^ [_825742, _825744, _825746, _825748, _825750, _825752] : [-(c_Wellfounded_Omlex__prod(_825752, _825748, _825744) = c_Wellfounded_Omlex__prod(_825750, _825746, _825742)), _825752 = _825750, _825748 = _825746, _825744 = _825742], (3192 ^ _777081) ^ [_825963, _825965] : [_825965 = _825963, -(c_Int_Oint__ge__less__than(_825965) = c_Int_Oint__ge__less__than(_825963))], (3198 ^ _777081) ^ [_826048, _826050] : [_826050 = _826048, -(c_Int_Oint__ge__less__than2(_826050) = c_Int_Oint__ge__less__than2(_826048))], (3204 ^ _777081) ^ [_826133, _826135, _826137, _826139, _826141, _826143, _826145, _826147] : [-(c_Recdef_Osame__fst(_826147, _826143, _826139, _826135) = c_Recdef_Osame__fst(_826145, _826141, _826137, _826133)), _826147 = _826145, _826143 = _826141, _826139 = _826137, _826135 = _826133], (3222 ^ _777081) ^ [_826434, _826436, _826438, _826440, _826442, _826444] : [-(c_FunDef_Oin__rel(_826444, _826440, _826436) = c_FunDef_Oin__rel(_826442, _826438, _826434)), _826444 = _826442, _826440 = _826438, _826436 = _826434], (3236 ^ _777081) ^ [_826655, _826657, _826659, _826661] : [-(c_Predicate_OPowp(_826661, _826657) = c_Predicate_OPowp(_826659, _826655)), _826661 = _826659, _826657 = _826655], (3246 ^ _777081) ^ [_826804, _826806, _826808, _826810] : [-(c_Option_Omap(_826810, _826806) = c_Option_Omap(_826808, _826804)), _826810 = _826808, _826806 = _826804], (3256 ^ _777081) ^ [_826953, _826955, _826957, _826959, _826961, _826963] : [-(c_Map_Oran(_826963, _826959, _826955) = c_Map_Oran(_826961, _826957, _826953)), _826963 = _826961, _826959 = _826957, _826955 = _826953], (3270 ^ _777081) ^ [_827174, _827176, _827178, _827180] : [-(c_List_Olenlex(_827180, _827176) = c_List_Olenlex(_827178, _827174)), _827180 = _827178, _827176 = _827174], (3280 ^ _777081) ^ [_827323, _827325, _827327, _827329, _827331, _827333, _827335, _827337, _827339, _827341, _827343, _827345] : [-(c_Product__Type_Omap__pair(_827345, _827341, _827337, _827333, _827329, _827325) = c_Product__Type_Omap__pair(_827343, _827339, _827335, _827331, _827327, _827323)), _827345 = _827343, _827341 = _827339, _827337 = _827335, _827333 = _827331, _827329 = _827327, _827325 = _827323], (3306 ^ _777081) ^ [_827808, _827810, _827812, _827814, _827816, _827818, _827820, _827822] : [-(c_Wellfounded_Olex__prod(_827822, _827818, _827814, _827810) = c_Wellfounded_Olex__prod(_827820, _827816, _827812, _827808)), _827822 = _827820, _827818 = _827816, _827814 = _827812, _827810 = _827808], (3324 ^ _777081) ^ [_828109, _828111, _828113, _828115] : [-(c_List_Olexn(_828115, _828111) = c_List_Olexn(_828113, _828109)), _828115 = _828113, _828111 = _828109], (3334 ^ _777081) ^ [_828258, _828260, _828262, _828264, _828266, _828268, _828270, _828272] : [-(c_Map_Orestrict__map(_828272, _828268, _828264, _828260) = c_Map_Orestrict__map(_828270, _828266, _828262, _828258)), _828272 = _828270, _828268 = _828266, _828264 = _828262, _828260 = _828258], (3352 ^ _777081) ^ [_828559, _828561] : [_828561 = _828559, -(c_Groups_Oabs__class_Oabs(_828561) = c_Groups_Oabs__class_Oabs(_828559))], (3358 ^ _777081) ^ [_828644, _828646, _828648, _828650, _828652, _828654, _828656, _828658] : [-(c_Nitpick_Osetsum_H(_828658, _828654, _828650, _828646) = c_Nitpick_Osetsum_H(_828656, _828652, _828648, _828644)), _828658 = _828656, _828654 = _828652, _828650 = _828648, _828646 = _828644], (3376 ^ _777081) ^ [_828945, _828947, _828949, _828951] : [-(c_Nitpick_Ocard_H(_828951, _828947) = c_Nitpick_Ocard_H(_828949, _828945)), _828951 = _828949, _828947 = _828945], (3386 ^ _777081) ^ [_829094, _829096, _829098, _829100] : [-(c_Hilbert__Choice_OEps(_829100, _829096) = c_Hilbert__Choice_OEps(_829098, _829094)), _829100 = _829098, _829096 = _829094], (3396 ^ _777081) ^ [_829243, _829245, _829247, _829249, _829251, _829253, _829255, _829257] : [-(c_Hilbert__Choice_OLeastM(_829257, _829253, _829249, _829245) = c_Hilbert__Choice_OLeastM(_829255, _829251, _829247, _829243)), _829257 = _829255, _829253 = _829251, _829249 = _829247, _829245 = _829243], (3414 ^ _777081) ^ [_829544, _829546] : [_829546 = _829544, -(c_Hilbert__Choice_OGreatest(_829546) = c_Hilbert__Choice_OGreatest(_829544))], (3420 ^ _777081) ^ [_829629, _829631, _829633, _829635, _829637, _829639] : [-(c_Hilbert__Choice_OGreatestM(_829639, _829635, _829631) = c_Hilbert__Choice_OGreatestM(_829637, _829633, _829629)), _829639 = _829637, _829635 = _829633, _829631 = _829629], (3434 ^ _777081) ^ [_829850, _829852, _829854, _829856, _829858, _829860] : [-(c_List_Olist_Olist__size(_829860, _829856, _829852) = c_List_Olist_Olist__size(_829858, _829854, _829850)), _829860 = _829858, _829856 = _829854, _829852 = _829850], (3448 ^ _777081) ^ [_830071, _830073, _830075, _830077, _830079, _830081, _830083, _830085] : [-(c_Lazy__Sequence_Oanamorph(_830085, _830081, _830077, _830073) = c_Lazy__Sequence_Oanamorph(_830083, _830079, _830075, _830071)), _830085 = _830083, _830081 = _830079, _830077 = _830075, _830073 = _830071], (3466 ^ _777081) ^ [_830372, _830374, _830376, _830378, _830380, _830382] : [-(c_List_Oset__Cons(_830382, _830378, _830374) = c_List_Oset__Cons(_830380, _830376, _830372)), _830382 = _830380, _830378 = _830376, _830374 = _830372], (3480 ^ _777081) ^ [_830593, _830595, _830597, _830599] : [-(c_List_Olistset(_830599, _830595) = c_List_Olistset(_830597, _830593)), _830599 = _830597, _830595 = _830593], (3490 ^ _777081) ^ [_830742, _830744, _830746, _830748, _830750, _830752, _830754, _830756] : [-(c_Nat_Onat_Onat__case(_830756, _830752, _830748, _830744) = c_Nat_Onat_Onat__case(_830754, _830750, _830746, _830742)), _830756 = _830754, _830752 = _830750, _830748 = _830746, _830744 = _830742], (3508 ^ _777081) ^ [_831043, _831045, _831047, _831049] : [-(c_Fun_Ofun__upd(_831049, _831045) = c_Fun_Ofun__upd(_831047, _831043)), _831049 = _831047, _831045 = _831043], (3518 ^ _777081) ^ [_831192, _831194, _831196, _831198] : [-(c_List_Olexord(_831198, _831194) = c_List_Olexord(_831196, _831192)), _831198 = _831196, _831194 = _831192], (3528 ^ _777081) ^ [_831341, _831343] : [_831343 = _831341, -(c_Set_OBall(_831343) = c_Set_OBall(_831341))], (3534 ^ _777081) ^ [_831426, _831428] : [_831428 = _831426, -(c_SetInterval_Oord__class_OgreaterThan(_831428) = c_SetInterval_Oord__class_OgreaterThan(_831426))], (3540 ^ _777081) ^ [_831511, _831513, _831515, _831517, _831519, _831521] : [-(c_List_Opartition(_831521, _831517, _831513) = c_List_Opartition(_831519, _831515, _831511)), _831521 = _831519, _831517 = _831515, _831513 = _831511], (3554 ^ _777081) ^ [_831732, _831734, _831736, _831738] : [-(c_List_Olists(_831738, _831734) = c_List_Olists(_831736, _831732)), _831738 = _831736, _831734 = _831732], (3564 ^ _777081) ^ [_831881, _831883, _831885, _831887] : [-(c_List_Olistsp(_831887, _831883) = c_List_Olistsp(_831885, _831881)), _831887 = _831885, _831883 = _831881], (3574 ^ _777081) ^ [_832030, _832032, _832034, _832036, _832038, _832040, _832042, _832044] : [-(c_Option_Ooption_Ooption__case(_832044, _832040, _832036, _832032) = c_Option_Ooption_Ooption__case(_832042, _832038, _832034, _832030)), _832044 = _832042, _832040 = _832038, _832036 = _832034, _832032 = _832030], (3592 ^ _777081) ^ [_832331, _832333, _832335, _832337, _832339, _832341, _832343, _832345] : [-(c_List_Omap__filter(_832345, _832341, _832337, _832333) = c_List_Omap__filter(_832343, _832339, _832335, _832331)), _832345 = _832343, _832341 = _832339, _832337 = _832335, _832333 = _832331], (3610 ^ _777081) ^ [_832632, _832634] : [_832634 = _832632, -(c_If(_832634) = c_If(_832632))], (3616 ^ _777081) ^ [_832717, _832719, _832721, _832723, _832725, _832727] : [-(c_List_Osublist(_832727, _832723, _832719) = c_List_Osublist(_832725, _832721, _832717)), _832727 = _832725, _832723 = _832721, _832719 = _832717], (3630 ^ _777081) ^ [_832938, _832940, _832942, _832944] : [-(c_List_Oupto(_832944, _832940) = c_List_Oupto(_832942, _832938)), _832944 = _832942, _832940 = _832938], (3640 ^ _777081) ^ [_833087, _833089, _833091, _833093, _833095, _833097, _833099, _833101, _833103, _833105] : [-(c_List_Olinorder__class_Oinsort__insert__key(_833105, _833101, _833097, _833093, _833089) = c_List_Olinorder__class_Oinsort__insert__key(_833103, _833099, _833095, _833091, _833087)), _833105 = _833103, _833101 = _833099, _833097 = _833095, _833093 = _833091, _833089 = _833087], (3662 ^ _777081) ^ [_833476, _833478, _833480, _833482, _833484, _833486] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_833486, _833482, _833478) = c_SetInterval_Oord__class_OatLeastAtMost(_833484, _833480, _833476)), _833486 = _833484, _833482 = _833480, _833478 = _833476], (3676 ^ _777081) ^ [_833697, _833699] : [_833699 = _833697, -(c_SetInterval_Oord__class_OlessThan(_833699) = c_SetInterval_Oord__class_OlessThan(_833697))], (3682 ^ _777081) ^ [_833782, _833784, _833786, _833788, _833790, _833792] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_833792, _833788, _833784) = c_SetInterval_Oord__class_OgreaterThanAtMost(_833790, _833786, _833782)), _833792 = _833790, _833788 = _833786, _833784 = _833782], (3696 ^ _777081) ^ [_834003, _834005, _834007, _834009, _834011, _834013] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_834013, _834009, _834005) = c_SetInterval_Oord__class_OgreaterThanLessThan(_834011, _834007, _834003)), _834013 = _834011, _834009 = _834007, _834005 = _834003], (3710 ^ _777081) ^ [_834224, _834226] : [_834226 = _834224, -(c_SetInterval_Oord__class_OatMost(_834226) = c_SetInterval_Oord__class_OatMost(_834224))], (3716 ^ _777081) ^ [_834309, _834311, _834313, _834315] : [-(c_List_Oupt(_834315, _834311) = c_List_Oupt(_834313, _834309)), _834315 = _834313, _834311 = _834309], (3726 ^ _777081) ^ [_834458, _834460, _834462, _834464, _834466, _834468, _834470, _834472, _834474, _834476] : [-(c_List_Ofoldr(_834476, _834472, _834468, _834464, _834460) = c_List_Ofoldr(_834474, _834470, _834466, _834462, _834458)), _834476 = _834474, _834472 = _834470, _834468 = _834466, _834464 = _834462, _834460 = _834458], (3748 ^ _777081) ^ [_834847, _834849, _834851, _834853] : [-(c_Wellfounded_Oaccp(_834853, _834849) = c_Wellfounded_Oaccp(_834851, _834847)), _834853 = _834851, _834849 = _834847], (3758 ^ _777081) ^ [_834996, _834998] : [_834998 = _834996, -(c_List_Otranspose__rel(_834998) = c_List_Otranspose__rel(_834996))], (3764 ^ _777081) ^ [_835081, _835083, _835085, _835087, _835089, _835091, _835093, _835095] : [-(c_List_Olist_Olist__case(_835095, _835091, _835087, _835083) = c_List_Olist_Olist__case(_835093, _835089, _835085, _835081)), _835095 = _835093, _835091 = _835089, _835087 = _835085, _835083 = _835081], (3782 ^ _777081) ^ [_835382, _835384, _835386, _835388] : [-(c_List_Otranspose(_835388, _835384) = c_List_Otranspose(_835386, _835382)), _835388 = _835386, _835384 = _835382], (3792 ^ _777081) ^ [_835531, _835533, _835535, _835537, _835539, _835541, _835543, _835545, _835547, _835549] : [-(c_Map_Omap__upds(_835549, _835545, _835541, _835537, _835533) = c_Map_Omap__upds(_835547, _835543, _835539, _835535, _835531)), _835549 = _835547, _835545 = _835543, _835541 = _835539, _835537 = _835535, _835533 = _835531], (3814 ^ _777081) ^ [_835920, _835922, _835924, _835926, _835928, _835930, _835932, _835934] : [-(c_Map_Omap__add(_835934, _835930, _835926, _835922) = c_Map_Omap__add(_835932, _835928, _835924, _835920)), _835934 = _835932, _835930 = _835928, _835926 = _835924, _835922 = _835920], (3832 ^ _777081) ^ [_836221, _836223, _836225, _836227] : [-(c_List_Olast(_836227, _836223) = c_List_Olast(_836225, _836221)), _836227 = _836225, _836223 = _836221], (3842 ^ _777081) ^ [_836370, _836372, _836374, _836376] : [-(c_List_Obutlast(_836376, _836372) = c_List_Obutlast(_836374, _836370)), _836376 = _836374, _836372 = _836370], (3852 ^ _777081) ^ [_836519, _836521] : [_836521 = _836519, -(c_List_Oreturn__list(_836521) = c_List_Oreturn__list(_836519))], (3858 ^ _777081) ^ [_836604, _836606] : [_836606 = _836604, -(c_List_Oembed__list(_836606) = c_List_Oembed__list(_836604))], (3864 ^ _777081) ^ [_836689, _836691] : [_836691 = _836689, -(c_List_Otl(_836691) = c_List_Otl(_836689))], (3870 ^ _777081) ^ [_836774, _836776] : [_836776 = _836774, -(c_List_Ohd(_836776) = c_List_Ohd(_836774))], (3876 ^ _777081) ^ [_836859, _836861] : [_836861 = _836859, -(c_Power_Opower__class_Opower(_836861) = c_Power_Opower__class_Opower(_836859))], (3882 ^ _777081) ^ [_836944, _836946, _836948, _836950] : [-(c_HOL_OLet(_836950, _836946) = c_HOL_OLet(_836948, _836944)), _836950 = _836948, _836946 = _836944], (3892 ^ _777081) ^ [_837093, _837095, _837097, _837099] : [-(c_Enum_Osublists(_837099, _837095) = c_Enum_Osublists(_837097, _837093)), _837099 = _837097, _837095 = _837093], (3902 ^ _777081) ^ [_837242, _837244, _837246, _837248] : [-(c_Enum_Oenum__the(_837248, _837244) = c_Enum_Oenum__the(_837246, _837242)), _837248 = _837246, _837244 = _837242], (3912 ^ _777081) ^ [_837391, _837393, _837395, _837397, _837399, _837401, _837403, _837405] : [-(c_Enum_Oproduct(_837405, _837401, _837397, _837393) = c_Enum_Oproduct(_837403, _837399, _837395, _837391)), _837405 = _837403, _837401 = _837399, _837397 = _837395, _837393 = _837391], (3930 ^ _777081) ^ [_837692, _837694, _837696, _837698] : [-(c_List_Olinorder__class_Osorted__list__of__set(_837698, _837694) = c_List_Olinorder__class_Osorted__list__of__set(_837696, _837692)), _837698 = _837696, _837694 = _837692], (3940 ^ _777081) ^ [_837841, _837843, _837845, _837847, _837849, _837851, _837853, _837855] : [-(c_List_Olinorder__class_Osort__key(_837855, _837851, _837847, _837843) = c_List_Olinorder__class_Osort__key(_837853, _837849, _837845, _837841)), _837855 = _837853, _837851 = _837849, _837847 = _837845, _837843 = _837841], (3958 ^ _777081) ^ [_838142, _838144, _838146, _838148, _838150, _838152] : [-(c_Enum_On__lists(_838152, _838148, _838144) = c_Enum_On__lists(_838150, _838146, _838142)), _838152 = _838150, _838148 = _838146, _838144 = _838142], (3972 ^ _777081) ^ [_838363, _838365, _838367, _838369] : [-(c_Sum__Type_OInl(_838369, _838365) = c_Sum__Type_OInl(_838367, _838363)), _838369 = _838367, _838365 = _838363], (3982 ^ _777081) ^ [_838512, _838514, _838516, _838518] : [-(c_Sum__Type_OInr(_838518, _838514) = c_Sum__Type_OInr(_838516, _838512)), _838518 = _838516, _838514 = _838512], (3992 ^ _777081) ^ [_838661, _838663] : [_838663 = _838661, -(c_Enum_Oenum__class_Oenum__ex(_838663) = c_Enum_Oenum__class_Oenum__ex(_838661))], (3998 ^ _777081) ^ [_838746, _838748] : [_838748 = _838746, -(c_Enum_Oenum__class_Oenum__all(_838748) = c_Enum_Oenum__class_Oenum__all(_838746))], (4004 ^ _777081) ^ [_838831, _838833] : [_838833 = _838831, -(c_Option_Othe(_838833) = c_Option_Othe(_838831))], (4010 ^ _777081) ^ [_838916, _838918] : [_838918 = _838916, -(c_Enum_Oenum__class_Oenum(_838918) = c_Enum_Oenum__class_Oenum(_838916))], (4016 ^ _777081) ^ [_839001, _839003] : [_839003 = _839001, -(c_Equiv__Relations_Oquotient(_839003) = c_Equiv__Relations_Oquotient(_839001))], (4022 ^ _777081) ^ [_839086, _839088] : [_839088 = _839086, -(c_Set_OPow(_839088) = c_Set_OPow(_839086))], (4028 ^ _777081) ^ [_839171, _839173, _839175, _839177, _839179, _839181] : [-(c_Set_Ovimage(_839181, _839177, _839173) = c_Set_Ovimage(_839179, _839175, _839171)), _839181 = _839179, _839177 = _839175, _839173 = _839171], (4042 ^ _777081) ^ [_839392, _839394] : [_839394 = _839392, -(c_HOL_OAll(_839394) = c_HOL_OAll(_839392))], (4048 ^ _777081) ^ [_839477, _839479] : [_839479 = _839477, -(c_List_Odrop(_839479) = c_List_Odrop(_839477))], (4054 ^ _777081) ^ [_839562, _839564, _839566, _839568] : [-(c_List_Olist__update(_839568, _839564) = c_List_Olist__update(_839566, _839562)), _839568 = _839566, _839564 = _839562], (4064 ^ _777081) ^ [_839711, _839713, _839715, _839717, _839719, _839721] : [-(c_List_Oremove1(_839721, _839717, _839713) = c_List_Oremove1(_839719, _839715, _839711)), _839721 = _839719, _839717 = _839715, _839713 = _839711], (4078 ^ _777081) ^ [_839932, _839934, _839936, _839938] : [-(c_List_OremoveAll(_839938, _839934) = c_List_OremoveAll(_839936, _839932)), _839938 = _839936, _839934 = _839932], (4088 ^ _777081) ^ [_840081, _840083, _840085, _840087] : [-(c_List_Oremdups(_840087, _840083) = c_List_Oremdups(_840085, _840081)), _840087 = _840085, _840083 = _840081], (4098 ^ _777081) ^ [_840230, _840232, _840234, _840236, _840238, _840240] : [-(c_List_Oinsert(_840240, _840236, _840232) = c_List_Oinsert(_840238, _840234, _840230)), _840240 = _840238, _840236 = _840234, _840232 = _840230], (4112 ^ _777081) ^ [_840451, _840453, _840455, _840457, _840459, _840461, _840463, _840465] : [-(c_List_Omaps(_840465, _840461, _840457, _840453) = c_List_Omaps(_840463, _840459, _840455, _840451)), _840465 = _840463, _840461 = _840459, _840457 = _840455, _840453 = _840451], (4130 ^ _777081) ^ [_840752, _840754, _840756, _840758] : [-(c_List_Oconcat(_840758, _840754) = c_List_Oconcat(_840756, _840752)), _840758 = _840756, _840754 = _840752], (4140 ^ _777081) ^ [_840901, _840903, _840905, _840907] : [-(c_List_Olex(_840907, _840903) = c_List_Olex(_840905, _840901)), _840907 = _840905, _840903 = _840901], (4150 ^ _777081) ^ [_841050, _841052, _841054, _841056] : [-(c_List_Omeasures(_841056, _841052) = c_List_Omeasures(_841054, _841050)), _841056 = _841054, _841052 = _841050], (4160 ^ _777081) ^ [_841199, _841201] : [_841201 = _841199, -(c_List_Otake(_841201) = c_List_Otake(_841199))], (4166 ^ _777081) ^ [_841284, _841286, _841288, _841290] : [-(c_List_Ozip(_841290, _841286) = c_List_Ozip(_841288, _841284)), _841290 = _841288, _841286 = _841284], (4176 ^ _777081) ^ [_841433, _841435, _841437, _841439] : [-(c_Map_Omap__of(_841439, _841435) = c_Map_Omap__of(_841437, _841433)), _841439 = _841437, _841435 = _841433], (4186 ^ _777081) ^ [_841582, _841584, _841586, _841588, _841590, _841592] : [-(c_Predicate_ODomainP(_841592, _841588, _841584) = c_Predicate_ODomainP(_841590, _841586, _841582)), _841592 = _841590, _841588 = _841586, _841584 = _841582], (4200 ^ _777081) ^ [_841803, _841805, _841807, _841809, _841811, _841813] : [-(c_Predicate_ORangeP(_841813, _841809, _841805) = c_Predicate_ORangeP(_841811, _841807, _841803)), _841813 = _841811, _841809 = _841807, _841805 = _841803], (4214 ^ _777081) ^ [_842024, _842026, _842028, _842030, _842032, _842034] : [-(c_List_OdropWhile(_842034, _842030, _842026) = c_List_OdropWhile(_842032, _842028, _842024)), _842034 = _842032, _842030 = _842028, _842026 = _842024], (4228 ^ _777081) ^ [_842245, _842247, _842249, _842251, _842253, _842255] : [-(c_Map_Odom(_842255, _842251, _842247) = c_Map_Odom(_842253, _842249, _842245)), _842255 = _842253, _842251 = _842249, _842247 = _842245], (4242 ^ _777081) ^ [_842466, _842468] : [_842468 = _842466, -(c_Option_Ooption_ONone(_842468) = c_Option_Ooption_ONone(_842466))], (4248 ^ _777081) ^ [_842551, _842553] : [_842553 = _842551, -(c_List_Odistinct(_842553) = c_List_Odistinct(_842551))], (4254 ^ _777081) ^ [_842636, _842638, _842640, _842642, _842644, _842646] : [-(c_List_OtakeWhile(_842646, _842642, _842638) = c_List_OtakeWhile(_842644, _842640, _842636)), _842646 = _842644, _842642 = _842640, _842638 = _842636], (4268 ^ _777081) ^ [_842857, _842859, _842861, _842863, _842865, _842867] : [-(c_List_Olinorder__class_Oinsort__key(_842867, _842863, _842859) = c_List_Olinorder__class_Oinsort__key(_842865, _842861, _842857)), _842867 = _842865, _842863 = _842861, _842859 = _842857], (4282 ^ _777081) ^ [_843078, _843080] : [_843080 = _843078, -(c_Finite__Set_Ocard(_843080) = c_Finite__Set_Ocard(_843078))], (4288 ^ _777081) ^ [_843163, _843165, _843167, _843169] : [-(c_Wellfounded_Omax__ext(_843169, _843165) = c_Wellfounded_Omax__ext(_843167, _843163)), _843169 = _843167, _843165 = _843163], (4298 ^ _777081) ^ [_843312, _843314, _843316, _843318, _843320, _843322] : [-(c_Set_Oimage(_843322, _843318, _843314) = c_Set_Oimage(_843320, _843316, _843312)), _843322 = _843320, _843318 = _843316, _843314 = _843312], (4312 ^ _777081) ^ [_843533, _843535] : [_843535 = _843533, -(c_List_Orev(_843535) = c_List_Orev(_843533))], (4318 ^ _777081) ^ [_843618, _843620, _843622, _843624] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_843624, _843620) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_843622, _843618)), _843624 = _843622, _843620 = _843618], (4328 ^ _777081) ^ [_843767, _843769, _843771, _843773] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_843773, _843769) = c_SetInterval_Oord__class_OatLeastLessThan(_843771, _843767)), _843773 = _843771, _843769 = _843767], (4338 ^ _777081) ^ [_843916, _843918, _843920, _843922, _843924, _843926, _843928, _843930] : [-(c_Random_Oiterate(_843930, _843926, _843922, _843918) = c_Random_Oiterate(_843928, _843924, _843920, _843916)), _843930 = _843928, _843926 = _843924, _843922 = _843920, _843918 = _843916], (4356 ^ _777081) ^ [_844217, _844219, _844221, _844223] : [-(c_Random_Olog(_844223, _844219) = c_Random_Olog(_844221, _844217)), _844223 = _844221, _844219 = _844217], (4366 ^ _777081) ^ [_844366, _844368, _844370, _844372, _844374, _844376] : [-(c_Random_Ominus__shift(_844376, _844372, _844368) = c_Random_Ominus__shift(_844374, _844370, _844366)), _844376 = _844374, _844372 = _844370, _844368 = _844366], (4380 ^ _777081) ^ [_844587, _844589, _844591, _844593] : [-(c_Random_Oinc__shift(_844593, _844589) = c_Random_Oinc__shift(_844591, _844587)), _844593 = _844591, _844589 = _844587], (4390 ^ _777081) ^ [_844736, _844738] : [_844738 = _844736, -(c_List_Olist_ONil(_844738) = c_List_Olist_ONil(_844736))], (4396 ^ _777081) ^ [_844821, _844823, _844825, _844827] : [-(c_Product__Type_Osnd(_844827, _844823) = c_Product__Type_Osnd(_844825, _844821)), _844827 = _844825, _844823 = _844821], (4406 ^ _777081) ^ [_844970, _844972, _844974, _844976] : [-(c_List_Ofilter(_844976, _844972) = c_List_Ofilter(_844974, _844970)), _844976 = _844974, _844972 = _844970], (4416 ^ _777081) ^ [_845119, _845121, _845123, _845125] : [-(c_Random_Oselect__weight(_845125, _845121) = c_Random_Oselect__weight(_845123, _845119)), _845125 = _845123, _845121 = _845119], (4426 ^ _777081) ^ [_845268, _845270] : [_845270 = _845268, -(c_List_Omonoid__add__class_Olistsum(_845270) = c_List_Omonoid__add__class_Olistsum(_845268))], (4432 ^ _777081) ^ [_845353, _845355, _845357, _845359] : [-(c_Random_Opick(_845359, _845355) = c_Random_Opick(_845357, _845353)), _845359 = _845357, _845355 = _845353], (4442 ^ _777081) ^ [_845502, _845504, _845506, _845508] : [-(c_List_Omap(_845508, _845504) = c_List_Omap(_845506, _845502)), _845508 = _845506, _845504 = _845502], (4452 ^ _777081) ^ [_845651, _845653, _845655, _845657] : [-(c_Product__Type_Ofst(_845657, _845653) = c_Product__Type_Ofst(_845655, _845651)), _845657 = _845655, _845653 = _845651], (4462 ^ _777081) ^ [_845800, _845802, _845804, _845806] : [-(c_Random_Oselect(_845806, _845802) = c_Random_Oselect(_845804, _845800)), _845806 = _845804, _845802 = _845800], (4472 ^ _777081) ^ [_845949, _845951, _845953, _845955, _845957, _845959, _845961, _845963] : [-(c_Product__Type_Oscomp(_845963, _845959, _845955, _845951) = c_Product__Type_Oscomp(_845961, _845957, _845953, _845949)), _845963 = _845961, _845959 = _845957, _845955 = _845953, _845951 = _845949], (4490 ^ _777081) ^ [_846250, _846252] : [_846252 = _846250, -(c_Random_Orange(_846252) = c_Random_Orange(_846250))], (4496 ^ _777081) ^ [_846335, _846337] : [_846337 = _846335, -(c_List_Onth(_846337) = c_List_Onth(_846335))], (4502 ^ _777081) ^ [_846420, _846422] : [_846422 = _846420, -(c_Nat_Osemiring__1__class_Oof__nat(_846422) = c_Nat_Osemiring__1__class_Oof__nat(_846420))], (4508 ^ _777081) ^ [_846505, _846507, _846509, _846511] : [-(c_Code__Numeral_Onat__of__aux(_846511, _846507) = c_Code__Numeral_Onat__of__aux(_846509, _846505)), _846511 = _846509, _846507 = _846505], (4518 ^ _777081) ^ [_846654, _846656, _846658, _846660] : [-(c_Wellfounded_Oacc(_846660, _846656) = c_Wellfounded_Oacc(_846658, _846654)), _846660 = _846658, _846656 = _846654], (4528 ^ _777081) ^ [_846803, _846805] : [_846805 = _846803, -(c_Nat_Osize__class_Osize(_846805) = c_Nat_Osize__class_Osize(_846803))], (4534 ^ _777081) ^ [_846888, _846890, _846892, _846894] : [-(c_List_Olistrel(_846894, _846890) = c_List_Olistrel(_846892, _846888)), _846894 = _846892, _846890 = _846888], (4544 ^ _777081) ^ [_847037, _847039] : [_847039 = _847037, -(c_Code__Numeral_OSuc__code__numeral(_847039) = c_Code__Numeral_OSuc__code__numeral(_847037))], (4550 ^ _777081) ^ [_847122, _847124, _847126, _847128] : [-(c_Product__Type_OSigma(_847128, _847124) = c_Product__Type_OSigma(_847126, _847122)), _847128 = _847126, _847124 = _847122], (4560 ^ _777081) ^ [_847271, _847273] : [_847273 = _847271, -(c_Lazy__Sequence_Ohb__not__seq(_847273) = c_Lazy__Sequence_Ohb__not__seq(_847271))], (4566 ^ _777081) ^ [_847356, _847358] : [_847358 = _847356, -(c_Int_Onumber__class_Onumber__of(_847358) = c_Int_Onumber__class_Onumber__of(_847356))], (4572 ^ _777081) ^ [_847441, _847443] : [_847443 = _847441, -(c_Int_OBit1(_847443) = c_Int_OBit1(_847441))], (4578 ^ _777081) ^ [_847526, _847528, _847530, _847532] : [-(c_List_Olistrel1(_847532, _847528) = c_List_Olistrel1(_847530, _847526)), _847532 = _847530, _847528 = _847526], (4588 ^ _777081) ^ [_847675, _847677] : [_847677 = _847675, -(c_Relation_OField(_847677) = c_Relation_OField(_847675))], (4594 ^ _777081) ^ [_847760, _847762, _847764, _847766] : [-(c_Relation_Oinv__image(_847766, _847762) = c_Relation_Oinv__image(_847764, _847760)), _847766 = _847764, _847762 = _847760], (4604 ^ _777081) ^ [_847909, _847911] : [_847911 = _847909, -(c_Groups_Ouminus__class_Ouminus(_847911) = c_Groups_Ouminus__class_Ouminus(_847909))], (4610 ^ _777081) ^ [_847994, _847996, _847998, _848000, _848002, _848004] : [-(c_Product__Type_Oprod_Oprod__case(_848004, _848000, _847996) = c_Product__Type_Oprod_Oprod__case(_848002, _847998, _847994)), _848004 = _848002, _848000 = _847998, _847996 = _847994], (4624 ^ _777081) ^ [_848215, _848217, _848219, _848221] : [-(c_Relation_ORange(_848221, _848217) = c_Relation_ORange(_848219, _848215)), _848221 = _848219, _848217 = _848215], (4634 ^ _777081) ^ [_848364, _848366, _848368, _848370] : [-(c_Relation_ODomain(_848370, _848366) = c_Relation_ODomain(_848368, _848364)), _848370 = _848368, _848366 = _848364], (4644 ^ _777081) ^ [_848513, _848515, _848517, _848519] : [-(c_Relation_OId__on(_848519, _848515) = c_Relation_OId__on(_848517, _848513)), _848519 = _848517, _848515 = _848513], (4654 ^ _777081) ^ [_848662, _848664] : [_848664 = _848662, -(c_Set_OCollect(_848664) = c_Set_OCollect(_848662))], (4660 ^ _777081) ^ [_848747, _848749] : [_848749 = _848747, -(c_HOL_OEx(_848749) = c_HOL_OEx(_848747))], (4666 ^ _777081) ^ [_848832, _848834, _848836, _848838, _848840, _848842] : [-(c_Relation_OImage(_848842, _848838, _848834) = c_Relation_OImage(_848840, _848836, _848832)), _848842 = _848840, _848838 = _848836, _848834 = _848832], (4680 ^ _777081) ^ [_849053, _849055, _849057, _849059] : [-(c_Relation_Oconverse(_849059, _849055) = c_Relation_Oconverse(_849057, _849053)), _849059 = _849057, _849055 = _849053], (4690 ^ _777081) ^ [_849202, _849204] : [_849204 = _849202, -(c_Fun_Oid(_849204) = c_Fun_Oid(_849202))], (4696 ^ _777081) ^ [_849287, _849289, _849291, _849293, _849295, _849297, _849299, _849301] : [-(c_Fun_Ocomp(_849301, _849297, _849293, _849289) = c_Fun_Ocomp(_849299, _849295, _849291, _849287)), _849301 = _849299, _849297 = _849295, _849293 = _849291, _849289 = _849287], (4714 ^ _777081) ^ [_849588, _849590] : [_849590 = _849588, -(c_Groups_Oone__class_Oone(_849590) = c_Groups_Oone__class_Oone(_849588))], (4720 ^ _777081) ^ [_849673, _849675, _849677, _849679, _849681, _849683] : [-(c_Relation_Orel__comp(_849683, _849679, _849675) = c_Relation_Orel__comp(_849681, _849677, _849673)), _849683 = _849681, _849679 = _849677, _849675 = _849673], (4734 ^ _777081) ^ [_849894, _849896] : [_849896 = _849894, -(c_Orderings_Oord__class_Oless(_849896) = c_Orderings_Oord__class_Oless(_849894))], (4740 ^ _777081) ^ [_849979, _849981] : [_849981 = _849979, -(c_Nat_Ofunpow(_849981) = c_Nat_Ofunpow(_849979))], (4746 ^ _777081) ^ [_850064, _850066, _850068, _850070] : [-(c_List_Orotate(_850070, _850066) = c_List_Orotate(_850068, _850064)), _850070 = _850068, _850066 = _850064], (4756 ^ _777081) ^ [_850213, _850215] : [_850215 = _850213, -(c_List_Orotate1(_850215) = c_List_Orotate1(_850213))], (4762 ^ _777081) ^ [_850298, _850300] : [_850300 = _850298, -(c_Groups_Ozero__class_Ozero(_850300) = c_Groups_Ozero__class_Ozero(_850298))], (4768 ^ _777081) ^ [_850383, _850385, _850387, _850389, _850391, _850393, _850395, _850397] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_850397, _850393, _850389, _850385) = c_New__Random__Sequence_Opos__not__random__dseq(_850395, _850391, _850387, _850383)), _850397 = _850395, _850393 = _850391, _850389 = _850387, _850385 = _850383], (4786 ^ _777081) ^ [_850684, _850686] : [_850686 = _850684, -(c_New__DSequence_Opos__not__seq(_850686) = c_New__DSequence_Opos__not__seq(_850684))], (4792 ^ _777081) ^ [_850769, _850771, _850773, _850775] : [-(c_Nat_Ocompow(_850775, _850771) = c_Nat_Ocompow(_850773, _850769)), _850775 = _850773, _850771 = _850769], (4802 ^ _777081) ^ [_850918, _850920, _850922, _850924] : [-(c_Transitive__Closure_Otrancl(_850924, _850920) = c_Transitive__Closure_Otrancl(_850922, _850918)), _850924 = _850922, _850920 = _850918], (4812 ^ _777081) ^ [_851067, _851069, _851071, _851073] : [-(c_Transitive__Closure_Ortrancl(_851073, _851069) = c_Transitive__Closure_Ortrancl(_851071, _851067)), _851073 = _851071, _851069 = _851067], (4822 ^ _777081) ^ [_851216, _851218] : [_851218 = _851216, -(c_Relation_OId(_851218) = c_Relation_OId(_851216))], (4828 ^ _777081) ^ [_851301, _851303, _851305, _851307] : [-(c_Product__Type_OPair(_851307, _851303) = c_Product__Type_OPair(_851305, _851301)), _851307 = _851305, _851303 = _851301], (4838 ^ _777081) ^ [_851450, _851452] : [_851452 = _851450, -(c_List_Oappend(_851452) = c_List_Oappend(_851450))], (4844 ^ _777081) ^ [_851535, _851537] : [_851537 = _851535, -(c_List_Olist_OCons(_851537) = c_List_Olist_OCons(_851535))], (4850 ^ _777081) ^ [_851620, _851622] : [_851622 = _851620, -(c_Groups_Oplus__class_Oplus(_851622) = c_Groups_Oplus__class_Oplus(_851620))], (4856 ^ _777081) ^ [_851705, _851707, _851709, _851711] : [-(c_Divides_Odiv__class_Odiv(_851711, _851707) = c_Divides_Odiv__class_Odiv(_851709, _851705)), _851711 = _851709, _851707 = _851705], (4866 ^ _777081) ^ [_851854, _851856, _851858, _851860, _851862, _851864] : [-(c_Divides_Odiv__class_Omod(_851864, _851860, _851856) = c_Divides_Odiv__class_Omod(_851862, _851858, _851854)), _851864 = _851862, _851860 = _851858, _851856 = _851854], (4880 ^ _777081) ^ [_852075, _852077, _852079, _852081, _852083, _852085] : [-(c_Finite__Set_Ofold__image(_852085, _852081, _852077) = c_Finite__Set_Ofold__image(_852083, _852079, _852075)), _852085 = _852083, _852081 = _852079, _852077 = _852075], (4894 ^ _777081) ^ [_852296, _852298, _852300, _852302] : [-(c_HOL_OThe(_852302, _852298) = c_HOL_OThe(_852300, _852296)), _852302 = _852300, _852298 = _852296], (4904 ^ _777081) ^ [_852445, _852447, _852449, _852451, _852453, _852455, _852457, _852459, _852461, _852463] : [-(c_Finite__Set_Ofold__graph(_852463, _852459, _852455, _852451, _852447) = c_Finite__Set_Ofold__graph(_852461, _852457, _852453, _852449, _852445)), _852463 = _852461, _852459 = _852457, _852455 = _852453, _852451 = _852449, _852447 = _852445], (4926 ^ _777081) ^ [_852834, _852836, _852838, _852840] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_852840, _852836) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_852838, _852834)), _852840 = _852838, _852836 = _852834], (4936 ^ _777081) ^ [_852983, _852985] : [_852985 = _852983, -(c_List_Oset(_852985) = c_List_Oset(_852983))], (4942 ^ _777081) ^ [_853068, _853070, _853072, _853074, _853076, _853078, _853080, _853082] : [-(c_List_Ofoldl(_853082, _853078, _853074, _853070) = c_List_Ofoldl(_853080, _853076, _853072, _853068)), _853082 = _853080, _853078 = _853076, _853074 = _853072, _853070 = _853068], (4960 ^ _777081) ^ [_853369, _853371] : [_853371 = _853369, -(c_Orderings_Oord__class_Oless__eq(_853371) = c_Orderings_Oord__class_Oless__eq(_853369))], (4966 ^ _777081) ^ [_853454, _853456, _853458, _853460] : [-(c_Complete__Lattice_OSup__class_OSup(_853460, _853456) = c_Complete__Lattice_OSup__class_OSup(_853458, _853454)), _853460 = _853458, _853456 = _853454], (4976 ^ _777081) ^ [_853603, _853605, _853607, _853609] : [-(c_Complete__Lattice_OInf__class_OInf(_853609, _853605) = c_Complete__Lattice_OInf__class_OInf(_853607, _853603)), _853609 = _853607, _853605 = _853603], (4986 ^ _777081) ^ [_853752, _853754] : [_853754 = _853752, -(c_Orderings_Otop__class_Otop(_853754) = c_Orderings_Otop__class_Otop(_853752))], (4992 ^ _777081) ^ [_853837, _853839, _853841, _853843] : [-(c_Finite__Set_Ofold1(_853843, _853839) = c_Finite__Set_Ofold1(_853841, _853837)), _853843 = _853841, _853839 = _853837], (5002 ^ _777081) ^ [_853986, _853988] : [_853988 = _853986, -(c_Groups_Otimes__class_Otimes(_853988) = c_Groups_Otimes__class_Otimes(_853986))], (5008 ^ _777081) ^ [_854071, _854073, _854075, _854077] : [-(c_Big__Operators_Olattice__class_OSup__fin(_854077, _854073) = c_Big__Operators_Olattice__class_OSup__fin(_854075, _854071)), _854077 = _854075, _854073 = _854071], (5018 ^ _777081) ^ [_854220, _854222, _854224, _854226] : [-(c_Big__Operators_Olattice__class_OInf__fin(_854226, _854222) = c_Big__Operators_Olattice__class_OInf__fin(_854224, _854220)), _854226 = _854224, _854222 = _854220], (5028 ^ _777081) ^ [_854369, _854371] : [_854371 = _854369, -(c_Lattices_Osemilattice__inf__class_Oinf(_854371) = c_Lattices_Osemilattice__inf__class_Oinf(_854369))], (5034 ^ _777081) ^ [_854454, _854456, _854458, _854460] : [-(c_Big__Operators_Olinorder__class_OMin(_854460, _854456) = c_Big__Operators_Olinorder__class_OMin(_854458, _854454)), _854460 = _854458, _854456 = _854454], (5044 ^ _777081) ^ [_854603, _854605, _854607, _854609] : [-(c_Big__Operators_Olinorder__class_OMax(_854609, _854605) = c_Big__Operators_Olinorder__class_OMax(_854607, _854603)), _854609 = _854607, _854605 = _854603], (5054 ^ _777081) ^ [_854752, _854754, _854756, _854758, _854760, _854762] : [-(c_Big__Operators_Olattice_OInf__fin(_854762, _854758, _854754) = c_Big__Operators_Olattice_OInf__fin(_854760, _854756, _854752)), _854762 = _854760, _854758 = _854756, _854754 = _854752], (5068 ^ _777081) ^ [_854973, _854975] : [_854975 = _854973, -(c_Orderings_Oord__class_Omin(_854975) = c_Orderings_Oord__class_Omin(_854973))], (5074 ^ _777081) ^ [_855058, _855060, _855062, _855064, _855066, _855068] : [-(c_Big__Operators_Olattice_OSup__fin(_855068, _855064, _855060) = c_Big__Operators_Olattice_OSup__fin(_855066, _855062, _855058)), _855068 = _855066, _855064 = _855062, _855060 = _855058], (5088 ^ _777081) ^ [_855279, _855281] : [_855281 = _855279, -(c_Orderings_Oord__class_Omax(_855281) = c_Orderings_Oord__class_Omax(_855279))], (5094 ^ _777081) ^ [_855364, _855366] : [_855366 = _855364, -(c_Groups_Ominus__class_Ominus(_855366) = c_Groups_Ominus__class_Ominus(_855364))], (5100 ^ _777081) ^ [_855449, _855451] : [_855451 = _855449, -(c_member(_855451) = c_member(_855449))], (5106 ^ _777081) ^ [_855534, _855536] : [_855536 = _855534, -(c_Set_Oinsert(_855536) = c_Set_Oinsert(_855534))], (5112 ^ _777081) ^ [_855619, _855621] : [_855621 = _855619, -(c_Finite__Set_Ofinite(_855621) = c_Finite__Set_Ofinite(_855619))], (5118 ^ _777081) ^ [_855704, _855706, _855708, _855710] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855710, _855706) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855708, _855704)), _855710 = _855708, _855706 = _855704], (5128 ^ _777081) ^ [_855853, _855855, _855857, _855859, _855861, _855863] : [-(c_Finite__Set_Ofold(_855863, _855859, _855855) = c_Finite__Set_Ofold(_855861, _855857, _855853)), _855863 = _855861, _855859 = _855857, _855855 = _855853], (5142 ^ _777081) ^ [_856074, _856076] : [_856076 = _856074, -(c_Lattices_Osemilattice__sup__class_Osup(_856076) = c_Lattices_Osemilattice__sup__class_Osup(_856074))], (5148 ^ _777081) ^ [_856159, _856161] : [_856161 = _856159, -(c_Orderings_Obot__class_Obot(_856161) = c_Orderings_Obot__class_Obot(_856159))], (5154 ^ _777081) ^ [_856244, _856246, _856248, _856250] : [-(tc_fun(_856250, _856246) = tc_fun(_856248, _856244)), _856250 = _856248, _856246 = _856244], (5164 ^ _777081) ^ [_856393, _856395] : [_856395 = _856393, -(tc_List_Olist(_856395) = tc_List_Olist(_856393))], (5170 ^ _777081) ^ [_856478, _856480, _856482, _856484] : [-(tc_sum(_856484, _856480) = tc_sum(_856482, _856478)), _856484 = _856482, _856480 = _856478], (5180 ^ _777081) ^ [_856627, _856629] : [_856629 = _856627, -(tc_Option_Ooption(_856629) = tc_Option_Ooption(_856627))], (5186 ^ _777081) ^ [_856712, _856714, _856716, _856718] : [-(tc_Nitpick_Opair__box(_856718, _856714) = tc_Nitpick_Opair__box(_856716, _856712)), _856718 = _856716, _856714 = _856712], (5196 ^ _777081) ^ [_856861, _856863, _856865, _856867] : [-(tc_prod(_856867, _856863) = tc_prod(_856865, _856861)), _856867 = _856865, _856863 = _856861], (5206 ^ _777081) ^ [_857010, _857012] : [_857012 = _857010, -(tc_Hoare__Mirabelle_Otriple(_857012) = tc_Hoare__Mirabelle_Otriple(_857010))], (5212 ^ _777081) ^ [_857095, _857097] : [_857097 = _857095, -(tc_Lazy__Sequence_Olazy__sequence(_857097) = tc_Lazy__Sequence_Olazy__sequence(_857095))], (5218 ^ _777081) ^ [_857180, _857182] : [_857182 = _857180, -(c_COMBI(_857182) = c_COMBI(_857180))], (5224 ^ _777081) ^ [_857265, _857267, _857269, _857271] : [-(c_COMBK(_857271, _857267) = c_COMBK(_857269, _857265)), _857271 = _857269, _857267 = _857265], (5234 ^ _777081) ^ [_857414, _857416, _857418, _857420, _857422, _857424] : [-(c_COMBB(_857424, _857420, _857416) = c_COMBB(_857422, _857418, _857414)), _857424 = _857422, _857420 = _857418, _857416 = _857414], (5248 ^ _777081) ^ [_857635, _857637, _857639, _857641, _857643, _857645] : [-(c_COMBC(_857645, _857641, _857637) = c_COMBC(_857643, _857639, _857635)), _857645 = _857643, _857641 = _857639, _857637 = _857635], (5262 ^ _777081) ^ [_857856, _857858, _857860, _857862, _857864, _857866] : [-(c_COMBS(_857866, _857862, _857858) = c_COMBS(_857864, _857860, _857856)), _857866 = _857864, _857862 = _857860, _857858 = _857856], (5276 ^ _777081) ^ [_858077, _858079] : [_858079 = _858077, -(c_Option_Ooption_OSome(_858079) = c_Option_Ooption_OSome(_858077))], (5282 ^ _777081) ^ [_858158, _858160, _858162, _858164] : [-(hAPP(_858164, _858160) = hAPP(_858162, _858158)), _858164 = _858162, _858160 = _858158], (5292 ^ _777081) ^ [_860807, _860809] : [hAPP(_860807, 5293 ^ [_860807, _860809]) = hAPP(_860809, 5293 ^ [_860807, _860809]), -(_860807 = _860809)], (5299 ^ _777081) ^ [_860933, _860935] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _860933) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _860935), -(hBOOL(hAPP(c_Com_OWT, _860935)))], (5309 ^ _777081) ^ [_861090, _861092, _861094] : [hAPP(c_Option_Ooption_OSome(_861090), _861092) = hAPP(c_Option_Ooption_OSome(_861090), _861094), -(_861092 = _861094)], (5315 ^ _777081) ^ [_861185, _861187, _861189] : [_861187 = _861189, -(hAPP(c_Option_Ooption_OSome(_861185), _861187) = hAPP(c_Option_Ooption_OSome(_861185), _861189))], (5321 ^ _777081) ^ [_861298] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _861298))), -(hAPP(c_Com_Obody, _861298) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 5324 ^ [_861298]))], (5328 ^ _777081) ^ [_861401] : [5329 ^ _777081 : [(5330 ^ _777081) ^ [_861449] : [hAPP(c_Com_Obody, _861401) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _861449)]], -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _861401))))], (5334 ^ _777081) ^ [] : [c_Hoare__Mirabelle_Ostate__not__singleton, 5337 ^ [] = 5338 ^ []], (5342 ^ _777081) ^ [] : [5343 ^ _777081 : [(5344 ^ _777081) ^ [_861605, _861607] : [-(_861607 = _861605)]], -(c_Hoare__Mirabelle_Ostate__not__singleton)], (5348 ^ _777081) ^ [] : [c_Hoare__Mirabelle_Ostate__not__singleton, 5352 ^ _777081 : [(5353 ^ _777081) ^ [_861687] : [5351 ^ [_861687] = _861687]]], (5355 ^ _777081) ^ [_861719] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _861719))), -(hAPP(c_Com_Obody, _861719) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 5358 ^ [_861719]))], (5362 ^ _777081) ^ [_861830, _861832, _861834, _861836, _861838] : [-(c_Option_Ooption_Ooption__rec(_861830, _861832, _861834, _861836, hAPP(c_Option_Ooption_OSome(_861832), _861838)) = hAPP(_861836, _861838))], (5364 ^ _777081) ^ [_861875, _861877, _861879, _861881, _861883] : [-(hAPP(c_Option_Ooption_Ooption__case(_861875, _861877, _861879, _861881), hAPP(c_Option_Ooption_OSome(_861877), _861883)) = hAPP(_861881, _861883))], (5366 ^ _777081) ^ [_861934, _861936] : [c_Option_Ois__none(_861934, hAPP(c_Option_Ooption_OSome(_861934), _861936))], (5368 ^ _777081) ^ [_861994, _861996, _861998, _862000, _862002, _862004, _862006] : [c_Map_Omap__comp(_861994, _861996, _861998, _862000, _862002, _862004) = hAPP(c_Option_Ooption_OSome(_861996), _862006), 5372 ^ _777081 : [(5373 ^ _777081) ^ [] : [-(hAPP(_862002, _862004) = hAPP(c_Option_Ooption_OSome(_861994), 5371 ^ [_861994, _861996, _861998, _862000, _862002, _862004, _862006]))], (5375 ^ _777081) ^ [] : [-(hAPP(_862000, 5371 ^ [_861994, _861996, _861998, _862000, _862002, _862004, _862006]) = hAPP(c_Option_Ooption_OSome(_861996), _862006))]]], (5377 ^ _777081) ^ [_862198, _862200, _862202, _862204, _862206, _862208, _862210] : [-(c_Map_Omap__comp(_862198, _862200, _862202, _862204, _862206, _862208) = hAPP(c_Option_Ooption_OSome(_862200), _862210)), 5378 ^ _777081 : [(5379 ^ _777081) ^ [_862276] : [hAPP(_862206, _862208) = hAPP(c_Option_Ooption_OSome(_862198), _862276), hAPP(_862204, _862276) = hAPP(c_Option_Ooption_OSome(_862200), _862210)]]], (5387 ^ _777081) ^ [_862438, _862440, _862442, _862444, _862446, _862448, _862450] : [hAPP(_862438, _862440) = hAPP(c_Option_Ooption_OSome(_862442), _862444), -(c_Map_Omap__comp(_862442, _862446, _862448, _862450, _862438, _862440) = hAPP(_862450, _862444))], (5393 ^ _777081) ^ [_862561, _862563] : [-(hAPP(hAPP(c_Option_Obind(_862561, _862561), _862563), c_Option_Ooption_OSome(_862561)) = _862563)], (5395 ^ _777081) ^ [_862612, _862614] : [hAPP(c_Com_Ocom_OBODY, _862612) = hAPP(c_Com_Ocom_OBODY, _862614), -(_862612 = _862614)], (5401 ^ _777081) ^ [_862697, _862699] : [_862697 = _862699, -(hAPP(c_Com_Ocom_OBODY, _862697) = hAPP(c_Com_Ocom_OBODY, _862699))], (5407 ^ _777081) ^ [_862788, _862790, _862792, _862794] : [-(hAPP(hAPP(c_Option_Obind(_862788, _862790), hAPP(c_Option_Ooption_OSome(_862788), _862792)), _862794) = hAPP(_862794, _862792))], (5409 ^ _777081) ^ [_862830] : [-(hAPP(c_Com_Obody, _862830) = c_Option_Ooption_ONone(tc_Com_Ocom)), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _862830))))], (5415 ^ _777081) ^ [_862872, _862874, _862876] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_862872, _862874, _862876))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _862874))))], (5421 ^ _777081) ^ [_862991, _862993, _862995] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_862991, _862993, _862995))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _862993))))], (5427 ^ _777081) ^ [_863088, _863090, _863092] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _863090))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_863088, _863090, _863092))))], (5433 ^ _777081) ^ [_863191, _863193, _863195] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _863191))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_863193, _863191, _863195))))], (5439 ^ _777081) ^ [_863319, _863321, _863323, _863325, _863327, _863329] : [c_Map_Omap__comp(_863319, _863321, _863323, _863325, _863327, _863329) = c_Option_Ooption_ONone(_863321), -(hAPP(_863327, _863329) = c_Option_Ooption_ONone(_863319)), 5447 ^ _777081 : [(5448 ^ _777081) ^ [] : [-(hAPP(_863327, _863329) = hAPP(c_Option_Ooption_OSome(_863319), 5446 ^ [_863319, _863321, _863323, _863325, _863327, _863329]))], (5450 ^ _777081) ^ [] : [-(hAPP(_863325, 5446 ^ [_863319, _863321, _863323, _863325, _863327, _863329]) = c_Option_Ooption_ONone(_863321))]]], (5452 ^ _777081) ^ [_863545, _863547, _863549, _863551, _863553, _863555] : [-(c_Map_Omap__comp(_863545, _863547, _863549, _863551, _863553, _863555) = c_Option_Ooption_ONone(_863547)), 5453 ^ _777081 : [(5454 ^ _777081) ^ [] : [hAPP(_863553, _863555) = c_Option_Ooption_ONone(_863545)], (5456 ^ _777081) ^ [_863657] : [hAPP(_863553, _863555) = hAPP(c_Option_Ooption_OSome(_863545), _863657), hAPP(_863551, _863657) = c_Option_Ooption_ONone(_863547)]]], (5464 ^ _777081) ^ [_863810, _863812, _863814, _863816, _863818, _863820, _863822, _863824, _863826, _863828] : [-(c_Com_Ocom_Ocom__case(_863810, _863812, _863814, _863816, _863818, _863820, _863822, _863824, _863826, hAPP(c_Com_Ocom_OBODY, _863828)) = hAPP(_863824, _863828))], (5466 ^ _777081) ^ [_863868, _863870] : [-(hAPP(c_Option_Othe(_863868), hAPP(c_Option_Ooption_OSome(_863868), _863870)) = _863870)], (5468 ^ _777081) ^ [_863903, _863905, _863907, _863909] : [-(c_Option_Ooption_Ooption__rec(_863903, _863905, _863907, _863909, c_Option_Ooption_ONone(_863905)) = _863907)], (5470 ^ _777081) ^ [_863940, _863942] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_863940, _863942))), 5473 ^ _777081 : [(5474 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _863940)))], (5476 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _863942)))]]], (5478 ^ _777081) ^ [_864065, _864067, _864069] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_864065, _864067, _864069))), 5481 ^ _777081 : [(5482 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _864067)))], (5484 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _864069)))]]], (5486 ^ _777081) ^ [_864194] : [-(c_Option_Ois__none(_864194, c_Option_Ooption_ONone(_864194)))], (5488 ^ _777081) ^ [_864231, _864233] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_864231, _864233)], (5490 ^ _777081) ^ [_864274, _864276, _864278] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCall(_864274, _864276, _864278)], (5492 ^ _777081) ^ [_864320, _864322, _864324] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_864320, _864322, _864324)], (5494 ^ _777081) ^ [_864363, _864365] : [c_Com_Ocom_OSemi(_864363, _864365) = c_Com_Ocom_OSKIP], (5496 ^ _777081) ^ [_864412, _864414, _864416, _864418, _864420] : [c_Com_Ocom_OSemi(_864412, _864414) = c_Com_Ocom_OCall(_864416, _864418, _864420)], (5498 ^ _777081) ^ [_864471, _864473, _864475, _864477, _864479] : [c_Com_Ocom_OSemi(_864471, _864473) = c_Com_Ocom_OCond(_864475, _864477, _864479)], (5500 ^ _777081) ^ [_864524, _864526, _864528] : [c_Com_Ocom_OCall(_864524, _864526, _864528) = c_Com_Ocom_OSKIP], (5502 ^ _777081) ^ [_864570, _864572, _864574] : [c_Com_Ocom_OCond(_864570, _864572, _864574) = c_Com_Ocom_OSKIP], (5504 ^ _777081) ^ [_864622, _864624, _864626, _864628, _864630] : [c_Com_Ocom_OCall(_864622, _864624, _864626) = c_Com_Ocom_OSemi(_864628, _864630)], (5506 ^ _777081) ^ [_864681, _864683, _864685, _864687, _864689] : [c_Com_Ocom_OCond(_864681, _864683, _864685) = c_Com_Ocom_OSemi(_864687, _864689)], (5508 ^ _777081) ^ [_864743, _864745, _864747, _864749, _864751, _864753] : [c_Com_Ocom_OCall(_864743, _864745, _864747) = c_Com_Ocom_OCond(_864749, _864751, _864753)], (5510 ^ _777081) ^ [_864808, _864810, _864812, _864814, _864816, _864818] : [c_Com_Ocom_OCond(_864808, _864810, _864812) = c_Com_Ocom_OCall(_864814, _864816, _864818)], (5512 ^ _777081) ^ [_864870, _864872, _864874, _864876] : [c_Com_Ocom_OSemi(_864870, _864872) = c_Com_Ocom_OSemi(_864874, _864876), 5515 ^ _777081 : [(5516 ^ _777081) ^ [] : [-(_864870 = _864874)], (5518 ^ _777081) ^ [] : [-(_864872 = _864876)]]], (5520 ^ _777081) ^ [_864985, _864987, _864989, _864991] : [-(c_Com_Ocom_OSemi(_864985, _864987) = c_Com_Ocom_OSemi(_864989, _864991)), _864985 = _864989, _864987 = _864991], (5530 ^ _777081) ^ [_865163, _865165, _865167, _865169, _865171, _865173] : [c_Com_Ocom_OCall(_865163, _865165, _865167) = c_Com_Ocom_OCall(_865169, _865171, _865173), 5533 ^ _777081 : [(5534 ^ _777081) ^ [] : [-(_865163 = _865169)], (5536 ^ _777081) ^ [] : [-(_865165 = _865171)], (5538 ^ _777081) ^ [] : [-(_865167 = _865173)]]], (5540 ^ _777081) ^ [_865310, _865312, _865314, _865316, _865318, _865320] : [-(c_Com_Ocom_OCall(_865310, _865312, _865314) = c_Com_Ocom_OCall(_865316, _865318, _865320)), _865310 = _865316, _865312 = _865318, _865314 = _865320], (5554 ^ _777081) ^ [_865560, _865562, _865564, _865566, _865568, _865570] : [c_Com_Ocom_OCond(_865560, _865562, _865564) = c_Com_Ocom_OCond(_865566, _865568, _865570), 5557 ^ _777081 : [(5558 ^ _777081) ^ [] : [-(_865560 = _865566)], (5560 ^ _777081) ^ [] : [-(_865562 = _865568)], (5562 ^ _777081) ^ [] : [-(_865564 = _865570)]]], (5564 ^ _777081) ^ [_865707, _865709, _865711, _865713, _865715, _865717] : [-(c_Com_Ocom_OCond(_865707, _865709, _865711) = c_Com_Ocom_OCond(_865713, _865715, _865717)), _865707 = _865713, _865709 = _865715, _865711 = _865717], (5578 ^ _777081) ^ [_865930, _865932, _865934, _865936, _865938, _865940, _865942, _865944, _865946] : [-(c_Com_Ocom_Ocom__case(_865930, _865932, _865934, _865936, _865938, _865940, _865942, _865944, _865946, c_Com_Ocom_OSKIP) = _865932)], (5580 ^ _777081) ^ [_865980, _865982, _865984, _865986, _865988, _865990, _865992, _865994, _865996, _865998, _866000] : [-(c_Com_Ocom_Ocom__case(_865980, _865982, _865984, _865986, _865988, _865990, _865992, _865994, _865996, c_Com_Ocom_OSemi(_865998, _866000)) = hAPP(hAPP(_865988, _865998), _866000))], (5582 ^ _777081) ^ [_866043, _866045, _866047, _866049, _866051, _866053, _866055, _866057, _866059, _866061, _866063, _866065] : [-(c_Com_Ocom_Ocom__case(_866043, _866045, _866047, _866049, _866051, _866053, _866055, _866057, _866059, c_Com_Ocom_OCall(_866061, _866063, _866065)) = hAPP(hAPP(hAPP(_866059, _866061), _866063), _866065))], (5584 ^ _777081) ^ [_866112, _866114, _866116, _866118, _866120, _866122, _866124, _866126, _866128, _866130, _866132, _866134] : [-(c_Com_Ocom_Ocom__case(_866112, _866114, _866116, _866118, _866120, _866122, _866124, _866126, _866128, c_Com_Ocom_OCond(_866130, _866132, _866134)) = hAPP(hAPP(hAPP(_866122, _866130), _866132), _866134))], (5586 ^ _777081) ^ [_866193, _866195] : [c_Option_Ooption_ONone(_866193) = hAPP(c_Option_Ooption_OSome(_866193), _866195)], (5588 ^ _777081) ^ [_866237, _866239] : [hAPP(c_Option_Ooption_OSome(_866237), _866239) = c_Option_Ooption_ONone(_866237)], (5590 ^ _777081) ^ [_866278, _866280] : [-(_866278 = hAPP(c_Option_Ooption_OSome(_866280), 5591 ^ [_866278, _866280])), -(_866278 = c_Option_Ooption_ONone(_866280))], (5597 ^ _777081) ^ [_866324, _866326] : [_866324 = c_Option_Ooption_ONone(_866326), 5600 ^ _777081 : [(5601 ^ _777081) ^ [_866396] : [_866324 = hAPP(c_Option_Ooption_OSome(_866326), _866396)]]], (5603 ^ _777081) ^ [_866439, _866441] : [-(_866439 = c_Option_Ooption_ONone(_866441)), -(_866439 = hAPP(c_Option_Ooption_OSome(_866441), 5606 ^ [_866439, _866441]))], (5610 ^ _777081) ^ [_866485, _866487] : [5611 ^ _777081 : [(5612 ^ _777081) ^ [_866533] : [_866485 = hAPP(c_Option_Ooption_OSome(_866487), _866533)]], _866485 = c_Option_Ooption_ONone(_866487)], (5616 ^ _777081) ^ [_866592, _866594, _866596, _866598] : [-(hAPP(c_Option_Ooption_Ooption__case(_866592, _866594, _866596, _866598), c_Option_Ooption_ONone(_866594)) = _866596)], (5618 ^ _777081) ^ [_866631, _866633, _866635] : [-(hAPP(hAPP(c_Option_Obind(_866631, _866633), c_Option_Ooption_ONone(_866631)), _866635) = c_Option_Ooption_ONone(_866633))], (5620 ^ _777081) ^ [_866689, _866691, _866693, _866695] : [c_Com_Ocom_OCall(_866689, _866691, _866693) = hAPP(c_Com_Ocom_OBODY, _866695)], (5622 ^ _777081) ^ [_866743, _866745, _866747, _866749] : [hAPP(c_Com_Ocom_OBODY, _866743) = c_Com_Ocom_OCall(_866745, _866747, _866749)], (5624 ^ _777081) ^ [_866797, _866799, _866801] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_866797, _866799, _866801))), 5627 ^ _777081 : [(5628 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _866799)))], (5630 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _866801)))]]], (5632 ^ _777081) ^ [_866918, _866920, _866922] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_866918, _866920, _866922)))), hBOOL(hAPP(c_Com_OWT, _866920)), hBOOL(hAPP(c_Com_OWT, _866922))], (5642 ^ _777081) ^ [_867073, _867075, _867077] : [hBOOL(hAPP(c_Com_OWT, _867073)), hBOOL(hAPP(c_Com_OWT, _867075)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_867077, _867073, _867075))))], (5652 ^ _777081) ^ [_867244, _867246, _867248, _867250] : [c_Com_Ocom_OCond(_867244, _867246, _867248) = hAPP(c_Com_Ocom_OBODY, _867250)], (5654 ^ _777081) ^ [_867298, _867300, _867302, _867304] : [hAPP(c_Com_Ocom_OBODY, _867298) = c_Com_Ocom_OCond(_867300, _867302, _867304)], (5656 ^ _777081) ^ [_867334, _867336, _867338, _867340, _867342, _867344] : [hAPP(_867334, _867336) = c_Option_Ooption_ONone(_867338), -(c_Map_Omap__comp(_867338, _867340, _867342, _867344, _867334, _867336) = c_Option_Ooption_ONone(_867340))], (5662 ^ _777081) ^ [_867462, _867464] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_867462, _867464))), 5665 ^ _777081 : [(5666 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _867462)))], (5668 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _867464)))]]], (5670 ^ _777081) ^ [_867579, _867581] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_867579, _867581)))), hBOOL(hAPP(c_Com_OWT, _867579)), hBOOL(hAPP(c_Com_OWT, _867581))], (5680 ^ _777081) ^ [_867728, _867730] : [hBOOL(hAPP(c_Com_OWT, _867728)), hBOOL(hAPP(c_Com_OWT, _867730)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_867728, _867730))))], (5690 ^ _777081) ^ [_867890, _867892, _867894] : [c_Com_Ocom_OSemi(_867890, _867892) = hAPP(c_Com_Ocom_OBODY, _867894)], (5692 ^ _777081) ^ [_867938, _867940, _867942] : [hAPP(c_Com_Ocom_OBODY, _867938) = c_Com_Ocom_OSemi(_867940, _867942)], (5694 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (5696 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (5698 ^ _777081) ^ [_868016] : [hAPP(c_Com_Ocom_OBODY, _868016) = c_Com_Ocom_OSKIP], (5700 ^ _777081) ^ [_868051] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _868051)], (5702 ^ _777081) ^ [_868092, _868094] : [c_Option_Ois__none(_868092, _868094), -(_868094 = c_Option_Ooption_ONone(_868092))], (5708 ^ _777081) ^ [_868169, _868171] : [_868171 = c_Option_Ooption_ONone(_868169), -(c_Option_Ois__none(_868169, _868171))], (5714 ^ _777081) ^ [_868248, _868250] : [-(_868248 = c_Option_Ooption_ONone(_868250)), -(_868248 = hAPP(c_Option_Ooption_OSome(_868250), 5717 ^ [_868248, _868250]))], (5721 ^ _777081) ^ [_868298, _868300, _868302, _868304, _868306, _868308] : [hAPP(c_Map_Omap__add(_868298, _868300, _868302, _868304), _868306) = hAPP(c_Option_Ooption_OSome(_868300), _868308), -(hAPP(_868304, _868306) = hAPP(c_Option_Ooption_OSome(_868300), _868308)), 5728 ^ _777081 : [(5729 ^ _777081) ^ [] : [-(hAPP(_868304, _868306) = c_Option_Ooption_ONone(_868300))], (5731 ^ _777081) ^ [] : [-(hAPP(_868302, _868306) = hAPP(c_Option_Ooption_OSome(_868300), _868308))]]], (5733 ^ _777081) ^ [_868534, _868536, _868538, _868540, _868542, _868544] : [hAPP(c_Map_Omap__add(_868534, _868536, _868538, _868540), _868542) = hAPP(c_Option_Ooption_OSome(_868536), _868544), -(hAPP(_868540, _868542) = hAPP(c_Option_Ooption_OSome(_868536), _868544)), 5740 ^ _777081 : [(5741 ^ _777081) ^ [] : [-(hAPP(_868540, _868542) = c_Option_Ooption_ONone(_868536))], (5743 ^ _777081) ^ [] : [-(hAPP(_868538, _868542) = hAPP(c_Option_Ooption_OSome(_868536), _868544))]]], (5745 ^ _777081) ^ [_868739, _868741, _868743, _868745, _868747, _868749] : [-(hAPP(c_Map_Omap__add(_868739, _868741, _868743, _868745), _868747) = hAPP(c_Option_Ooption_OSome(_868741), _868749)), 5746 ^ _777081 : [(5747 ^ _777081) ^ [] : [hAPP(_868745, _868747) = hAPP(c_Option_Ooption_OSome(_868741), _868749)], (5749 ^ _777081) ^ [] : [hAPP(_868745, _868747) = c_Option_Ooption_ONone(_868741), hAPP(_868743, _868747) = hAPP(c_Option_Ooption_OSome(_868741), _868749)]]], (5757 ^ _777081) ^ [_868990, _868992, _868994, _868996, _868998, _869000, _869002, _869004, _869006] : [-(c_Com_Ocom_Ocom__rec(_868990, _868992, _868994, _868996, _868998, _869000, _869002, _869004, _869006, c_Com_Ocom_OSKIP) = _868992)], (5759 ^ _777081) ^ [_869040, _869042, _869044, _869046, _869048, _869050, _869052, _869054, _869056, _869058, _869060] : [-(c_Com_Ocom_Ocom__rec(_869040, _869042, _869044, _869046, _869048, _869050, _869052, _869054, _869056, c_Com_Ocom_OSemi(_869058, _869060)) = hAPP(hAPP(hAPP(hAPP(_869048, _869058), _869060), c_Com_Ocom_Ocom__rec(_869040, _869042, _869044, _869046, _869048, _869050, _869052, _869054, _869056, _869058)), c_Com_Ocom_Ocom__rec(_869040, _869042, _869044, _869046, _869048, _869050, _869052, _869054, _869056, _869060)))], (5761 ^ _777081) ^ [_869131, _869133, _869135, _869137, _869139, _869141, _869143, _869145, _869147, _869149, _869151, _869153] : [-(c_Com_Ocom_Ocom__rec(_869131, _869133, _869135, _869137, _869139, _869141, _869143, _869145, _869147, c_Com_Ocom_OCall(_869149, _869151, _869153)) = hAPP(hAPP(hAPP(_869147, _869149), _869151), _869153))], (5763 ^ _777081) ^ [_869200, _869202, _869204, _869206, _869208, _869210, _869212, _869214, _869216, _869218, _869220, _869222] : [-(c_Com_Ocom_Ocom__rec(_869200, _869202, _869204, _869206, _869208, _869210, _869212, _869214, _869216, c_Com_Ocom_OCond(_869218, _869220, _869222)) = hAPP(hAPP(hAPP(hAPP(hAPP(_869210, _869218), _869220), _869222), c_Com_Ocom_Ocom__rec(_869200, _869202, _869204, _869206, _869208, _869210, _869212, _869214, _869216, _869220)), c_Com_Ocom_Ocom__rec(_869200, _869202, _869204, _869206, _869208, _869210, _869212, _869214, _869216, _869222)))], (5765 ^ _777081) ^ [_869297, _869299, _869301] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_869297, _869299, _869301))), -(hBOOL(hAPP(c_Com_OWT, _869301)))], (5771 ^ _777081) ^ [_869392, _869394, _869396, _869398, _869400, _869402, _869404, _869406, _869408, _869410] : [-(c_Com_Ocom_Ocom__rec(_869392, _869394, _869396, _869398, _869400, _869402, _869404, _869406, _869408, hAPP(c_Com_Ocom_OBODY, _869410)) = hAPP(_869406, _869410))], (5773 ^ _777081) ^ [_869450, _869452, _869454] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _869450))), _869452), _869454)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _869450)), _869452), _869454)))], (5779 ^ _777081) ^ [_869575, _869577, _869579] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _869575)), _869577), _869579)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _869575))), _869577), _869579)))], (5785 ^ _777081) ^ [_869699, _869701, _869703, _869705, _869707] : [-(hBOOL(hAPP(_869699, _869701))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869703), _869701), _869705)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_869699, _869707, _869703)), _869701), _869705)))], (5795 ^ _777081) ^ [_869876, _869878, _869880, _869882, _869884] : [hBOOL(hAPP(_869876, _869878)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_869880), _869878), _869882)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_869876, _869880, _869884)), _869878), _869882)))], (5805 ^ _777081) ^ [_870057, _870059, _870061, _870063, _870065] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_870057, _870059, _870061)), _870063), _870065)), 5810 ^ _777081 : [(5811 ^ _777081) ^ [] : [-(hBOOL(hAPP(_870057, _870063)))], (5813 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_870059), _870063), _870065)))]], 5814 ^ _777081 : [(5815 ^ _777081) ^ [] : [hBOOL(hAPP(_870057, _870063))], (5817 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_870061), _870063), _870065)))]]], (5819 ^ _777081) ^ [_870325, _870327, _870329, _870331, _870333] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_870325), _870327), _870329)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_870331), _870329), _870333)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_870325, _870331)), _870327), _870333)))], (5829 ^ _777081) ^ [_870514] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _870514), _870514)))], (5831 ^ _777081) ^ [_870542, _870544] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _870542), _870544)), -(_870544 = _870542)], (5837 ^ _777081) ^ [_870629, _870631, _870633, _870635] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_870629), _870631), _870633)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_870629), _870631), _870635)), -(_870635 = _870633)], (5847 ^ _777081) ^ [_870794, _870796, _870798, _870800, _870802, _870804, _870806, _870808, _870810, _870812, _870814, _870816] : [-(c_Com_Ocom_Ocom__rec(_870794, _870796, _870798, _870800, _870802, _870804, _870806, _870808, _870810, c_Com_Ocom_OLocal(_870812, _870814, _870816)) = hAPP(hAPP(hAPP(hAPP(_870800, _870812), _870814), _870816), c_Com_Ocom_Ocom__rec(_870794, _870796, _870798, _870800, _870802, _870804, _870806, _870808, _870810, _870816)))], (5849 ^ _777081) ^ [_870877, _870879, _870881, _870883, _870885, _870887, _870889, _870891, _870893, _870895, _870897] : [-(c_Com_Ocom_Ocom__rec(_870877, _870879, _870881, _870883, _870885, _870887, _870889, _870891, _870893, c_Com_Ocom_OAss(_870895, _870897)) = hAPP(hAPP(_870881, _870895), _870897))], (5851 ^ _777081) ^ [_870967, _870969, _870971, _870973, _870975, _870977] : [c_Com_Ocom_OLocal(_870967, _870969, _870971) = c_Com_Ocom_OLocal(_870973, _870975, _870977), 5854 ^ _777081 : [(5855 ^ _777081) ^ [] : [-(_870967 = _870973)], (5857 ^ _777081) ^ [] : [-(_870969 = _870975)], (5859 ^ _777081) ^ [] : [-(_870971 = _870977)]]], (5861 ^ _777081) ^ [_871114, _871116, _871118, _871120, _871122, _871124] : [-(c_Com_Ocom_OLocal(_871114, _871116, _871118) = c_Com_Ocom_OLocal(_871120, _871122, _871124)), _871114 = _871120, _871116 = _871122, _871118 = _871124], (5875 ^ _777081) ^ [_871358, _871360, _871362, _871364] : [c_Com_Ocom_OAss(_871358, _871360) = c_Com_Ocom_OAss(_871362, _871364), 5878 ^ _777081 : [(5879 ^ _777081) ^ [] : [-(_871358 = _871362)], (5881 ^ _777081) ^ [] : [-(_871360 = _871364)]]], (5883 ^ _777081) ^ [_871473, _871475, _871477, _871479] : [-(c_Com_Ocom_OAss(_871473, _871475) = c_Com_Ocom_OAss(_871477, _871479)), _871473 = _871477, _871475 = _871479], (5893 ^ _777081) ^ [_871624, _871626, _871628, _871630, _871632] : [-(c_Map_Omap__add(_871624, _871626, _871628, c_Map_Omap__add(_871624, _871626, _871630, _871632)) = c_Map_Omap__add(_871624, _871626, c_Map_Omap__add(_871624, _871626, _871628, _871630), _871632))], (5895 ^ _777081) ^ [_871696, _871698, _871700, _871702, _871704] : [c_Com_Ocom_OLocal(_871696, _871698, _871700) = c_Com_Ocom_OAss(_871702, _871704)], (5897 ^ _777081) ^ [_871755, _871757, _871759, _871761, _871763] : [c_Com_Ocom_OAss(_871755, _871757) = c_Com_Ocom_OLocal(_871759, _871761, _871763)], (5899 ^ _777081) ^ [_871817, _871819, _871821, _871823, _871825] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_871817, _871819, _871821)), _871823), _871825)), 5904 ^ _777081 : [(5905 ^ _777081) ^ [] : [-(hBOOL(hAPP(_871817, _871823)))], (5907 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_871819), _871823), _871825)))]], 5908 ^ _777081 : [(5909 ^ _777081) ^ [] : [hBOOL(hAPP(_871817, _871823))], (5911 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_871821), _871823), _871825)))]]], (5913 ^ _777081) ^ [_872075, _872077, _872079, _872081, _872083] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_872075, _872077, _872079)), _872081), _872083))), 5914 ^ _777081 : [(5915 ^ _777081) ^ [] : [hBOOL(hAPP(_872075, _872081)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_872077), _872081), _872083))], (5921 ^ _777081) ^ [] : [-(hBOOL(hAPP(_872075, _872081))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_872079), _872081), _872083))]]], (5929 ^ _777081) ^ [_872392, _872394, _872396, _872398, _872400] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_872392, _872394, _872396)), _872398), _872400)), 5934 ^ _777081 : [(5935 ^ _777081) ^ [] : [-(hBOOL(hAPP(_872392, _872398)))], (5937 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_872394), _872398), _872400)))]], 5938 ^ _777081 : [(5939 ^ _777081) ^ [] : [hBOOL(hAPP(_872392, _872398))], (5941 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_872396), _872398), _872400)))]]], (5943 ^ _777081) ^ [_872650, _872652, _872654, _872656, _872658] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(_872650, _872652, _872654)), _872656), _872658))), 5944 ^ _777081 : [(5945 ^ _777081) ^ [] : [hBOOL(hAPP(_872650, _872656)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_872652), _872656), _872658))], (5951 ^ _777081) ^ [] : [-(hBOOL(hAPP(_872650, _872656))), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_872654), _872656), _872658))]]], (5959 ^ _777081) ^ [_872964, _872966, _872968, _872970] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_872964, _872966)), _872968), _872970)), 5963 ^ _777081 : [(5964 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_872964), _872968), 5962 ^ [_872964, _872966, _872968, _872970])))], (5966 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_872966), 5962 ^ [_872964, _872966, _872968, _872970]), _872970)))]]], (5968 ^ _777081) ^ [_873142, _873144, _873146, _873148] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_873142, _873144)), _873146), _873148))), 5969 ^ _777081 : [(5970 ^ _777081) ^ [_873210] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_873142), _873146), _873210)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_873144), _873210), _873148))]]], (5978 ^ _777081) ^ [_873360] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP), _873360), _873360)))], (5980 ^ _777081) ^ [_873412, _873414, _873416, _873418, _873420] : [hAPP(c_Map_Omap__add(_873412, _873414, _873416, _873418), _873420) = c_Option_Ooption_ONone(_873414), 5983 ^ _777081 : [(5984 ^ _777081) ^ [] : [-(hAPP(_873418, _873420) = c_Option_Ooption_ONone(_873414))], (5986 ^ _777081) ^ [] : [-(hAPP(_873416, _873420) = c_Option_Ooption_ONone(_873414))]]], (5988 ^ _777081) ^ [_873557, _873559, _873561, _873563, _873565] : [-(hAPP(c_Map_Omap__add(_873557, _873559, _873561, _873563), _873565) = c_Option_Ooption_ONone(_873559)), hAPP(_873563, _873565) = c_Option_Ooption_ONone(_873559), hAPP(_873561, _873565) = c_Option_Ooption_ONone(_873559)], (5998 ^ _777081) ^ [_873740, _873742, _873744, _873746, _873748, _873750] : [hAPP(_873740, _873742) = hAPP(c_Option_Ooption_OSome(_873744), _873746), -(hAPP(c_Map_Omap__add(_873748, _873744, _873750, _873740), _873742) = hAPP(c_Option_Ooption_OSome(_873744), _873746))], (6004 ^ _777081) ^ [_873882, _873884, _873886] : [hAPP(c_Com_Ocom_OBODY, _873882) = c_Com_Ocom_OAss(_873884, _873886)], (6006 ^ _777081) ^ [_873930, _873932, _873934] : [c_Com_Ocom_OAss(_873930, _873932) = hAPP(c_Com_Ocom_OBODY, _873934)], (6008 ^ _777081) ^ [_873963, _873965] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_873963, _873965))))], (6010 ^ _777081) ^ [_873993, _873995] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OAss(_873993, _873995))))], (6012 ^ _777081) ^ [_874041, _874043, _874045, _874047] : [hAPP(c_Com_Ocom_OBODY, _874041) = c_Com_Ocom_OLocal(_874043, _874045, _874047)], (6014 ^ _777081) ^ [_874095, _874097, _874099, _874101] : [c_Com_Ocom_OLocal(_874095, _874097, _874099) = hAPP(c_Com_Ocom_OBODY, _874101)], (6016 ^ _777081) ^ [_874131, _874133, _874135] : [hBOOL(hAPP(c_Com_OWT, _874131)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_874133, _874135, _874131))))], (6022 ^ _777081) ^ [_874244, _874246, _874248] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_874244, _874246, _874248))), -(hBOOL(hAPP(c_Com_OWT, _874248)))], (6028 ^ _777081) ^ [_874335, _874337, _874339] : [hBOOL(hAPP(c_Com_OWT, _874339)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_874335, _874337, _874339))))], (6034 ^ _777081) ^ [_874453, _874455, _874457, _874459, _874461] : [c_Com_Ocom_OCond(_874453, _874455, _874457) = c_Com_Ocom_OAss(_874459, _874461)], (6036 ^ _777081) ^ [_874512, _874514, _874516, _874518, _874520] : [c_Com_Ocom_OAss(_874512, _874514) = c_Com_Ocom_OCond(_874516, _874518, _874520)], (6038 ^ _777081) ^ [_874574, _874576, _874578, _874580, _874582, _874584] : [c_Com_Ocom_OLocal(_874574, _874576, _874578) = c_Com_Ocom_OCond(_874580, _874582, _874584)], (6040 ^ _777081) ^ [_874639, _874641, _874643, _874645, _874647, _874649] : [c_Com_Ocom_OCond(_874639, _874641, _874643) = c_Com_Ocom_OLocal(_874645, _874647, _874649)], (6042 ^ _777081) ^ [_874701, _874703, _874705, _874707, _874709] : [c_Com_Ocom_OCall(_874701, _874703, _874705) = c_Com_Ocom_OAss(_874707, _874709)], (6044 ^ _777081) ^ [_874760, _874762, _874764, _874766, _874768] : [c_Com_Ocom_OAss(_874760, _874762) = c_Com_Ocom_OCall(_874764, _874766, _874768)], (6046 ^ _777081) ^ [_874816, _874818, _874820, _874822] : [c_Com_Ocom_OSemi(_874816, _874818) = c_Com_Ocom_OAss(_874820, _874822)], (6048 ^ _777081) ^ [_874869, _874871, _874873, _874875] : [c_Com_Ocom_OAss(_874869, _874871) = c_Com_Ocom_OSemi(_874873, _874875)], (6050 ^ _777081) ^ [_874916, _874918] : [c_Com_Ocom_OAss(_874916, _874918) = c_Com_Ocom_OSKIP], (6052 ^ _777081) ^ [_874956, _874958] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OAss(_874956, _874958)], (6054 ^ _777081) ^ [_875008, _875010, _875012, _875014, _875016, _875018] : [c_Com_Ocom_OLocal(_875008, _875010, _875012) = c_Com_Ocom_OCall(_875014, _875016, _875018)], (6056 ^ _777081) ^ [_875073, _875075, _875077, _875079, _875081, _875083] : [c_Com_Ocom_OCall(_875073, _875075, _875077) = c_Com_Ocom_OLocal(_875079, _875081, _875083)], (6058 ^ _777081) ^ [_875135, _875137, _875139, _875141, _875143] : [c_Com_Ocom_OLocal(_875135, _875137, _875139) = c_Com_Ocom_OSemi(_875141, _875143)], (6060 ^ _777081) ^ [_875194, _875196, _875198, _875200, _875202] : [c_Com_Ocom_OSemi(_875194, _875196) = c_Com_Ocom_OLocal(_875198, _875200, _875202)], (6062 ^ _777081) ^ [_875247, _875249, _875251] : [c_Com_Ocom_OLocal(_875247, _875249, _875251) = c_Com_Ocom_OSKIP], (6064 ^ _777081) ^ [_875293, _875295, _875297] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_875293, _875295, _875297)], (6066 ^ _777081) ^ [_875342, _875344, _875346] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _875342)), _875344), _875346)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _875342))), _875344), _875346)))], (6072 ^ _777081) ^ [_875463, _875465, _875467] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _875463))), _875465), _875467)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _875463)), _875465), _875467)))], (6078 ^ _777081) ^ [_875590, _875592, _875594, _875596, _875598, _875600, _875602, _875604, _875606, _875608, _875610] : [-(c_Com_Ocom_Ocom__case(_875590, _875592, _875594, _875596, _875598, _875600, _875602, _875604, _875606, c_Com_Ocom_OAss(_875608, _875610)) = hAPP(hAPP(_875594, _875608), _875610))], (6080 ^ _777081) ^ [_875653, _875655, _875657, _875659, _875661, _875663, _875665, _875667, _875669, _875671, _875673, _875675] : [-(c_Com_Ocom_Ocom__case(_875653, _875655, _875657, _875659, _875661, _875663, _875665, _875667, _875669, c_Com_Ocom_OLocal(_875671, _875673, _875675)) = hAPP(hAPP(hAPP(_875659, _875671), _875673), _875675))], (6082 ^ _777081) ^ [_875722, _875724, _875726, _875728] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(_875722, _875724)), _875726), _875728)), 6086 ^ _777081 : [(6087 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_875722), _875726), 6085 ^ [_875722, _875724, _875726, _875728])))], (6089 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_875724), 6085 ^ [_875722, _875724, _875726, _875728]), _875728)))]]], (6091 ^ _777081) ^ [_875908, _875910, _875912] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_875908, _875910)), _875912), hAPP(hAPP(hAPP(c_Natural_Oupdate, _875912), _875908), hAPP(_875910, _875912)))))], (6093 ^ _777081) ^ [_875957, _875959, _875961, _875963] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_875957, _875959)), _875961), _875963)), -(_875963 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _875961), _875957), hAPP(_875959, _875961)))], (6099 ^ _777081) ^ [_876082, _876084, _876086] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(_876082, _876084)), _876086), hAPP(hAPP(hAPP(c_Natural_Oupdate, _876086), _876082), hAPP(_876084, _876086)))))], (6101 ^ _777081) ^ [_876131, _876133, _876135, _876137, _876139, _876141] : [-(c_Map_Omap__add(_876131, _876133, _876135, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_876131, tc_Option_Ooption(_876133)), _876137), _876139), hAPP(c_Option_Ooption_OSome(_876133), _876141))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_876131, tc_Option_Ooption(_876133)), c_Map_Omap__add(_876131, _876133, _876135, _876137)), _876139), hAPP(c_Option_Ooption_OSome(_876133), _876141)))], (6103 ^ _777081) ^ [_876212, _876214, _876216, _876218] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _876212))), _876214), _876216), _876218)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _876212)), _876214), hAPP(c_Nat_OSuc, _876216)), _876218)))], (6109 ^ _777081) ^ [_876361, _876363] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_876361, _876363))), -(hBOOL(hAPP(c_Com_OWT, _876363)))], (6115 ^ _777081) ^ [_876452, _876454, _876456, _876458, _876460, _876462, _876464, _876466, _876468, _876470, _876472] : [-(c_Com_Ocom_Ocom__case(_876452, _876454, _876456, _876458, _876460, _876462, _876464, _876466, _876468, c_Com_Ocom_OWhile(_876470, _876472)) = hAPP(hAPP(_876464, _876470), _876472))], (6117 ^ _777081) ^ [_876536, _876538, _876540, _876542] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _876536)), _876538), hAPP(c_Nat_OSuc, _876540)), _876542)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _876536))), _876538), _876540), _876542)))], (6123 ^ _777081) ^ [_876681, _876683, _876685, _876687] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _876681))), _876683), _876685), _876687)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _876681)), _876683), hAPP(c_Nat_OSuc, _876685)), _876687)))], (6129 ^ _777081) ^ [_876828, _876830, _876832] : [-(hBOOL(hAPP(_876828, _876830))), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_876828, _876832)), _876830), _876830)))], (6135 ^ _777081) ^ [_876878, _876880, _876882, _876884, _876886] : [hBOOL(hAPP(_876878, _876880)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_876882), _876880), _876884)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_876878, _876882)), _876884), _876886)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_876878, _876882)), _876880), _876886)))], (6149 ^ _777081) ^ [_877135, _877137, _877139, _877141, _877143] : [c_Map_Omap__le(_877135, _877137, c_Map_Omap__add(_877135, _877137, _877139, _877141), _877143), -(c_Map_Omap__le(_877135, _877137, _877141, _877143))], (6155 ^ _777081) ^ [_877232, _877234, _877236, _877238] : [-(hBOOL(hAPP(_877232, _877234))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_877232, _877236)), _877234), _877238), _877234)))], (6161 ^ _777081) ^ [_877288, _877290, _877292, _877294, _877296, _877298] : [hBOOL(hAPP(_877288, _877290)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _877292), _877290), _877294), _877296)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_877288, _877292)), _877296), _877294), _877298)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_877288, _877292)), _877290), _877294), _877298)))], (6175 ^ _777081) ^ [_877575, _877577, _877579, _877581, _877583, _877585] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_877575, _877577, _877579)), _877581), _877583), _877585)), 6180 ^ _777081 : [(6181 ^ _777081) ^ [] : [-(hBOOL(hAPP(_877575, _877581)))], (6183 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _877577), _877581), _877583), _877585)))]], 6184 ^ _777081 : [(6185 ^ _777081) ^ [] : [hBOOL(hAPP(_877575, _877581))], (6187 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _877579), _877581), _877583), _877585)))]]], (6189 ^ _777081) ^ [_877871, _877873, _877875, _877877, _877879, _877881] : [hBOOL(hAPP(_877871, _877873)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _877875), _877873), _877877), _877879)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_877871, _877875, _877881)), _877873), _877877), _877879)))], (6199 ^ _777081) ^ [_878071, _878073, _878075, _878077, _878079, _878081] : [-(hBOOL(hAPP(_878071, _878073))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _878075), _878073), _878077), _878079)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_878071, _878081, _878075)), _878073), _878077), _878079)))], (6209 ^ _777081) ^ [_878268, _878270, _878272, _878274, _878276, _878278] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _878268), _878270), _878272), _878274)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _878276), _878274), _878272), _878278)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_878268, _878276)), _878270), _878272), _878278)))], (6219 ^ _777081) ^ [_878485, _878487, _878489] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _878485), _878487), _878489)), -(_878489 = _878485)], (6225 ^ _777081) ^ [_878580, _878582] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _878580), _878582), _878580)))], (6227 ^ _777081) ^ [_878613, _878615, _878617, _878619, _878621] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OAss(_878613, _878615)), _878617), _878619), _878621)), -(_878621 = hAPP(hAPP(hAPP(c_Natural_Oupdate, _878617), _878613), hAPP(_878615, _878617)))], (6233 ^ _777081) ^ [_878748, _878750, _878752, _878754] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OAss(_878748, _878750)), _878752), _878754), hAPP(hAPP(hAPP(c_Natural_Oupdate, _878752), _878748), hAPP(_878750, _878752)))))], (6235 ^ _777081) ^ [_878824, _878826, _878828, _878830] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_878824, _878826)), _878828), _878830), _878828)), hBOOL(hAPP(_878824, _878828)), 6243 ^ _777081 : [(6244 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _878826), _878828), _878830), 6242 ^ [_878824, _878826, _878828, _878830])))], (6246 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_878824, _878826)), 6242 ^ [_878824, _878826, _878828, _878830]), _878830), _878828)))]]], (6248 ^ _777081) ^ [_879092, _879094, _879096, _879098] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_879092, _879094)), _879096), _879098), _879096))), 6249 ^ _777081 : [(6250 ^ _777081) ^ [] : [-(hBOOL(hAPP(_879092, _879096)))], (6252 ^ _777081) ^ [_879206] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _879094), _879096), _879098), _879206)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_879092, _879094)), _879206), _879098), _879096))]]], (6260 ^ _777081) ^ [_879408, _879410, _879412, _879414, _879416] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_879408, _879410)), _879412), _879414), _879416)), 6265 ^ _777081 : [(6266 ^ _777081) ^ [] : [-(_879416 = _879412)], (6268 ^ _777081) ^ [] : [hBOOL(hAPP(_879408, _879412))]], 6269 ^ _777081 : [(6270 ^ _777081) ^ [] : [-(hBOOL(hAPP(_879408, _879412)))], (6273 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _879410), _879412), _879414), 6271 ^ [_879408, _879410, _879412, _879414, _879416])))], (6275 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_879408, _879410)), 6271 ^ [_879408, _879410, _879412, _879414, _879416]), _879414), _879416)))]]], (6277 ^ _777081) ^ [_879747, _879749, _879751, _879753, _879755] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_879747, _879749)), _879751), _879753), _879755))), 6278 ^ _777081 : [(6279 ^ _777081) ^ [] : [_879755 = _879751, -(hBOOL(hAPP(_879747, _879751)))], (6285 ^ _777081) ^ [] : [hBOOL(hAPP(_879747, _879751)), 6288 ^ _777081 : [(6289 ^ _777081) ^ [_879984] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _879749), _879751), _879753), _879984)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_879747, _879749)), _879984), _879753), _879755))]]]]], (6297 ^ _777081) ^ [_880168, _880170, _880172, _880174] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _880168), _880170), _880172), _880174)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _880168), _880170), hAPP(c_Nat_OSuc, _880172)), _880174)))], (6303 ^ _777081) ^ [_880299, _880301, _880303] : [-(c_Map_Omap__le(_880299, _880301, _880303, _880303))], (6305 ^ _777081) ^ [_880349, _880351, _880353, _880355] : [c_Com_Ocom_OWhile(_880349, _880351) = c_Com_Ocom_OWhile(_880353, _880355), 6308 ^ _777081 : [(6309 ^ _777081) ^ [] : [-(_880349 = _880353)], (6311 ^ _777081) ^ [] : [-(_880351 = _880355)]]], (6313 ^ _777081) ^ [_880464, _880466, _880468, _880470] : [-(c_Com_Ocom_OWhile(_880464, _880466) = c_Com_Ocom_OWhile(_880468, _880470)), _880464 = _880468, _880466 = _880470], (6323 ^ _777081) ^ [_880615, _880617, _880619, _880621, _880623, _880625] : [c_Map_Omap__le(_880615, _880617, _880619, _880621), -(c_Map_Omap__le(_880615, _880617, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_880615, tc_Option_Ooption(_880617)), _880619), _880623), _880625), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_880615, tc_Option_Ooption(_880617)), _880621), _880623), _880625)))], (6329 ^ _777081) ^ [_880764, _880766, _880768, _880770] : [c_Map_Omap__le(_880764, _880766, _880768, _880770), c_Map_Omap__le(_880764, _880766, _880770, _880768), -(_880768 = _880770)], (6339 ^ _777081) ^ [_880909, _880911, _880913, _880915, _880917] : [c_Map_Omap__le(_880909, _880911, _880913, _880915), c_Map_Omap__le(_880909, _880911, _880915, _880917), -(c_Map_Omap__le(_880909, _880911, _880913, _880917))], (6349 ^ _777081) ^ [_881062, _881064, _881066, _881068] : [-(c_Map_Omap__le(_881062, _881064, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_881062, tc_Option_Ooption(_881064)), _881066), _881068), c_Option_Ooption_ONone(_881064)), _881066))], (6351 ^ _777081) ^ [_881109, _881111, _881113, _881115] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OAss(_881109, _881111)), _881113), _881115), hAPP(hAPP(hAPP(c_Natural_Oupdate, _881113), _881109), hAPP(_881111, _881113)))))], (6353 ^ _777081) ^ [_881164, _881166, _881168, _881170, _881172, _881174] : [c_Map_Omap__le(_881164, _881166, _881168, _881170), -(c_Map_Omap__le(_881164, _881166, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_881164, tc_Option_Ooption(_881166)), _881168), _881172), c_Option_Ooption_ONone(_881166)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_881164, tc_Option_Ooption(_881166)), _881170), _881172), hAPP(c_Option_Ooption_OSome(_881166), _881174))))], (6359 ^ _777081) ^ [_881357, _881359, _881361, _881363, _881365, _881367, _881369] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_881357, tc_Option_Ooption(_881359)), _881361), _881363), hAPP(c_Option_Ooption_OSome(_881359), _881365)), _881367) = hAPP(c_Option_Ooption_OSome(_881359), _881369), 6364 ^ _777081 : [(6365 ^ _777081) ^ [] : [-(_881367 = _881363)], (6367 ^ _777081) ^ [] : [-(_881365 = _881369)]], 6368 ^ _777081 : [(6369 ^ _777081) ^ [] : [_881367 = _881363], (6371 ^ _777081) ^ [] : [-(hAPP(_881361, _881367) = hAPP(c_Option_Ooption_OSome(_881359), _881369))]]], (6373 ^ _777081) ^ [_881635, _881637, _881639, _881641, _881643, _881645, _881647] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_881635, tc_Option_Ooption(_881637)), _881639), _881641), hAPP(c_Option_Ooption_OSome(_881637), _881643)), _881645) = hAPP(c_Option_Ooption_OSome(_881637), _881647)), 6374 ^ _777081 : [(6375 ^ _777081) ^ [] : [_881645 = _881641, _881643 = _881647], (6381 ^ _777081) ^ [] : [-(_881645 = _881641), hAPP(_881639, _881645) = hAPP(c_Option_Ooption_OSome(_881637), _881647)]]], (6389 ^ _777081) ^ [_881952, _881954, _881956, _881958, _881960] : [hAPP(_881952, _881954) = hAPP(c_Option_Ooption_OSome(_881956), _881958), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_881960, tc_Option_Ooption(_881956)), _881952), _881954), hAPP(c_Option_Ooption_OSome(_881956), _881958)) = _881952)], (6395 ^ _777081) ^ [_882089, _882091, _882093, _882095, _882097, _882099, _882101] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_882089, tc_Option_Ooption(_882091)), _882093), _882095), hAPP(c_Option_Ooption_OSome(_882091), _882097)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_882089, tc_Option_Ooption(_882091)), _882099), _882095), hAPP(c_Option_Ooption_OSome(_882091), _882101)), -(_882097 = _882101)], (6401 ^ _777081) ^ [_882252, _882254, _882256, _882258] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _882252), _882254), _882256), _882258)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_882252), _882254), _882258)))], (6407 ^ _777081) ^ [_882387, _882389, _882391] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_882387), _882389), _882391)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _882387), _882389), 6410 ^ [_882387, _882389, _882391]), _882391)))], (6414 ^ _777081) ^ [_882512, _882514, _882516] : [6415 ^ _777081 : [(6416 ^ _777081) ^ [_882571] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _882512), _882514), _882571), _882516))]], -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_882512), _882514), _882516)))], (6420 ^ _777081) ^ [_882669, _882671, _882673, _882675, _882677, _882679] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_882669, _882671, _882673)), _882675), _882677), _882679)), 6425 ^ _777081 : [(6426 ^ _777081) ^ [] : [-(hBOOL(hAPP(_882669, _882675)))], (6428 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _882671), _882675), _882677), _882679)))]], 6429 ^ _777081 : [(6430 ^ _777081) ^ [] : [hBOOL(hAPP(_882669, _882675))], (6432 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _882673), _882675), _882677), _882679)))]]], (6434 ^ _777081) ^ [_882955, _882957, _882959, _882961, _882963, _882965] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_882955, _882957, _882959)), _882961), _882963), _882965))), 6435 ^ _777081 : [(6436 ^ _777081) ^ [] : [hBOOL(hAPP(_882955, _882961)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _882957), _882961), _882963), _882965))], (6442 ^ _777081) ^ [] : [-(hBOOL(hAPP(_882955, _882961))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _882959), _882961), _882963), _882965))]]], (6450 ^ _777081) ^ [_883305, _883307, _883309, _883311, _883313, _883315] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_883305, _883307, _883309)), _883311), _883313), _883315)), 6455 ^ _777081 : [(6456 ^ _777081) ^ [] : [-(hBOOL(hAPP(_883305, _883311)))], (6458 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _883307), _883311), _883313), _883315)))]], 6459 ^ _777081 : [(6460 ^ _777081) ^ [] : [hBOOL(hAPP(_883305, _883311))], (6462 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _883309), _883311), _883313), _883315)))]]], (6464 ^ _777081) ^ [_883591, _883593, _883595, _883597, _883599, _883601] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCond(_883591, _883593, _883595)), _883597), _883599), _883601))), 6465 ^ _777081 : [(6466 ^ _777081) ^ [] : [hBOOL(hAPP(_883591, _883597)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _883593), _883597), _883599), _883601))], (6472 ^ _777081) ^ [] : [-(hBOOL(hAPP(_883591, _883597))), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _883595), _883597), _883599), _883601))]]], (6480 ^ _777081) ^ [_883938, _883940, _883942, _883944, _883946] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_883938, _883940)), _883942), _883944), _883946)), 6484 ^ _777081 : [(6485 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _883938), _883942), _883944), 6483 ^ [_883938, _883940, _883942, _883944, _883946])))], (6487 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _883940), 6483 ^ [_883938, _883940, _883942, _883944, _883946]), _883944), _883946)))]]], (6489 ^ _777081) ^ [_884146, _884148, _884150, _884152, _884154] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_884146, _884148)), _884150), _884152), _884154))), 6490 ^ _777081 : [(6491 ^ _777081) ^ [_884228] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _884146), _884150), _884152), _884228)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _884148), _884228), _884152), _884154))]]], (6499 ^ _777081) ^ [_884400, _884402] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSKIP), _884400), _884402), _884400)))], (6501 ^ _777081) ^ [_884454, _884456, _884458, _884460] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884454, _884456)), _884458), _884460)), 6506 ^ _777081 : [(6507 ^ _777081) ^ [] : [-(_884460 = _884458)], (6509 ^ _777081) ^ [] : [hBOOL(hAPP(_884454, _884458))]], 6510 ^ _777081 : [(6511 ^ _777081) ^ [] : [-(hBOOL(hAPP(_884454, _884458)))], (6514 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_884456), _884458), 6512 ^ [_884454, _884456, _884458, _884460])))], (6516 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884454, _884456)), 6512 ^ [_884454, _884456, _884458, _884460]), _884460)))]]], (6518 ^ _777081) ^ [_884761, _884763, _884765, _884767] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884761, _884763)), _884765), _884767))), 6519 ^ _777081 : [(6520 ^ _777081) ^ [] : [_884767 = _884765, -(hBOOL(hAPP(_884761, _884765)))], (6526 ^ _777081) ^ [] : [hBOOL(hAPP(_884761, _884765)), 6529 ^ _777081 : [(6530 ^ _777081) ^ [_884980] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_884763), _884765), _884980)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_884761, _884763)), _884980), _884767))]]]]], (6538 ^ _777081) ^ [_885160, _885162, _885164] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_885160, _885162)), _885164), _885164)), hBOOL(hAPP(_885160, _885164)), 6546 ^ _777081 : [(6547 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885162), _885164), 6545 ^ [_885160, _885162, _885164])))], (6549 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_885160, _885162)), 6545 ^ [_885160, _885162, _885164]), _885164)))]]], (6551 ^ _777081) ^ [_885396, _885398, _885400] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_885396, _885398)), _885400), _885400))), 6552 ^ _777081 : [(6553 ^ _777081) ^ [] : [-(hBOOL(hAPP(_885396, _885400)))], (6555 ^ _777081) ^ [_885496] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_885398), _885400), _885496)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_885396, _885398)), _885496), _885400))]]], (6563 ^ _777081) ^ [_885667, _885669] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_885667, _885669))), -(hBOOL(hAPP(c_Com_OWT, _885669)))], (6569 ^ _777081) ^ [_885754, _885756] : [hBOOL(hAPP(c_Com_OWT, _885756)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_885754, _885756))))], (6575 ^ _777081) ^ [_885847, _885849] : [hBOOL(hAPP(c_Com_OWT, _885847)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_885849, _885847))))], (6581 ^ _777081) ^ [_885953, _885955, _885957] : [c_Com_Ocom_OWhile(_885953, _885955) = hAPP(c_Com_Ocom_OBODY, _885957)], (6583 ^ _777081) ^ [_886001, _886003, _886005] : [hAPP(c_Com_Ocom_OBODY, _886001) = c_Com_Ocom_OWhile(_886003, _886005)], (6585 ^ _777081) ^ [_886055, _886057, _886059, _886061, _886063] : [c_Com_Ocom_OWhile(_886055, _886057) = c_Com_Ocom_OCond(_886059, _886061, _886063)], (6587 ^ _777081) ^ [_886114, _886116, _886118, _886120, _886122] : [c_Com_Ocom_OCond(_886114, _886116, _886118) = c_Com_Ocom_OWhile(_886120, _886122)], (6589 ^ _777081) ^ [_886170, _886172, _886174, _886176] : [c_Com_Ocom_OAss(_886170, _886172) = c_Com_Ocom_OWhile(_886174, _886176)], (6591 ^ _777081) ^ [_886223, _886225, _886227, _886229] : [c_Com_Ocom_OWhile(_886223, _886225) = c_Com_Ocom_OAss(_886227, _886229)], (6593 ^ _777081) ^ [_886276, _886278, _886280, _886282] : [c_Com_Ocom_OSemi(_886276, _886278) = c_Com_Ocom_OWhile(_886280, _886282)], (6595 ^ _777081) ^ [_886329, _886331, _886333, _886335] : [c_Com_Ocom_OWhile(_886329, _886331) = c_Com_Ocom_OSemi(_886333, _886335)], (6597 ^ _777081) ^ [_886385, _886387, _886389, _886391, _886393] : [c_Com_Ocom_OWhile(_886385, _886387) = c_Com_Ocom_OCall(_886389, _886391, _886393)], (6599 ^ _777081) ^ [_886444, _886446, _886448, _886450, _886452] : [c_Com_Ocom_OCall(_886444, _886446, _886448) = c_Com_Ocom_OWhile(_886450, _886452)], (6601 ^ _777081) ^ [_886503, _886505, _886507, _886509, _886511] : [c_Com_Ocom_OWhile(_886503, _886505) = c_Com_Ocom_OLocal(_886507, _886509, _886511)], (6603 ^ _777081) ^ [_886562, _886564, _886566, _886568, _886570] : [c_Com_Ocom_OLocal(_886562, _886564, _886566) = c_Com_Ocom_OWhile(_886568, _886570)], (6605 ^ _777081) ^ [_886612, _886614] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_886612, _886614)], (6607 ^ _777081) ^ [_886652, _886654] : [c_Com_Ocom_OWhile(_886652, _886654) = c_Com_Ocom_OSKIP], (6609 ^ _777081) ^ [_886680, _886682, _886684, _886686, _886688, _886690, _886692, _886694, _886696, _886698, _886700] : [-(c_Com_Ocom_Ocom__rec(_886680, _886682, _886684, _886686, _886688, _886690, _886692, _886694, _886696, c_Com_Ocom_OWhile(_886698, _886700)) = hAPP(hAPP(hAPP(_886692, _886698), _886700), c_Com_Ocom_Ocom__rec(_886680, _886682, _886684, _886686, _886688, _886690, _886692, _886694, _886696, _886700)))], (6611 ^ _777081) ^ [_886757, _886759, _886761, _886763] : [-(c_Map_Omap__le(_886757, _886759, _886761, c_Map_Omap__add(_886757, _886759, _886763, _886761)))], (6613 ^ _777081) ^ [_886814, _886816, _886818, _886820] : [c_Map_Omap__le(_886814, _886816, _886818, c_Map_Omap__add(_886814, _886816, _886818, _886820)), -(c_Map_Omap__add(_886814, _886816, _886818, _886820) = c_Map_Omap__add(_886814, _886816, _886820, _886818))], (6619 ^ _777081) ^ [_886925, _886927, _886929, _886931] : [c_Map_Omap__add(_886925, _886927, _886929, _886931) = c_Map_Omap__add(_886925, _886927, _886931, _886929), -(c_Map_Omap__le(_886925, _886927, _886929, c_Map_Omap__add(_886925, _886927, _886929, _886931)))], (6625 ^ _777081) ^ [_887042, _887044, _887046, _887048, _887050] : [c_Map_Omap__le(_887042, _887044, _887046, _887048), c_Map_Omap__le(_887042, _887044, _887050, _887048), c_Map_Omap__le(_887042, _887044, _887046, c_Map_Omap__add(_887042, _887044, _887046, _887050)), -(c_Map_Omap__le(_887042, _887044, c_Map_Omap__add(_887042, _887044, _887046, _887050), _887048))], (6639 ^ _777081) ^ [_887277, _887279, _887281, _887283] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_887277, _887279), _887281), _887283), hAPP(_887281, _887283)) = _887281)], (6641 ^ _777081) ^ [_887321, _887323, _887325, _887327] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _887321)), _887323), _887325), _887327)), 6645 ^ _777081 : [(6646 ^ _777081) ^ [] : [-(_887325 = hAPP(c_Nat_OSuc, 6644 ^ [_887321, _887323, _887325, _887327]))], (6648 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _887321))), _887323), 6644 ^ [_887321, _887323, _887325, _887327]), _887327)))]]], (6650 ^ _777081) ^ [_887527, _887529, _887531, _887533, _887535] : [hAPP(_887527, _887529) = _887531, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_887533, _887535), _887527), _887529), _887531) = _887527)], (6656 ^ _777081) ^ [_887636, _887638, _887640, _887642, _887644, _887646] : [-(_887636 = _887638), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_887640, _887642), _887644), _887638), _887646), _887636) = hAPP(_887644, _887636))], (6662 ^ _777081) ^ [_887694, _887696, _887698, _887700, _887702, _887704, _887706] : [-(_887694 = _887696), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_887698, _887700), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_887698, _887700), _887702), _887694), _887704)), _887696), _887706) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_887698, _887700), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_887698, _887700), _887702), _887696), _887706)), _887694), _887704))], (6668 ^ _777081) ^ [_887809, _887811, _887813, _887815, _887817, _887819] : [_887809 = _887811, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_887813, _887815), _887817), _887811), _887819), _887809) = _887819)], (6674 ^ _777081) ^ [_887918, _887920, _887922, _887924, _887926, _887928] : [-(_887918 = _887920), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_887922, _887924), _887926), _887920), _887928), _887918) = hAPP(_887926, _887918))], (6680 ^ _777081) ^ [_887982, _887984, _887986, _887988, _887990] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_887982, _887984), _887986), _887988), _887990), _887988) = _887990)], (6682 ^ _777081) ^ [_888028, _888030, _888032, _888034, _888036, _888038] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_888028, _888030), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_888028, _888030), _888032), _888034), _888036)), _888034), _888038) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_888028, _888030), _888032), _888034), _888038))], (6684 ^ _777081) ^ [_888121, _888123, _888125, _888127, _888129] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_888121, _888123), _888125), _888127), _888129) = _888125, -(hAPP(_888125, _888127) = _888129)], (6690 ^ _777081) ^ [_888230, _888232, _888234, _888236, _888238] : [hAPP(_888234, _888236) = _888238, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_888230, _888232), _888234), _888236), _888238) = _888234)], (6696 ^ _777081) ^ [_888345, _888347, _888349, _888351, _888353] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OSemi(_888345, _888347)), _888349), _888351), _888353)), 6700 ^ _777081 : [(6701 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _888345), _888349), _888351), 6699 ^ [_888345, _888347, _888349, _888351, _888353])))], (6703 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _888347), 6699 ^ [_888345, _888347, _888349, _888351, _888353]), _888351), _888353)))]]], (6705 ^ _777081) ^ [_888570] : [_888570 = hAPP(c_Nat_OSuc, _888570)], (6707 ^ _777081) ^ [_888605] : [hAPP(c_Nat_OSuc, _888605) = _888605], (6709 ^ _777081) ^ [_888646, _888648] : [hAPP(c_Nat_OSuc, _888646) = hAPP(c_Nat_OSuc, _888648), -(_888646 = _888648)], (6715 ^ _777081) ^ [_888731, _888733] : [_888731 = _888733, -(hAPP(c_Nat_OSuc, _888731) = hAPP(c_Nat_OSuc, _888733))], (6721 ^ _777081) ^ [_888822, _888824] : [hAPP(c_Nat_OSuc, _888822) = hAPP(c_Nat_OSuc, _888824), -(_888822 = _888824)], (6727 ^ _777081) ^ [_888911, _888913, _888915, _888917] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_888911, _888913)), _888915), _888917)), 6732 ^ _777081 : [(6733 ^ _777081) ^ [] : [-(_888917 = _888915)], (6735 ^ _777081) ^ [] : [hBOOL(hAPP(_888911, _888915))]], 6736 ^ _777081 : [(6737 ^ _777081) ^ [] : [-(hBOOL(hAPP(_888911, _888915)))], (6740 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_888913), _888915), 6738 ^ [_888911, _888913, _888915, _888917])))], (6742 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(_888911, _888913)), 6738 ^ [_888911, _888913, _888915, _888917]), _888917)))]]], (6744 ^ _777081) ^ [_889224, _889226, _889228, _889230, _889232] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_889224, _889226)), _889228), _889230), _889232)), 6749 ^ _777081 : [(6750 ^ _777081) ^ [] : [-(_889232 = _889228)], (6752 ^ _777081) ^ [] : [hBOOL(hAPP(_889224, _889228))]], 6753 ^ _777081 : [(6754 ^ _777081) ^ [] : [-(hBOOL(hAPP(_889224, _889228)))], (6757 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _889226), _889228), _889230), 6755 ^ [_889224, _889226, _889228, _889230, _889232])))], (6759 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OWhile(_889224, _889226)), 6755 ^ [_889224, _889226, _889228, _889230, _889232]), _889230), _889232)))]]], (6761 ^ _777081) ^ [_889569, _889571, _889573] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_889569), _889571), _889573)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _889569), _889571), 6764 ^ [_889569, _889571, _889573]), _889573)))], (6768 ^ _777081) ^ [_889722, _889724, _889726, _889728, _889730] : [c_Hoare__Mirabelle_Otriple__valid(_889722, _889724, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_889722), _889726), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _889728))), _889730)), -(c_Hoare__Mirabelle_Otriple__valid(_889722, hAPP(c_Nat_OSuc, _889724), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_889722), _889726), hAPP(c_Com_Ocom_OBODY, _889728)), _889730)))], (6774 ^ _777081) ^ [_889873, _889875, _889877, _889879, _889881] : [c_Hoare__Mirabelle_Otriple__valid(_889873, hAPP(c_Nat_OSuc, _889875), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_889873), _889877), hAPP(c_Com_Ocom_OBODY, _889879)), _889881)), -(c_Hoare__Mirabelle_Otriple__valid(_889873, _889875, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_889873), _889877), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _889879))), _889881)))], (6780 ^ _777081) ^ [_890030, _890032, _890034, _890036, _890038] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(_890030), hAPP(hAPP(hAPP(c_Natural_Oupdate, _890032), c_Com_Ovname_OLoc(_890034)), hAPP(_890036, _890032))), _890038)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_890034, _890036, _890030)), _890032), hAPP(hAPP(hAPP(c_Natural_Oupdate, _890038), c_Com_Ovname_OLoc(_890034)), hAPP(hAPP(c_Natural_Ogetlocs, _890032), _890034)))))], (6786 ^ _777081) ^ [_890211, _890213, _890215, _890217, _890219, _890221] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _890211), hAPP(hAPP(hAPP(c_Natural_Oupdate, _890213), c_Com_Ovname_OLoc(_890215)), hAPP(_890217, _890213))), _890219), _890221)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OLocal(_890215, _890217, _890211)), _890213), _890219), hAPP(hAPP(hAPP(c_Natural_Oupdate, _890221), c_Com_Ovname_OLoc(_890215)), hAPP(hAPP(c_Natural_Ogetlocs, _890213), _890215)))))], (6792 ^ _777081) ^ [_890410, _890412, _890414, _890416, _890418] : [hAPP(_890410, _890412) = c_Option_Ooption_ONone(_890414), -(c_Map_Oran(_890416, _890414, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_890416, tc_Option_Ooption(_890414)), _890410), _890412), hAPP(c_Option_Ooption_OSome(_890414), _890418))) = hAPP(hAPP(c_Set_Oinsert(_890414), _890418), c_Map_Oran(_890416, _890414, _890410)))], (6798 ^ _777081) ^ [_890588, _890590] : [c_Com_Ovname_OLoc(_890588) = c_Com_Ovname_OLoc(_890590), -(_890588 = _890590)], (6804 ^ _777081) ^ [_890669, _890671] : [_890669 = _890671, -(c_Com_Ovname_OLoc(_890669) = c_Com_Ovname_OLoc(_890671))], (6810 ^ _777081) ^ [_890786, _890788, _890790, _890792, _890794, _890796, _890798] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_890786), _890788), _890790), _890792) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_890786), _890794), _890796), _890798), 6813 ^ _777081 : [(6814 ^ _777081) ^ [] : [-(_890788 = _890794)], (6816 ^ _777081) ^ [] : [-(_890790 = _890796)], (6818 ^ _777081) ^ [] : [-(_890792 = _890798)]]], (6820 ^ _777081) ^ [_890963, _890965, _890967, _890969, _890971, _890973, _890975] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_890963), _890965), _890967), _890969) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_890963), _890971), _890973), _890975)), _890965 = _890971, _890967 = _890973, _890969 = _890975], (6848 ^ _777081) ^ [_891598, _891600, _891602, _891604, _891606] : [6851 ^ _777081 : [(6852 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_891602, 6849 ^ [_891598, _891600, _891602, _891604, _891606]), 6850 ^ [_891598, _891600, _891602, _891604, _891606])))], (6855 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _891604), 6850 ^ [_891598, _891600, _891602, _891604, _891606]), _891600), 6853 ^ [_891598, _891600, _891602, _891604, _891606])))], (6857 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_891606, 6849 ^ [_891598, _891600, _891602, _891604, _891606]), 6853 ^ [_891598, _891600, _891602, _891604, _891606]))]], -(c_Hoare__Mirabelle_Otriple__valid(_891598, _891600, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_891598), _891602), _891604), _891606)))], (6834 ^ _777081) ^ [_891244, _891246, _891248, _891250, _891252] : [c_Hoare__Mirabelle_Otriple__valid(_891244, _891246, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_891244), _891248), _891250), _891252)), 6837 ^ _777081 : [(6838 ^ _777081) ^ [_891374, _891376] : [hBOOL(hAPP(hAPP(_891248, _891376), _891374)), 6841 ^ _777081 : [(6842 ^ _777081) ^ [_891473] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _891250), _891374), _891246), _891473)), -(hBOOL(hAPP(hAPP(_891252, _891376), _891473)))]]]]], (6861 ^ _777081) ^ [_892033, _892035, _892037, _892039, _892041, _892043] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OLocal(_892033, _892035, _892037)), _892039), _892041), hAPP(hAPP(hAPP(c_Natural_Oupdate, _892043), c_Com_Ovname_OLoc(_892033)), hAPP(hAPP(c_Natural_Ogetlocs, _892039), _892033)))), 6865 ^ _777081 : [(6866 ^ _777081) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, _892043), c_Com_Ovname_OLoc(_892033)), hAPP(hAPP(c_Natural_Ogetlocs, _892039), _892033)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6864 ^ [_892033, _892035, _892037, _892039, _892041, _892043]), c_Com_Ovname_OLoc(_892033)), hAPP(hAPP(c_Natural_Ogetlocs, _892039), _892033)))], (6868 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _892037), hAPP(hAPP(hAPP(c_Natural_Oupdate, _892039), c_Com_Ovname_OLoc(_892033)), hAPP(_892035, _892039))), _892041), 6864 ^ [_892033, _892035, _892037, _892039, _892041, _892043])))]]], (6870 ^ _777081) ^ [_892357, _892359, _892361, _892363, _892365, _892367] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OLocal(_892357, _892359, _892361)), _892363), _892365), hAPP(hAPP(hAPP(c_Natural_Oupdate, _892367), c_Com_Ovname_OLoc(_892357)), hAPP(hAPP(c_Natural_Ogetlocs, _892363), _892357))))), 6871 ^ _777081 : [(6872 ^ _777081) ^ [_892496] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, _892367), c_Com_Ovname_OLoc(_892357)), hAPP(hAPP(c_Natural_Ogetlocs, _892363), _892357)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, _892496), c_Com_Ovname_OLoc(_892357)), hAPP(hAPP(c_Natural_Ogetlocs, _892363), _892357)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _892361), hAPP(hAPP(hAPP(c_Natural_Oupdate, _892363), c_Com_Ovname_OLoc(_892357)), hAPP(_892359, _892363))), _892365), _892496))]]], (6880 ^ _777081) ^ [_892786, _892788, _892790, _892792, _892794] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_892786, _892788, _892790)), _892792), hAPP(hAPP(hAPP(c_Natural_Oupdate, _892794), c_Com_Ovname_OLoc(_892786)), hAPP(hAPP(c_Natural_Ogetlocs, _892792), _892786)))), 6884 ^ _777081 : [(6885 ^ _777081) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, _892794), c_Com_Ovname_OLoc(_892786)), hAPP(hAPP(c_Natural_Ogetlocs, _892792), _892786)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6883 ^ [_892786, _892788, _892790, _892792, _892794]), c_Com_Ovname_OLoc(_892786)), hAPP(hAPP(c_Natural_Ogetlocs, _892792), _892786)))], (6887 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_892790), hAPP(hAPP(hAPP(c_Natural_Oupdate, _892792), c_Com_Ovname_OLoc(_892786)), hAPP(_892788, _892792))), 6883 ^ [_892786, _892788, _892790, _892792, _892794])))]]], (6889 ^ _777081) ^ [_893088, _893090, _893092, _893094, _893096] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_893088, _893090, _893092)), _893094), hAPP(hAPP(hAPP(c_Natural_Oupdate, _893096), c_Com_Ovname_OLoc(_893088)), hAPP(hAPP(c_Natural_Ogetlocs, _893094), _893088))))), 6890 ^ _777081 : [(6891 ^ _777081) ^ [_893217] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, _893096), c_Com_Ovname_OLoc(_893088)), hAPP(hAPP(c_Natural_Ogetlocs, _893094), _893088)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, _893217), c_Com_Ovname_OLoc(_893088)), hAPP(hAPP(c_Natural_Ogetlocs, _893094), _893088)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(_893092), hAPP(hAPP(hAPP(c_Natural_Oupdate, _893094), c_Com_Ovname_OLoc(_893088)), hAPP(_893090, _893094))), _893217))]]], (6899 ^ _777081) ^ [_893469, _893471, _893473] : [c_Hoare__Mirabelle_Otriple__valid(_893469, hAPP(c_Nat_OSuc, _893471), _893473), -(c_Hoare__Mirabelle_Otriple__valid(_893469, _893471, _893473))], (6905 ^ _777081) ^ [_893558, _893560, _893562, _893564, _893566] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OLocal(_893558, _893560, _893562)), _893564), _893566)), 6909 ^ _777081 : [(6910 ^ _777081) ^ [] : [-(_893566 = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6908 ^ [_893558, _893560, _893562, _893564, _893566]), c_Com_Ovname_OLoc(_893558)), hAPP(hAPP(c_Natural_Ogetlocs, _893564), _893558)))], (6912 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(_893562), hAPP(hAPP(hAPP(c_Natural_Oupdate, _893564), c_Com_Ovname_OLoc(_893558)), hAPP(_893560, _893564))), 6908 ^ [_893558, _893560, _893562, _893564, _893566])))]]], (6914 ^ _777081) ^ [_893800, _893802, _893804, _893806, _893808, _893810] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OLocal(_893800, _893802, _893804)), _893806), _893808), _893810)), 6918 ^ _777081 : [(6919 ^ _777081) ^ [] : [-(_893810 = hAPP(hAPP(hAPP(c_Natural_Oupdate, 6917 ^ [_893800, _893802, _893804, _893806, _893808, _893810]), c_Com_Ovname_OLoc(_893800)), hAPP(hAPP(c_Natural_Ogetlocs, _893806), _893800)))], (6921 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _893804), hAPP(hAPP(hAPP(c_Natural_Oupdate, _893806), c_Com_Ovname_OLoc(_893800)), hAPP(_893802, _893806))), _893808), 6917 ^ [_893800, _893802, _893804, _893806, _893808, _893810])))]]], (6923 ^ _777081) ^ [_894064, _894066, _894068, _894070, _894072, _894074] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_894064, _894066, _894068, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_894064), _894070), _894072), _894074)) = hAPP(hAPP(hAPP(_894068, _894070), _894072), _894074))], (6925 ^ _777081) ^ [_894122, _894124, _894126, _894128, _894130, _894132] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_894122, _894124, _894126, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_894122), _894128), _894130), _894132)) = hAPP(hAPP(hAPP(_894126, _894128), _894130), _894132))], (6927 ^ _777081) ^ [_894180, _894182, _894184, _894186] : [-(c_Com_Ovname_Ovname__rec(_894180, _894182, _894184, c_Com_Ovname_OLoc(_894186)) = hAPP(_894184, _894186))], (6929 ^ _777081) ^ [_894219, _894221, _894223, _894225] : [-(c_Com_Ovname_Ovname__case(_894219, _894221, _894223, c_Com_Ovname_OLoc(_894225)) = hAPP(_894223, _894225))], (6931 ^ _777081) ^ [_894258, _894260, _894262, _894264] : [-(c_Hoare__Mirabelle_Otriple__valid(_894258, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_894258), _894260), hAPP(c_Com_Ocom_OBODY, _894262)), _894264)))], (6943 ^ _777081) ^ [_894437, _894439, _894441, _894443] : [6944 ^ _777081 : [(6945 ^ _777081) ^ [] : [_894439 = _894443], (6947 ^ _777081) ^ [] : [hBOOL(hAPP(_894441, _894443))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_894437), _894439), _894441), _894443)))], (6933 ^ _777081) ^ [_894323, _894325, _894327, _894329] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_894323), _894325), _894327), _894329)), -(_894325 = _894329), -(hBOOL(hAPP(_894327, _894329)))], (6951 ^ _777081) ^ [_894582, _894584, _894586, _894588] : [-(hAPP(hAPP(c_Set_Oinsert(_894582), _894584), hAPP(hAPP(c_Set_Oinsert(_894582), _894586), _894588)) = hAPP(hAPP(c_Set_Oinsert(_894582), _894586), hAPP(hAPP(c_Set_Oinsert(_894582), _894584), _894588)))], (6953 ^ _777081) ^ [_894643, _894645, _894647] : [-(hAPP(hAPP(c_Set_Oinsert(_894643), _894645), hAPP(hAPP(c_Set_Oinsert(_894643), _894645), _894647)) = hAPP(hAPP(c_Set_Oinsert(_894643), _894645), _894647))], (6955 ^ _777081) ^ [_894694, _894696, _894698, _894700, _894702] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _894694)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894696), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_894698, _894696))), _894700)), -(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_894702, _894694, _894698)), _894696), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894700), hAPP(c_Natural_Ogetlocs, _894696))), _894702), hAPP(hAPP(c_Natural_Ogetlocs, _894700), c_Com_ORes)))))], (6961 ^ _777081) ^ [_894903, _894905, _894907, _894909, _894911, _894913] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _894903)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894905), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_894907, _894905))), _894909), _894911)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCall(_894913, _894903, _894907)), _894905), _894909), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _894911), hAPP(c_Natural_Ogetlocs, _894905))), _894913), hAPP(hAPP(c_Natural_Ogetlocs, _894911), c_Com_ORes)))))], (6967 ^ _777081) ^ [_895139] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _895139)], (6969 ^ _777081) ^ [_895174] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _895174)], (6971 ^ _777081) ^ [_895209] : [hAPP(c_Nat_OSuc, _895209) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6973 ^ _777081) ^ [_895244] : [hAPP(c_Nat_OSuc, _895244) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6975 ^ _777081) ^ [_895279] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _895279)], (6977 ^ _777081) ^ [_895314] : [hAPP(c_Nat_OSuc, _895314) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6979 ^ _777081) ^ [_895367, _895369, _895371, _895373, _895375, _895377] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCall(_895367, _895369, _895371)), _895373), _895375), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895377), hAPP(c_Natural_Ogetlocs, _895373))), _895367), hAPP(hAPP(c_Natural_Ogetlocs, _895377), c_Com_ORes)))), 6983 ^ _777081 : [(6984 ^ _777081) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895377), hAPP(c_Natural_Ogetlocs, _895373))), _895367), hAPP(hAPP(c_Natural_Ogetlocs, _895377), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 6982 ^ [_895367, _895369, _895371, _895373, _895375, _895377]), hAPP(c_Natural_Ogetlocs, _895373))), _895367), hAPP(hAPP(c_Natural_Ogetlocs, 6982 ^ [_895367, _895369, _895371, _895373, _895375, _895377]), c_Com_ORes)))], (6986 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _895369)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895373), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_895371, _895373))), _895375), 6982 ^ [_895367, _895369, _895371, _895373, _895375, _895377])))]]], (6988 ^ _777081) ^ [_895762, _895764, _895766, _895768, _895770, _895772] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCall(_895762, _895764, _895766)), _895768), _895770), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895772), hAPP(c_Natural_Ogetlocs, _895768))), _895762), hAPP(hAPP(c_Natural_Ogetlocs, _895772), c_Com_ORes))))), 6989 ^ _777081 : [(6990 ^ _777081) ^ [_895929] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895772), hAPP(c_Natural_Ogetlocs, _895768))), _895762), hAPP(hAPP(c_Natural_Ogetlocs, _895772), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895929), hAPP(c_Natural_Ogetlocs, _895768))), _895762), hAPP(hAPP(c_Natural_Ogetlocs, _895929), c_Com_ORes)), hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _895764)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _895768), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_895766, _895768))), _895770), _895929))]]], (6998 ^ _777081) ^ [_896268, _896270, _896272, _896274, _896276] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_896268, _896270, _896272)), _896274), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _896276), hAPP(c_Natural_Ogetlocs, _896274))), _896268), hAPP(hAPP(c_Natural_Ogetlocs, _896276), c_Com_ORes)))), 7002 ^ _777081 : [(7003 ^ _777081) ^ [] : [-(hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _896276), hAPP(c_Natural_Ogetlocs, _896274))), _896268), hAPP(hAPP(c_Natural_Ogetlocs, _896276), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 7001 ^ [_896268, _896270, _896272, _896274, _896276]), hAPP(c_Natural_Ogetlocs, _896274))), _896268), hAPP(hAPP(c_Natural_Ogetlocs, 7001 ^ [_896268, _896270, _896272, _896274, _896276]), c_Com_ORes)))], (7005 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _896270)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _896274), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_896272, _896274))), 7001 ^ [_896268, _896270, _896272, _896274, _896276])))]]], (7007 ^ _777081) ^ [_896639, _896641, _896643, _896645, _896647] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_896639, _896641, _896643)), _896645), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _896647), hAPP(c_Natural_Ogetlocs, _896645))), _896639), hAPP(hAPP(c_Natural_Ogetlocs, _896647), c_Com_ORes))))), 7008 ^ _777081 : [(7009 ^ _777081) ^ [_896796] : [hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _896647), hAPP(c_Natural_Ogetlocs, _896645))), _896639), hAPP(hAPP(c_Natural_Ogetlocs, _896647), c_Com_ORes)) = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _896796), hAPP(c_Natural_Ogetlocs, _896645))), _896639), hAPP(hAPP(c_Natural_Ogetlocs, _896796), c_Com_ORes)), hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _896641)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _896645), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_896643, _896645))), _896796))]]], (7017 ^ _777081) ^ [_897097, _897099, _897101, _897103, _897105] : [hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCall(_897097, _897099, _897101)), _897103), _897105)), 7021 ^ _777081 : [(7022 ^ _777081) ^ [] : [-(_897105 = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 7020 ^ [_897097, _897099, _897101, _897103, _897105]), hAPP(c_Natural_Ogetlocs, _897103))), _897097), hAPP(hAPP(c_Natural_Ogetlocs, 7020 ^ [_897097, _897099, _897101, _897103, _897105]), c_Com_ORes)))], (7024 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY, _897099)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _897103), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_897101, _897103))), 7020 ^ [_897097, _897099, _897101, _897103, _897105])))]]], (7026 ^ _777081) ^ [_897380, _897382, _897384, _897386, _897388, _897390] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, c_Com_Ocom_OCall(_897380, _897382, _897384)), _897386), _897388), _897390)), 7030 ^ _777081 : [(7031 ^ _777081) ^ [] : [-(_897390 = hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, 7029 ^ [_897380, _897382, _897384, _897386, _897388, _897390]), hAPP(c_Natural_Ogetlocs, _897386))), _897380), hAPP(hAPP(c_Natural_Ogetlocs, 7029 ^ [_897380, _897382, _897384, _897386, _897388, _897390]), c_Com_ORes)))], (7033 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, hAPP(c_Com_Ocom_OBODY, _897382)), hAPP(hAPP(hAPP(c_Natural_Oupdate, hAPP(hAPP(c_Natural_Osetlocs, _897386), c_Natural_Onewlocs)), c_Com_Ovname_OLoc(c_Com_OArg)), hAPP(_897384, _897386))), _897388), 7029 ^ [_897380, _897382, _897384, _897386, _897388, _897390])))]]], (7035 ^ _777081) ^ [_897687, _897689, _897691, _897693, _897695] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_897687, _897689, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_897687), _897691), _897693), _897695)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7037 ^ _777081) ^ [_897733] : [-(c_Com_Ovname_Ovname__size(c_Com_Ovname_OLoc(_897733)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7039 ^ _777081) ^ [_897760, _897762, _897764, _897766] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_897760)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_897760), _897762), _897764), _897766)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7041 ^ _777081) ^ [_897807] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname), c_Com_Ovname_OLoc(_897807)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7043 ^ _777081) ^ [_897835, _897837, _897839, _897841] : [-(c_Com_Ovname_Ovname__case(_897835, _897837, _897839, c_Com_Ovname_OGlb(_897841)) = hAPP(_897837, _897841))], (7045 ^ _777081) ^ [_897874, _897876, _897878, _897880] : [-(c_Com_Ovname_Ovname__rec(_897874, _897876, _897878, c_Com_Ovname_OGlb(_897880)) = hAPP(_897876, _897880))], (7047 ^ _777081) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7049 ^ _777081) ^ [_897931, _897933, _897935] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(_897931, _897933, _897935)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7051 ^ _777081) ^ [_897964, _897966] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(_897964, _897966)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7053 ^ _777081) ^ [_898009, _898011] : [c_Com_Ovname_OGlb(_898009) = c_Com_Ovname_OGlb(_898011), -(_898009 = _898011)], (7059 ^ _777081) ^ [_898090, _898092] : [_898090 = _898092, -(c_Com_Ovname_OGlb(_898090) = c_Com_Ovname_OGlb(_898092))], (7065 ^ _777081) ^ [_898177] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ovname), c_Com_Ovname_OGlb(_898177)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7067 ^ _777081) ^ [_898205] : [-(c_Com_Ovname_Ovname__size(c_Com_Ovname_OGlb(_898205)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7069 ^ _777081) ^ [_898244, _898246] : [c_Com_Ovname_OGlb(_898244) = c_Com_Ovname_OLoc(_898246)], (7071 ^ _777081) ^ [_898285, _898287] : [c_Com_Ovname_OLoc(_898285) = c_Com_Ovname_OGlb(_898287)], (7073 ^ _777081) ^ [_898314] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _898314)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7075 ^ _777081) ^ [_898342, _898344, _898346] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_898342, _898344, _898346)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_898346)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7077 ^ _777081) ^ [_898383, _898385] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_898383, _898385)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_898383)), c_Com_Ocom_Ocom__size(_898385))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7079 ^ _777081) ^ [_898429, _898431, _898433] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_898429, _898431, _898433)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_898431)), c_Com_Ocom_Ocom__size(_898433))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7081 ^ _777081) ^ [_898478, _898480] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_898478, _898480)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_898480)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7083 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7085 ^ _777081) ^ [_898534, _898536, _898538] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCall(_898534, _898536, _898538)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7087 ^ _777081) ^ [_898568, _898570] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OAss(_898568, _898570)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7089 ^ _777081) ^ [_898599] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _898599)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7091 ^ _777081) ^ [_898628, _898630] : [-(c_Option_Ooption_Ooption__size(_898628, _898630, c_Option_Ooption_ONone(_898628)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7093 ^ _777081) ^ [_898659, _898661] : [class_Groups_Ozero(_898659), 7096 ^ _777081 : [(7097 ^ _777081) ^ [] : [c_Groups_Ozero__class_Ozero(_898659) = _898661, -(_898661 = c_Groups_Ozero__class_Ozero(_898659))], (7103 ^ _777081) ^ [] : [_898661 = c_Groups_Ozero__class_Ozero(_898659), -(c_Groups_Ozero__class_Ozero(_898659) = _898661)]]], (7109 ^ _777081) ^ [_898894, _898896, _898898] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898894), _898896) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898898), _898896), -(_898894 = _898898)], (7115 ^ _777081) ^ [_898993, _898995, _898997] : [_898993 = _898997, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898993), _898995) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _898997), _898995))], (7121 ^ _777081) ^ [_899116, _899118, _899120] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899116), _899118) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899116), _899120), -(_899118 = _899120)], (7127 ^ _777081) ^ [_899215, _899217, _899219] : [_899217 = _899219, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899215), _899217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899215), _899219))], (7133 ^ _777081) ^ [_899320, _899322, _899324] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899320), _899322)), _899324) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899320), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899322), _899324)))], (7135 ^ _777081) ^ [_899371, _899373, _899375] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899373), _899375)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899373), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899371), _899375)))], (7137 ^ _777081) ^ [_899422, _899424] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899422), _899424) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _899424), _899422))], (7139 ^ _777081) ^ [_899459, _899461, _899463, _899465] : [class_Groups_Oab__semigroup__add(_899459), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899459), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899459), _899461), _899463)), _899465) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899459), _899461), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899459), _899463), _899465)))], (7145 ^ _777081) ^ [_899602, _899604, _899606, _899608] : [class_Groups_Ocancel__semigroup__add(_899602), 7148 ^ _777081 : [(7149 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899602), _899604), _899606) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899602), _899604), _899608), -(_899606 = _899608)], (7155 ^ _777081) ^ [] : [_899606 = _899608, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899602), _899604), _899606) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899602), _899604), _899608))]]], (7161 ^ _777081) ^ [_899867, _899869, _899871, _899873] : [class_Groups_Ocancel__semigroup__add(_899867), 7164 ^ _777081 : [(7165 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899867), _899869), _899871) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899867), _899873), _899871), -(_899869 = _899873)], (7171 ^ _777081) ^ [] : [_899869 = _899873, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899867), _899869), _899871) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_899867), _899873), _899871))]]], (7177 ^ _777081) ^ [_900132, _900134, _900136, _900138] : [class_Groups_Ocancel__semigroup__add(_900132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900132), _900134), _900136) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900132), _900134), _900138), -(_900136 = _900138)], (7187 ^ _777081) ^ [_900299, _900301, _900303, _900305] : [class_Groups_Ocancel__ab__semigroup__add(_900299), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900299), _900301), _900303) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900299), _900301), _900305), -(_900303 = _900305)], (7197 ^ _777081) ^ [_900466, _900468, _900470, _900472] : [class_Groups_Ocancel__semigroup__add(_900466), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900466), _900468), _900470) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900466), _900472), _900470), -(_900468 = _900472)], (7207 ^ _777081) ^ [_900633, _900635] : [class_Groups_Omonoid__add(_900633), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900633), c_Groups_Ozero__class_Ozero(_900633)), _900635) = _900635)], (7213 ^ _777081) ^ [_900728, _900730] : [class_Groups_Ocomm__monoid__add(_900728), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900728), c_Groups_Ozero__class_Ozero(_900728)), _900730) = _900730)], (7219 ^ _777081) ^ [_900823, _900825] : [class_Groups_Olinordered__ab__group__add(_900823), 7222 ^ _777081 : [(7223 ^ _777081) ^ [] : [c_Groups_Ozero__class_Ozero(_900823) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900823), _900825), _900825), -(_900825 = c_Groups_Ozero__class_Ozero(_900823))], (7229 ^ _777081) ^ [] : [_900825 = c_Groups_Ozero__class_Ozero(_900823), -(c_Groups_Ozero__class_Ozero(_900823) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_900823), _900825), _900825))]]], (7235 ^ _777081) ^ [_901064, _901066] : [class_Groups_Omonoid__add(_901064), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901064), _901066), c_Groups_Ozero__class_Ozero(_901064)) = _901066)], (7241 ^ _777081) ^ [_901159, _901161] : [class_Groups_Ocomm__monoid__add(_901159), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_901159), _901161), c_Groups_Ozero__class_Ozero(_901159)) = _901161)], (7247 ^ _777081) ^ [_901254, _901256] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901254), _901256) = _901254, -(_901256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7253 ^ _777081) ^ [_901358, _901360] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901358), _901360) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 7256 ^ _777081 : [(7257 ^ _777081) ^ [] : [-(_901358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7259 ^ _777081) ^ [] : [-(_901360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7261 ^ _777081) ^ [_901469, _901471] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901469), _901471) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _901471 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7271 ^ _777081) ^ [_901612] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901612), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _901612)], (7273 ^ _777081) ^ [_901641] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _901641) = _901641)], (7275 ^ _777081) ^ [_901667, _901669] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901667), hAPP(c_Nat_OSuc, _901669)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901667), _901669)))], (7277 ^ _777081) ^ [_901710, _901712] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _901710)), _901712) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901710), _901712)))], (7279 ^ _777081) ^ [_901753, _901755] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _901753)), _901755) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _901753), hAPP(c_Nat_OSuc, _901755)))], (7281 ^ _777081) ^ [_901796, _901798, _901800] : [-(c_Option_Ooption_Ooption__size(_901796, _901798, hAPP(c_Option_Ooption_OSome(_901796), _901800)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_901798, _901800)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7283 ^ _777081) ^ [_901841, _901843] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_901841, _901843)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _901843)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7285 ^ _777081) ^ [_901881, _901883, _901885] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_901881, _901883, _901885)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _901883)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _901885))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7287 ^ _777081) ^ [_901933, _901935] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_901933, _901935)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _901933)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _901935))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7289 ^ _777081) ^ [_901982, _901984, _901986] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_901982, _901984, _901986)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _901986)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7291 ^ _777081) ^ [_902040, _902042] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _902040), _902042) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7296 ^ _777081 : [(7297 ^ _777081) ^ [] : [-(_902040 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7299 ^ _777081) ^ [] : [-(_902042 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 7300 ^ _777081 : [(7301 ^ _777081) ^ [] : [-(_902040 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7303 ^ _777081) ^ [] : [-(_902042 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7305 ^ _777081) ^ [_902224, _902226] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _902224), _902226) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 7306 ^ _777081 : [(7307 ^ _777081) ^ [] : [_902224 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _902226 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7313 ^ _777081) ^ [] : [_902224 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _902226 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7321 ^ _777081) ^ [_902465, _902467] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _902465), _902467), 7326 ^ _777081 : [(7327 ^ _777081) ^ [] : [-(_902465 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7329 ^ _777081) ^ [] : [-(_902467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 7330 ^ _777081 : [(7331 ^ _777081) ^ [] : [-(_902465 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7333 ^ _777081) ^ [] : [-(_902467 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (7335 ^ _777081) ^ [_902649, _902651] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _902649), _902651)), 7336 ^ _777081 : [(7337 ^ _777081) ^ [] : [_902649 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _902651 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7343 ^ _777081) ^ [] : [_902649 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _902651 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7351 ^ _777081) ^ [_902875] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _902875)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_902875)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7353 ^ _777081) ^ [_902911] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _902911)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _902911)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7355 ^ _777081) ^ [_902949, _902951] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_902949)), hAPP(c_Option_Ooption_OSome(_902949), _902951)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7357 ^ _777081) ^ [_902986] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_902986)), c_Option_Ooption_ONone(_902986)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7359 ^ _777081) ^ [_903018, _903020] : [class_Rings_Ocomm__semiring__1(_903018), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903018), c_Groups_Ozero__class_Ozero(_903018)), _903020) = _903020)], (7365 ^ _777081) ^ [_903113, _903115] : [class_Rings_Ocomm__semiring__1(_903113), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903113), _903115), c_Groups_Ozero__class_Ozero(_903113)) = _903115)], (7371 ^ _777081) ^ [_903208, _903210, _903212] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_903208), 7374 ^ _777081 : [(7375 ^ _777081) ^ [] : [_903210 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903208), _903210), _903212), -(_903212 = c_Groups_Ozero__class_Ozero(_903208))], (7381 ^ _777081) ^ [] : [_903212 = c_Groups_Ozero__class_Ozero(_903208), -(_903210 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903208), _903210), _903212))]]], (7387 ^ _777081) ^ [_903449, _903451] : [class_Groups_Olinordered__ab__group__add(_903449), 7390 ^ _777081 : [(7391 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903449), _903451), _903451) = c_Groups_Ozero__class_Ozero(_903449), -(_903451 = c_Groups_Ozero__class_Ozero(_903449))], (7397 ^ _777081) ^ [] : [_903451 = c_Groups_Ozero__class_Ozero(_903449), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903449), _903451), _903451) = c_Groups_Ozero__class_Ozero(_903449))]]], (7403 ^ _777081) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7405 ^ _777081) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7407 ^ _777081) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7409 ^ _777081) ^ [_903744] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _903744) = _903744)], (7411 ^ _777081) ^ [] : [-(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))], (7413 ^ _777081) ^ [_903788, _903790, _903792, _903794, _903796] : [class_Rings_Ocomm__semiring__1(_903788), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903788), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903788), _903790), _903792)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903788), _903794), _903796)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903788), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903788), _903790), _903794)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903788), _903792), _903796)))], (7419 ^ _777081) ^ [_903965, _903967, _903969, _903971] : [class_Rings_Ocomm__semiring__1(_903965), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903965), _903967), _903969)), _903971) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_903965), _903967), _903971)), _903969))], (7425 ^ _777081) ^ [_904108, _904110, _904112, _904114] : [class_Rings_Ocomm__semiring__1(_904108), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904108), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904108), _904110), _904112)), _904114) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904108), _904110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904108), _904112), _904114)))], (7431 ^ _777081) ^ [_904251, _904253, _904255, _904257] : [class_Rings_Ocomm__semiring__1(_904251), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904251), _904253), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904251), _904255), _904257)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904251), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904251), _904253), _904255)), _904257))], (7437 ^ _777081) ^ [_904394, _904396, _904398, _904400] : [class_Rings_Ocomm__semiring__1(_904394), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904394), _904396), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904394), _904398), _904400)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904394), _904398), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904394), _904396), _904400)))], (7443 ^ _777081) ^ [_904537, _904539, _904541] : [class_Rings_Ocomm__semiring__1(_904537), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904537), _904539), _904541) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_904537), _904541), _904539))], (7449 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7451 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7453 ^ _777081) ^ [_904682, _904684, _904686, _904688] : [class_Rings_Osemiring__1(_904682), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_904682, _904684, hAPP(c_Nat_OSuc, _904686), _904688) = c_Nat_Osemiring__1__class_Oof__nat__aux(_904682, _904684, _904686, hAPP(_904684, _904688)))], (7459 ^ _777081) ^ [_904793, _904795, _904797] : [class_Rings_Osemiring__1(_904793), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_904793, _904795, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _904797) = _904797)], (7465 ^ _777081) ^ [_904880, _904882, _904884, _904886, _904888, _904890] : [-(c_Nitpick_Opair__box_Opair__box__size(_904880, _904882, _904884, _904886, c_Nitpick_Opair__box_OPairBox(_904880, _904882, _904888, _904890)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_904884, _904888)), hAPP(_904886, _904890))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7467 ^ _777081) ^ [_904942, _904944, _904946, _904948, _904950, _904952, _904954, _904956] : [c_Hoare__Mirabelle_Ohoare__derivs(_904942, _904944, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_904942)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_904942), _904946), hAPP(c_Com_Ocom_OBODY, _904948)), hAPP(hAPP(c_COMBC(_904942, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _904942), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _904950)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), hAPP(hAPP(c_COMBB(tc_Com_Ostate, tc_fun(tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), tc_Com_Ostate), c_Natural_Oupdate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Oloc, tc_Nat_Onat), tc_Com_Ostate), c_Natural_Osetlocs), hAPP(c_Natural_Ogetlocs, _904952)))), _904954)), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Oloc, tc_Nat_Onat), c_Natural_Ogetlocs), c_Com_ORes))))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_904942), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_904942, _904944, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_904942)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_904942), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _904942), hAPP(c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj), hAPP(c_fequal, _904952)))), hAPP(hAPP(c_COMBC(_904942, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _904942), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _904946)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), hAPP(hAPP(c_COMBB(tc_Com_Ostate, tc_fun(tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), tc_Com_Ostate), c_Natural_Oupdate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Oloc, tc_Nat_Onat), tc_Com_Ostate), c_Natural_Osetlocs), c_Natural_Onewlocs))), c_Com_Ovname_OLoc(c_Com_OArg))), _904956)))), c_Com_Ocom_OCall(_904954, _904948, _904956)), _904950)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_904942), tc_HOL_Obool)))))], (7473 ^ _777081) ^ [_905327, _905329, _905331, _905333, _905335] : [-(c_Sum__Type_Osum_Osum__size(_905327, _905329, _905331, _905333, hAPP(c_Sum__Type_OInl(_905327, _905329), _905335)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_905331, _905335)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7475 ^ _777081) ^ [_905379, _905381, _905383, _905385, _905387] : [-(c_Sum__Type_Osum_Osum__size(_905379, _905381, _905383, _905385, hAPP(c_Sum__Type_OInr(_905381, _905379), _905387)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_905385, _905387)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7477 ^ _777081) ^ [_905431, _905433, _905435, _905437, _905439] : [-(c_Map_Orestrict__map(_905431, _905433, _905435, hAPP(hAPP(c_Set_Oinsert(_905431), _905437), _905439)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_905431, tc_Option_Ooption(_905433)), c_Map_Orestrict__map(_905431, _905433, _905435, _905439)), _905437), hAPP(_905435, _905437)))], (7479 ^ _777081) ^ [_905497, _905499, _905501, _905503, _905505] : [hAPP(_905497, _905499) = hAPP(c_Option_Ooption_OSome(_905501), _905503), -(hBOOL(hAPP(hAPP(c_member(_905501), _905503), c_Map_Oran(_905505, _905501, _905497))))], (7485 ^ _777081) ^ [_905618, _905620, _905622, _905624] : [_905618 = _905620, 7490 ^ _777081 : [(7491 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_905622), _905624), _905618)))], (7493 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_905622), _905624), _905620)))]], 7494 ^ _777081 : [(7495 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_905622), _905624), _905618))], (7497 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_905622), _905624), _905620))]]], (7499 ^ _777081) ^ [_905893, _905895] : [hBOOL(hAPP(hAPP(c_member(_905893), _905895), c_Orderings_Obot__class_Obot(tc_fun(_905893, tc_HOL_Obool))))], (7501 ^ _777081) ^ [_905930, _905932, _905934, _905936] : [hBOOL(hAPP(hAPP(c_member(_905930), _905932), hAPP(hAPP(c_Set_Oinsert(_905930), _905934), _905936))), -(_905932 = _905934), -(hBOOL(hAPP(hAPP(c_member(_905930), _905932), _905936)))], (7511 ^ _777081) ^ [_906070, _906072, _906074, _906076] : [7512 ^ _777081 : [(7513 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_906070), _906072), _906074))], (7515 ^ _777081) ^ [] : [_906072 = _906076]], -(hBOOL(hAPP(hAPP(c_member(_906070), _906072), hAPP(hAPP(c_Set_Oinsert(_906070), _906076), _906074))))], (7519 ^ _777081) ^ [_906235, _906237, _906239, _906241, _906243] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_906235, _906237, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_906235)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_906235), hAPP(hAPP(c_COMBC(_906235, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _906235), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _906235), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _906239))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _906241))), c_Com_Ocom_OWhile(_906241, _906243)), _906239)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_906235), tc_HOL_Obool)))))], (7521 ^ _777081) ^ [_906331, _906333, _906335, _906337] : [c_Hoare__Mirabelle_Ohoare__derivs(_906331, _906333, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_906331)), _906335), _906337)), 7524 ^ _777081 : [(7525 ^ _777081) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_906331, _906333, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_906331)), _906335), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_906331), tc_HOL_Obool)))))], (7527 ^ _777081) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_906331, _906333, _906337))]]], (7529 ^ _777081) ^ [_906498, _906500, _906502, _906504] : [c_Hoare__Mirabelle_Ohoare__derivs(_906498, _906500, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_906498)), _906502), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_906498), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_906498, _906500, _906504), -(c_Hoare__Mirabelle_Ohoare__derivs(_906498, _906500, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_906498)), _906502), _906504)))], (7539 ^ _777081) ^ [_906695, _906697, _906699, _906701] : [-(hAPP(c_Map_Orestrict__map(_906695, _906697, _906699, c_Orderings_Obot__class_Obot(tc_fun(_906695, tc_HOL_Obool))), _906701) = c_Option_Ooption_ONone(_906697))], (7541 ^ _777081) ^ [_906757, _906759, _906761, _906763, _906765] : [hBOOL(hAPP(hAPP(c_member(_906757), _906759), _906761)), -(hAPP(c_Map_Orestrict__map(_906757, _906763, _906765, _906761), _906759) = hAPP(_906765, _906759))], (7547 ^ _777081) ^ [_906870, _906872, _906874, _906876, _906878] : [-(hBOOL(hAPP(hAPP(c_member(_906870), _906872), _906874))), -(hAPP(c_Map_Orestrict__map(_906870, _906876, _906878, _906874), _906872) = c_Option_Ooption_ONone(_906876))], (7553 ^ _777081) ^ [_906931, _906933, _906935, _906937] : [-(hAPP(c_Map_Orestrict__map(_906931, _906933, hAPP(c_COMBK(tc_Option_Ooption(_906933), _906931), c_Option_Ooption_ONone(_906933)), _906935), _906937) = c_Option_Ooption_ONone(_906933))], (7555 ^ _777081) ^ [_906980, _906982] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_906980, _906982, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_906980), tc_HOL_Obool))))], (7557 ^ _777081) ^ [_907013, _907015] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_907013, _907015, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_907013), tc_HOL_Obool))))], (7559 ^ _777081) ^ [_907073, _907075, _907077, _907079, _907081, _907083] : [c_Nitpick_Opair__box_OPairBox(_907073, _907075, _907077, _907079) = c_Nitpick_Opair__box_OPairBox(_907073, _907075, _907081, _907083), 7562 ^ _777081 : [(7563 ^ _777081) ^ [] : [-(_907077 = _907081)], (7565 ^ _777081) ^ [] : [-(_907079 = _907083)]]], (7567 ^ _777081) ^ [_907200, _907202, _907204, _907206, _907208, _907210] : [-(c_Nitpick_Opair__box_OPairBox(_907200, _907202, _907204, _907206) = c_Nitpick_Opair__box_OPairBox(_907200, _907202, _907208, _907210)), _907204 = _907208, _907206 = _907210], (7577 ^ _777081) ^ [_907367, _907369, _907371, _907373] : [c_Hoare__Mirabelle_Ohoare__derivs(_907367, _907369, _907371), c_Hoare__Mirabelle_Ohoare__derivs(_907367, _907373, _907369), -(c_Hoare__Mirabelle_Ohoare__derivs(_907367, _907373, _907371))], (7587 ^ _777081) ^ [_907510, _907512, _907514, _907516, _907518] : [hBOOL(hAPP(hAPP(c_member(_907510), _907512), _907514)), -(hAPP(c_Map_Orestrict__map(_907510, _907516, _907518, _907514), _907512) = hAPP(_907518, _907512))], (7593 ^ _777081) ^ [_907629, _907631, _907633, _907635] : [_907629 = _907631, hBOOL(hAPP(hAPP(c_member(_907633), _907631), _907635)), -(hBOOL(hAPP(hAPP(c_member(_907633), _907629), _907635)))], (7603 ^ _777081) ^ [_907794, _907796, _907798, _907800] : [_907794 = _907796, 7606 ^ _777081 : [(7607 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_907798), _907794), _907800)), -(hBOOL(hAPP(hAPP(c_member(_907798), _907796), _907800)))], (7613 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_907798), _907796), _907800)), -(hBOOL(hAPP(hAPP(c_member(_907798), _907794), _907800)))]]], (7619 ^ _777081) ^ [_908055, _908057, _908059, _908061] : [_908055 = _908057, 7622 ^ _777081 : [(7623 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_908059), _908061), _908055)), -(hBOOL(hAPP(hAPP(c_member(_908059), _908061), _908057)))], (7629 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_908059), _908061), _908057)), -(hBOOL(hAPP(hAPP(c_member(_908059), _908061), _908055)))]]], (7635 ^ _777081) ^ [_908316, _908318, _908320] : [_908316 = c_Orderings_Obot__class_Obot(tc_fun(_908318, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_908318), _908320), _908316))], (7641 ^ _777081) ^ [_908438, _908440, _908442] : [hBOOL(hAPP(hAPP(c_member(_908438), _908440), _908442)), -(hBOOL(hAPP(_908442, _908440)))], (7647 ^ _777081) ^ [_908531, _908533, _908535] : [hBOOL(hAPP(_908535, _908533)), -(hBOOL(hAPP(hAPP(c_member(_908531), _908533), _908535)))], (7653 ^ _777081) ^ [_908642, _908644] : [hBOOL(hAPP(hAPP(c_member(_908642), _908644), c_Orderings_Obot__class_Obot(tc_fun(_908642, tc_HOL_Obool))))], (7655 ^ _777081) ^ [_908694, _908696] : [7656 ^ _777081 : [(7657 ^ _777081) ^ [_908747] : [hBOOL(hAPP(hAPP(c_member(_908694), _908747), _908696))]], _908696 = c_Orderings_Obot__class_Obot(tc_fun(_908694, tc_HOL_Obool))], (7661 ^ _777081) ^ [_908803, _908805] : [-(_908805 = c_Orderings_Obot__class_Obot(tc_fun(_908803, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_908803), 7664 ^ [_908803, _908805]), _908805)))], (7668 ^ _777081) ^ [_908869, _908871] : [-(hBOOL(hAPP(hAPP(c_member(_908869), 7669 ^ [_908869, _908871]), _908871))), -(_908871 = c_Orderings_Obot__class_Obot(tc_fun(_908869, tc_HOL_Obool)))], (7675 ^ _777081) ^ [_908920, _908922] : [_908922 = c_Orderings_Obot__class_Obot(tc_fun(_908920, tc_HOL_Obool)), 7678 ^ _777081 : [(7679 ^ _777081) ^ [_909000] : [hBOOL(hAPP(hAPP(c_member(_908920), _909000), _908922))]]], (7681 ^ _777081) ^ [_909057, _909059, _909061, _909063, _909065, _909067] : [_909057 = _909059, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909061, _909063), _909065), _909059), _909067), _909057) = _909067)], (7687 ^ _777081) ^ [_909166, _909168, _909170, _909172, _909174, _909176] : [-(_909166 = _909168), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909170, _909172), _909174), _909168), _909176), _909166) = hAPP(_909174, _909166))], (7693 ^ _777081) ^ [_909230, _909232, _909234] : [hBOOL(hAPP(hAPP(c_member(_909230), _909232), hAPP(hAPP(c_Set_Oinsert(_909230), _909234), c_Orderings_Obot__class_Obot(tc_fun(_909230, tc_HOL_Obool))))), -(_909232 = _909234)], (7699 ^ _777081) ^ [_909367, _909369, _909371] : [hBOOL(hAPP(hAPP(c_member(_909367), _909369), hAPP(hAPP(c_Set_Oinsert(_909367), _909371), c_Orderings_Obot__class_Obot(tc_fun(_909367, tc_HOL_Obool))))), -(_909369 = _909371)], (7705 ^ _777081) ^ [_909482, _909484, _909486] : [_909484 = _909486, -(hBOOL(hAPP(hAPP(c_member(_909482), _909484), hAPP(hAPP(c_Set_Oinsert(_909482), _909486), c_Orderings_Obot__class_Obot(tc_fun(_909482, tc_HOL_Obool))))))], (7711 ^ _777081) ^ [_909599, _909601, _909603, _909605, _909607] : [-(hBOOL(hAPP(hAPP(c_member(_909599), _909601), _909603))), -(hAPP(c_Map_Orestrict__map(_909599, _909605, _909607, _909603), _909601) = c_Option_Ooption_ONone(_909605))], (7717 ^ _777081) ^ [_909658, _909660, _909662, _909664, _909666, _909668] : [-(hAPP(hAPP(c_Option_Obind(_909658, _909660), hAPP(hAPP(c_Option_Obind(_909662, _909658), _909664), _909666)), _909668) = hAPP(hAPP(c_Option_Obind(_909662, _909660), _909664), hAPP(hAPP(c_COMBC(_909662, tc_fun(_909658, tc_Option_Ooption(_909660)), tc_Option_Ooption(_909660)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_909658), tc_fun(tc_fun(_909658, tc_Option_Ooption(_909660)), tc_Option_Ooption(_909660)), _909662), c_Option_Obind(_909658, _909660)), _909666)), _909668)))], (7719 ^ _777081) ^ [_909760, _909762] : [-(c_Map_Oran(_909760, _909762, hAPP(c_COMBK(tc_Option_Ooption(_909762), _909760), c_Option_Ooption_ONone(_909762))) = c_Orderings_Obot__class_Obot(tc_fun(_909762, tc_HOL_Obool)))], (7721 ^ _777081) ^ [_909804, _909806, _909808, _909810, _909812] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_909804, _909806, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_909804)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_909804), hAPP(hAPP(c_COMBC(_909804, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _909804), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _909808)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _909810)), _909812))), c_Com_Ocom_OAss(_909810, _909812)), _909808)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_909804), tc_HOL_Obool)))))], (7723 ^ _777081) ^ [_909896, _909898, _909900, _909902, _909904] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_909896, _909898, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_909896)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_909896), hAPP(hAPP(c_COMBC(_909896, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _909896), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _909900)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), _909902)), _909904))), c_Com_Ocom_OAss(_909902, _909904)), _909900)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_909896), tc_HOL_Obool)))))], (7725 ^ _777081) ^ [_909988, _909990, _909992, _909994] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_909988, tc_Option_Ooption(_909990)), hAPP(c_COMBK(tc_Option_Ooption(_909990), _909988), c_Option_Ooption_ONone(_909990))), _909992), c_Option_Ooption_ONone(_909990)), _909994) = c_Option_Ooption_ONone(_909990))], (7727 ^ _777081) ^ [_910048, _910050, _910052] : [-(c_Map_Omap__add(_910048, _910050, _910052, hAPP(c_COMBK(tc_Option_Ooption(_910050), _910048), c_Option_Ooption_ONone(_910050))) = _910052)], (7729 ^ _777081) ^ [_910090, _910092, _910094] : [-(c_Map_Omap__add(_910090, _910092, hAPP(c_COMBK(tc_Option_Ooption(_910092), _910090), c_Option_Ooption_ONone(_910092)), _910094) = _910094)], (7731 ^ _777081) ^ [_910132, _910134, _910136, _910138, _910140] : [-(hAPP(c_Map_Omap__add(_910132, _910134, _910136, _910138), _910140) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_910134), _910134, hAPP(_910136, _910140), c_Option_Ooption_OSome(_910134)), hAPP(_910138, _910140)))], (7733 ^ _777081) ^ [_910189, _910191, _910193] : [-(c_Map_Omap__le(_910189, _910191, hAPP(c_COMBK(tc_Option_Ooption(_910191), _910189), c_Option_Ooption_ONone(_910191)), _910193))], (7735 ^ _777081) ^ [_910228, _910230, _910232] : [-(hAPP(hAPP(c_Option_Obind(_910228, _910230), _910232), hAPP(c_COMBK(tc_Option_Ooption(_910230), _910228), c_Option_Ooption_ONone(_910230))) = c_Option_Ooption_ONone(_910230))], (7737 ^ _777081) ^ [_910276, _910278, _910280, _910282, _910284, _910286] : [-(c_Map_Omap__comp(_910276, _910278, _910280, _910282, _910284, _910286) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_910278), _910276, c_Option_Ooption_ONone(_910278), _910282), hAPP(_910284, _910286)))], (7739 ^ _777081) ^ [_910331, _910333, _910335, _910337, _910339] : [-(c_Map_Omap__comp(_910331, _910333, _910335, _910337, hAPP(c_COMBK(tc_Option_Ooption(_910331), _910335), c_Option_Ooption_ONone(_910331)), _910339) = c_Option_Ooption_ONone(_910333))], (7741 ^ _777081) ^ [_910381, _910383, _910385, _910387, _910389] : [-(c_Map_Omap__comp(_910381, _910383, _910385, hAPP(c_COMBK(tc_Option_Ooption(_910383), _910381), c_Option_Ooption_ONone(_910383)), _910387, _910389) = c_Option_Ooption_ONone(_910383))], (7743 ^ _777081) ^ [_910431, _910433, _910435] : [-(hBOOL(hAPP(hAPP(c_member(_910431), _910433), hAPP(hAPP(c_Set_Oinsert(_910431), _910433), _910435))))], (7755 ^ _777081) ^ [_910628, _910630, _910632, _910634] : [7756 ^ _777081 : [(7757 ^ _777081) ^ [] : [_910630 = _910632], (7759 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_910628), _910630), _910634))]], -(hBOOL(hAPP(hAPP(c_member(_910628), _910630), hAPP(hAPP(c_Set_Oinsert(_910628), _910632), _910634))))], (7745 ^ _777081) ^ [_910494, _910496, _910498, _910500] : [hBOOL(hAPP(hAPP(c_member(_910494), _910496), hAPP(hAPP(c_Set_Oinsert(_910494), _910498), _910500))), -(_910496 = _910498), -(hBOOL(hAPP(hAPP(c_member(_910494), _910496), _910500)))], (7763 ^ _777081) ^ [_910792, _910794, _910796, _910798] : [-(hBOOL(hAPP(hAPP(c_member(_910792), _910794), _910796))), -(hBOOL(hAPP(hAPP(c_member(_910792), _910794), _910798))), 7770 ^ _777081 : [(7771 ^ _777081) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_910792), _910794), _910796) = hAPP(hAPP(c_Set_Oinsert(_910792), _910794), _910798), -(_910796 = _910798)], (7777 ^ _777081) ^ [] : [_910796 = _910798, -(hAPP(hAPP(c_Set_Oinsert(_910792), _910794), _910796) = hAPP(hAPP(c_Set_Oinsert(_910792), _910794), _910798))]]], (7783 ^ _777081) ^ [_911137, _911139, _911141, _911143] : [hBOOL(hAPP(hAPP(c_member(_911137), _911139), _911141)), -(hBOOL(hAPP(hAPP(c_member(_911137), _911139), hAPP(hAPP(c_Set_Oinsert(_911137), _911143), _911141))))], (7789 ^ _777081) ^ [_911262, _911264, _911266] : [hBOOL(hAPP(hAPP(c_member(_911262), _911264), _911266)), -(hAPP(hAPP(c_Set_Oinsert(_911262), _911264), _911266) = _911266)], (7795 ^ _777081) ^ [_911371, _911373, _911375, _911377, _911379, _911381, _911383] : [c_Hoare__Mirabelle_Ohoare__derivs(_911371, _911373, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_911371)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_911371), _911375), _911377), _911379)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_911371), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_911371, _911373, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_911371)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_911371), _911379), _911381), _911383)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_911371), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_911371, _911373, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_911371)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_911371), _911375), c_Com_Ocom_OSemi(_911377, _911381)), _911383)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_911371), tc_HOL_Obool)))))], (7805 ^ _777081) ^ [_911700, _911702, _911704] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_911700, _911702, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_911700)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_911700), _911704), c_Com_Ocom_OSKIP), _911704)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_911700), tc_HOL_Obool)))))], (7807 ^ _777081) ^ [_911756, _911758, _911760] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_911756, _911758, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_911756)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_911756), _911760), c_Com_Ocom_OSKIP), _911760)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_911756), tc_HOL_Obool)))))], (7809 ^ _777081) ^ [_911827, _911829, _911831] : [c_Orderings_Obot__class_Obot(tc_fun(_911827, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_911827), _911829), _911831)], (7811 ^ _777081) ^ [_911882, _911884, _911886] : [hAPP(hAPP(c_Set_Oinsert(_911882), _911884), _911886) = c_Orderings_Obot__class_Obot(tc_fun(_911882, tc_HOL_Obool))], (7813 ^ _777081) ^ [_911946, _911948, _911950, _911952, _911954] : [hAPP(hAPP(c_Set_Oinsert(_911946), _911948), hAPP(hAPP(c_Set_Oinsert(_911946), _911950), c_Orderings_Obot__class_Obot(tc_fun(_911946, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_911946), _911952), hAPP(hAPP(c_Set_Oinsert(_911946), _911954), c_Orderings_Obot__class_Obot(tc_fun(_911946, tc_HOL_Obool)))), 7818 ^ _777081 : [(7819 ^ _777081) ^ [] : [-(_911948 = _911952)], (7821 ^ _777081) ^ [] : [-(_911950 = _911954)]], 7822 ^ _777081 : [(7823 ^ _777081) ^ [] : [-(_911948 = _911954)], (7825 ^ _777081) ^ [] : [-(_911950 = _911952)]]], (7827 ^ _777081) ^ [_912208, _912210, _912212, _912214, _912216] : [-(hAPP(hAPP(c_Set_Oinsert(_912208), _912210), hAPP(hAPP(c_Set_Oinsert(_912208), _912212), c_Orderings_Obot__class_Obot(tc_fun(_912208, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_912208), _912214), hAPP(hAPP(c_Set_Oinsert(_912208), _912216), c_Orderings_Obot__class_Obot(tc_fun(_912208, tc_HOL_Obool))))), 7828 ^ _777081 : [(7829 ^ _777081) ^ [] : [_912210 = _912214, _912212 = _912216], (7835 ^ _777081) ^ [] : [_912210 = _912216, _912212 = _912214]]], (7843 ^ _777081) ^ [_912524, _912526, _912528] : [hAPP(hAPP(c_Set_Oinsert(_912524), _912526), c_Orderings_Obot__class_Obot(tc_fun(_912524, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_912524), _912528), c_Orderings_Obot__class_Obot(tc_fun(_912524, tc_HOL_Obool))), -(_912526 = _912528)], (7849 ^ _777081) ^ [_912655, _912657, _912659, _912661, _912663, _912665, _912667, _912669] : [c_Hoare__Mirabelle_Ohoare__derivs(_912655, _912657, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_912655)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_912655), _912659), _912661), hAPP(hAPP(c_COMBC(_912655, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _912655), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _912663)), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), c_Com_Ovname_OLoc(_912665))), hAPP(hAPP(c_Natural_Ogetlocs, _912667), _912665))))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_912655), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_912655, _912657, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_912655)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_912655), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _912655), hAPP(c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj), hAPP(c_fequal, _912667)))), hAPP(hAPP(c_COMBC(_912655, tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_fun(tc_Com_Ostate, tc_Com_Ostate), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _912655), c_COMBB(tc_Com_Ostate, tc_HOL_Obool, tc_Com_Ostate)), _912659)), hAPP(hAPP(c_COMBS(tc_Com_Ostate, tc_Nat_Onat, tc_Com_Ostate), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ovname, tc_fun(tc_Nat_Onat, tc_Com_Ostate)), c_Natural_Oupdate), c_Com_Ovname_OLoc(_912665))), _912669)))), c_Com_Ocom_OLocal(_912665, _912669, _912661)), _912663)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_912655), tc_HOL_Obool)))))], (7855 ^ _777081) ^ [_913063, _913065, _913067, _913069, _913071] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_913063, tc_Option_Ooption(_913065)), _913067), _913069), hAPP(c_Option_Ooption_OSome(_913065), _913071)) = hAPP(c_COMBK(tc_Option_Ooption(_913065), _913063), c_Option_Ooption_ONone(_913065))], (7857 ^ _777081) ^ [_913123, _913125, _913127, _913129, _913131] : [c_Hoare__Mirabelle_Ohoare__derivs(_913123, _913125, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_913123)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_913123), _913127), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _913129))), _913131)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_913123), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_913123, _913125, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_913123)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_913123), _913127), hAPP(c_Com_Ocom_OBODY, _913129)), _913131)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_913123), tc_HOL_Obool)))))], (7863 ^ _777081) ^ [_913340, _913342, _913344, _913346, _913348] : [c_Hoare__Mirabelle_Ohoare__derivs(_913340, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_913340)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_913340), _913342), hAPP(c_Com_Ocom_OBODY, _913344)), _913346)), _913348), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_913340)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_913340), _913342), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _913344))), _913346)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_913340), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_913340, _913348, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_913340)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_913340), _913342), hAPP(c_Com_Ocom_OBODY, _913344)), _913346)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_913340), tc_HOL_Obool)))))], (7869 ^ _777081) ^ [_913605, _913607, _913609, _913611] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_913605, _913607)), c_Nitpick_Opair__box_OPairBox(_913605, _913607, _913609, _913611)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7871 ^ _777081) ^ [_913647, _913649, _913651, _913653, _913655, _913657] : [-(c_Nitpick_Opair__box_Opair__box__rec(_913647, _913649, _913651, _913653, c_Nitpick_Opair__box_OPairBox(_913647, _913649, _913655, _913657)) = hAPP(hAPP(_913653, _913655), _913657))], (7873 ^ _777081) ^ [_913697, _913699, _913701, _913703, _913705, _913707] : [-(c_Nitpick_Opair__box_Opair__box__case(_913697, _913699, _913701, _913703, c_Nitpick_Opair__box_OPairBox(_913697, _913699, _913705, _913707)) = hAPP(hAPP(_913703, _913705), _913707))], (7875 ^ _777081) ^ [_913747, _913749] : [-(c_Set_Othe__elem(_913747, hAPP(hAPP(c_Set_Oinsert(_913747), _913749), c_Orderings_Obot__class_Obot(tc_fun(_913747, tc_HOL_Obool)))) = _913749)], (7877 ^ _777081) ^ [_913806, _913808, _913810, _913812] : [hAPP(c_Sum__Type_OInl(_913806, _913808), _913810) = hAPP(c_Sum__Type_OInr(_913808, _913806), _913812)], (7879 ^ _777081) ^ [_913865, _913867, _913869, _913871] : [hAPP(c_Sum__Type_OInl(_913865, _913867), _913869) = hAPP(c_Sum__Type_OInr(_913867, _913865), _913871)], (7881 ^ _777081) ^ [_913924, _913926, _913928, _913930] : [hAPP(c_Sum__Type_OInr(_913924, _913926), _913928) = hAPP(c_Sum__Type_OInl(_913926, _913924), _913930)], (7883 ^ _777081) ^ [_913983, _913985, _913987, _913989] : [hAPP(c_Sum__Type_OInr(_913983, _913985), _913987) = hAPP(c_Sum__Type_OInl(_913985, _913983), _913989)], (7885 ^ _777081) ^ [_914024, _914026, _914028] : [class_Orderings_Obot(_914024), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_914026, _914024)), _914028) = c_Orderings_Obot__class_Obot(_914024))], (7891 ^ _777081) ^ [_914136, _914138] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_914136, tc_HOL_Obool)), _914138)), -(hBOOL(hAPP(hAPP(c_member(_914136), _914138), c_Orderings_Obot__class_Obot(tc_fun(_914136, tc_HOL_Obool)))))], (7897 ^ _777081) ^ [_914247, _914249] : [hBOOL(hAPP(hAPP(c_member(_914247), _914249), c_Orderings_Obot__class_Obot(tc_fun(_914247, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_914247, tc_HOL_Obool)), _914249)))], (7903 ^ _777081) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7905 ^ _777081) ^ [_914400, _914402, _914404] : [hBOOL(hAPP(hAPP(c_member(_914400), _914402), hAPP(c_fequal, _914404))), -(_914402 = _914404)], (7911 ^ _777081) ^ [_914495, _914497, _914499] : [_914497 = _914499, -(hBOOL(hAPP(hAPP(c_member(_914495), _914497), hAPP(c_fequal, _914499))))], (7917 ^ _777081) ^ [_914596, _914598, _914600, _914602] : [hAPP(c_Sum__Type_OInr(_914596, _914598), _914600) = hAPP(c_Sum__Type_OInr(_914596, _914598), _914602), -(_914600 = _914602)], (7923 ^ _777081) ^ [_914722, _914724, _914726, _914728] : [hAPP(c_Sum__Type_OInr(_914722, _914724), _914726) = hAPP(c_Sum__Type_OInr(_914722, _914724), _914728), -(_914726 = _914728)], (7929 ^ _777081) ^ [_914823, _914825, _914827, _914829] : [_914827 = _914829, -(hAPP(c_Sum__Type_OInr(_914823, _914825), _914827) = hAPP(c_Sum__Type_OInr(_914823, _914825), _914829))], (7935 ^ _777081) ^ [_914930, _914932, _914934, _914936] : [hAPP(c_Sum__Type_OInl(_914930, _914932), _914934) = hAPP(c_Sum__Type_OInl(_914930, _914932), _914936), -(_914934 = _914936)], (7941 ^ _777081) ^ [_915056, _915058, _915060, _915062] : [hAPP(c_Sum__Type_OInl(_915056, _915058), _915060) = hAPP(c_Sum__Type_OInl(_915056, _915058), _915062), -(_915060 = _915062)], (7947 ^ _777081) ^ [_915157, _915159, _915161, _915163] : [_915161 = _915163, -(hAPP(c_Sum__Type_OInl(_915157, _915159), _915161) = hAPP(c_Sum__Type_OInl(_915157, _915159), _915163))], (7953 ^ _777081) ^ [_915282, _915284, _915286] : [hAPP(hAPP(c_COMBC(_915282, tc_fun(_915282, tc_HOL_Obool), tc_HOL_Obool), c_member(_915282)), _915284) = hAPP(hAPP(c_COMBC(_915282, tc_fun(_915282, tc_HOL_Obool), tc_HOL_Obool), c_member(_915282)), _915286), -(_915284 = _915286)], (7959 ^ _777081) ^ [_915417, _915419, _915421] : [_915419 = _915421, -(hAPP(hAPP(c_COMBC(_915417, tc_fun(_915417, tc_HOL_Obool), tc_HOL_Obool), c_member(_915417)), _915419) = hAPP(hAPP(c_COMBC(_915417, tc_fun(_915417, tc_HOL_Obool), tc_HOL_Obool), c_member(_915417)), _915421))], (7965 ^ _777081) ^ [_915558, _915560, _915562] : [class_Orderings_Obot(_915558), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_915560, _915558)), _915562) = c_Orderings_Obot__class_Obot(_915558))], (7971 ^ _777081) ^ [_915655, _915657, _915659] : [-(c_Sum__Type_OProjl(_915655, _915657, hAPP(c_Sum__Type_OInl(_915655, _915657), _915659)) = _915659)], (7973 ^ _777081) ^ [_915692, _915694, _915696] : [-(c_Sum__Type_OProjr(_915692, _915694, hAPP(c_Sum__Type_OInr(_915694, _915692), _915696)) = _915696)], (7975 ^ _777081) ^ [_915729, _915731] : [-(c_Option_Oset(_915729, hAPP(c_Option_Ooption_OSome(_915729), _915731)) = hAPP(hAPP(c_Set_Oinsert(_915729), _915731), c_Orderings_Obot__class_Obot(tc_fun(_915729, tc_HOL_Obool))))], (7977 ^ _777081) ^ [_915775, _915777, _915779] : [-(hAPP(c_Nat_Osize__class_Osize(tc_sum(_915775, _915777)), hAPP(c_Sum__Type_OInl(_915775, _915777), _915779)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7979 ^ _777081) ^ [_915816, _915818, _915820] : [-(hAPP(c_Nat_Osize__class_Osize(tc_sum(_915816, _915818)), hAPP(c_Sum__Type_OInr(_915818, _915816), _915820)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7981 ^ _777081) ^ [_915857, _915859] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY, _915857))), _915859), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _915857)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _915859, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY, _915857))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (7987 ^ _777081) ^ [_916010, _916012, _916014] : [-(c_Smallcheck_Oorelse(_916010, _916012, _916014) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_916010), _916010, _916014, c_Option_Ooption_OSome(_916010)), _916012))], (7989 ^ _777081) ^ [_916071, _916073, _916075, _916077, _916079] : [hBOOL(hAPP(hAPP(c_member(_916071), _916073), _916075)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_916071, tc_Option_Ooption(_916077)), c_Map_Orestrict__map(_916071, _916077, _916079, _916075)), _916073), c_Option_Ooption_ONone(_916077)) = c_Map_Orestrict__map(_916071, _916077, _916079, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916071, tc_HOL_Obool)), _916075), hAPP(hAPP(c_Set_Oinsert(_916071), _916073), c_Orderings_Obot__class_Obot(tc_fun(_916071, tc_HOL_Obool))))))], (7995 ^ _777081) ^ [_916262, _916264, _916266, _916268, _916270] : [-(hBOOL(hAPP(hAPP(c_member(_916262), _916264), _916266))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_916262, tc_Option_Ooption(_916268)), c_Map_Orestrict__map(_916262, _916268, _916270, _916266)), _916264), c_Option_Ooption_ONone(_916268)) = c_Map_Orestrict__map(_916262, _916268, _916270, _916266))], (8001 ^ _777081) ^ [_916339, _916341, _916343, _916345, _916347] : [8004 ^ _777081 : [(8005 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_916339, 8002 ^ [_916339, _916341, _916343, _916345, _916347]), 8003 ^ [_916339, _916341, _916343, _916345, _916347])))], (8007 ^ _777081) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_916341, _916343, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_916341)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_916341), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _916341), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 8003 ^ [_916339, _916341, _916343, _916345, _916347]))), _916345), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _916341), hAPP(_916347, 8002 ^ [_916339, _916341, _916343, _916345, _916347])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_916341), tc_HOL_Obool))))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_916341, _916343, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_916341)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_916341), _916339), _916345), _916347)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_916341), tc_HOL_Obool)))))], (8011 ^ _777081) ^ [_916782, _916784, _916786, _916788] : [c_Map_Odom(_916782, _916784, _916786) = hAPP(hAPP(c_Set_Oinsert(_916782), _916788), c_Orderings_Obot__class_Obot(tc_fun(_916782, tc_HOL_Obool))), -(_916786 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_916782, tc_Option_Ooption(_916784)), hAPP(c_COMBK(tc_Option_Ooption(_916784), _916782), c_Option_Ooption_ONone(_916784))), _916788), hAPP(c_Option_Ooption_OSome(_916784), 8014 ^ [_916782, _916784, _916786, _916788])))], (8018 ^ _777081) ^ [_916967, _916969, _916971, _916973] : [8019 ^ _777081 : [(8020 ^ _777081) ^ [_917056] : [_916971 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_916967, tc_Option_Ooption(_916969)), hAPP(c_COMBK(tc_Option_Ooption(_916969), _916967), c_Option_Ooption_ONone(_916969))), _916973), hAPP(c_Option_Ooption_OSome(_916969), _917056))]], -(c_Map_Odom(_916967, _916969, _916971) = hAPP(hAPP(c_Set_Oinsert(_916967), _916973), c_Orderings_Obot__class_Obot(tc_fun(_916967, tc_HOL_Obool))))], (8024 ^ _777081) ^ [_917155, _917157, _917159, _917161] : [hBOOL(hAPP(hAPP(c_member(_917155), _917157), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917155, tc_HOL_Obool)), _917159), _917161))), 8027 ^ _777081 : [(8028 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_917155), _917157), _917159)))], (8030 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_917155), _917157), _917161))]]], (8032 ^ _777081) ^ [_917334, _917336, _917338, _917340] : [hBOOL(hAPP(hAPP(c_member(_917334), _917336), _917338)), -(hBOOL(hAPP(hAPP(c_member(_917334), _917336), _917340))), -(hBOOL(hAPP(hAPP(c_member(_917334), _917336), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917334, tc_HOL_Obool)), _917338), _917340))))], (8042 ^ _777081) ^ [_917494, _917496, _917498] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917494, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917494, tc_HOL_Obool)), _917496), _917498)), _917498) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917494, tc_HOL_Obool)), _917496), _917498))], (8044 ^ _777081) ^ [_917554, _917556, _917558, _917560, _917562] : [class_Groups_Oab__group__add(_917554), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_917554), _917556), _917558) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_917554), _917560), _917562), 8051 ^ _777081 : [(8052 ^ _777081) ^ [] : [_917556 = _917558, -(_917560 = _917562)], (8058 ^ _777081) ^ [] : [_917560 = _917562, -(_917556 = _917558)]]], (8064 ^ _777081) ^ [_917867, _917869] : [class_Groups_Ogroup__add(_917867), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_917867), _917869), c_Groups_Ozero__class_Ozero(_917867)) = _917869)], (8070 ^ _777081) ^ [_917962, _917964] : [class_Groups_Ogroup__add(_917962), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_917962), _917964), _917964) = c_Groups_Ozero__class_Ozero(_917962))], (8076 ^ _777081) ^ [_918057, _918059, _918061] : [class_Groups_Oab__group__add(_918057), 8079 ^ _777081 : [(8080 ^ _777081) ^ [] : [_918059 = _918061, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918057), _918059), _918061) = c_Groups_Ozero__class_Ozero(_918057))], (8086 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918057), _918059), _918061) = c_Groups_Ozero__class_Ozero(_918057), -(_918059 = _918061)]]], (8092 ^ _777081) ^ [_918298, _918300, _918302] : [class_Groups_Ogroup__add(_918298), 8095 ^ _777081 : [(8096 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918298), _918300), _918302) = c_Groups_Ozero__class_Ozero(_918298), -(_918300 = _918302)], (8102 ^ _777081) ^ [] : [_918300 = _918302, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918298), _918300), _918302) = c_Groups_Ozero__class_Ozero(_918298))]]], (8108 ^ _777081) ^ [_918539, _918541, _918543, _918545, _918547] : [hAPP(_918539, _918541) = c_Option_Ooption_ONone(_918543), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918545, tc_HOL_Obool)), c_Map_Odom(_918545, _918543, _918539)), hAPP(hAPP(c_Set_Oinsert(_918545), _918541), _918547)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918545, tc_HOL_Obool)), c_Map_Odom(_918545, _918543, _918539)), _918547))], (8114 ^ _777081) ^ [_918708, _918710, _918712] : [class_Groups_Ogroup__add(_918708), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918708), _918710), _918712)), _918712) = _918710)], (8120 ^ _777081) ^ [_918817, _918819, _918821] : [class_Groups_Ogroup__add(_918817), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918817), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_918817), _918819), _918821)), _918821) = _918819)], (8126 ^ _777081) ^ [_918926, _918928, _918930, _918932] : [hBOOL(hAPP(hAPP(c_member(_918926), _918928), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918926, tc_HOL_Obool)), _918930), _918932))), hBOOL(hAPP(hAPP(c_member(_918926), _918928), _918932))], (8132 ^ _777081) ^ [_919058, _919060, _919062, _919064] : [hBOOL(hAPP(hAPP(c_member(_919058), _919060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919058, tc_HOL_Obool)), _919062), _919064))), -(hBOOL(hAPP(hAPP(c_member(_919058), _919060), _919062)))], (8138 ^ _777081) ^ [_919210, _919212, _919214, _919216] : [hBOOL(hAPP(hAPP(c_member(_919210), _919212), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919210, tc_HOL_Obool)), _919214), _919216))), 8141 ^ _777081 : [(8142 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_919210), _919212), _919214)))], (8144 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_919210), _919212), _919216))]]], (8146 ^ _777081) ^ [_919385, _919387, _919389, _919391] : [-(hBOOL(hAPP(hAPP(c_member(_919385), _919387), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919385, tc_HOL_Obool)), _919389), _919391)))), hBOOL(hAPP(hAPP(c_member(_919385), _919387), _919389)), -(hBOOL(hAPP(hAPP(c_member(_919385), _919387), _919391)))], (8156 ^ _777081) ^ [_919591, _919593] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919591, tc_HOL_Obool)), _919593), _919593) = c_Orderings_Obot__class_Obot(tc_fun(_919591, tc_HOL_Obool)))], (8158 ^ _777081) ^ [_919632, _919634] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919632, tc_HOL_Obool)), _919634), c_Orderings_Obot__class_Obot(tc_fun(_919632, tc_HOL_Obool))) = _919634)], (8160 ^ _777081) ^ [_919673, _919675] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919673, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_919673, tc_HOL_Obool))), _919675) = c_Orderings_Obot__class_Obot(tc_fun(_919673, tc_HOL_Obool)))], (8172 ^ _777081) ^ [_919945, _919947, _919949, _919951] : [8174 ^ _777081 : [(8175 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_919945), 8173 ^ [_919945, _919947, _919949, _919951]), c_Map_Odom(_919945, _919947, _919949))))], (8177 ^ _777081) ^ [] : [hAPP(_919949, 8173 ^ [_919945, _919947, _919949, _919951]) = hAPP(_919951, 8173 ^ [_919945, _919947, _919949, _919951])]], -(c_Map_Omap__le(_919945, _919947, _919949, _919951))], (8162 ^ _777081) ^ [_919740, _919742, _919744, _919746] : [c_Map_Omap__le(_919740, _919742, _919744, _919746), 8165 ^ _777081 : [(8166 ^ _777081) ^ [_919828] : [hBOOL(hAPP(hAPP(c_member(_919740), _919828), c_Map_Odom(_919740, _919742, _919744))), -(hAPP(_919744, _919828) = hAPP(_919746, _919828))]]], (8181 ^ _777081) ^ [_920159, _920161, _920163, _920165] : [hBOOL(hAPP(hAPP(c_member(_920159), _920161), _920163)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920159, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_920159), _920161), _920165)), _920163) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920159, tc_HOL_Obool)), _920165), _920163))], (8187 ^ _777081) ^ [_920329, _920331, _920333, _920335] : [hBOOL(hAPP(hAPP(c_member(_920329), _920331), _920333)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920329, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_920329), _920331), _920335)), _920333) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920329, tc_HOL_Obool)), _920335), _920333))], (8193 ^ _777081) ^ [_920478, _920480, _920482, _920484] : [-(hBOOL(hAPP(hAPP(c_member(_920478), _920480), _920482))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920478, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_920478), _920480), _920484)), _920482) = hAPP(hAPP(c_Set_Oinsert(_920478), _920480), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920478, tc_HOL_Obool)), _920484), _920482)))], (8199 ^ _777081) ^ [_920565, _920567, _920569] : [-(hAPP(hAPP(c_Set_Oinsert(_920565), _920567), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920565, tc_HOL_Obool)), _920569), hAPP(hAPP(c_Set_Oinsert(_920565), _920567), c_Orderings_Obot__class_Obot(tc_fun(_920565, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_920565), _920567), _920569))], (8201 ^ _777081) ^ [_920632, _920634, _920636, _920638] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920632, tc_HOL_Obool)), _920634), hAPP(hAPP(c_Set_Oinsert(_920632), _920636), _920638)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920632, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920632, tc_HOL_Obool)), _920634), hAPP(hAPP(c_Set_Oinsert(_920632), _920636), c_Orderings_Obot__class_Obot(tc_fun(_920632, tc_HOL_Obool))))), _920638))], (8203 ^ _777081) ^ [_920715, _920717, _920719, _920721] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920715, tc_HOL_Obool)), _920717), hAPP(hAPP(c_Set_Oinsert(_920715), _920719), _920721)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920715, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920715, tc_HOL_Obool)), _920717), _920721)), hAPP(hAPP(c_Set_Oinsert(_920715), _920719), c_Orderings_Obot__class_Obot(tc_fun(_920715, tc_HOL_Obool)))))], (8205 ^ _777081) ^ [_920816, _920818, _920820, _920822, _920824] : [_920816 = c_Option_Ooption_ONone(_920818), -(c_Map_Odom(_920820, _920818, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_920820, tc_Option_Ooption(_920818)), _920822), _920824), _920816)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920820, tc_HOL_Obool)), c_Map_Odom(_920820, _920818, _920822)), hAPP(hAPP(c_Set_Oinsert(_920820), _920824), c_Orderings_Obot__class_Obot(tc_fun(_920820, tc_HOL_Obool)))))], (8211 ^ _777081) ^ [_920989, _920991, _920993, _920995, _920997] : [-(_920989 = c_Option_Ooption_ONone(_920991)), -(c_Map_Odom(_920993, _920991, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_920993, tc_Option_Ooption(_920991)), _920995), _920997), _920989)) = hAPP(hAPP(c_Set_Oinsert(_920993), _920997), c_Map_Odom(_920993, _920991, _920995)))], (8217 ^ _777081) ^ [_921086, _921088, _921090, _921092] : [hBOOL(hAPP(hAPP(c_member(_921086), _921088), c_Map_Odom(_921086, _921090, _921092))), hAPP(_921092, _921088) = c_Option_Ooption_ONone(_921090)], (8223 ^ _777081) ^ [_921194, _921196, _921198, _921200] : [-(hAPP(_921200, _921196) = c_Option_Ooption_ONone(_921198)), -(hBOOL(hAPP(hAPP(c_member(_921194), _921196), c_Map_Odom(_921194, _921198, _921200))))], (8229 ^ _777081) ^ [_921252, _921254, _921256, _921258, _921260] : [hAPP(_921252, _921254) = hAPP(c_Option_Ooption_OSome(_921256), _921258), -(hBOOL(hAPP(hAPP(c_member(_921260), _921254), c_Map_Odom(_921260, _921256, _921252))))], (8235 ^ _777081) ^ [_921373, _921375, _921377, _921379, _921381] : [hAPP(_921373, _921375) = hAPP(c_Option_Ooption_OSome(_921377), _921379), -(hAPP(hAPP(c_Set_Oinsert(_921381), _921375), c_Map_Odom(_921381, _921377, _921373)) = c_Map_Odom(_921381, _921377, _921373))], (8241 ^ _777081) ^ [_921504, _921506, _921508, _921510, _921512] : [hBOOL(hAPP(hAPP(c_member(_921504), _921506), c_Map_Odom(_921504, _921508, _921510))), -(hAPP(c_Map_Omap__add(_921504, _921508, _921512, _921510), _921506) = hAPP(_921510, _921506))], (8247 ^ _777081) ^ [_921627, _921629, _921631, _921633, _921635] : [-(hBOOL(hAPP(hAPP(c_member(_921627), _921629), c_Map_Odom(_921627, _921631, _921633)))), -(hAPP(c_Map_Omap__add(_921627, _921631, _921635, _921633), _921629) = hAPP(_921635, _921629))], (8253 ^ _777081) ^ [_921687, _921689, _921691, _921693, _921695] : [-(hBOOL(hAPP(hAPP(c_member(_921687), _921689), c_Map_Odom(_921687, _921691, _921693)))), -(hAPP(c_Map_Omap__add(_921687, _921691, _921693, _921695), _921689) = hAPP(_921695, _921689))], (8259 ^ _777081) ^ [_921751, _921753] : [-(c_Map_Odom(_921751, _921753, hAPP(c_COMBK(tc_Option_Ooption(_921753), _921751), c_Option_Ooption_ONone(_921753))) = c_Orderings_Obot__class_Obot(tc_fun(_921751, tc_HOL_Obool)))], (8261 ^ _777081) ^ [_921813, _921815, _921817] : [c_Map_Odom(_921813, _921815, _921817) = c_Orderings_Obot__class_Obot(tc_fun(_921813, tc_HOL_Obool)), -(_921817 = hAPP(c_COMBK(tc_Option_Ooption(_921815), _921813), c_Option_Ooption_ONone(_921815)))], (8267 ^ _777081) ^ [_921926, _921928, _921930] : [_921930 = hAPP(c_COMBK(tc_Option_Ooption(_921928), _921926), c_Option_Ooption_ONone(_921928)), -(c_Map_Odom(_921926, _921928, _921930) = c_Orderings_Obot__class_Obot(tc_fun(_921926, tc_HOL_Obool)))], (8273 ^ _777081) ^ [_922041, _922043, _922045] : [-(hBOOL(hAPP(hAPP(c_member(_922041), _922043), _922045))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922041, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_922041), _922043), _922045)), hAPP(hAPP(c_Set_Oinsert(_922041), _922043), c_Orderings_Obot__class_Obot(tc_fun(_922041, tc_HOL_Obool)))) = _922045)], (8279 ^ _777081) ^ [_922118, _922120, _922122] : [hBOOL(hAPP(hAPP(c_member(_922118), _922120), _922122)), -(hAPP(hAPP(c_Set_Oinsert(_922118), _922120), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922118, tc_HOL_Obool)), _922122), hAPP(hAPP(c_Set_Oinsert(_922118), _922120), c_Orderings_Obot__class_Obot(tc_fun(_922118, tc_HOL_Obool))))) = _922122)], (8285 ^ _777081) ^ [_922275] : [-(c_Hoare__Mirabelle_OMGT(_922275) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), c_fequal), _922275), c_Natural_Oevalc(_922275)))], (8287 ^ _777081) ^ [_922308, _922310, _922312, _922314, _922316, _922318] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_922308, tc_Option_Ooption(_922310)), c_Map_Orestrict__map(_922308, _922310, _922312, _922314)), _922316), _922318) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_922308, tc_Option_Ooption(_922310)), c_Map_Orestrict__map(_922308, _922310, _922312, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922308, tc_HOL_Obool)), _922314), hAPP(hAPP(c_Set_Oinsert(_922308), _922316), c_Orderings_Obot__class_Obot(tc_fun(_922308, tc_HOL_Obool)))))), _922316), _922318))], (8289 ^ _777081) ^ [_922399, _922401, _922403, _922405, _922407, _922409] : [-(hBOOL(hAPP(hAPP(c_member(_922399), _922401), c_Map_Odom(_922399, _922403, _922405)))), -(c_Map_Omap__add(_922399, _922403, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_922399, tc_Option_Ooption(_922403)), _922407), _922401), hAPP(c_Option_Ooption_OSome(_922403), _922409)), _922405) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_922399, tc_Option_Ooption(_922403)), c_Map_Omap__add(_922399, _922403, _922407, _922405)), _922401), hAPP(c_Option_Ooption_OSome(_922403), _922409)))], (8295 ^ _777081) ^ [_922523, _922525, _922527, _922529, _922531, _922533] : [hBOOL(hAPP(hAPP(c_member(_922523), _922525), _922527)), -(c_Map_Orestrict__map(_922523, _922529, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_922523, tc_Option_Ooption(_922529)), _922531), _922525), _922533), _922527) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_922523, tc_Option_Ooption(_922529)), c_Map_Orestrict__map(_922523, _922529, _922531, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922523, tc_HOL_Obool)), _922527), hAPP(hAPP(c_Set_Oinsert(_922523), _922525), c_Orderings_Obot__class_Obot(tc_fun(_922523, tc_HOL_Obool)))))), _922525), _922533))], (8301 ^ _777081) ^ [_922740, _922742, _922744, _922746, _922748, _922750] : [-(hBOOL(hAPP(hAPP(c_member(_922740), _922742), _922744))), -(c_Map_Orestrict__map(_922740, _922746, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_922740, tc_Option_Ooption(_922746)), _922748), _922742), _922750), _922744) = c_Map_Orestrict__map(_922740, _922746, _922748, _922744))], (8307 ^ _777081) ^ [_922817, _922819, _922821, _922823, _922825, _922827] : [hBOOL(hAPP(hAPP(c_member(_922817), _922819), _922821)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_922817, tc_Option_Ooption(_922823)), c_Map_Orestrict__map(_922817, _922823, _922825, _922821)), _922819), _922827) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_922817, tc_Option_Ooption(_922823)), c_Map_Orestrict__map(_922817, _922823, _922825, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922817, tc_HOL_Obool)), _922821), hAPP(hAPP(c_Set_Oinsert(_922817), _922819), c_Orderings_Obot__class_Obot(tc_fun(_922817, tc_HOL_Obool)))))), _922819), _922827))], (8313 ^ _777081) ^ [_923058, _923060, _923062] : [hBOOL(hAPP(hAPP(c_member(_923058), _923060), c_Option_Oset(_923058, _923062))), -(_923062 = hAPP(c_Option_Ooption_OSome(_923058), _923060))], (8319 ^ _777081) ^ [_923163, _923165, _923167] : [_923167 = hAPP(c_Option_Ooption_OSome(_923163), _923165), -(hBOOL(hAPP(hAPP(c_member(_923163), _923165), c_Option_Oset(_923163, _923167))))], (8325 ^ _777081) ^ [_923289, _923291] : [c_Option_Oset(_923289, _923291) = c_Orderings_Obot__class_Obot(tc_fun(_923289, tc_HOL_Obool)), -(_923291 = c_Option_Ooption_ONone(_923289))], (8331 ^ _777081) ^ [_923382, _923384] : [_923384 = c_Option_Ooption_ONone(_923382), -(c_Option_Oset(_923382, _923384) = c_Orderings_Obot__class_Obot(tc_fun(_923382, tc_HOL_Obool)))], (8337 ^ _777081) ^ [_923481] : [-(c_Option_Oset(_923481, c_Option_Ooption_ONone(_923481)) = c_Orderings_Obot__class_Obot(tc_fun(_923481, tc_HOL_Obool)))], (8339 ^ _777081) ^ [_923514, _923516] : [c_Hoare__Mirabelle_Ostate__not__singleton, 8345 ^ _777081 : [(8346 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), 8344 ^ [_923514, _923516]), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (8348 ^ _777081) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _923514, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY, 8344 ^ [_923514, _923516]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))]], hBOOL(hAPP(c_Com_OWT, _923516)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _923514, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(_923516)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (8356 ^ _777081) ^ [_923820, _923822, _923824] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(_923820)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _923822), _923820), _923824)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _923822), _923820), _923824)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (8366 ^ _777081) ^ [_924035, _924037] : [c_Hoare__Mirabelle_Ostate__not__singleton, c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _924035, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_Com_Ostate), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies)), c_Natural_Oevalc(_924037))))), c_fequal))), _924037), c_fequal)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _924035, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(_924037)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (8376 ^ _777081) ^ [_924248, _924250, _924252, _924254, _924256, _924258, _924260] : [hBOOL(hAPP(hAPP(c_member(_924248), _924250), _924252)), c_Nitpick_Ofold__graph_H(_924248, _924254, _924256, _924258, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924248, tc_HOL_Obool)), _924252), hAPP(hAPP(c_Set_Oinsert(_924248), _924250), c_Orderings_Obot__class_Obot(tc_fun(_924248, tc_HOL_Obool)))), _924260), -(c_Nitpick_Ofold__graph_H(_924248, _924254, _924256, _924258, _924252, hAPP(hAPP(_924256, _924250), _924260)))], (8386 ^ _777081) ^ [_924487, _924489, _924491, _924493, _924495] : [class_Groups_Ominus(_924487), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924489, _924487)), _924491), _924493), _924495) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_924487), hAPP(_924491, _924495)), hAPP(_924493, _924495)))], (8392 ^ _777081) ^ [_924624, _924626] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _924624, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), c_Hoare__Mirabelle_OMGT(_924626)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _924624, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_Com_Ostate), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies)), c_Natural_Oevalc(_924626))))), c_fequal))), _924626), c_fequal)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (8398 ^ _777081) ^ [_924791, _924793, _924795, _924797, _924799] : [class_Groups_Ominus(_924791), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_924793, _924791)), _924795), _924797), _924799) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_924791), hAPP(_924795, _924799)), hAPP(_924797, _924799)))], (8404 ^ _777081) ^ [_924928, _924930, _924932, _924934, _924936] : [hBOOL(hAPP(hAPP(c_member(_924928), _924930), c_Map_Oran(_924932, _924928, c_Map_Orestrict__map(_924932, _924928, _924934, _924936)))), 8408 ^ _777081 : [(8409 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_924932), 8407 ^ [_924928, _924930, _924932, _924934, _924936]), _924936)))], (8411 ^ _777081) ^ [] : [-(hAPP(_924934, 8407 ^ [_924928, _924930, _924932, _924934, _924936]) = hAPP(c_Option_Ooption_OSome(_924928), _924930))]]], (8413 ^ _777081) ^ [_925130, _925132] : [-(c_Set_Othe__elem(_925130, _925132) = c_HOL_OThe(_925130, hAPP(hAPP(c_COMBB(tc_fun(_925130, tc_HOL_Obool), tc_HOL_Obool, _925130), hAPP(c_fequal, _925132)), hAPP(hAPP(c_COMBC(_925130, tc_fun(_925130, tc_HOL_Obool), tc_fun(_925130, tc_HOL_Obool)), c_Set_Oinsert(_925130)), c_Orderings_Obot__class_Obot(tc_fun(_925130, tc_HOL_Obool))))))], (8415 ^ _777081) ^ [_925200, _925202, _925204, _925206, _925208, _925210] : [c_Hoare__Mirabelle_Ohoare__derivs(_925200, _925202, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_925200)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_925200), _925204), _925206), _925208)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_925200), tc_HOL_Obool)))), 8422 ^ _777081 : [(8423 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_925210, 8420 ^ [_925200, _925202, _925204, _925206, _925208, _925210]), 8421 ^ [_925200, _925202, _925204, _925206, _925208, _925210])))], (8425 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_925204, 8420 ^ [_925200, _925202, _925204, _925206, _925208, _925210]), 8421 ^ [_925200, _925202, _925204, _925206, _925208, _925210]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_925200, _925202, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_925200)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_925200), _925210), _925206), _925208)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_925200), tc_HOL_Obool)))))], (8429 ^ _777081) ^ [_925629] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _925629) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8431 ^ _777081) ^ [_925655] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _925655), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _925655)], (8433 ^ _777081) ^ [_925684] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _925684), _925684) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8435 ^ _777081) ^ [_925713, _925715] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _925713), _925715) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _925715), _925713) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_925713 = _925715)], (8445 ^ _777081) ^ [_925866, _925868, _925870] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _925866)), _925868)), hAPP(c_Nat_OSuc, _925870)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _925866), _925868)), _925870))], (8447 ^ _777081) ^ [_925923, _925925] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _925923)), hAPP(c_Nat_OSuc, _925925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _925923), _925925))], (8449 ^ _777081) ^ [_925966, _925968] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _925966), _925968)), _925968) = _925966)], (8451 ^ _777081) ^ [_926003, _926005] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _926003), _926005)), _926003) = _926005)], (8453 ^ _777081) ^ [_926040, _926042, _926044] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926040), _926042)), _926044) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926040), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _926042), _926044)))], (8455 ^ _777081) ^ [_926091, _926093, _926095] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _926091), _926093)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _926091), _926095)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926093), _926095))], (8457 ^ _777081) ^ [_926142, _926144, _926146] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _926142), _926144)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _926146), _926144)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _926142), _926146))], (8459 ^ _777081) ^ [_926211, _926213, _926215] : [c_Hoare__Mirabelle_Otriple__valid(_926211, _926213, _926215), -(hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(_926211, tc_HOL_Obool, hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_HOL_Obool))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_HOL_Obool)), tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_926211, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_HOL_OAll(_926211)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_HOL_Obool))), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_HOL_Obool)), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_HOL_Obool), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, _926211), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBC(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(_926211, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBS(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_926211, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _926211), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _926211), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _926211), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_926211, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_Com_Ocom), c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _926211)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))), hAPP(hAPP(c_COMBC(tc_Com_Ocom, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_Natural_Oevaln)), _926213))))))))), _926215)))], (8465 ^ _777081) ^ [_927256, _927258, _927260] : [hBOOL(c_Hoare__Mirabelle_Otriple_Otriple__case(_927256, tc_HOL_Obool, hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_HOL_Obool))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_HOL_Obool)), tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_HOL_Obool), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_927256, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_HOL_OAll(_927256)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_HOL_Obool))), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_HOL_Obool)), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_HOL_Obool), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, _927256), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBC(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))))), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBB(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(_927256, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_COMBS(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_927256, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _927256), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _927256), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_HOL_Obool), _927256), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_HOL_Obool, tc_Com_Ostate), c_HOL_OAll(tc_Com_Ostate))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(_927256, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)))), tc_Com_Ocom), c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _927256)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(tc_Com_Ostate, tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Com_Ostate), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_Com_Ocom), hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Com_Ostate), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fimplies))), hAPP(hAPP(c_COMBC(tc_Com_Ocom, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_fun(tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), tc_Com_Ocom), c_COMBC(tc_Com_Ostate, tc_Nat_Onat, tc_fun(tc_Com_Ostate, tc_HOL_Obool))), c_Natural_Oevaln)), _927258))))))))), _927260)), -(c_Hoare__Mirabelle_Otriple__valid(_927256, _927258, _927260))], (8471 ^ _777081) ^ [_928307, _928309] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _928307), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _928307), _928309)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8473 ^ _777081) ^ [_928344, _928346, _928348, _928350] : [-(c_Nitpick_Ofold__graph_H(_928344, _928346, _928348, _928350, c_Orderings_Obot__class_Obot(tc_fun(_928344, tc_HOL_Obool)), _928350))], (8475 ^ _777081) ^ [_928382, _928384, _928386, _928388] : [-(c_Nitpick_Ofold__graph_H(_928382, _928384, _928386, _928388, c_Orderings_Obot__class_Obot(tc_fun(_928382, tc_HOL_Obool)), _928388))], (8477 ^ _777081) ^ [_928420, _928422, _928424] : [c_Hoare__Mirabelle_Ohoare__derivs(_928420, _928422, _928424), -(c_Hoare__Mirabelle_Ohoare__valids(_928420, _928422, _928424))], (8483 ^ _777081) ^ [_928533, _928535, _928537, _928539, _928541, _928543, _928545] : [c_Nitpick_Ofold__graph_H(_928533, _928535, _928537, _928539, _928541, hAPP(hAPP(_928537, _928543), _928545)), 8488 ^ _777081 : [(8489 ^ _777081) ^ [] : [-(_928541 = c_Orderings_Obot__class_Obot(tc_fun(_928533, tc_HOL_Obool)))], (8491 ^ _777081) ^ [] : [-(hAPP(hAPP(_928537, _928543), _928545) = _928539)]], 8494 ^ _777081 : [(8495 ^ _777081) ^ [] : [-(hAPP(hAPP(_928537, _928543), _928545) = hAPP(hAPP(_928537, 8492 ^ [_928533, _928535, _928537, _928539, _928541, _928543, _928545]), 8493 ^ [_928533, _928535, _928537, _928539, _928541, _928543, _928545]))], (8497 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928533), 8492 ^ [_928533, _928535, _928537, _928539, _928541, _928543, _928545]), _928541)))], (8499 ^ _777081) ^ [] : [-(c_Nitpick_Ofold__graph_H(_928533, _928535, _928537, _928539, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928533, tc_HOL_Obool)), _928541), hAPP(hAPP(c_Set_Oinsert(_928533), 8492 ^ [_928533, _928535, _928537, _928539, _928541, _928543, _928545]), c_Orderings_Obot__class_Obot(tc_fun(_928533, tc_HOL_Obool)))), 8493 ^ [_928533, _928535, _928537, _928539, _928541, _928543, _928545]))]]], (8501 ^ _777081) ^ [_928970, _928972, _928974, _928976, _928978, _928980, _928982] : [-(c_Nitpick_Ofold__graph_H(_928970, _928972, _928974, _928976, _928978, hAPP(hAPP(_928974, _928980), _928982))), 8502 ^ _777081 : [(8503 ^ _777081) ^ [] : [_928978 = c_Orderings_Obot__class_Obot(tc_fun(_928970, tc_HOL_Obool)), hAPP(hAPP(_928974, _928980), _928982) = _928976], (8509 ^ _777081) ^ [_929199, _929201] : [hAPP(hAPP(_928974, _928980), _928982) = hAPP(hAPP(_928974, _929201), _929199), hBOOL(hAPP(hAPP(c_member(_928970), _929201), _928978)), c_Nitpick_Ofold__graph_H(_928970, _928972, _928974, _928976, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928970, tc_HOL_Obool)), _928978), hAPP(hAPP(c_Set_Oinsert(_928970), _929201), c_Orderings_Obot__class_Obot(tc_fun(_928970, tc_HOL_Obool)))), _929199)]]], (8521 ^ _777081) ^ [_929491, _929493, _929495, _929497, _929499, _929501] : [c_Hoare__Mirabelle_Ohoare__derivs(_929491, _929493, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_929491)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_929491), _929495), _929497), _929499)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_929491), tc_HOL_Obool)))), 8528 ^ _777081 : [(8529 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_929499, 8526 ^ [_929491, _929493, _929495, _929497, _929499, _929501]), 8527 ^ [_929491, _929493, _929495, _929497, _929499, _929501])))], (8531 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_929501, 8526 ^ [_929491, _929493, _929495, _929497, _929499, _929501]), 8527 ^ [_929491, _929493, _929495, _929497, _929499, _929501]))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_929491, _929493, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_929491)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_929491), _929495), _929497), _929501)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_929491), tc_HOL_Obool)))))], (8535 ^ _777081) ^ [_929920, _929922, _929924] : [-(hAPP(c_Option_Omap(_929920, _929922), _929924) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_929922), _929920, c_Option_Ooption_ONone(_929922), hAPP(hAPP(c_COMBB(_929922, tc_Option_Ooption(_929922), _929920), c_Option_Ooption_OSome(_929922)), _929924)))], (8537 ^ _777081) ^ [_929976, _929978] : [-(c_HOL_OThe(_929976, hAPP(c_fequal, _929978)) = _929978)], (8539 ^ _777081) ^ [_930007, _930009] : [-(c_HOL_OThe(_930007, hAPP(hAPP(c_COMBC(_930007, _930007, tc_HOL_Obool), c_fequal), _930009)) = _930009)], (8541 ^ _777081) ^ [_930045, _930047, _930049, _930051, _930053, _930055] : [-(c_Sum__Type_Osum_Osum__rec(_930045, _930047, _930049, _930051, _930053, hAPP(c_Sum__Type_OInl(_930045, _930049), _930055)) = hAPP(_930051, _930055))], (8543 ^ _777081) ^ [_930094, _930096, _930098, _930100, _930102, _930104] : [-(c_Sum__Type_Osum_Osum__rec(_930094, _930096, _930098, _930100, _930102, hAPP(c_Sum__Type_OInr(_930098, _930094), _930104)) = hAPP(_930102, _930104))], (8545 ^ _777081) ^ [_930143, _930145, _930147, _930149, _930151] : [-(c_Map_Orestrict__map(_930143, _930145, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_930143, tc_Option_Ooption(_930145)), _930147), _930149), hAPP(c_Option_Ooption_OSome(_930145), _930151)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_930143, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_930143), _930149), c_Orderings_Obot__class_Obot(tc_fun(_930143, tc_HOL_Obool))))) = c_Map_Orestrict__map(_930143, _930145, _930147, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_930143, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_930143), _930149), c_Orderings_Obot__class_Obot(tc_fun(_930143, tc_HOL_Obool))))))], (8547 ^ _777081) ^ [_930245, _930247, _930249, _930251] : [-(c_Map_Orestrict__map(_930245, _930247, _930249, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_930245, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_930245), _930251), c_Orderings_Obot__class_Obot(tc_fun(_930245, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_930245, tc_Option_Ooption(_930247)), _930249), _930251), c_Option_Ooption_ONone(_930247)))], (8549 ^ _777081) ^ [_930316, _930318, _930320, _930322, _930324] : [hBOOL(hAPP(hAPP(c_member(_930316), _930318), _930320)), -(hBOOL(hAPP(hAPP(c_member(tc_sum(_930316, _930322)), hAPP(c_Sum__Type_OInl(_930316, _930322), _930318)), c_Sum__Type_OPlus(_930316, _930322, _930320, _930324))))], (8555 ^ _777081) ^ [_930451, _930453, _930455] : [-(hBOOL(hAPP(hAPP(c_member(_930451), _930453), _930455))), -(hBOOL(hAPP(hAPP(c_member(_930451), _930453), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_930451, tc_HOL_Obool)), _930455))))], (8561 ^ _777081) ^ [_930511, _930513, _930515, _930517, _930519] : [hBOOL(hAPP(hAPP(c_member(_930511), _930513), _930515)), -(hBOOL(hAPP(hAPP(c_member(tc_sum(_930517, _930511)), hAPP(c_Sum__Type_OInr(_930511, _930517), _930513)), c_Sum__Type_OPlus(_930517, _930511, _930519, _930515))))], (8567 ^ _777081) ^ [_930650, _930652, _930654] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _930650), _930652)), _930654) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _930650), _930654)), _930652))], (8569 ^ _777081) ^ [_930701, _930703, _930705, _930707] : [class_Groups_Ouminus(_930701), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_930703, _930701)), _930705), _930707) = hAPP(c_Groups_Ouminus__class_Ouminus(_930701), hAPP(_930705, _930707)))], (8575 ^ _777081) ^ [_930818, _930820, _930822] : [class_Lattices_Oboolean__algebra(_930818), 8578 ^ _777081 : [(8579 ^ _777081) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_930818), _930820) = hAPP(c_Groups_Ouminus__class_Ouminus(_930818), _930822), -(_930820 = _930822)], (8585 ^ _777081) ^ [] : [_930820 = _930822, -(hAPP(c_Groups_Ouminus__class_Ouminus(_930818), _930820) = hAPP(c_Groups_Ouminus__class_Ouminus(_930818), _930822))]]], (8591 ^ _777081) ^ [_931059, _931061, _931063, _931065] : [class_Groups_Ouminus(_931059), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_931061, _931059)), _931063), _931065) = hAPP(c_Groups_Ouminus__class_Ouminus(_931059), hAPP(_931063, _931065)))], (8597 ^ _777081) ^ [_931176, _931178] : [class_Lattices_Oboolean__algebra(_931176), -(hAPP(c_Groups_Ouminus__class_Ouminus(_931176), hAPP(c_Groups_Ouminus__class_Ouminus(_931176), _931178)) = _931178)], (8603 ^ _777081) ^ [_931289, _931291, _931293] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_931289, tc_HOL_Obool)), _931291) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_931289, tc_HOL_Obool)), _931293), -(_931291 = _931293)], (8609 ^ _777081) ^ [_931396, _931398, _931400] : [_931398 = _931400, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_931396, tc_HOL_Obool)), _931398) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_931396, tc_HOL_Obool)), _931400))], (8615 ^ _777081) ^ [_931509, _931511] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_931509, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_931509, tc_HOL_Obool)), _931511)) = _931511)], (8617 ^ _777081) ^ [_931550, _931552, _931554] : [class_Groups_Ogroup__add(_931550), 8620 ^ _777081 : [(8621 ^ _777081) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_931550), _931552) = hAPP(c_Groups_Ouminus__class_Ouminus(_931550), _931554), -(_931552 = _931554)], (8627 ^ _777081) ^ [] : [_931552 = _931554, -(hAPP(c_Groups_Ouminus__class_Ouminus(_931550), _931552) = hAPP(c_Groups_Ouminus__class_Ouminus(_931550), _931554))]]], (8633 ^ _777081) ^ [_931791, _931793, _931795] : [class_Groups_Ogroup__add(_931791), 8636 ^ _777081 : [(8637 ^ _777081) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_931791), _931793) = _931795, -(hAPP(c_Groups_Ouminus__class_Ouminus(_931791), _931795) = _931793)], (8643 ^ _777081) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_931791), _931795) = _931793, -(hAPP(c_Groups_Ouminus__class_Ouminus(_931791), _931793) = _931795)]]], (8649 ^ _777081) ^ [_932032, _932034, _932036] : [class_Groups_Ogroup__add(_932032), 8652 ^ _777081 : [(8653 ^ _777081) ^ [] : [_932034 = hAPP(c_Groups_Ouminus__class_Ouminus(_932032), _932036), -(_932036 = hAPP(c_Groups_Ouminus__class_Ouminus(_932032), _932034))], (8659 ^ _777081) ^ [] : [_932036 = hAPP(c_Groups_Ouminus__class_Ouminus(_932032), _932034), -(_932034 = hAPP(c_Groups_Ouminus__class_Ouminus(_932032), _932036))]]], (8665 ^ _777081) ^ [_932273, _932275] : [class_Groups_Ogroup__add(_932273), -(hAPP(c_Groups_Ouminus__class_Ouminus(_932273), hAPP(c_Groups_Ouminus__class_Ouminus(_932273), _932275)) = _932275)], (8671 ^ _777081) ^ [_932368] : [class_Groups_Ogroup__add(_932368), -(hAPP(c_Groups_Ouminus__class_Ouminus(_932368), c_Groups_Ozero__class_Ozero(_932368)) = c_Groups_Ozero__class_Ozero(_932368))], (8677 ^ _777081) ^ [_932459, _932461] : [class_Groups_Ogroup__add(_932459), 8680 ^ _777081 : [(8681 ^ _777081) ^ [] : [c_Groups_Ozero__class_Ozero(_932459) = hAPP(c_Groups_Ouminus__class_Ouminus(_932459), _932461), -(c_Groups_Ozero__class_Ozero(_932459) = _932461)], (8687 ^ _777081) ^ [] : [c_Groups_Ozero__class_Ozero(_932459) = _932461, -(c_Groups_Ozero__class_Ozero(_932459) = hAPP(c_Groups_Ouminus__class_Ouminus(_932459), _932461))]]], (8693 ^ _777081) ^ [_932691, _932693] : [class_Groups_Olinordered__ab__group__add(_932691), 8696 ^ _777081 : [(8697 ^ _777081) ^ [] : [_932693 = hAPP(c_Groups_Ouminus__class_Ouminus(_932691), _932693), -(_932693 = c_Groups_Ozero__class_Ozero(_932691))], (8703 ^ _777081) ^ [] : [_932693 = c_Groups_Ozero__class_Ozero(_932691), -(_932693 = hAPP(c_Groups_Ouminus__class_Ouminus(_932691), _932693))]]], (8709 ^ _777081) ^ [_932917, _932919] : [class_Groups_Ogroup__add(_932917), 8712 ^ _777081 : [(8713 ^ _777081) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_932917), _932919) = c_Groups_Ozero__class_Ozero(_932917), -(_932919 = c_Groups_Ozero__class_Ozero(_932917))], (8719 ^ _777081) ^ [] : [_932919 = c_Groups_Ozero__class_Ozero(_932917), -(hAPP(c_Groups_Ouminus__class_Ouminus(_932917), _932919) = c_Groups_Ozero__class_Ozero(_932917))]]], (8725 ^ _777081) ^ [_933149, _933151] : [class_Groups_Olinordered__ab__group__add(_933149), 8728 ^ _777081 : [(8729 ^ _777081) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_933149), _933151) = _933151, -(_933151 = c_Groups_Ozero__class_Ozero(_933149))], (8735 ^ _777081) ^ [] : [_933151 = c_Groups_Ozero__class_Ozero(_933149), -(hAPP(c_Groups_Ouminus__class_Ouminus(_933149), _933151) = _933151)]]], (8741 ^ _777081) ^ [_933375, _933377, _933379] : [class_Groups_Oab__group__add(_933375), -(hAPP(c_Groups_Ouminus__class_Ouminus(_933375), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933375), _933377), _933379)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933375), hAPP(c_Groups_Ouminus__class_Ouminus(_933375), _933377)), hAPP(c_Groups_Ouminus__class_Ouminus(_933375), _933379)))], (8747 ^ _777081) ^ [_933514, _933516, _933518] : [class_Groups_Ogroup__add(_933514), -(hAPP(c_Groups_Ouminus__class_Ouminus(_933514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933514), _933516), _933518)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933514), hAPP(c_Groups_Ouminus__class_Ouminus(_933514), _933518)), hAPP(c_Groups_Ouminus__class_Ouminus(_933514), _933516)))], (8753 ^ _777081) ^ [_933653, _933655, _933657] : [class_Groups_Ogroup__add(_933653), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933653), _933655), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933653), hAPP(c_Groups_Ouminus__class_Ouminus(_933653), _933655)), _933657)) = _933657)], (8759 ^ _777081) ^ [_933772, _933774, _933776] : [class_Groups_Ogroup__add(_933772), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933772), hAPP(c_Groups_Ouminus__class_Ouminus(_933772), _933774)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933772), _933774), _933776)) = _933776)], (8765 ^ _777081) ^ [_933891, _933893, _933895] : [hBOOL(hAPP(hAPP(c_member(_933891), _933893), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_933891, tc_HOL_Obool)), _933895))), hBOOL(hAPP(hAPP(c_member(_933891), _933893), _933895))], (8771 ^ _777081) ^ [_934015, _934017, _934019] : [hBOOL(hAPP(hAPP(c_member(_934015), _934017), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_934015, tc_HOL_Obool)), _934019))), hBOOL(hAPP(hAPP(c_member(_934015), _934017), _934019))], (8777 ^ _777081) ^ [_934157, _934159, _934161] : [hBOOL(hAPP(hAPP(c_member(_934157), _934159), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_934157, tc_HOL_Obool)), _934161))), hBOOL(hAPP(hAPP(c_member(_934157), _934159), _934161))], (8783 ^ _777081) ^ [_934275, _934277, _934279] : [-(hBOOL(hAPP(hAPP(c_member(_934275), _934277), _934279))), -(hBOOL(hAPP(hAPP(c_member(_934275), _934277), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_934275, tc_HOL_Obool)), _934279))))], (8789 ^ _777081) ^ [_934337, _934339, _934341] : [class_Groups_Oab__group__add(_934337), -(hAPP(c_Groups_Ouminus__class_Ouminus(_934337), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_934337), _934339), _934341)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_934337), _934341), _934339))], (8795 ^ _777081) ^ [_934477, _934479, _934481, _934483] : [hAPP(hAPP(c_Option_Omap(_934477, _934479), _934481), _934483) = c_Option_Ooption_ONone(_934479), -(_934483 = c_Option_Ooption_ONone(_934477))], (8801 ^ _777081) ^ [_934580, _934582, _934584, _934586] : [_934586 = c_Option_Ooption_ONone(_934580), -(hAPP(hAPP(c_Option_Omap(_934580, _934582), _934584), _934586) = c_Option_Ooption_ONone(_934582))], (8807 ^ _777081) ^ [_934689, _934691, _934693] : [-(hAPP(hAPP(c_Option_Omap(_934689, _934691), _934693), c_Option_Ooption_ONone(_934689)) = c_Option_Ooption_ONone(_934691))], (8809 ^ _777081) ^ [_934753, _934755, _934757, _934759, _934761] : [hAPP(hAPP(c_Option_Omap(_934753, _934755), _934757), _934759) = hAPP(c_Option_Ooption_OSome(_934755), _934761), 8813 ^ _777081 : [(8814 ^ _777081) ^ [] : [-(_934759 = hAPP(c_Option_Ooption_OSome(_934753), 8812 ^ [_934753, _934755, _934757, _934759, _934761]))], (8816 ^ _777081) ^ [] : [-(hAPP(_934757, 8812 ^ [_934753, _934755, _934757, _934759, _934761]) = _934761)]]], (8818 ^ _777081) ^ [_934933, _934935, _934937, _934939, _934941] : [-(hAPP(hAPP(c_Option_Omap(_934933, _934935), _934937), _934939) = hAPP(c_Option_Ooption_OSome(_934935), _934941)), 8819 ^ _777081 : [(8820 ^ _777081) ^ [_935001] : [_934939 = hAPP(c_Option_Ooption_OSome(_934933), _935001), hAPP(_934937, _935001) = _934941]]], (8828 ^ _777081) ^ [_935145, _935147, _935149, _935151] : [-(hAPP(hAPP(c_Option_Omap(_935145, _935147), _935149), hAPP(c_Option_Ooption_OSome(_935145), _935151)) = hAPP(c_Option_Ooption_OSome(_935147), hAPP(_935149, _935151)))], (8830 ^ _777081) ^ [_935217, _935219, _935221, _935223] : [c_Sum__Type_OPlus(_935217, _935219, _935221, _935223) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_935217, _935219), tc_HOL_Obool)), 8833 ^ _777081 : [(8834 ^ _777081) ^ [] : [-(_935221 = c_Orderings_Obot__class_Obot(tc_fun(_935217, tc_HOL_Obool)))], (8836 ^ _777081) ^ [] : [-(_935223 = c_Orderings_Obot__class_Obot(tc_fun(_935219, tc_HOL_Obool)))]]], (8838 ^ _777081) ^ [_935366, _935368, _935370, _935372] : [-(c_Sum__Type_OPlus(_935366, _935368, _935370, _935372) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_935366, _935368), tc_HOL_Obool))), _935370 = c_Orderings_Obot__class_Obot(tc_fun(_935366, tc_HOL_Obool)), _935372 = c_Orderings_Obot__class_Obot(tc_fun(_935368, tc_HOL_Obool))], (8848 ^ _777081) ^ [_935551, _935553, _935555] : [class_Groups_Ogroup__add(_935551), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935551), _935553), _935555) = c_Groups_Ozero__class_Ozero(_935551), -(hAPP(c_Groups_Ouminus__class_Ouminus(_935551), _935553) = _935555)], (8858 ^ _777081) ^ [_935712, _935714] : [class_Groups_Oab__group__add(_935712), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935712), hAPP(c_Groups_Ouminus__class_Ouminus(_935712), _935714)), _935714) = c_Groups_Ozero__class_Ozero(_935712))], (8864 ^ _777081) ^ [_935817, _935819] : [class_Groups_Ogroup__add(_935817), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935817), hAPP(c_Groups_Ouminus__class_Ouminus(_935817), _935819)), _935819) = c_Groups_Ozero__class_Ozero(_935817))], (8870 ^ _777081) ^ [_935922, _935924, _935926] : [class_Groups_Ogroup__add(_935922), 8873 ^ _777081 : [(8874 ^ _777081) ^ [] : [_935924 = hAPP(c_Groups_Ouminus__class_Ouminus(_935922), _935926), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935922), _935924), _935926) = c_Groups_Ozero__class_Ozero(_935922))], (8880 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_935922), _935924), _935926) = c_Groups_Ozero__class_Ozero(_935922), -(_935924 = hAPP(c_Groups_Ouminus__class_Ouminus(_935922), _935926))]]], (8886 ^ _777081) ^ [_936178, _936180] : [class_Groups_Ogroup__add(_936178), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936178), _936180), hAPP(c_Groups_Ouminus__class_Ouminus(_936178), _936180)) = c_Groups_Ozero__class_Ozero(_936178))], (8892 ^ _777081) ^ [_936283, _936285] : [class_Groups_Ogroup__add(_936283), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_936283), c_Groups_Ozero__class_Ozero(_936283)), _936285) = hAPP(c_Groups_Ouminus__class_Ouminus(_936283), _936285))], (8898 ^ _777081) ^ [_936388, _936390, _936392] : [class_Groups_Ogroup__add(_936388), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_936388), _936390), _936392) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936388), _936390), hAPP(c_Groups_Ouminus__class_Ouminus(_936388), _936392)))], (8904 ^ _777081) ^ [_936507, _936509, _936511] : [class_Groups_Oab__group__add(_936507), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_936507), _936509), _936511) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936507), _936509), hAPP(c_Groups_Ouminus__class_Ouminus(_936507), _936511)))], (8910 ^ _777081) ^ [_936626, _936628, _936630] : [class_Rings_Ocomm__ring__1(_936626), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_936626), _936628), _936630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936626), _936628), hAPP(c_Groups_Ouminus__class_Ouminus(_936626), _936630)))], (8916 ^ _777081) ^ [_936745, _936747, _936749] : [class_Groups_Ogroup__add(_936745), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_936745), _936747), hAPP(c_Groups_Ouminus__class_Ouminus(_936745), _936749)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_936745), _936747), _936749))], (8922 ^ _777081) ^ [_936864, _936866, _936868, _936870, _936872] : [-(c_Map_Odom(_936864, _936866, hAPP(hAPP(c_COMBS(_936864, tc_Option_Ooption(_936868), tc_Option_Ooption(_936866)), hAPP(hAPP(c_COMBB(tc_fun(_936868, _936866), tc_fun(tc_Option_Ooption(_936868), tc_Option_Ooption(_936866)), _936864), c_Option_Omap(_936868, _936866)), _936870)), _936872)) = c_Map_Odom(_936864, _936868, _936872))], (8924 ^ _777081) ^ [_936940, _936942] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _936940), hAPP(c_Nat_OSuc, _936942)) = 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), _936940), _936942)))], (8926 ^ _777081) ^ [_936985, _936987, _936989, _936991] : [-(c_Sum__Type_Osum_Osum__case(_936985, _936987, _936989, hAPP(hAPP(c_COMBB(tc_sum(_936985, _936989), _936987, _936985), _936991), c_Sum__Type_OInl(_936985, _936989)), hAPP(hAPP(c_COMBB(tc_sum(_936985, _936989), _936987, _936989), _936991), c_Sum__Type_OInr(_936989, _936985))) = _936991)], (8928 ^ _777081) ^ [_937073, _937075, _937077, _937079, _937081, _937083] : [hBOOL(hAPP(hAPP(c_member(_937073), _937075), _937077)), -(hAPP(c_Set_Oimage(_937073, _937079, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_937073, _937079), _937081), _937075), _937083)), _937077) = hAPP(hAPP(c_Set_Oinsert(_937079), _937083), hAPP(c_Set_Oimage(_937073, _937079, _937081), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_937073, tc_HOL_Obool)), _937077), hAPP(hAPP(c_Set_Oinsert(_937073), _937075), c_Orderings_Obot__class_Obot(tc_fun(_937073, tc_HOL_Obool)))))))], (8934 ^ _777081) ^ [_937282, _937284, _937286, _937288, _937290, _937292] : [-(hBOOL(hAPP(hAPP(c_member(_937282), _937284), _937286))), -(hAPP(c_Set_Oimage(_937282, _937288, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_937282, _937288), _937290), _937284), _937292)), _937286) = hAPP(c_Set_Oimage(_937282, _937288, _937290), _937286))], (8940 ^ _777081) ^ [_937361, _937363, _937365, _937367, _937369] : [hBOOL(hAPP(hAPP(c_member(tc_sum(_937361, _937363)), _937365), c_Sum__Type_OPlus(_937361, _937363, _937367, _937369))), 8946 ^ _777081 : [(8947 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_937361), 8945 ^ [_937361, _937363, _937365, _937367, _937369]), _937367)))], (8949 ^ _777081) ^ [] : [-(_937365 = hAPP(c_Sum__Type_OInl(_937361, _937363), 8945 ^ [_937361, _937363, _937365, _937367, _937369]))]], 8951 ^ _777081 : [(8952 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_937363), 8950 ^ [_937361, _937363, _937365, _937367, _937369]), _937369)))], (8954 ^ _777081) ^ [] : [-(_937365 = hAPP(c_Sum__Type_OInr(_937363, _937361), 8950 ^ [_937361, _937363, _937365, _937367, _937369]))]]], (8956 ^ _777081) ^ [_937693, _937695, _937697, _937699, _937701] : [-(hAPP(c_Sum__Type_OSuml(_937693, _937695, _937697, _937699), hAPP(c_Sum__Type_OInl(_937693, _937697), _937701)) = hAPP(_937699, _937701))], (8958 ^ _777081) ^ [_937741, _937743, _937745, _937747, _937749] : [-(hAPP(c_Fun_Othe__inv__into(_937741, _937743, _937745, _937747), _937749) = c_HOL_OThe(_937741, hAPP(hAPP(c_COMBS(_937741, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _937741), c_fconj), hAPP(hAPP(c_COMBC(_937741, tc_fun(_937741, tc_HOL_Obool), tc_HOL_Obool), c_member(_937741)), _937745))), hAPP(hAPP(c_COMBC(_937741, _937743, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_937743, tc_fun(_937743, tc_HOL_Obool), _937741), c_fequal), _937747)), _937749))))], (8960 ^ _777081) ^ [_937841, _937843] : [class_Int_Oring__char__0(_937841), hBOOL(hAPP(hAPP(c_member(_937841), _937843), c_Int_Oring__1__class_OInts(_937841))), 8967 ^ _777081 : [(8968 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937841), _937843), _937843) = c_Groups_Ozero__class_Ozero(_937841), -(_937843 = c_Groups_Ozero__class_Ozero(_937841))], (8974 ^ _777081) ^ [] : [_937843 = c_Groups_Ozero__class_Ozero(_937841), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_937841), _937843), _937843) = c_Groups_Ozero__class_Ozero(_937841))]]], (8980 ^ _777081) ^ [_938161, _938163] : [_938161 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938161), _938163) = _938163)], (8986 ^ _777081) ^ [_938244, _938246] : [-(_938244 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938244), _938246) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _938244), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _938246)))], (8992 ^ _777081) ^ [_938303, _938305, _938307, _938309, _938311] : [-(hAPP(c_Sum__Type_OSumr(_938303, _938305, _938307, _938309), hAPP(c_Sum__Type_OInr(_938303, _938307), _938311)) = hAPP(_938309, _938311))], (9010 ^ _777081) ^ [_938704, _938706, _938708, _938710] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938704, tc_HOL_Obool)), _938706), hAPP(hAPP(c_Set_Oinsert(_938704), _938708), _938710)))), 9013 ^ _777081 : [(9014 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_938704), _938708), _938706)))], (9016 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938704, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938704, tc_HOL_Obool)), _938706), hAPP(hAPP(c_Set_Oinsert(_938704), _938708), c_Orderings_Obot__class_Obot(tc_fun(_938704, tc_HOL_Obool))))), _938710))]], 9017 ^ _777081 : [(9018 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_938704), _938708), _938706))], (9020 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938704, tc_HOL_Obool)), _938706), _938710))]]], (8994 ^ _777081) ^ [_938372, _938374, _938376, _938378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938372, tc_HOL_Obool)), _938374), hAPP(hAPP(c_Set_Oinsert(_938372), _938376), _938378))), 8997 ^ _777081 : [(8998 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_938372), _938376), _938374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938372, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_938372, tc_HOL_Obool)), _938374), hAPP(hAPP(c_Set_Oinsert(_938372), _938376), c_Orderings_Obot__class_Obot(tc_fun(_938372, tc_HOL_Obool))))), _938378)))], (9004 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_938372), _938376), _938374))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938372, tc_HOL_Obool)), _938374), _938378)))]]], (9024 ^ _777081) ^ [_939068, _939070] : [class_Orderings_Opreorder(_939068), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939068), _939070), _939070)))], (9030 ^ _777081) ^ [_939157, _939159, _939161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939157, tc_HOL_Obool)), _939159), _939161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939157, tc_HOL_Obool)), _939161), _939159)), -(_939159 = _939161)], (9040 ^ _777081) ^ [_939330, _939332, _939334, _939336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939330, tc_HOL_Obool)), _939332), _939334)), hBOOL(hAPP(hAPP(c_member(_939330), _939336), _939332)), -(hBOOL(hAPP(hAPP(c_member(_939330), _939336), _939334)))], (9050 ^ _777081) ^ [_939515, _939517, _939519, _939521, _939523, _939525] : [_939515 = hAPP(_939517, _939519), hBOOL(hAPP(hAPP(c_member(_939521), _939519), _939523)), -(hBOOL(hAPP(hAPP(c_member(_939525), _939515), hAPP(c_Set_Oimage(_939521, _939525, _939517), _939523))))], (9060 ^ _777081) ^ [_939708, _939710] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939708, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_939708, tc_HOL_Obool))), _939710)))], (9062 ^ _777081) ^ [_939748, _939750, _939752, _939754, _939756] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939748, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939748, tc_HOL_Obool)), hAPP(c_Set_Oimage(_939750, _939748, _939752), _939754)), hAPP(c_Set_Oimage(_939750, _939748, _939752), _939756))), hAPP(c_Set_Oimage(_939750, _939748, _939752), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939750, tc_HOL_Obool)), _939754), _939756)))))], (9064 ^ _777081) ^ [_939832, _939834, _939836, _939838, _939840, _939842] : [-(hAPP(c_Set_Oimage(_939832, _939834, _939836), hAPP(c_Set_Oimage(_939838, _939832, _939840), _939842)) = hAPP(c_Set_Oimage(_939838, _939834, hAPP(hAPP(c_COMBB(_939832, _939834, _939838), _939836), _939840)), _939842))], (9066 ^ _777081) ^ [_939896, _939898] : [-(hAPP(c_Set_Oimage(_939896, _939896, c_COMBI(_939896)), _939898) = _939898)], (9068 ^ _777081) ^ [_939930, _939932] : [class_Groups_Oone(_939930), 9071 ^ _777081 : [(9072 ^ _777081) ^ [] : [c_Groups_Oone__class_Oone(_939930) = _939932, -(_939932 = c_Groups_Oone__class_Oone(_939930))], (9078 ^ _777081) ^ [] : [_939932 = c_Groups_Oone__class_Oone(_939930), -(c_Groups_Oone__class_Oone(_939930) = _939932)]]], (9084 ^ _777081) ^ [_940147, _940149] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940147, tc_HOL_Obool)), _940149), _940149)))], (9086 ^ _777081) ^ [_940200, _940202, _940204] : [_940200 = _940202, 9089 ^ _777081 : [(9090 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940204, tc_HOL_Obool)), _940200), _940202)))], (9092 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940204, tc_HOL_Obool)), _940202), _940200)))]]], (9094 ^ _777081) ^ [_940341, _940343, _940345] : [-(_940341 = _940343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940345, tc_HOL_Obool)), _940341), _940343)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940345, tc_HOL_Obool)), _940343), _940341))], (9104 ^ _777081) ^ [_940540, _940542, _940544, _940546, _940548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940540, tc_HOL_Obool)), _940542), hAPP(c_Set_Oimage(_940544, _940540, _940546), _940548))), 9108 ^ _777081 : [(9109 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940544, tc_HOL_Obool)), 9107 ^ [_940540, _940542, _940544, _940546, _940548]), _940548)))], (9111 ^ _777081) ^ [] : [-(_940542 = hAPP(c_Set_Oimage(_940544, _940540, _940546), 9107 ^ [_940540, _940542, _940544, _940546, _940548]))]]], (9113 ^ _777081) ^ [_940744, _940746, _940748, _940750, _940752] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940744, tc_HOL_Obool)), _940746), hAPP(c_Set_Oimage(_940748, _940744, _940750), _940752)))), 9114 ^ _777081 : [(9115 ^ _777081) ^ [_940824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940748, tc_HOL_Obool)), _940824), _940752)), _940746 = hAPP(c_Set_Oimage(_940748, _940744, _940750), _940824)]]], (9123 ^ _777081) ^ [_940989, _940991, _940993] : [_940989 = _940991, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940993, tc_HOL_Obool)), _940989), _940991)))], (9129 ^ _777081) ^ [_941088, _941090, _941092] : [_941088 = _941090, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941092, tc_HOL_Obool)), _941090), _941088)))], (9135 ^ _777081) ^ [_941187, _941189, _941191, _941193, _941195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941187, tc_HOL_Obool)), _941189), _941191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941193, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941187, _941193, _941195), _941189)), hAPP(c_Set_Oimage(_941187, _941193, _941195), _941191))))], (9141 ^ _777081) ^ [_941338, _941340, _941342, _941344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941338, tc_HOL_Obool)), _941340), _941342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941338, tc_HOL_Obool)), _941342), _941344)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941338, tc_HOL_Obool)), _941340), _941344)))], (9151 ^ _777081) ^ [_941535, _941537, _941539] : [_941535 = _941537, 9154 ^ _777081 : [(9155 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941539, tc_HOL_Obool)), _941535), _941537)))], (9157 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941539, tc_HOL_Obool)), _941537), _941535)))]]], (9159 ^ _777081) ^ [_941684, _941686, _941688, _941690] : [class_Orderings_Oord(_941684), 9162 ^ _777081 : [(9163 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941686, _941684)), _941688), _941690)), 9166 ^ _777081 : [(9167 ^ _777081) ^ [_941841] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941684), hAPP(_941688, _941841)), hAPP(_941690, _941841))))]]], (9169 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_941684), hAPP(_941688, 9170 ^ [_941684, _941686, _941688, _941690])), hAPP(_941690, 9170 ^ [_941684, _941686, _941688, _941690]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941686, _941684)), _941688), _941690)))]]], (9176 ^ _777081) ^ [_942030, _942032, _942034] : [class_Orderings_Olinorder(_942030), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942030), _942032), _942034))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942030), _942034), _942032)))], (9186 ^ _777081) ^ [_942148, _942150, _942152] : [class_Orderings_Oorder(_942148), 9189 ^ _777081 : [(9190 ^ _777081) ^ [] : [_942150 = _942152, 9193 ^ _777081 : [(9194 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942148), _942150), _942152)))], (9196 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942148), _942152), _942150)))]]], (9198 ^ _777081) ^ [] : [-(_942150 = _942152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942148), _942150), _942152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942148), _942152), _942150))]]], (9208 ^ _777081) ^ [_942475, _942477, _942479, _942481] : [hBOOL(hAPP(_942475, _942477)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942479, tc_HOL_Obool)), _942475), _942481)), -(hBOOL(hAPP(_942481, _942477)))], (9218 ^ _777081) ^ [_942640, _942642, _942644] : [class_Orderings_Opreorder(_942640), _942642 = _942644, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942640), _942642), _942644)))], (9228 ^ _777081) ^ [_942785, _942787, _942789, _942791, _942793] : [class_Orderings_Oord(_942785), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942787, _942785)), _942789), _942791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942785), hAPP(_942789, _942793)), hAPP(_942791, _942793))))], (9238 ^ _777081) ^ [_942970, _942972, _942974] : [class_Orderings_Oorder(_942970), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942970), _942972), _942974)), 9245 ^ _777081 : [(9246 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942970), _942974), _942972)), -(_942974 = _942972)], (9252 ^ _777081) ^ [] : [_942974 = _942972, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_942970), _942974), _942972)))]]], (9258 ^ _777081) ^ [_943270, _943272, _943274, _943276, _943278, _943280, _943282] : [_943270 = _943272, -(hAPP(c_Sum__Type_Osum_Osum__case(_943274, _943276, _943278, _943280, _943282), _943270) = hAPP(c_Sum__Type_Osum_Osum__case(_943274, _943276, _943278, _943280, _943282), _943272))], (9264 ^ _777081) ^ [_943393, _943395, _943397, _943399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943393, tc_HOL_Obool)), _943395), _943397)), hBOOL(hAPP(_943395, _943399)), -(hBOOL(hAPP(_943397, _943399)))], (9274 ^ _777081) ^ [_943558, _943560, _943562, _943564] : [class_Orderings_Oord(_943558), _943560 = _943562, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943558), _943562), _943564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943558), _943560), _943564)))], (9288 ^ _777081) ^ [_943777, _943779, _943781, _943783] : [class_Orderings_Oorder(_943777), _943779 = _943781, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943777), _943783), _943781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943777), _943783), _943779)))], (9302 ^ _777081) ^ [_943996, _943998, _944000, _944002] : [class_Orderings_Oord(_943996), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943996), _943998), _944000)), _944000 = _944002, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_943996), _943998), _944002)))], (9316 ^ _777081) ^ [_944215, _944217, _944219, _944221] : [class_Orderings_Oorder(_944215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944215), _944217), _944219)), _944217 = _944221, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944215), _944221), _944219)))], (9330 ^ _777081) ^ [_944434, _944436, _944438] : [class_Orderings_Oorder(_944434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944434), _944436), _944438)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944434), _944438), _944436)), -(_944436 = _944438)], (9344 ^ _777081) ^ [_944647, _944649, _944651, _944653] : [class_Orderings_Opreorder(_944647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944647), _944649), _944651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944647), _944651), _944653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944647), _944649), _944653)))], (9358 ^ _777081) ^ [_944880, _944882, _944884] : [class_Orderings_Oorder(_944880), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944880), _944882), _944884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944880), _944884), _944882)), -(_944884 = _944882)], (9372 ^ _777081) ^ [_945093, _945095, _945097, _945099] : [class_Orderings_Oorder(_945093), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945093), _945095), _945097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945093), _945099), _945095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945093), _945099), _945097)))], (9386 ^ _777081) ^ [_945326, _945328, _945330, _945332, _945334] : [class_Orderings_Oord(_945326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945328, _945326)), _945330), _945332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945326), hAPP(_945330, _945334)), hAPP(_945332, _945334))))], (9396 ^ _777081) ^ [_945511, _945513, _945515, _945517, _945519, _945521, _945523] : [c_Sum__Type_Osum_Osum__case(_945511, _945513, _945515, _945517, _945519) = c_Sum__Type_Osum_Osum__case(_945511, _945513, _945515, _945521, _945523), 9399 ^ _777081 : [(9400 ^ _777081) ^ [] : [-(_945517 = _945521)], (9402 ^ _777081) ^ [] : [-(_945519 = _945523)]]], (9404 ^ _777081) ^ [_945652, _945654, _945656] : [class_Orderings_Olinorder(_945652), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945652), _945654), _945656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945652), _945656), _945654)))], (9414 ^ _777081) ^ [_945772] : [class_Rings_Oring__1(_945772), -(hBOOL(hAPP(hAPP(c_member(_945772), c_Groups_Oone__class_Oone(_945772)), c_Int_Oring__1__class_OInts(_945772))))], (9420 ^ _777081) ^ [_945867, _945869, _945871, _945873, _945875] : [c_Sum__Type_OSumr(_945867, _945869, _945871, _945873) = c_Sum__Type_OSumr(_945867, _945869, _945871, _945875), -(_945873 = _945875)], (9426 ^ _777081) ^ [_945970, _945972, _945974, _945976, _945978] : [c_Sum__Type_OSuml(_945970, _945972, _945974, _945976) = c_Sum__Type_OSuml(_945970, _945972, _945974, _945978), -(_945976 = _945978)], (9432 ^ _777081) ^ [_946097, _946099, _946101, _946103, _946105] : [hBOOL(hAPP(hAPP(c_member(_946097), _946099), hAPP(c_Set_Oimage(_946101, _946097, _946103), _946105))), 9436 ^ _777081 : [(9437 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_946101), 9435 ^ [_946097, _946099, _946101, _946103, _946105]), _946105)))], (9439 ^ _777081) ^ [] : [-(_946099 = hAPP(_946103, 9435 ^ [_946097, _946099, _946101, _946103, _946105]))]]], (9441 ^ _777081) ^ [_946281, _946283, _946285, _946287, _946289] : [-(hBOOL(hAPP(hAPP(c_member(_946281), _946283), hAPP(c_Set_Oimage(_946285, _946281, _946287), _946289)))), 9442 ^ _777081 : [(9443 ^ _777081) ^ [_946351] : [hBOOL(hAPP(hAPP(c_member(_946285), _946351), _946289)), _946283 = hAPP(_946287, _946351)]]], (9451 ^ _777081) ^ [_946499, _946501, _946503, _946505, _946507] : [hBOOL(hAPP(hAPP(c_member(_946499), _946501), _946503)), -(hBOOL(hAPP(hAPP(c_member(_946505), hAPP(_946507, _946501)), hAPP(c_Set_Oimage(_946499, _946505, _946507), _946503))))], (9457 ^ _777081) ^ [_946630, _946632, _946634, _946636, _946638, _946640] : [hBOOL(hAPP(hAPP(c_member(_946630), _946632), _946634)), _946636 = hAPP(_946638, _946632), -(hBOOL(hAPP(hAPP(c_member(_946640), _946636), hAPP(c_Set_Oimage(_946630, _946640, _946638), _946634))))], (9467 ^ _777081) ^ [_946844, _946846, _946848, _946850] : [c_Orderings_Obot__class_Obot(tc_fun(_946844, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_946846, _946844, _946848), _946850), -(_946850 = c_Orderings_Obot__class_Obot(tc_fun(_946846, tc_HOL_Obool)))], (9473 ^ _777081) ^ [_946955, _946957, _946959, _946961] : [_946961 = c_Orderings_Obot__class_Obot(tc_fun(_946957, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_946955, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_946957, _946955, _946959), _946961))], (9479 ^ _777081) ^ [_947072, _947074, _947076] : [-(hAPP(c_Set_Oimage(_947072, _947074, _947076), c_Orderings_Obot__class_Obot(tc_fun(_947072, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_947074, tc_HOL_Obool)))], (9481 ^ _777081) ^ [_947137, _947139, _947141, _947143] : [hAPP(c_Set_Oimage(_947137, _947139, _947141), _947143) = c_Orderings_Obot__class_Obot(tc_fun(_947139, tc_HOL_Obool)), -(_947143 = c_Orderings_Obot__class_Obot(tc_fun(_947137, tc_HOL_Obool)))], (9487 ^ _777081) ^ [_947248, _947250, _947252, _947254] : [_947254 = c_Orderings_Obot__class_Obot(tc_fun(_947248, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_947248, _947250, _947252), _947254) = c_Orderings_Obot__class_Obot(tc_fun(_947250, tc_HOL_Obool)))], (9493 ^ _777081) ^ [_947365, _947367, _947369, _947371, _947373] : [-(hAPP(c_Set_Oimage(_947365, _947367, _947369), hAPP(hAPP(c_Set_Oinsert(_947365), _947371), _947373)) = hAPP(hAPP(c_Set_Oinsert(_947367), hAPP(_947369, _947371)), hAPP(c_Set_Oimage(_947365, _947367, _947369), _947373)))], (9495 ^ _777081) ^ [_947429, _947431, _947433, _947435, _947437] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_947429, _947431, _947433, hAPP(c_COMBK(_947431, _947429), _947435), hAPP(c_COMBK(_947431, _947433), _947435)), _947437) = _947435)], (9497 ^ _777081) ^ [_947481, _947483, _947485, _947487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947481, tc_HOL_Obool)), _947483), _947485)), hBOOL(hAPP(hAPP(c_member(_947481), _947487), _947483)), -(hBOOL(hAPP(hAPP(c_member(_947481), _947487), _947485)))], (9507 ^ _777081) ^ [_947666, _947668, _947670, _947672] : [hBOOL(hAPP(hAPP(c_member(_947666), _947668), _947670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947666, tc_HOL_Obool)), _947670), _947672)), -(hBOOL(hAPP(hAPP(c_member(_947666), _947668), _947672)))], (9517 ^ _777081) ^ [_947851, _947853, _947855, _947857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_947851, tc_HOL_Obool)), _947853), _947855)), hBOOL(hAPP(hAPP(c_member(_947851), _947857), _947853)), -(hBOOL(hAPP(hAPP(c_member(_947851), _947857), _947855)))], (9527 ^ _777081) ^ [_948036, _948038, _948040, _948042] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_948036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948036), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948036), _948038), _948040)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948036), _948038), _948042))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948036), _948040), _948042)))], (9537 ^ _777081) ^ [_948231, _948233, _948235, _948237] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_948231), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948231), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948231), _948233), _948235)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948231), _948237), _948235))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948231), _948233), _948237)))], (9547 ^ _777081) ^ [_948426, _948428, _948430, _948432, _948434] : [class_Groups_Oordered__ab__semigroup__add(_948426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948426), _948428), _948430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948426), _948432), _948434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948426), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948426), _948428), _948432)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948426), _948430), _948434))))], (9561 ^ _777081) ^ [_948697, _948699, _948701, _948703] : [class_Groups_Oordered__ab__semigroup__add(_948697), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948697), _948699), _948701)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948697), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948697), _948703), _948699)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948697), _948703), _948701))))], (9571 ^ _777081) ^ [_948892, _948894, _948896, _948898] : [class_Groups_Oordered__ab__semigroup__add(_948892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948892), _948894), _948896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948892), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948892), _948894), _948898)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948892), _948896), _948898))))], (9581 ^ _777081) ^ [_949087, _949089, _949091, _949093] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_949087), 9584 ^ _777081 : [(9585 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949087), _949089), _949091)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949087), _949089), _949093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949087), _949091), _949093)))], (9591 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949087), _949091), _949093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949087), _949089), _949091)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949087), _949089), _949093))))]]], (9597 ^ _777081) ^ [_949394, _949396, _949398, _949400] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_949394), 9600 ^ _777081 : [(9601 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949394), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949394), _949396), _949398)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949394), _949400), _949398))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949394), _949396), _949400)))], (9607 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949394), _949396), _949400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949394), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949394), _949396), _949398)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949394), _949400), _949398))))]]], (9613 ^ _777081) ^ [_949701, _949703] : [class_Orderings_Obot(_949701), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949701), c_Orderings_Obot__class_Obot(_949701)), _949703)))], (9619 ^ _777081) ^ [_949794, _949796, _949798, _949800, _949802] : [class_Groups_Oordered__ab__group__add(_949794), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_949794), _949796), _949798) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_949794), _949800), _949802), 9626 ^ _777081 : [(9627 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949794), _949796), _949798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949794), _949800), _949802)))], (9633 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949794), _949800), _949802)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949794), _949796), _949798)))]]], (9639 ^ _777081) ^ [_950164, _950166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950164, tc_HOL_Obool)), _950166), c_Orderings_Obot__class_Obot(tc_fun(_950164, tc_HOL_Obool)))), -(_950166 = c_Orderings_Obot__class_Obot(tc_fun(_950164, tc_HOL_Obool)))], (9645 ^ _777081) ^ [_950277, _950279] : [_950279 = c_Orderings_Obot__class_Obot(tc_fun(_950277, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950277, tc_HOL_Obool)), _950279), c_Orderings_Obot__class_Obot(tc_fun(_950277, tc_HOL_Obool)))))], (9651 ^ _777081) ^ [_950396, _950398, _950400, _950402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950396, tc_HOL_Obool)), _950398), _950400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950396, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_950396), _950402), _950398)), hAPP(hAPP(c_Set_Oinsert(_950396), _950402), _950400))))], (9657 ^ _777081) ^ [_950549, _950551, _950553, _950555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950549, tc_HOL_Obool)), _950551), _950553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950549, tc_HOL_Obool)), _950551), hAPP(hAPP(c_Set_Oinsert(_950549), _950555), _950553))))], (9663 ^ _777081) ^ [_950686, _950688, _950690] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950686, tc_HOL_Obool)), _950688), hAPP(hAPP(c_Set_Oinsert(_950686), _950690), _950688))))], (9665 ^ _777081) ^ [_950731, _950733, _950735] : [class_Groups_Oordered__ab__group__add(_950731), 9668 ^ _777081 : [(9669 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950731), _950733), hAPP(c_Groups_Ouminus__class_Ouminus(_950731), _950735))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950731), _950735), hAPP(c_Groups_Ouminus__class_Ouminus(_950731), _950733))))], (9675 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950731), _950735), hAPP(c_Groups_Ouminus__class_Ouminus(_950731), _950733))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950731), _950733), hAPP(c_Groups_Ouminus__class_Ouminus(_950731), _950735))))]]], (9681 ^ _777081) ^ [_951014, _951016, _951018] : [class_Groups_Oordered__ab__group__add(_951014), 9684 ^ _777081 : [(9685 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951014), hAPP(c_Groups_Ouminus__class_Ouminus(_951014), _951016)), _951018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951014), hAPP(c_Groups_Ouminus__class_Ouminus(_951014), _951018)), _951016)))], (9691 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951014), hAPP(c_Groups_Ouminus__class_Ouminus(_951014), _951018)), _951016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951014), hAPP(c_Groups_Ouminus__class_Ouminus(_951014), _951016)), _951018)))]]], (9697 ^ _777081) ^ [_951297, _951299, _951301] : [class_Groups_Oordered__ab__group__add(_951297), 9700 ^ _777081 : [(9701 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951297), hAPP(c_Groups_Ouminus__class_Ouminus(_951297), _951299)), hAPP(c_Groups_Ouminus__class_Ouminus(_951297), _951301))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951297), _951301), _951299)))], (9707 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951297), _951301), _951299)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951297), hAPP(c_Groups_Ouminus__class_Ouminus(_951297), _951299)), hAPP(c_Groups_Ouminus__class_Ouminus(_951297), _951301))))]]], (9713 ^ _777081) ^ [_951580, _951582, _951584] : [class_Groups_Oordered__ab__group__add(_951580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951580), _951582), _951584)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951580), hAPP(c_Groups_Ouminus__class_Ouminus(_951580), _951584)), hAPP(c_Groups_Ouminus__class_Ouminus(_951580), _951582))))], (9723 ^ _777081) ^ [_951759, _951761, _951763] : [class_Lattices_Oboolean__algebra(_951759), 9726 ^ _777081 : [(9727 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951759), hAPP(c_Groups_Ouminus__class_Ouminus(_951759), _951761)), hAPP(c_Groups_Ouminus__class_Ouminus(_951759), _951763))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951759), _951763), _951761)))], (9733 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951759), _951763), _951761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_951759), hAPP(c_Groups_Ouminus__class_Ouminus(_951759), _951761)), hAPP(c_Groups_Ouminus__class_Ouminus(_951759), _951763))))]]], (9739 ^ _777081) ^ [_952042, _952044, _952046] : [class_Lattices_Oboolean__algebra(_952042), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952042), _952044), _952046)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_952042), hAPP(c_Groups_Ouminus__class_Ouminus(_952042), _952046)), hAPP(c_Groups_Ouminus__class_Ouminus(_952042), _952044))))], (9749 ^ _777081) ^ [_952221, _952223, _952225] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952221, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952221, tc_HOL_Obool)), _952223), _952225)), _952223)))], (9751 ^ _777081) ^ [_952269, _952271, _952273, _952275, _952277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952269, tc_HOL_Obool)), _952271), _952273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952269, tc_HOL_Obool)), _952275), _952277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952269, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952269, tc_HOL_Obool)), _952271), _952277)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952269, tc_HOL_Obool)), _952273), _952275))))], (9761 ^ _777081) ^ [_952514, _952516, _952518, _952520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952514, tc_HOL_Obool)), _952516), _952518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952514, tc_HOL_Obool)), _952518), _952520)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952514, tc_HOL_Obool)), _952518), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_952514, tc_HOL_Obool)), _952520), _952516)) = _952516)], (9771 ^ _777081) ^ [_952753, _952755, _952757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952753, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952753, tc_HOL_Obool)), _952755)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952753, tc_HOL_Obool)), _952757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952753, tc_HOL_Obool)), _952757), _952755)))], (9777 ^ _777081) ^ [_952900, _952902, _952904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952900, tc_HOL_Obool)), _952904), _952902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_952900, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952900, tc_HOL_Obool)), _952902)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952900, tc_HOL_Obool)), _952904))))], (9783 ^ _777081) ^ [_953053, _953055, _953057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953053, tc_HOL_Obool)), _953055), _953057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953053, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_953053, tc_HOL_Obool)), _953057)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_953053, tc_HOL_Obool)), _953055))))], (9789 ^ _777081) ^ [_953204, _953206, _953208, _953210] : [c_Hoare__Mirabelle_Ohoare__derivs(_953204, _953206, _953208), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_953204), tc_HOL_Obool)), _953206), _953210)), -(c_Hoare__Mirabelle_Ohoare__derivs(_953204, _953210, _953208))], (9799 ^ _777081) ^ [_953369, _953371, _953373, _953375] : [c_Hoare__Mirabelle_Ohoare__derivs(_953369, _953371, _953373), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_953369), tc_HOL_Obool)), _953375), _953373)), -(c_Hoare__Mirabelle_Ohoare__derivs(_953369, _953371, _953375))], (9809 ^ _777081) ^ [_953534, _953536, _953538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_953534), tc_HOL_Obool)), _953536), _953538)), -(c_Hoare__Mirabelle_Ohoare__derivs(_953534, _953538, _953536))], (9815 ^ _777081) ^ [_953657, _953659, _953661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953657, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_953657, tc_fun(_953657, tc_HOL_Obool), tc_HOL_Obool), c_member(_953657)), _953659)), hAPP(hAPP(c_COMBC(_953657, tc_fun(_953657, tc_HOL_Obool), tc_HOL_Obool), c_member(_953657)), _953661))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953657, tc_HOL_Obool)), _953659), _953661)))], (9821 ^ _777081) ^ [_953832, _953834, _953836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953832, tc_HOL_Obool)), _953834), _953836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953832, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_953832, tc_fun(_953832, tc_HOL_Obool), tc_HOL_Obool), c_member(_953832)), _953834)), hAPP(hAPP(c_COMBC(_953832, tc_fun(_953832, tc_HOL_Obool), tc_HOL_Obool), c_member(_953832)), _953836))))], (9827 ^ _777081) ^ [_954013, _954015] : [class_Int_Oring__char__0(_954013), hBOOL(hAPP(hAPP(c_member(_954013), _954015), c_Int_Oring__1__class_OInts(_954013))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954013), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954013), c_Groups_Oone__class_Oone(_954013)), _954015)), _954015) = c_Groups_Ozero__class_Ozero(_954013)], (9837 ^ _777081) ^ [_954199, _954201, _954203, _954205, _954207] : [hBOOL(hAPP(hAPP(c_member(_954199), _954201), _954203)), -(hAPP(hAPP(c_Set_Oinsert(_954205), hAPP(_954207, _954201)), hAPP(c_Set_Oimage(_954199, _954205, _954207), _954203)) = hAPP(c_Set_Oimage(_954199, _954205, _954207), _954203))], (9843 ^ _777081) ^ [_954346, _954348] : [class_Groups_Olinordered__ab__group__add(_954346), 9846 ^ _777081 : [(9847 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954346), c_Groups_Ozero__class_Ozero(_954346)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954346), _954348), _954348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954346), c_Groups_Ozero__class_Ozero(_954346)), _954348)))], (9853 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954346), c_Groups_Ozero__class_Ozero(_954346)), _954348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954346), c_Groups_Ozero__class_Ozero(_954346)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954346), _954348), _954348))))]]], (9859 ^ _777081) ^ [_954629, _954631] : [class_Groups_Olinordered__ab__group__add(_954629), 9862 ^ _777081 : [(9863 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954629), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954629), _954631), _954631)), c_Groups_Ozero__class_Ozero(_954629))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954629), _954631), c_Groups_Ozero__class_Ozero(_954629))))], (9869 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954629), _954631), c_Groups_Ozero__class_Ozero(_954629))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954629), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954629), _954631), _954631)), c_Groups_Ozero__class_Ozero(_954629))))]]], (9875 ^ _777081) ^ [_954912, _954914, _954916] : [class_Groups_Oordered__comm__monoid__add(_954912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954912), c_Groups_Ozero__class_Ozero(_954912)), _954914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954912), c_Groups_Ozero__class_Ozero(_954912)), _954916)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_954912), c_Groups_Ozero__class_Ozero(_954912)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954912), _954914), _954916))))], (9889 ^ _777081) ^ [_955167, _955169, _955171] : [class_Groups_Oordered__comm__monoid__add(_955167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955167), c_Groups_Ozero__class_Ozero(_955167)), _955169)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955167), c_Groups_Ozero__class_Ozero(_955167)), _955171)), 9900 ^ _777081 : [(9901 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955167), _955169), _955171) = c_Groups_Ozero__class_Ozero(_955167), 9904 ^ _777081 : [(9905 ^ _777081) ^ [] : [-(_955169 = c_Groups_Ozero__class_Ozero(_955167))], (9907 ^ _777081) ^ [] : [-(_955171 = c_Groups_Ozero__class_Ozero(_955167))]]], (9909 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955167), _955169), _955171) = c_Groups_Ozero__class_Ozero(_955167)), _955169 = c_Groups_Ozero__class_Ozero(_955167), _955171 = c_Groups_Ozero__class_Ozero(_955167)]]], (9919 ^ _777081) ^ [_955638, _955640, _955642, _955644] : [class_Groups_Oordered__comm__monoid__add(_955638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955638), c_Groups_Ozero__class_Ozero(_955638)), _955640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955638), _955642), _955644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955638), _955642), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955638), _955640), _955644))))], (9933 ^ _777081) ^ [_955891, _955893, _955895, _955897] : [class_Groups_Oordered__comm__monoid__add(_955891), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955891), c_Groups_Ozero__class_Ozero(_955891)), _955893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955891), _955895), _955897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955891), _955895), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_955891), _955897), _955893))))], (9947 ^ _777081) ^ [_956144, _956146, _956148] : [class_Groups_Oordered__comm__monoid__add(_956144), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956144), _956146), c_Groups_Ozero__class_Ozero(_956144))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956144), _956148), c_Groups_Ozero__class_Ozero(_956144))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956144), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956144), _956146), _956148)), c_Groups_Ozero__class_Ozero(_956144))))], (9961 ^ _777081) ^ [_956399, _956401, _956403] : [class_Groups_Oordered__ab__group__add(_956399), 9964 ^ _777081 : [(9965 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956399), _956401), _956403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_956399), _956401), _956403)), c_Groups_Ozero__class_Ozero(_956399))))], (9971 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956399), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_956399), _956401), _956403)), c_Groups_Ozero__class_Ozero(_956399))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956399), _956401), _956403)))]]], (9977 ^ _777081) ^ [_956682, _956684] : [class_Groups_Olinordered__ab__group__add(_956682), 9980 ^ _777081 : [(9981 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956682), hAPP(c_Groups_Ouminus__class_Ouminus(_956682), _956684)), _956684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956682), c_Groups_Ozero__class_Ozero(_956682)), _956684)))], (9987 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956682), c_Groups_Ozero__class_Ozero(_956682)), _956684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956682), hAPP(c_Groups_Ouminus__class_Ouminus(_956682), _956684)), _956684)))]]], (9993 ^ _777081) ^ [_956950, _956952] : [class_Groups_Oordered__ab__group__add(_956950), 9996 ^ _777081 : [(9997 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956950), hAPP(c_Groups_Ouminus__class_Ouminus(_956950), _956952)), c_Groups_Ozero__class_Ozero(_956950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956950), c_Groups_Ozero__class_Ozero(_956950)), _956952)))], (10003 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956950), c_Groups_Ozero__class_Ozero(_956950)), _956952)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956950), hAPP(c_Groups_Ouminus__class_Ouminus(_956950), _956952)), c_Groups_Ozero__class_Ozero(_956950))))]]], (10009 ^ _777081) ^ [_957224, _957226] : [class_Groups_Olinordered__ab__group__add(_957224), 10012 ^ _777081 : [(10013 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957224), _957226), hAPP(c_Groups_Ouminus__class_Ouminus(_957224), _957226))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957224), _957226), c_Groups_Ozero__class_Ozero(_957224))))], (10019 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957224), _957226), c_Groups_Ozero__class_Ozero(_957224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957224), _957226), hAPP(c_Groups_Ouminus__class_Ouminus(_957224), _957226))))]]], (10025 ^ _777081) ^ [_957492, _957494] : [class_Groups_Oordered__ab__group__add(_957492), 10028 ^ _777081 : [(10029 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957492), c_Groups_Ozero__class_Ozero(_957492)), hAPP(c_Groups_Ouminus__class_Ouminus(_957492), _957494))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957492), _957494), c_Groups_Ozero__class_Ozero(_957492))))], (10035 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957492), _957494), c_Groups_Ozero__class_Ozero(_957492))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957492), c_Groups_Ozero__class_Ozero(_957492)), hAPP(c_Groups_Ouminus__class_Ouminus(_957492), _957494))))]]], (10041 ^ _777081) ^ [_957787, _957789, _957791, _957793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957787, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_957787), _957789), _957791)), _957793)), 10044 ^ _777081 : [(10045 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_957787), _957789), _957793)))], (10047 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957787, tc_HOL_Obool)), _957791), _957793)))]]], (10049 ^ _777081) ^ [_957960, _957962, _957964, _957966] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957960, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_957960), _957962), _957964)), _957966))), hBOOL(hAPP(hAPP(c_member(_957960), _957962), _957966)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957960, tc_HOL_Obool)), _957964), _957966))], (10059 ^ _777081) ^ [_958168, _958170, _958172, _958174] : [-(hBOOL(hAPP(hAPP(c_member(_958168), _958170), _958172))), 10062 ^ _777081 : [(10063 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958168, tc_HOL_Obool)), _958172), hAPP(hAPP(c_Set_Oinsert(_958168), _958170), _958174))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958168, tc_HOL_Obool)), _958172), _958174)))], (10069 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958168, tc_HOL_Obool)), _958172), _958174)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958168, tc_HOL_Obool)), _958172), hAPP(hAPP(c_Set_Oinsert(_958168), _958170), _958174))))]]], (10075 ^ _777081) ^ [_958476, _958478, _958480] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958476, tc_HOL_Obool)), _958478), hAPP(hAPP(c_Set_Oinsert(_958476), _958480), c_Orderings_Obot__class_Obot(tc_fun(_958476, tc_HOL_Obool))))), -(_958478 = c_Orderings_Obot__class_Obot(tc_fun(_958476, tc_HOL_Obool))), -(_958478 = hAPP(hAPP(c_Set_Oinsert(_958476), _958480), c_Orderings_Obot__class_Obot(tc_fun(_958476, tc_HOL_Obool))))], (10085 ^ _777081) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10087 ^ _777081) ^ [_958668] : [-(hAPP(c_Nat_OSuc, _958668) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _958668))], (10089 ^ _777081) ^ [_958697] : [-(hAPP(c_Nat_OSuc, _958697) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _958697), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10091 ^ _777081) ^ [_958729] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _958729)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _958729)], (10093 ^ _777081) ^ [_958761, _958763] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _958761), hAPP(c_Nat_OSuc, _958763)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _958761), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _958763))], (10095 ^ _777081) ^ [_958822, _958824, _958826, _958828] : [_958822 = c_Orderings_Obot__class_Obot(tc_fun(_958824, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_958824, _958826, hAPP(c_COMBK(_958826, _958824), _958828)), _958822) = c_Orderings_Obot__class_Obot(tc_fun(_958826, tc_HOL_Obool)))], (10101 ^ _777081) ^ [_958943, _958945, _958947, _958949] : [-(_958943 = c_Orderings_Obot__class_Obot(tc_fun(_958945, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_958945, _958947, hAPP(c_COMBK(_958947, _958945), _958949)), _958943) = hAPP(hAPP(c_Set_Oinsert(_958947), _958949), c_Orderings_Obot__class_Obot(tc_fun(_958947, tc_HOL_Obool))))], (10107 ^ _777081) ^ [_959031, _959033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_959031, tc_HOL_Obool)), _959033), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_959031, tc_HOL_Obool)), _959033))), -(_959033 = c_Orderings_Obot__class_Obot(tc_fun(_959031, tc_HOL_Obool)))], (10113 ^ _777081) ^ [_959150, _959152] : [_959152 = c_Orderings_Obot__class_Obot(tc_fun(_959150, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_959150, tc_HOL_Obool)), _959152), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_959150, tc_HOL_Obool)), _959152))))], (10119 ^ _777081) ^ [_959275, _959277, _959279, _959281, _959283, _959285] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_959275, _959277, _959279, _959281, _959283), hAPP(c_Sum__Type_OInr(_959279, _959275), _959285)) = hAPP(_959283, _959285))], (10121 ^ _777081) ^ [_959326, _959328, _959330, _959332, _959334, _959336] : [-(hAPP(c_Sum__Type_Osum_Osum__case(_959326, _959328, _959330, _959332, _959334), hAPP(c_Sum__Type_OInl(_959326, _959330), _959336)) = hAPP(_959332, _959336))], (10123 ^ _777081) ^ [_959377, _959379, _959381, _959383] : [c_Map_Omap__le(_959377, _959379, _959381, _959383), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_959377, tc_HOL_Obool)), c_Map_Odom(_959377, _959379, _959381)), c_Map_Odom(_959377, _959379, _959383))))], (10129 ^ _777081) ^ [_959498, _959500, _959502] : [-(c_Nat_Onat_Onat__case(_959498, _959500, _959502, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _959500)], (10131 ^ _777081) ^ [_959530, _959532, _959534, _959536] : [-(c_Nat_Onat_Onat__case(_959530, _959532, _959534, hAPP(c_Nat_OSuc, _959536)) = hAPP(_959534, _959536))], (10133 ^ _777081) ^ [_959570] : [class_Rings_Oring__1(_959570), -(hBOOL(hAPP(hAPP(c_member(_959570), c_Groups_Ozero__class_Ozero(_959570)), c_Int_Oring__1__class_OInts(_959570))))], (10139 ^ _777081) ^ [_959665, _959667, _959669] : [class_Rings_Oring__1(_959665), hBOOL(hAPP(hAPP(c_member(_959665), _959667), c_Int_Oring__1__class_OInts(_959665))), hBOOL(hAPP(hAPP(c_member(_959665), _959669), c_Int_Oring__1__class_OInts(_959665))), -(hBOOL(hAPP(hAPP(c_member(_959665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959665), _959667), _959669)), c_Int_Oring__1__class_OInts(_959665))))], (10153 ^ _777081) ^ [_959920, _959922, _959924] : [class_Rings_Oring__1(_959920), hBOOL(hAPP(hAPP(c_member(_959920), _959922), c_Int_Oring__1__class_OInts(_959920))), hBOOL(hAPP(hAPP(c_member(_959920), _959924), c_Int_Oring__1__class_OInts(_959920))), -(hBOOL(hAPP(hAPP(c_member(_959920), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_959920), _959922), _959924)), c_Int_Oring__1__class_OInts(_959920))))], (10167 ^ _777081) ^ [_960175, _960177] : [class_Rings_Oring__1(_960175), hBOOL(hAPP(hAPP(c_member(_960175), _960177), c_Int_Oring__1__class_OInts(_960175))), -(hBOOL(hAPP(hAPP(c_member(_960175), hAPP(c_Groups_Ouminus__class_Ouminus(_960175), _960177)), c_Int_Oring__1__class_OInts(_960175))))], (10177 ^ _777081) ^ [_960344, _960346, _960348, _960350, _960352, _960354] : [-(hBOOL(hAPP(hAPP(c_member(_960344), _960346), _960348))), -(hAPP(c_Set_Oimage(_960344, tc_Option_Ooption(_960350), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_960344, tc_Option_Ooption(_960350)), _960352), _960346), hAPP(c_Option_Ooption_OSome(_960350), _960354))), _960348) = hAPP(c_Set_Oimage(_960344, tc_Option_Ooption(_960350), _960352), _960348))], (10183 ^ _777081) ^ [_960432, _960434, _960436, _960438, _960440] : [hBOOL(hAPP(hAPP(c_member(_960432), _960434), _960436)), -(hAPP(c_Set_Oimage(_960432, _960438, hAPP(c_COMBK(_960438, _960432), _960440)), _960436) = hAPP(hAPP(c_Set_Oinsert(_960438), _960440), c_Orderings_Obot__class_Obot(tc_fun(_960438, tc_HOL_Obool))))], (10189 ^ _777081) ^ [_960581, _960583, _960585, _960587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960581, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960581, tc_HOL_Obool)), _960583), hAPP(hAPP(c_Set_Oinsert(_960581), _960585), c_Orderings_Obot__class_Obot(tc_fun(_960581, tc_HOL_Obool))))), _960587)), hBOOL(hAPP(hAPP(c_member(_960581), _960585), _960583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_960581, tc_HOL_Obool)), _960583), hAPP(hAPP(c_Set_Oinsert(_960581), _960585), _960587))))], (10199 ^ _777081) ^ [_960836] : [class_Rings_Olinordered__semidom(_960836), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960836), c_Groups_Ozero__class_Ozero(_960836)), c_Groups_Oone__class_Oone(_960836))))], (10205 ^ _777081) ^ [_960931] : [class_Rings_Olinordered__semidom(_960931), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_960931), c_Groups_Oone__class_Oone(_960931)), c_Groups_Ozero__class_Ozero(_960931)))], (10211 ^ _777081) ^ [_961027, _961029, _961031, _961033, _961035, _961037] : [c_Hoare__Mirabelle_Ohoare__derivs(_961027, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_961027), tc_HOL_Obool)), _961029), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_961027), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_961027, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961027)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_961027, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961027))), hAPP(hAPP(c_COMBB(tc_fun(_961027, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_961027, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961027))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_961027)), _961031)), c_Com_Ocom_OBODY)), _961033)), _961035)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_961027), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_961027, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961027)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_961027, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961027))), hAPP(hAPP(c_COMBB(tc_fun(_961027, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_961027, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961027))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_961027)), _961031)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _961033)), _961035)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _961037), _961035)), -(c_Hoare__Mirabelle_Ohoare__derivs(_961027, _961029, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_961027)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_961027), hAPP(_961031, _961037)), hAPP(c_Com_Ocom_OBODY, _961037)), hAPP(_961033, _961037))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_961027), tc_HOL_Obool)))))], (10221 ^ _777081) ^ [_961570, _961572, _961574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961570, tc_HOL_Obool)), _961572), hAPP(hAPP(c_Set_Oinsert(_961570), _961574), c_Orderings_Obot__class_Obot(tc_fun(_961570, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_961570, _961574, _961572) = _961574)], (10227 ^ _777081) ^ [_961697, _961699, _961701] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961697, tc_HOL_Obool)), _961699), hAPP(hAPP(c_Set_Oinsert(_961697), _961701), c_Orderings_Obot__class_Obot(tc_fun(_961697, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_961697, _961701, _961699) = c_HOL_OThe(_961697, hAPP(hAPP(c_COMBC(_961697, tc_fun(_961697, tc_HOL_Obool), tc_HOL_Obool), c_member(_961697)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_961697, tc_HOL_Obool)), _961699), hAPP(hAPP(c_Set_Oinsert(_961697), _961701), c_Orderings_Obot__class_Obot(tc_fun(_961697, tc_HOL_Obool)))))))], (10233 ^ _777081) ^ [_961806] : [class_Rings_Ozero__neq__one(_961806), c_Groups_Ozero__class_Ozero(_961806) = c_Groups_Oone__class_Oone(_961806)], (10239 ^ _777081) ^ [_961888] : [class_Rings_Ozero__neq__one(_961888), c_Groups_Oone__class_Oone(_961888) = c_Groups_Ozero__class_Ozero(_961888)], (10245 ^ _777081) ^ [_961970, _961972, _961974, _961976, _961978] : [c_Hoare__Mirabelle_Ohoare__valids(_961970, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_961970), tc_HOL_Obool)), _961972), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_961970), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961970)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961970))), hAPP(hAPP(c_COMBB(tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961970))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_961970)), _961974)), c_Com_Ocom_OBODY)), _961976)), _961978)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_961970), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961970)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961970))), hAPP(hAPP(c_COMBB(tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961970))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_961970)), _961974)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _961976)), _961978)), -(c_Hoare__Mirabelle_Ohoare__valids(_961970, _961972, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_961970), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961970)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961970))), hAPP(hAPP(c_COMBB(tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_961970, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_961970))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_961970)), _961974)), c_Com_Ocom_OBODY)), _961976)), _961978)))], (10251 ^ _777081) ^ [_962491, _962493, _962495, _962497, _962499] : [c_Hoare__Mirabelle_Ohoare__derivs(_962491, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_962491), tc_HOL_Obool)), _962493), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_962491), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_962491)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_962491))), hAPP(hAPP(c_COMBB(tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_962491))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_962491)), _962495)), c_Com_Ocom_OBODY)), _962497)), _962499)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_962491), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_962491)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_962491))), hAPP(hAPP(c_COMBB(tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_962491))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_962491)), _962495)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _962497)), _962499)), -(c_Hoare__Mirabelle_Ohoare__derivs(_962491, _962493, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_962491), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_962491)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_962491))), hAPP(hAPP(c_COMBB(tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_962491, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_962491))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_962491)), _962495)), c_Com_Ocom_OBODY)), _962497)), _962499)))], (10257 ^ _777081) ^ [_963012, _963014] : [class_Rings_Olinordered__idom(_963012), hBOOL(hAPP(hAPP(c_member(_963012), _963014), c_Int_Oring__1__class_OInts(_963012))), 10264 ^ _777081 : [(10265 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963012), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963012), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963012), c_Groups_Oone__class_Oone(_963012)), _963014)), _963014)), c_Groups_Ozero__class_Ozero(_963012))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963012), _963014), c_Groups_Ozero__class_Ozero(_963012))))], (10271 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963012), _963014), c_Groups_Ozero__class_Ozero(_963012))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_963012), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963012), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_963012), c_Groups_Oone__class_Oone(_963012)), _963014)), _963014)), c_Groups_Ozero__class_Ozero(_963012))))]]], (10277 ^ _777081) ^ [_963404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963404), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10279 ^ _777081) ^ [_963432] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _963432)))], (10281 ^ _777081) ^ [_963457] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963457), hAPP(c_Nat_OSuc, _963457))))], (10283 ^ _777081) ^ [_963488, _963490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963488), _963490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _963488)), hAPP(c_Nat_OSuc, _963490))))], (10289 ^ _777081) ^ [_963597, _963599, _963601, _963603] : [10290 ^ _777081 : [(10291 ^ _777081) ^ [] : [hBOOL(hAPP(_963597, _963599))], (10293 ^ _777081) ^ [] : [hBOOL(hAPP(_963601, _963599))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963603, tc_HOL_Obool)), _963601), _963597), _963599)))], (10297 ^ _777081) ^ [_963752, _963754, _963756, _963758] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963752, tc_HOL_Obool)), _963754), _963756), _963758)), -(hBOOL(hAPP(_963754, _963758))), -(hBOOL(hAPP(_963756, _963758)))], (10307 ^ _777081) ^ [_963882, _963884, _963886, _963888] : [10308 ^ _777081 : [(10309 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_963882), _963884), _963886))], (10311 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_963882), _963884), _963888))]], -(hBOOL(hAPP(hAPP(c_member(_963882), _963884), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963882, tc_HOL_Obool)), _963888), _963886))))], (10315 ^ _777081) ^ [_964067, _964069, _964071, _964073] : [hBOOL(hAPP(hAPP(c_member(_964067), _964069), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964067, tc_HOL_Obool)), _964071), _964073))), -(hBOOL(hAPP(hAPP(c_member(_964067), _964069), _964071))), -(hBOOL(hAPP(hAPP(c_member(_964067), _964069), _964073)))], (10325 ^ _777081) ^ [_964227] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _964227))))], (10327 ^ _777081) ^ [_964255, _964257, _964259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964255), _964257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964255), _964259)), 10334 ^ _777081 : [(10335 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964257), _964255)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964259), _964255))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964257), _964259)))], (10341 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964257), _964259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964257), _964255)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964259), _964255))))]]], (10347 ^ _777081) ^ [_964608, _964610, _964612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964608), _964610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964612), _964608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964608), _964612)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _964610), _964612))))], (10357 ^ _777081) ^ [_964795, _964797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _964795)), _964797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964795), _964797)))], (10363 ^ _777081) ^ [_964898, _964900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _964898), _964900)), 10366 ^ _777081 : [(10367 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964900), hAPP(c_Nat_OSuc, _964898))), -(_964900 = _964898)], (10373 ^ _777081) ^ [] : [_964900 = _964898, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _964900), hAPP(c_Nat_OSuc, _964898))))]]], (10379 ^ _777081) ^ [_965139, _965141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965139), _965141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965139)), _965141)))], (10385 ^ _777081) ^ [_965242, _965244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965242), _965244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965242), hAPP(c_Nat_OSuc, _965244))))], (10391 ^ _777081) ^ [_965360, _965362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965360)), _965362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965360), _965362)))], (10397 ^ _777081) ^ [_965459, _965461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965459), _965461)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965459)), _965461)))], (10403 ^ _777081) ^ [_965579, _965581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965579), hAPP(c_Nat_OSuc, _965581))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965579), _965581)))], (10409 ^ _777081) ^ [_965678, _965680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _965678), _965680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965678), hAPP(c_Nat_OSuc, _965680))))], (10415 ^ _777081) ^ [_965798, _965800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965798), _965800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965798)), _965800)))], (10421 ^ _777081) ^ [_965897, _965899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _965897)), _965899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _965897), _965899)))], (10427 ^ _777081) ^ [_966002, _966004, _966006, _966008] : [class_Lattices_Osemilattice__sup(_966002), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966002), _966004), _966006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966002), _966004), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966002), _966008), _966006))))], (10437 ^ _777081) ^ [_966181, _966183, _966185, _966187] : [class_Lattices_Osemilattice__sup(_966181), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966181), _966183), _966185)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966181), _966183), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966181), _966185), _966187))))], (10447 ^ _777081) ^ [_966360, _966362, _966364, _966366, _966368] : [class_Lattices_Olattice(_966360), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_966362, _966360)), _966364), _966366), _966368) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966360), hAPP(_966364, _966368)), hAPP(_966366, _966368)))], (10453 ^ _777081) ^ [_966497, _966499, _966501, _966503] : [class_Lattices_Osemilattice__sup(_966497), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966497), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966497), _966499), _966501)), _966503) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966497), _966499), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966497), _966501), _966503)))], (10459 ^ _777081) ^ [_966640, _966642, _966644, _966646] : [class_Lattices_Olattice(_966640), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966640), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966640), _966642), _966644)), _966646) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966640), _966642), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966640), _966644), _966646)))], (10465 ^ _777081) ^ [_966783, _966785, _966787, _966789] : [class_Lattices_Osemilattice__sup(_966783), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966783), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966783), _966785), _966787)), _966789) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966783), _966785), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966783), _966787), _966789)))], (10471 ^ _777081) ^ [_966926, _966928, _966930, _966932] : [class_Lattices_Osemilattice__sup(_966926), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966926), _966928), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966926), _966930), _966932)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966926), _966930), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_966926), _966928), _966932)))], (10477 ^ _777081) ^ [_967069, _967071, _967073, _967075] : [class_Lattices_Olattice(_967069), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967069), _967071), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967069), _967073), _967075)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967069), _967073), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967069), _967071), _967075)))], (10483 ^ _777081) ^ [_967212, _967214, _967216, _967218] : [class_Lattices_Osemilattice__sup(_967212), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967212), _967214), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967212), _967216), _967218)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967212), _967216), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967212), _967214), _967218)))], (10489 ^ _777081) ^ [_967355, _967357, _967359] : [class_Lattices_Osemilattice__sup(_967355), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967355), _967357), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967355), _967357), _967359)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967355), _967357), _967359))], (10495 ^ _777081) ^ [_967480, _967482, _967484] : [class_Lattices_Olattice(_967480), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967480), _967482), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967480), _967482), _967484)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967480), _967482), _967484))], (10501 ^ _777081) ^ [_967605, _967607, _967609] : [class_Lattices_Osemilattice__sup(_967605), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967605), _967607), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967605), _967607), _967609)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967605), _967607), _967609))], (10507 ^ _777081) ^ [_967730, _967732, _967734] : [class_Lattices_Osemilattice__sup(_967730), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967730), _967732), _967734) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967730), _967734), _967732))], (10513 ^ _777081) ^ [_967839, _967841, _967843] : [class_Lattices_Olattice(_967839), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967839), _967841), _967843) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967839), _967843), _967841))], (10519 ^ _777081) ^ [_967948, _967950, _967952] : [class_Lattices_Osemilattice__sup(_967948), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967948), _967950), _967952) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_967948), _967952), _967950))], (10525 ^ _777081) ^ [_968057, _968059] : [class_Lattices_Osemilattice__sup(_968057), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_968057), _968059), _968059) = _968059)], (10531 ^ _777081) ^ [_968148, _968150] : [class_Lattices_Osemilattice__sup(_968148), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_968148), _968150), _968150) = _968150)], (10537 ^ _777081) ^ [_968239, _968241, _968243] : [class_Orderings_Olinorder(_968239), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968239), _968241), _968243))), -(_968241 = _968243), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968239), _968243), _968241)))], (10551 ^ _777081) ^ [_968374, _968376, _968378] : [class_Orderings_Opreorder(_968374), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968374), _968376), _968378)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968374), _968378), _968376))], (10561 ^ _777081) ^ [_968534, _968536, _968538, _968540] : [class_Orderings_Oorder(_968534), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968534), _968536), _968538)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968534), _968540), _968536)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968534), _968540), _968538)))], (10575 ^ _777081) ^ [_968767, _968769, _968771, _968773] : [class_Orderings_Opreorder(_968767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968767), _968769), _968771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968767), _968771), _968773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968767), _968769), _968773)))], (10589 ^ _777081) ^ [_969000, _969002, _969004, _969006] : [class_Orderings_Oorder(_969000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969000), _969002), _969004)), _969002 = _969006, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969000), _969006), _969004)))], (10603 ^ _777081) ^ [_969219, _969221, _969223, _969225] : [class_Orderings_Oord(_969219), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969219), _969221), _969223)), _969223 = _969225, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969219), _969221), _969225)))], (10617 ^ _777081) ^ [_969438, _969440, _969442, _969444] : [class_Orderings_Oorder(_969438), _969440 = _969442, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969438), _969444), _969442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969438), _969444), _969440)))], (10631 ^ _777081) ^ [_969657, _969659, _969661, _969663] : [class_Orderings_Oord(_969657), _969659 = _969661, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969657), _969661), _969663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969657), _969659), _969663)))], (10645 ^ _777081) ^ [_969876, _969878, _969880] : [class_Orderings_Oorder(_969876), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969876), _969878), _969880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969876), _969880), _969878))], (10655 ^ _777081) ^ [_970036, _970038, _970040] : [class_Orderings_Opreorder(_970036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970036), _970038), _970040)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970036), _970040), _970038))], (10665 ^ _777081) ^ [_970196, _970198, _970200] : [class_Orderings_Oorder(_970196), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970196), _970198), _970200)), _970200 = _970198], (10675 ^ _777081) ^ [_970342, _970344, _970346] : [class_Orderings_Oorder(_970342), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970342), _970344), _970346)), _970344 = _970346], (10685 ^ _777081) ^ [_970488, _970490, _970492] : [class_Orderings_Opreorder(_970488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970488), _970490), _970492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970488), _970492), _970490))], (10695 ^ _777081) ^ [_970648, _970650, _970652] : [class_Orderings_Opreorder(_970648), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970648), _970650), _970652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970648), _970652), _970650))], (10705 ^ _777081) ^ [_970808, _970810, _970812] : [class_Orderings_Oorder(_970808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970808), _970810), _970812)), _970810 = _970812], (10715 ^ _777081) ^ [_970954, _970956, _970958, _970960] : [hBOOL(hAPP(_970954, _970956)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_970958, tc_HOL_Obool)), _970960), _970954), _970956)))], (10721 ^ _777081) ^ [_971065, _971067, _971069, _971071] : [hBOOL(hAPP(_971065, _971067)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971069, tc_HOL_Obool)), _971065), _971071), _971067)))], (10727 ^ _777081) ^ [_971176, _971178, _971180] : [class_Orderings_Olinorder(_971176), -(_971178 = _971180), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971176), _971178), _971180))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971176), _971180), _971178)))], (10741 ^ _777081) ^ [_971311, _971313, _971315] : [class_Orderings_Olinorder(_971311), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971311), _971313), _971315))), 10748 ^ _777081 : [(10749 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971311), _971315), _971313))), -(_971315 = _971313)], (10755 ^ _777081) ^ [] : [_971315 = _971313, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971311), _971315), _971313))]]], (10761 ^ _777081) ^ [_971570, _971572, _971574] : [class_Orderings_Olinorder(_971570), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971570), _971572), _971574))), -(_971572 = _971574), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971570), _971574), _971572)))], (10775 ^ _777081) ^ [_971701, _971703, _971705] : [class_Orderings_Olinorder(_971701), 10778 ^ _777081 : [(10789 ^ _777081) ^ [] : [10790 ^ _777081 : [(10791 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971701), _971705), _971703))], (10793 ^ _777081) ^ [] : [_971703 = _971705]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971701), _971703), _971705))], (10779 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971701), _971703), _971705))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971701), _971705), _971703))), -(_971703 = _971705)]]], (10797 ^ _777081) ^ [_971955, _971957, _971959] : [class_Orderings_Olinorder(_971955), 10800 ^ _777081 : [(10811 ^ _777081) ^ [] : [10812 ^ _777081 : [(10813 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971955), _971957), _971959))], (10815 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971955), _971959), _971957))]], _971957 = _971959], (10801 ^ _777081) ^ [] : [-(_971957 = _971959), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971955), _971957), _971959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971955), _971959), _971957)))]]], (10819 ^ _777081) ^ [_972209, _972211] : [class_Orderings_Opreorder(_972209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972209), _972211), _972211))], (10825 ^ _777081) ^ [_972299, _972301, _972303] : [class_Rings_Olinordered__idom(_972299), -(_972301 = _972303), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972299), _972301), _972303))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972299), _972303), _972301)))], (10858 ^ _777081) ^ [_972877, _972879, _972881, _972883] : [10862 ^ _777081 : [(10863 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972877), 10861 ^ [_972877, _972879, _972881, _972883]), _972879)))], (10865 ^ _777081) ^ [] : [hBOOL(hAPP(_972883, 10861 ^ [_972877, _972879, _972881, _972883]))]], 10867 ^ _777081 : [(10868 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972877), 10866 ^ [_972877, _972879, _972881, _972883]), _972881)))], (10870 ^ _777081) ^ [] : [hBOOL(hAPP(_972883, 10866 ^ [_972877, _972879, _972881, _972883]))]], 10871 ^ _777081 : [(10872 ^ _777081) ^ [_973210] : [hBOOL(hAPP(hAPP(c_member(_972877), _973210), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972877, tc_HOL_Obool)), _972879), _972881))), -(hBOOL(hAPP(_972883, _973210)))]]], (10839 ^ _777081) ^ [_972455, _972457, _972459, _972461] : [10841 ^ _777081 : [(10842 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972455), 10840 ^ [_972455, _972457, _972459, _972461]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972455, tc_HOL_Obool)), _972457), _972459))))], (10844 ^ _777081) ^ [] : [hBOOL(hAPP(_972461, 10840 ^ [_972455, _972457, _972459, _972461]))]], 10845 ^ _777081 : [(10846 ^ _777081) ^ [_972675] : [hBOOL(hAPP(hAPP(c_member(_972455), _972675), _972457)), -(hBOOL(hAPP(_972461, _972675)))], (10852 ^ _777081) ^ [_972772] : [hBOOL(hAPP(hAPP(c_member(_972455), _972772), _972459)), -(hBOOL(hAPP(_972461, _972772)))]]], (10878 ^ _777081) ^ [_973362, _973364, _973366, _973368] : [10879 ^ _777081 : [(10880 ^ _777081) ^ [_973472] : [hBOOL(hAPP(hAPP(c_member(_973362), _973472), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_973362, tc_HOL_Obool)), _973364), _973366))), hBOOL(hAPP(_973368, _973472))]], 10888 ^ _777081 : [(10889 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_973362), 10887 ^ [_973362, _973364, _973366, _973368]), _973364)))], (10891 ^ _777081) ^ [] : [-(hBOOL(hAPP(_973368, 10887 ^ [_973362, _973364, _973366, _973368])))]], 10893 ^ _777081 : [(10894 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_973362), 10892 ^ [_973362, _973364, _973366, _973368]), _973366)))], (10896 ^ _777081) ^ [] : [-(hBOOL(hAPP(_973368, 10892 ^ [_973362, _973364, _973366, _973368])))]]], (10898 ^ _777081) ^ [_973761, _973763, _973765, _973767] : [10912 ^ _777081 : [(10913 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_973761), 10911 ^ [_973761, _973763, _973765, _973767]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_973761, tc_HOL_Obool)), _973763), _973765))))], (10915 ^ _777081) ^ [] : [-(hBOOL(hAPP(_973767, 10911 ^ [_973761, _973763, _973765, _973767])))]], 10899 ^ _777081 : [(10900 ^ _777081) ^ [_973874] : [hBOOL(hAPP(hAPP(c_member(_973761), _973874), _973763)), hBOOL(hAPP(_973767, _973874))], (10906 ^ _777081) ^ [_973970] : [hBOOL(hAPP(hAPP(c_member(_973761), _973970), _973765)), hBOOL(hAPP(_973767, _973970))]]], (10917 ^ _777081) ^ [_974164, _974166, _974168, _974170] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974164, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974164, tc_HOL_Obool)), _974166), _974168)), _974170) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974164, tc_HOL_Obool)), _974166), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974164, tc_HOL_Obool)), _974168), _974170)))], (10919 ^ _777081) ^ [_974237, _974239, _974241, _974243] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974237, tc_HOL_Obool)), _974239), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974237, tc_HOL_Obool)), _974241), _974243)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974237, tc_HOL_Obool)), _974241), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974237, tc_HOL_Obool)), _974239), _974243)))], (10921 ^ _777081) ^ [_974310, _974312, _974314] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974310, tc_HOL_Obool)), _974312), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974310, tc_HOL_Obool)), _974312), _974314)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974310, tc_HOL_Obool)), _974312), _974314))], (10923 ^ _777081) ^ [_974370, _974372, _974374] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974370, tc_HOL_Obool)), _974372), _974374) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974370, tc_HOL_Obool)), _974374), _974372))], (10925 ^ _777081) ^ [_974419, _974421] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974419, tc_HOL_Obool)), _974421), _974421) = _974421)], (10927 ^ _777081) ^ [_974455, _974457, _974459, _974461, _974463] : [class_Lattices_Olattice(_974455), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_974457, _974455)), _974459), _974461), _974463) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_974455), hAPP(_974459, _974463)), hAPP(_974461, _974463)))], (10933 ^ _777081) ^ [_974592] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _974592) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974592)))], (10935 ^ _777081) ^ [_974639, _974641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974639)), _974641)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974639), _974641)))], (10941 ^ _777081) ^ [_974742, _974744] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _974742), _974744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _974742)), _974744)))], (10947 ^ _777081) ^ [_974851, _974853, _974855, _974857] : [class_Lattices_Osemilattice__sup(_974851), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974851), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_974851), _974853), _974855)), _974857)), 10954 ^ _777081 : [(10955 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974851), _974853), _974857)))], (10957 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974851), _974855), _974857)))]]], (10959 ^ _777081) ^ [_975074, _975076, _975078, _975080, _975082] : [class_Lattices_Osemilattice__sup(_975074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975074), _975076), _975078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975074), _975080), _975082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975074), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_975074), _975076), _975080)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_975074), _975078), _975082))))], (10973 ^ _777081) ^ [_975345, _975347, _975349, _975351] : [class_Lattices_Osemilattice__sup(_975345), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975345), _975347), _975349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975345), _975351), _975349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975345), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_975345), _975347), _975351)), _975349)))], (10987 ^ _777081) ^ [_975594, _975596, _975598, _975600] : [class_Lattices_Osemilattice__sup(_975594), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975594), _975596), _975598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975594), _975600), _975598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975594), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_975594), _975596), _975600)), _975598)))], (11001 ^ _777081) ^ [_975843, _975845, _975847] : [class_Lattices_Osemilattice__sup(_975843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975843), _975845), _975847)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_975843), _975847), _975845) = _975847)], (11011 ^ _777081) ^ [_976004, _976006, _976008] : [class_Lattices_Osemilattice__sup(_976004), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976004), _976006), _976008)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976004), _976006), _976008) = _976008)], (11021 ^ _777081) ^ [_976165, _976167, _976169, _976171] : [class_Lattices_Osemilattice__sup(_976165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976165), _976167), _976169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976165), _976167), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976165), _976171), _976169))))], (11031 ^ _777081) ^ [_976344, _976346, _976348, _976350] : [class_Lattices_Osemilattice__sup(_976344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976344), _976346), _976348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976344), _976346), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976344), _976348), _976350))))], (11041 ^ _777081) ^ [_976523, _976525, _976527, _976529] : [class_Lattices_Osemilattice__sup(_976523), 11044 ^ _777081 : [(11045 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976523), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976523), _976525), _976527)), _976529)), 11048 ^ _777081 : [(11049 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976523), _976525), _976529)))], (11051 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976523), _976527), _976529)))]]], (11053 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976523), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976523), _976525), _976527)), _976529))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976523), _976525), _976529)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976523), _976527), _976529))]]], (11063 ^ _777081) ^ [_976903, _976905, _976907] : [class_Lattices_Osemilattice__sup(_976903), 11066 ^ _777081 : [(11067 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976903), _976905), _976907)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976903), _976905), _976907) = _976907)], (11073 ^ _777081) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976903), _976905), _976907) = _976907, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976903), _976905), _976907)))]]], (11079 ^ _777081) ^ [_977159, _977161, _977163] : [class_Lattices_Osemilattice__sup(_977159), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977159), _977161), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977159), _977163), _977161))))], (11085 ^ _777081) ^ [_977266, _977268, _977270] : [class_Lattices_Olattice(_977266), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977266), _977268), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977266), _977270), _977268))))], (11091 ^ _777081) ^ [_977373, _977375, _977377] : [class_Lattices_Osemilattice__sup(_977373), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977373), _977375), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977373), _977375), _977377))))], (11097 ^ _777081) ^ [_977480, _977482, _977484] : [class_Lattices_Olattice(_977480), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977480), _977482), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977480), _977482), _977484))))], (11103 ^ _777081) ^ [_977587, _977589] : [class_Lattices_Obounded__lattice__bot(_977587), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977587), c_Orderings_Obot__class_Obot(_977587)), _977589) = _977589)], (11109 ^ _777081) ^ [_977682, _977684] : [class_Lattices_Obounded__lattice__bot(_977682), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977682), _977684), c_Orderings_Obot__class_Obot(_977682)) = _977684)], (11115 ^ _777081) ^ [_977777, _977779, _977781] : [class_Lattices_Obounded__lattice__bot(_977777), 11118 ^ _777081 : [(11119 ^ _777081) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977777), _977779), _977781) = c_Orderings_Obot__class_Obot(_977777), 11122 ^ _777081 : [(11123 ^ _777081) ^ [] : [-(_977779 = c_Orderings_Obot__class_Obot(_977777))], (11125 ^ _777081) ^ [] : [-(_977781 = c_Orderings_Obot__class_Obot(_977777))]]], (11127 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_977777), _977779), _977781) = c_Orderings_Obot__class_Obot(_977777)), _977779 = c_Orderings_Obot__class_Obot(_977777), _977781 = c_Orderings_Obot__class_Obot(_977777)]]], (11137 ^ _777081) ^ [_978104, _978106, _978108, _978110] : [hBOOL(hAPP(hAPP(c_member(_978104), _978106), _978108)), -(hBOOL(hAPP(hAPP(c_member(_978104), _978106), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978104, tc_HOL_Obool)), _978110), _978108))))], (11143 ^ _777081) ^ [_978235, _978237, _978239, _978241] : [hBOOL(hAPP(hAPP(c_member(_978235), _978237), _978239)), -(hBOOL(hAPP(hAPP(c_member(_978235), _978237), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978235, tc_HOL_Obool)), _978239), _978241))))], (11159 ^ _777081) ^ [_978541, _978543, _978545, _978547] : [11160 ^ _777081 : [(11161 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_978541), _978543), _978545))], (11163 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_978541), _978543), _978547))]], -(hBOOL(hAPP(hAPP(c_member(_978541), _978543), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978541, tc_HOL_Obool)), _978545), _978547))))], (11149 ^ _777081) ^ [_978387, _978389, _978391, _978393] : [hBOOL(hAPP(hAPP(c_member(_978387), _978389), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978387, tc_HOL_Obool)), _978391), _978393))), -(hBOOL(hAPP(hAPP(c_member(_978387), _978389), _978391))), -(hBOOL(hAPP(hAPP(c_member(_978387), _978389), _978393)))], (11167 ^ _777081) ^ [_978726, _978728, _978730, _978732] : [class_Orderings_Oord(_978726), 11170 ^ _777081 : [(11171 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_978728, _978726)), _978730), _978732)), 11174 ^ _777081 : [(11175 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978728, _978726)), _978730), _978732)))], (11177 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978728, _978726)), _978732), _978730))]]], (11179 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_978728, _978726)), _978730), _978732))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978728, _978726)), _978730), _978732)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978728, _978726)), _978732), _978730)))]]], (11189 ^ _777081) ^ [_979118, _979120, _979122, _979124] : [class_Orderings_Oorder(_979118), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979118), _979120), _979122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979118), _979124), _979120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979118), _979124), _979122)))], (11203 ^ _777081) ^ [_979351, _979353, _979355, _979357] : [class_Orderings_Opreorder(_979351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979351), _979353), _979355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979351), _979355), _979357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979351), _979353), _979357)))], (11217 ^ _777081) ^ [_979584, _979586, _979588, _979590] : [class_Orderings_Oorder(_979584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979584), _979586), _979588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979584), _979590), _979586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979584), _979590), _979588)))], (11231 ^ _777081) ^ [_979817, _979819, _979821, _979823] : [class_Orderings_Opreorder(_979817), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979817), _979819), _979821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979817), _979821), _979823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_979817), _979819), _979823)))], (11245 ^ _777081) ^ [_980050, _980052, _980054] : [class_Orderings_Oorder(_980050), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980050), _980052), _980054)), -(_980054 = _980052), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980050), _980052), _980054)))], (11259 ^ _777081) ^ [_980224, _980226, _980228] : [class_Orderings_Oorder(_980224), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980224), _980226), _980228)), -(_980226 = _980228), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980224), _980226), _980228)))], (11273 ^ _777081) ^ [_980398, _980400, _980402] : [class_Orderings_Oorder(_980398), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980398), _980400), _980402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980398), _980400), _980402))), -(_980400 = _980402)], (11287 ^ _777081) ^ [_980570, _980572, _980574] : [class_Orderings_Olinorder(_980570), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980570), _980572), _980574)), 11294 ^ _777081 : [(11295 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980570), _980572), _980574))), -(_980572 = _980574)], (11301 ^ _777081) ^ [] : [_980572 = _980574, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980570), _980572), _980574))]]], (11307 ^ _777081) ^ [_980826, _980828, _980830] : [class_Orderings_Opreorder(_980826), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980826), _980828), _980830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980826), _980828), _980830)))], (11317 ^ _777081) ^ [_980985, _980987, _980989] : [class_Orderings_Olinorder(_980985), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980985), _980987), _980989)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980985), _980989), _980987))], (11327 ^ _777081) ^ [_981145, _981147, _981149] : [class_Orderings_Oorder(_981145), -(_981147 = _981149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981145), _981149), _981147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981145), _981149), _981147)))], (11341 ^ _777081) ^ [_981361, _981363, _981365] : [class_Orderings_Oorder(_981361), -(_981363 = _981365), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981361), _981363), _981365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981361), _981363), _981365)))], (11355 ^ _777081) ^ [_981577, _981579, _981581] : [class_Orderings_Olinorder(_981577), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981577), _981579), _981581))), 11362 ^ _777081 : [(11363 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981577), _981579), _981581)), -(_981579 = _981581)], (11369 ^ _777081) ^ [] : [_981579 = _981581, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981577), _981579), _981581)))]]], (11375 ^ _777081) ^ [_981880, _981882, _981884] : [class_Orderings_Olinorder(_981880), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981880), _981882), _981884))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981880), _981884), _981882)))], (11385 ^ _777081) ^ [_982000, _982002, _982004] : [class_Orderings_Olinorder(_982000), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982000), _982002), _982004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982000), _982004), _982002)))], (11395 ^ _777081) ^ [_982120, _982122, _982124] : [class_Orderings_Oorder(_982120), 11398 ^ _777081 : [(11409 ^ _777081) ^ [] : [11410 ^ _777081 : [(11411 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982120), _982122), _982124))], (11413 ^ _777081) ^ [] : [_982122 = _982124]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982120), _982122), _982124)))], (11399 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982120), _982122), _982124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982120), _982122), _982124))), -(_982122 = _982124)]]], (11417 ^ _777081) ^ [_982418, _982420, _982422] : [class_Orderings_Opreorder(_982418), 11420 ^ _777081 : [(11421 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982418), _982420), _982422)), 11424 ^ _777081 : [(11425 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982418), _982420), _982422)))], (11427 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982418), _982422), _982420))]]], (11429 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982418), _982420), _982422))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982418), _982420), _982422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982418), _982422), _982420)))]]], (11439 ^ _777081) ^ [_982775, _982777, _982779] : [class_Orderings_Oorder(_982775), 11442 ^ _777081 : [(11443 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982775), _982777), _982779)), 11446 ^ _777081 : [(11447 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982775), _982777), _982779)))], (11449 ^ _777081) ^ [] : [_982777 = _982779]]], (11451 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982775), _982777), _982779))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_982775), _982777), _982779)), -(_982777 = _982779)]]], (11461 ^ _777081) ^ [_983111, _983113, _983115] : [class_Orderings_Olinorder(_983111), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983111), _983113), _983115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983111), _983115), _983113)))], (11471 ^ _777081) ^ [_983229, _983231, _983233] : [class_Orderings_Olinorder(_983229), 11474 ^ _777081 : [(11475 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983229), _983231), _983233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983229), _983233), _983231)))], (11481 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983229), _983233), _983231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983229), _983231), _983233))]]], (11487 ^ _777081) ^ [_983438, _983440, _983442] : [class_Orderings_Olinorder(_983438), 11490 ^ _777081 : [(11491 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983438), _983440), _983442))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983438), _983442), _983440)))], (11497 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983438), _983442), _983440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983438), _983440), _983442))]]], (11503 ^ _777081) ^ [_983665, _983667, _983669] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_983665, tc_HOL_Obool)), _983667), _983669) = c_Orderings_Obot__class_Obot(tc_fun(_983665, tc_HOL_Obool)), 11506 ^ _777081 : [(11507 ^ _777081) ^ [] : [-(_983667 = c_Orderings_Obot__class_Obot(tc_fun(_983665, tc_HOL_Obool)))], (11509 ^ _777081) ^ [] : [-(_983669 = c_Orderings_Obot__class_Obot(tc_fun(_983665, tc_HOL_Obool)))]]], (11511 ^ _777081) ^ [_983818, _983820, _983822] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_983818, tc_HOL_Obool)), _983820), _983822) = c_Orderings_Obot__class_Obot(tc_fun(_983818, tc_HOL_Obool))), _983820 = c_Orderings_Obot__class_Obot(tc_fun(_983818, tc_HOL_Obool)), _983822 = c_Orderings_Obot__class_Obot(tc_fun(_983818, tc_HOL_Obool))], (11521 ^ _777081) ^ [_984005, _984007] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984005, tc_HOL_Obool)), _984007), c_Orderings_Obot__class_Obot(tc_fun(_984005, tc_HOL_Obool))) = _984007)], (11523 ^ _777081) ^ [_984046, _984048] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984046, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_984046, tc_HOL_Obool))), _984048) = _984048)], (11525 ^ _777081) ^ [_984087, _984089, _984091, _984093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_984087, tc_HOL_Obool)), _984089), _984091)), hBOOL(hAPP(hAPP(c_member(_984087), _984093), _984089)), -(hBOOL(hAPP(hAPP(c_member(_984087), _984093), _984091)))], (11535 ^ _777081) ^ [_984272, _984274, _984276, _984278] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984272, tc_HOL_Obool)), _984274), hAPP(hAPP(c_Set_Oinsert(_984272), _984276), _984278)) = hAPP(hAPP(c_Set_Oinsert(_984272), _984276), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984272, tc_HOL_Obool)), _984274), _984278)))], (11537 ^ _777081) ^ [_984339, _984341, _984343, _984345] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984339, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_984339), _984341), _984343)), _984345) = hAPP(hAPP(c_Set_Oinsert(_984339), _984341), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984339, tc_HOL_Obool)), _984343), _984345)))], (11539 ^ _777081) ^ [_984406, _984408, _984410, _984412] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_984406), 11542 ^ _777081 : [(11543 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984406), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984406), _984408), _984410)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984406), _984412), _984410))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984406), _984408), _984412)))], (11549 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984406), _984408), _984412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984406), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984406), _984408), _984410)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984406), _984412), _984410))))]]], (11555 ^ _777081) ^ [_984713, _984715, _984717, _984719] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_984713), 11558 ^ _777081 : [(11559 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984713), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984713), _984715), _984717)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984713), _984715), _984719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984713), _984717), _984719)))], (11565 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984713), _984717), _984719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984713), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984713), _984715), _984717)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_984713), _984715), _984719))))]]], (11571 ^ _777081) ^ [_985020, _985022, _985024, _985026] : [class_Groups_Oordered__cancel__ab__semigroup__add(_985020), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985020), _985022), _985024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985020), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985020), _985022), _985026)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985020), _985024), _985026))))], (11581 ^ _777081) ^ [_985215, _985217, _985219, _985221] : [class_Groups_Oordered__cancel__ab__semigroup__add(_985215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985215), _985217), _985219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985215), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985215), _985221), _985217)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985215), _985221), _985219))))], (11591 ^ _777081) ^ [_985410, _985412, _985414, _985416, _985418] : [class_Groups_Oordered__cancel__ab__semigroup__add(_985410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985410), _985412), _985414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985410), _985416), _985418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985410), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985410), _985412), _985416)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985410), _985414), _985418))))], (11605 ^ _777081) ^ [_985681, _985683, _985685, _985687] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_985681), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985681), _985683), _985685)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985681), _985687), _985685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985681), _985683), _985687)))], (11615 ^ _777081) ^ [_985876, _985878, _985880, _985882] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_985876), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985876), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985876), _985878), _985880)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_985876), _985878), _985882))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985876), _985880), _985882)))], (11625 ^ _777081) ^ [_986071, _986073, _986075, _986077, _986079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986071, tc_HOL_Obool)), _986073), _986075)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986071, tc_HOL_Obool)), _986077), _986079)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986071, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_986071, tc_HOL_Obool)), _986073), _986077)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_986071, tc_HOL_Obool)), _986075), _986079))))], (11635 ^ _777081) ^ [_986316, _986318, _986320, _986322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986316, tc_HOL_Obool)), _986318), _986320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986316, tc_HOL_Obool)), _986322), _986320)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986316, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_986316, tc_HOL_Obool)), _986318), _986322)), _986320)))], (11645 ^ _777081) ^ [_986535, _986537, _986539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986535, tc_HOL_Obool)), _986537), _986539)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_986535, tc_HOL_Obool)), _986539), _986537) = _986539)], (11651 ^ _777081) ^ [_986656, _986658, _986660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986656, tc_HOL_Obool)), _986658), _986660)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_986656, tc_HOL_Obool)), _986658), _986660) = _986660)], (11657 ^ _777081) ^ [_986795, _986797, _986799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986795, tc_HOL_Obool)), _986797), _986799)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_986795, tc_HOL_Obool)), _986797), _986799) = _986799)], (11663 ^ _777081) ^ [_986912, _986914, _986916] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_986912, tc_HOL_Obool)), _986914), _986916) = _986916, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_986912, tc_HOL_Obool)), _986914), _986916)))], (11669 ^ _777081) ^ [_987035, _987037, _987039] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_987035, tc_HOL_Obool)), _987037), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987035, tc_HOL_Obool)), _987039), _987037))))], (11671 ^ _777081) ^ [_987083, _987085, _987087] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_987083, tc_HOL_Obool)), _987085), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987083, tc_HOL_Obool)), _987085), _987087))))], (11673 ^ _777081) ^ [_987131, _987133, _987135, _987137, _987139] : [-(hAPP(c_Set_Oimage(_987131, _987133, _987135), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987131, tc_HOL_Obool)), _987137), _987139)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987133, tc_HOL_Obool)), hAPP(c_Set_Oimage(_987131, _987133, _987135), _987137)), hAPP(c_Set_Oimage(_987131, _987133, _987135), _987139)))], (11675 ^ _777081) ^ [_987217, _987219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_987217, tc_HOL_Obool)), _987219), c_Orderings_Obot__class_Obot(tc_fun(_987217, tc_HOL_Obool))))], (11677 ^ _777081) ^ [_987257, _987259, _987261, _987263, _987265] : [class_Groups_Oordered__ab__group__add(_987257), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_987257), _987259), _987261) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_987257), _987263), _987265), 11684 ^ _777081 : [(11685 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987257), _987259), _987261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987257), _987263), _987265)))], (11691 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987257), _987263), _987265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987257), _987259), _987261)))]]], (11697 ^ _777081) ^ [_987612, _987614, _987616, _987618] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987612, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987612, tc_HOL_Obool)), _987614), _987616)), _987618) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987612, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987612, tc_HOL_Obool)), _987614), _987618)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987612, tc_HOL_Obool)), _987616), _987618)))], (11699 ^ _777081) ^ [_987696, _987698, _987700] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987696, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987696, tc_HOL_Obool)), _987698), _987700)), _987700) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987696, tc_HOL_Obool)), _987698), _987700))], (11701 ^ _777081) ^ [_987756, _987758, _987760] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987756, tc_HOL_Obool)), _987758), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987756, tc_HOL_Obool)), _987760), _987758)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_987756, tc_HOL_Obool)), _987758), _987760))], (11703 ^ _777081) ^ [_987816, _987818, _987820] : [class_Groups_Oordered__ab__group__add(_987816), 11706 ^ _777081 : [(11707 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987816), hAPP(c_Groups_Ouminus__class_Ouminus(_987816), _987818)), hAPP(c_Groups_Ouminus__class_Ouminus(_987816), _987820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987816), _987820), _987818)))], (11713 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987816), _987820), _987818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987816), hAPP(c_Groups_Ouminus__class_Ouminus(_987816), _987818)), hAPP(c_Groups_Ouminus__class_Ouminus(_987816), _987820))))]]], (11719 ^ _777081) ^ [_988099, _988101, _988103] : [class_Groups_Oordered__ab__group__add(_988099), 11722 ^ _777081 : [(11723 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988099), hAPP(c_Groups_Ouminus__class_Ouminus(_988099), _988101)), _988103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988099), hAPP(c_Groups_Ouminus__class_Ouminus(_988099), _988103)), _988101)))], (11729 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988099), hAPP(c_Groups_Ouminus__class_Ouminus(_988099), _988103)), _988101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988099), hAPP(c_Groups_Ouminus__class_Ouminus(_988099), _988101)), _988103)))]]], (11735 ^ _777081) ^ [_988382, _988384, _988386] : [class_Groups_Oordered__ab__group__add(_988382), 11738 ^ _777081 : [(11739 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988382), _988384), hAPP(c_Groups_Ouminus__class_Ouminus(_988382), _988386))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988382), _988386), hAPP(c_Groups_Ouminus__class_Ouminus(_988382), _988384))))], (11745 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988382), _988386), hAPP(c_Groups_Ouminus__class_Ouminus(_988382), _988384))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988382), _988384), hAPP(c_Groups_Ouminus__class_Ouminus(_988382), _988386))))]]], (11751 ^ _777081) ^ [_988665, _988667, _988669, _988671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_988665, tc_HOL_Obool)), _988667), _988669)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_988665, tc_HOL_Obool)), _988669), _988671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_988665, tc_HOL_Obool)), _988667), _988671)))], (11761 ^ _777081) ^ [_988862, _988864, _988866, _988868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_988862, tc_HOL_Obool)), _988864), _988866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_988862, tc_HOL_Obool)), _988866), _988868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_988862, tc_HOL_Obool)), _988864), _988868)))], (11771 ^ _777081) ^ [_989059, _989061, _989063] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_989059, tc_HOL_Obool)), _989061), _989063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989059, tc_HOL_Obool)), _989061), _989063)))], (11787 ^ _777081) ^ [_989324, _989326, _989328] : [11788 ^ _777081 : [(11789 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_989324, tc_HOL_Obool)), _989326), _989328))], (11791 ^ _777081) ^ [] : [_989326 = _989328]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989324, tc_HOL_Obool)), _989326), _989328)))], (11777 ^ _777081) ^ [_989196, _989198, _989200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989196, tc_HOL_Obool)), _989198), _989200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_989196, tc_HOL_Obool)), _989198), _989200))), -(_989198 = _989200)], (11795 ^ _777081) ^ [_989501, _989503, _989505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_989501, tc_HOL_Obool)), _989503), _989505)), 11798 ^ _777081 : [(11799 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989501, tc_HOL_Obool)), _989503), _989505)))], (11801 ^ _777081) ^ [] : [_989503 = _989505]]], (11803 ^ _777081) ^ [_989650, _989652, _989654] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_989650, tc_HOL_Obool)), _989652), _989654))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989650, tc_HOL_Obool)), _989652), _989654)), -(_989652 = _989654)], (11813 ^ _777081) ^ [_989824] : [-(_989824 = 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)), _989824)))], (11819 ^ _777081) ^ [_989860, _989862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989860), _989862)), _989862 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11825 ^ _777081) ^ [_989957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989957), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11827 ^ _777081) ^ [_989991] : [-(_989991 = 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)), _989991)))], (11833 ^ _777081) ^ [_990023] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _990023)), _990023 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11839 ^ _777081) ^ [_990114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990114), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11841 ^ _777081) ^ [_990154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990154), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_990154 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11847 ^ _777081) ^ [_990235] : [_990235 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _990235), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11853 ^ _777081) ^ [_990322] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _990322)))], (11855 ^ _777081) ^ [_990356, _990358] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990356), _990358))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990358), hAPP(c_Nat_OSuc, _990356))))], (11861 ^ _777081) ^ [_990401, _990403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990403), hAPP(c_Nat_OSuc, _990401))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990401), _990403))], (11877 ^ _777081) ^ [_990634, _990636] : [11878 ^ _777081 : [(11879 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990634), _990636))], (11881 ^ _777081) ^ [] : [_990634 = _990636]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990634), hAPP(c_Nat_OSuc, _990636))))], (11867 ^ _777081) ^ [_990522, _990524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990522), hAPP(c_Nat_OSuc, _990524))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990522), _990524))), -(_990522 = _990524)], (11885 ^ _777081) ^ [_990792, _990794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _990792)), hAPP(c_Nat_OSuc, _990794))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990792), _990794)))], (11891 ^ _777081) ^ [_990897, _990899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _990897), _990899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _990897)), hAPP(c_Nat_OSuc, _990899))))], (11897 ^ _777081) ^ [_991007, _991009] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991007), _991009))), 11900 ^ _777081 : [(11901 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991007), hAPP(c_Nat_OSuc, _991009))), -(_991007 = _991009)], (11907 ^ _777081) ^ [] : [_991007 = _991009, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991007), hAPP(c_Nat_OSuc, _991009))))]]], (11913 ^ _777081) ^ [_991240, _991242] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991240), _991242))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991240), hAPP(c_Nat_OSuc, _991242))), -(_991242 = _991240)], (11923 ^ _777081) ^ [_991388, _991390] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991388), _991390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991388), hAPP(c_Nat_OSuc, _991390))))], (11929 ^ _777081) ^ [_991491, _991493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991491), _991493)), -(hAPP(c_Nat_OSuc, _991491) = _991493), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _991491)), _991493)))], (11939 ^ _777081) ^ [_991615, _991617, _991619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991615), _991617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991617), _991619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _991615)), _991619)))], (11949 ^ _777081) ^ [_991784, _991786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991784), hAPP(c_Nat_OSuc, _991786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991784), _991786))), -(_991784 = _991786)], (11959 ^ _777081) ^ [_991902, _991904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _991902)), _991904)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991902), _991904)))], (11965 ^ _777081) ^ [_992005, _992007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _992005)), hAPP(c_Nat_OSuc, _992007))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992005), _992007)))], (11971 ^ _777081) ^ [_992123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _992123)), _992123))], (11973 ^ _777081) ^ [_992163, _992165] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992163), _992165))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _992165)), _992163)))], (11979 ^ _777081) ^ [_992208, _992210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _992210)), _992208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992208), _992210))], (11995 ^ _777081) ^ [_992447, _992449] : [11996 ^ _777081 : [(11997 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992447), _992449))], (11999 ^ _777081) ^ [] : [_992447 = hAPP(c_Nat_OSuc, _992449)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992447), hAPP(c_Nat_OSuc, _992449))))], (11985 ^ _777081) ^ [_992329, _992331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992329), hAPP(c_Nat_OSuc, _992331))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992329), _992331))), -(_992329 = hAPP(c_Nat_OSuc, _992331))], (12003 ^ _777081) ^ [_992611, _992613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _992611)), hAPP(c_Nat_OSuc, _992613))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992611), _992613)))], (12009 ^ _777081) ^ [_992716, _992718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992716), _992718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _992716)), hAPP(c_Nat_OSuc, _992718))))], (12015 ^ _777081) ^ [_992827, _992829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992827), _992829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992827), hAPP(c_Nat_OSuc, _992829))))], (12021 ^ _777081) ^ [_992930, _992932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992930), hAPP(c_Nat_OSuc, _992932))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _992930), _992932))), -(_992930 = hAPP(c_Nat_OSuc, _992932))], (12031 ^ _777081) ^ [_993054, _993056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _993054)), _993056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993054), _993056)))], (12037 ^ _777081) ^ [_993157, _993159, _993161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993157), _993159)), _993161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993157), _993161)))], (12043 ^ _777081) ^ [_993268, _993270, _993272, _993274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993268), _993270)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993272), _993270) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993268), _993274), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993272), _993274)))], (12053 ^ _777081) ^ [_993449, _993451, _993453, _993455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993449), _993451)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993453), _993455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993449), _993453)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993451), _993455))))], (12063 ^ _777081) ^ [_993640, _993642, _993644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993640), _993642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993640), _993644)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993642), _993644))))], (12069 ^ _777081) ^ [_993763, _993765, _993767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993763), _993765)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993763), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993767), _993765))))], (12075 ^ _777081) ^ [_993874, _993876, _993878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993874), _993876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993874), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993876), _993878))))], (12081 ^ _777081) ^ [_994003, _994005, _994007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994003), _994005)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994003), _994007))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994005), _994007)))], (12087 ^ _777081) ^ [_994122, _994124, _994126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _994124), _994126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994122), _994124)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994122), _994126))))], (12093 ^ _777081) ^ [_994259, _994261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994259), _994261)), _994261))], (12095 ^ _777081) ^ [_994307, _994309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994307), _994309)), _994307))], (12097 ^ _777081) ^ [_994343, _994345, _994347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994343), _994345)), _994347)), 12100 ^ _777081 : [(12101 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994343), _994347)))], (12103 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994345), _994347)))]]], (12105 ^ _777081) ^ [_994494, _994496, _994498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994494), _994496)), _994498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994494), _994498)))], (12111 ^ _777081) ^ [_994605, _994607, _994609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994605), _994607)), _994609)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994607), _994609)))], (12117 ^ _777081) ^ [_994716, _994718, _994720, _994722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994716), _994718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994720), _994722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994716), _994720)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994718), _994722))))], (12127 ^ _777081) ^ [_994907, _994909, _994911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994907), _994909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994907), _994911)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994909), _994911))))], (12133 ^ _777081) ^ [_995030, _995032, _995034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995030), _995032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995030), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995034), _995032))))], (12139 ^ _777081) ^ [_995141, _995143, _995145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995141), _995143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995141), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995143), _995145))))], (12145 ^ _777081) ^ [_995270, _995272, _995274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995270), _995272)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995270), _995274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995272), _995274)))], (12151 ^ _777081) ^ [_995389, _995391, _995393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995391), _995393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995389), _995391)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995389), _995393))))], (12157 ^ _777081) ^ [_995529, _995531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995529), _995531)), -(_995531 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995529), 12160 ^ [_995529, _995531]))], (12164 ^ _777081) ^ [_995636, _995638] : [12165 ^ _777081 : [(12166 ^ _777081) ^ [_995686] : [_995638 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995636), _995686)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995636), _995638)))], (12170 ^ _777081) ^ [_995750, _995752] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995750), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995750), _995752))))], (12172 ^ _777081) ^ [_995786, _995788] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995786), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995788), _995786))))], (12174 ^ _777081) ^ [_995822, _995824, _995826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995822), _995824)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995822), _995826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _995826), _995824)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _995826), _995822))))], (12184 ^ _777081) ^ [_996009, _996011, _996013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _996009), _996011)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996009), _996013)), _996011)))], (12190 ^ _777081) ^ [_996120, _996122, _996124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996120), _996122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996120), _996124)), 12197 ^ _777081 : [(12198 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996122), _996120)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996124), _996120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996122), _996124)))], (12204 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996122), _996124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996122), _996120)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996124), _996120))))]]], (12210 ^ _777081) ^ [_996473, _996475, _996477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996473), _996475)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996473), _996477)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996475), _996473)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996477), _996473)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996475), _996477))], (12220 ^ _777081) ^ [_996674, _996676, _996678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996674), _996676)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996674), _996678)), 12227 ^ _777081 : [(12228 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996676), _996674) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996678), _996674), -(_996676 = _996678)], (12234 ^ _777081) ^ [] : [_996676 = _996678, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996676), _996674) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996678), _996674))]]], (12240 ^ _777081) ^ [_996997, _996999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996997), _996999)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996999), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _996999), _996997)) = _996997)], (12246 ^ _777081) ^ [_997108, _997110, _997112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997108), _997110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997108), _997112)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997110), _997112))))], (12252 ^ _777081) ^ [_997231, _997233, _997235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997231), _997233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997235), _997233)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997235), _997231))))], (12258 ^ _777081) ^ [_997354, _997356] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _997354), _997356)), _997354)))], (12260 ^ _777081) ^ [_997390, _997392, _997394, _997396, _997398] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _997390), _997392), _997394), _997396)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997394), _997398)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln, _997390), _997392), _997398), _997396)))], (12270 ^ _777081) ^ [_997585, _997587, _997589, _997591] : [class_Rings_Olinordered__semidom(_997585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997585), c_Groups_Ozero__class_Ozero(_997585)), _997587)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997585), _997589), _997591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997585), _997589), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_997585), _997587), _997591))))], (12284 ^ _777081) ^ [_997838] : [class_Rings_Olinordered__semidom(_997838), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997838), c_Groups_Oone__class_Oone(_997838)), c_Groups_Ozero__class_Ozero(_997838)))], (12290 ^ _777081) ^ [_997934] : [class_Rings_Olinordered__semidom(_997934), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997934), c_Groups_Ozero__class_Ozero(_997934)), c_Groups_Oone__class_Oone(_997934))))], (12296 ^ _777081) ^ [_998029, _998031] : [class_Rings_Olinordered__idom(_998029), 12299 ^ _777081 : [(12300 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998029), _998031), hAPP(c_Groups_Ouminus__class_Ouminus(_998029), _998031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998029), _998031), c_Groups_Ozero__class_Ozero(_998029))))], (12306 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998029), _998031), c_Groups_Ozero__class_Ozero(_998029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998029), _998031), hAPP(c_Groups_Ouminus__class_Ouminus(_998029), _998031))))]]], (12312 ^ _777081) ^ [_998297, _998299] : [class_Rings_Olinordered__semidom(_998297), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998297), _998299), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998297), _998299), c_Groups_Oone__class_Oone(_998297)))))], (12318 ^ _777081) ^ [_998427, _998429, _998431, _998433] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998427, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_998427, tc_fun(_998427, tc_HOL_Obool), tc_HOL_Obool), c_member(_998427)), _998429)), hAPP(hAPP(c_COMBC(_998427, tc_fun(_998427, tc_HOL_Obool), tc_HOL_Obool), c_member(_998427)), _998431)), _998433)), -(hBOOL(hAPP(hAPP(c_member(_998427), _998433), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998427, tc_HOL_Obool)), _998429), _998431))))], (12324 ^ _777081) ^ [_998626, _998628, _998630, _998632] : [hBOOL(hAPP(hAPP(c_member(_998626), _998632), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998626, tc_HOL_Obool)), _998628), _998630))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_998626, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_998626, tc_fun(_998626, tc_HOL_Obool), tc_HOL_Obool), c_member(_998626)), _998628)), hAPP(hAPP(c_COMBC(_998626, tc_fun(_998626, tc_HOL_Obool), tc_HOL_Obool), c_member(_998626)), _998630)), _998632)))], (12330 ^ _777081) ^ [_998831] : [class_Rings_Olinordered__semidom(_998831), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998831), c_Groups_Ozero__class_Ozero(_998831)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998831), c_Groups_Oone__class_Oone(_998831)), c_Groups_Oone__class_Oone(_998831)))))], (12336 ^ _777081) ^ [_998946, _998948, _998950, _998952, _998954] : [class_Groups_Oordered__cancel__ab__semigroup__add(_998946), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998946), _998948), _998950)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998946), _998952), _998954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998946), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998946), _998948), _998952)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_998946), _998950), _998954))))], (12350 ^ _777081) ^ [_999217, _999219, _999221, _999223, _999225] : [class_Groups_Oordered__cancel__ab__semigroup__add(_999217), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999217), _999219), _999221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999217), _999223), _999225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999217), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999217), _999219), _999223)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999217), _999221), _999225))))], (12364 ^ _777081) ^ [_999488, _999490, _999492] : [-(hAPP(hAPP(c_Set_Oinsert(_999488), _999490), _999492) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_999488, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_999488), _999490), c_Orderings_Obot__class_Obot(tc_fun(_999488, tc_HOL_Obool)))), _999492))], (12366 ^ _777081) ^ [_999547, _999549, _999551] : [class_Groups_Oordered__comm__monoid__add(_999547), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999547), _999549), c_Groups_Ozero__class_Ozero(_999547))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999547), _999551), c_Groups_Ozero__class_Ozero(_999547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999547), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999547), _999549), _999551)), c_Groups_Ozero__class_Ozero(_999547))))], (12380 ^ _777081) ^ [_999802, _999804, _999806] : [class_Groups_Oordered__comm__monoid__add(_999802), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999802), c_Groups_Ozero__class_Ozero(_999802)), _999804)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999802), c_Groups_Ozero__class_Ozero(_999802)), _999806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999802), c_Groups_Ozero__class_Ozero(_999802)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_999802), _999804), _999806))))], (12394 ^ _777081) ^ [_1000057, _1000059] : [class_Groups_Olinordered__ab__group__add(_1000057), 12397 ^ _777081 : [(12398 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000057), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000057), _1000059), _1000059)), c_Groups_Ozero__class_Ozero(_1000057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000057), _1000059), c_Groups_Ozero__class_Ozero(_1000057))))], (12404 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000057), _1000059), c_Groups_Ozero__class_Ozero(_1000057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000057), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000057), _1000059), _1000059)), c_Groups_Ozero__class_Ozero(_1000057))))]]], (12410 ^ _777081) ^ [_1000340, _1000342] : [class_Groups_Olinordered__ab__group__add(_1000340), 12413 ^ _777081 : [(12414 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000340), c_Groups_Ozero__class_Ozero(_1000340)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000340), _1000342), _1000342))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000340), c_Groups_Ozero__class_Ozero(_1000340)), _1000342)))], (12420 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000340), c_Groups_Ozero__class_Ozero(_1000340)), _1000342)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000340), c_Groups_Ozero__class_Ozero(_1000340)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000340), _1000342), _1000342))))]]], (12426 ^ _777081) ^ [_1000623, _1000625] : [class_Rings_Olinordered__idom(_1000623), 12429 ^ _777081 : [(12430 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000623), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000623), _1000625), _1000625)), c_Groups_Ozero__class_Ozero(_1000623))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000623), _1000625), c_Groups_Ozero__class_Ozero(_1000623))))], (12436 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000623), _1000625), c_Groups_Ozero__class_Ozero(_1000623))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000623), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000623), _1000625), _1000625)), c_Groups_Ozero__class_Ozero(_1000623))))]]], (12442 ^ _777081) ^ [_1000906, _1000908, _1000910] : [class_Groups_Oordered__ab__group__add(_1000906), 12445 ^ _777081 : [(12446 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000906), _1000908), _1000910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000906), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1000906), _1000908), _1000910)), c_Groups_Ozero__class_Ozero(_1000906))))], (12452 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000906), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1000906), _1000908), _1000910)), c_Groups_Ozero__class_Ozero(_1000906))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000906), _1000908), _1000910)))]]], (12458 ^ _777081) ^ [_1001189, _1001191] : [class_Groups_Oordered__ab__group__add(_1001189), 12461 ^ _777081 : [(12462 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001189), c_Groups_Ozero__class_Ozero(_1001189)), hAPP(c_Groups_Ouminus__class_Ouminus(_1001189), _1001191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001189), _1001191), c_Groups_Ozero__class_Ozero(_1001189))))], (12468 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001189), _1001191), c_Groups_Ozero__class_Ozero(_1001189))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001189), c_Groups_Ozero__class_Ozero(_1001189)), hAPP(c_Groups_Ouminus__class_Ouminus(_1001189), _1001191))))]]], (12474 ^ _777081) ^ [_1001463, _1001465] : [class_Groups_Oordered__ab__group__add(_1001463), 12477 ^ _777081 : [(12478 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001463), hAPP(c_Groups_Ouminus__class_Ouminus(_1001463), _1001465)), c_Groups_Ozero__class_Ozero(_1001463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001463), c_Groups_Ozero__class_Ozero(_1001463)), _1001465)))], (12484 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001463), c_Groups_Ozero__class_Ozero(_1001463)), _1001465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001463), hAPP(c_Groups_Ouminus__class_Ouminus(_1001463), _1001465)), c_Groups_Ozero__class_Ozero(_1001463))))]]], (12490 ^ _777081) ^ [_1001737, _1001739] : [class_Groups_Olinordered__ab__group__add(_1001737), 12493 ^ _777081 : [(12494 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001737), hAPP(c_Groups_Ouminus__class_Ouminus(_1001737), _1001739)), _1001739)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001737), c_Groups_Ozero__class_Ozero(_1001737)), _1001739)))], (12500 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001737), c_Groups_Ozero__class_Ozero(_1001737)), _1001739)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001737), hAPP(c_Groups_Ouminus__class_Ouminus(_1001737), _1001739)), _1001739)))]]], (12506 ^ _777081) ^ [_1002026, _1002028, _1002030, _1002032] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1002026, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002026, tc_HOL_Obool)), _1002028), _1002030)), _1002032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1002026, tc_HOL_Obool)), _1002028), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002026, tc_HOL_Obool)), _1002030), _1002032))))], (12512 ^ _777081) ^ [_1002187, _1002189, _1002191, _1002193] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1002187, tc_HOL_Obool)), _1002189), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002187, tc_HOL_Obool)), _1002191), _1002193))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1002187, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002187, tc_HOL_Obool)), _1002189), _1002191)), _1002193)))], (12518 ^ _777081) ^ [_1002354, _1002356, _1002358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1002354, tc_HOL_Obool)), _1002356), _1002358)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002354, tc_HOL_Obool)), _1002356), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1002354, tc_HOL_Obool)), _1002358), _1002356)) = _1002358)], (12524 ^ _777081) ^ [_1002512, _1002514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002512), hAPP(c_Nat_OSuc, _1002514))), -(_1002512 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 12532 ^ _777081 : [(12533 ^ _777081) ^ [] : [-(_1002512 = hAPP(c_Nat_OSuc, 12531 ^ [_1002512, _1002514]))], (12535 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 12531 ^ [_1002512, _1002514]), _1002514)))]]], (12537 ^ _777081) ^ [_1002692, _1002694] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002692), hAPP(c_Nat_OSuc, _1002694)))), 12538 ^ _777081 : [(12539 ^ _777081) ^ [] : [_1002692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12541 ^ _777081) ^ [_1002780] : [_1002692 = hAPP(c_Nat_OSuc, _1002780), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002780), _1002694))]]], (12549 ^ _777081) ^ [_1002926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002926), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1002926 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12555 ^ _777081) ^ [_1003007] : [_1003007 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003007), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (12561 ^ _777081) ^ [_1003106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1003106)), -(_1003106 = hAPP(c_Nat_OSuc, 12564 ^ [_1003106]))], (12568 ^ _777081) ^ [_1003197] : [12569 ^ _777081 : [(12570 ^ _777081) ^ [_1003239] : [_1003197 = hAPP(c_Nat_OSuc, _1003239)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1003197)))], (12584 ^ _777081) ^ [_1003422, _1003424] : [12585 ^ _777081 : [(12586 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1003422))], (12588 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1003424))]], -(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), _1003422), _1003424))))], (12574 ^ _777081) ^ [_1003312, _1003314] : [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), _1003312), _1003314))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1003312))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1003314)))], (12592 ^ _777081) ^ [_1003578, _1003580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003578), _1003580)), -(_1003580 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003578), 12595 ^ [_1003578, _1003580])))], (12599 ^ _777081) ^ [_1003691, _1003693] : [12600 ^ _777081 : [(12601 ^ _777081) ^ [_1003744] : [_1003693 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003691), _1003744))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003691), _1003693)))], (12605 ^ _777081) ^ [_1003811, _1003813] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003811), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003813), _1003811)))))], (12607 ^ _777081) ^ [_1003850, _1003852] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003850), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003850), _1003852)))))], (12609 ^ _777081) ^ [_1003889, _1003891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1003889)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1003891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003891), _1003889)), _1003891)))], (12619 ^ _777081) ^ [_1004063, _1004065] : [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), _1004063), _1004065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004065), _1004063)))], (12625 ^ _777081) ^ [_1004162, _1004164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004164), _1004162)), -(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), _1004162), _1004164))))], (12631 ^ _777081) ^ [_1004267, _1004269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004267), _1004269)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004267), _1004269) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12637 ^ _777081) ^ [_1004381, _1004383] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004381), _1004383) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004381), _1004383)))], (12643 ^ _777081) ^ [_1004476, _1004478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004476), _1004478)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004476), _1004478) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12649 ^ _777081) ^ [_1004577, _1004579] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004577), _1004579)), hAPP(c_Nat_OSuc, _1004577))))], (12651 ^ _777081) ^ [_1004616, _1004618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1004616), _1004618)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1004618)), _1004616) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004618), _1004616)))], (12657 ^ _777081) ^ [_1004735, _1004737] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004735), _1004737))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1004737), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004735), _1004737)) = _1004735)], (12663 ^ _777081) ^ [_1004806, _1004808, _1004810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004806), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004808), _1004810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1004806), _1004810)), _1004808)))], (12669 ^ _777081) ^ [_1004925, _1004927, _1004929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1004925), _1004929)), _1004927)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004925), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004927), _1004929))))], (12675 ^ _777081) ^ [_1005050, _1005052, _1005054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005050), _1005052)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005052), _1005054)), _1005050) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005052), _1005050)), _1005054))], (12681 ^ _777081) ^ [_1005187, _1005189, _1005191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005187), _1005189)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005189), _1005187)), _1005191) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005189), _1005191)), _1005187))], (12687 ^ _777081) ^ [_1005324, _1005326, _1005328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005324), _1005326)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005328), _1005326)), _1005324) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005328), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005326), _1005324)))], (12693 ^ _777081) ^ [_1005461, _1005463, _1005465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005461), _1005463)), 12696 ^ _777081 : [(12697 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005463), _1005461) = _1005465, -(_1005463 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005465), _1005461))], (12703 ^ _777081) ^ [] : [_1005463 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005465), _1005461), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005463), _1005461) = _1005465)]]], (12709 ^ _777081) ^ [_1005720, _1005722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005720), _1005722)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005722), _1005720)), _1005720) = _1005722)], (12715 ^ _777081) ^ [_1005831, _1005833, _1005835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005831), _1005833)), 12718 ^ _777081 : [(12719 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005835), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005833), _1005831))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005835), _1005831)), _1005833)))], (12725 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1005835), _1005831)), _1005833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005835), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1005833), _1005831))))]]], (12731 ^ _777081) ^ [_1006120, _1006122, _1006124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1006120), _1006122)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1006124), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1006122), _1006120)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1006124), _1006122)), _1006120))], (12737 ^ _777081) ^ [_1006257, _1006259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1006257), _1006259)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1006257), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1006259), _1006257)) = _1006259)], (12743 ^ _777081) ^ [_1006368, _1006370, _1006372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1006368), _1006370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1006372), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1006370), _1006372)), _1006368))))], (12749 ^ _777081) ^ [_1006509, _1006511, _1006513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1006509), _1006511)), _1006513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1006509), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1006513), _1006511))))], (12755 ^ _777081) ^ [_1006628, _1006630, _1006632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1006628), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1006632), _1006630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1006628), _1006630)), _1006632)))], (12761 ^ _777081) ^ [_1006753, _1006755, _1006757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1006753), _1006755)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1006757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1006755), _1006753)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1006757), _1006753)), _1006755))], (12767 ^ _777081) ^ [_1006890, _1006892, _1006894] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006890, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1006890, tc_HOL_Obool)), _1006892), _1006894)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006890, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1006890, tc_HOL_Obool)), _1006892)), _1006894))], (12769 ^ _777081) ^ [_1006955, _1006957, _1006959, _1006961] : [-(c_Map_Odom(_1006955, _1006957, c_Map_Omap__add(_1006955, _1006957, _1006959, _1006961)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006955, tc_HOL_Obool)), c_Map_Odom(_1006955, _1006957, _1006961)), c_Map_Odom(_1006955, _1006957, _1006959)))], (12771 ^ _777081) ^ [_1007012, _1007014, _1007016] : [class_Groups_Oordered__comm__monoid__add(_1007012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007012), _1007014), c_Groups_Ozero__class_Ozero(_1007012))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007012), _1007016), c_Groups_Ozero__class_Ozero(_1007012))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007012), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007012), _1007014), _1007016)), c_Groups_Ozero__class_Ozero(_1007012))))], (12785 ^ _777081) ^ [_1007267, _1007269, _1007271] : [class_Groups_Oordered__comm__monoid__add(_1007267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007267), _1007269), c_Groups_Ozero__class_Ozero(_1007267))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007267), _1007271), c_Groups_Ozero__class_Ozero(_1007267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007267), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007267), _1007269), _1007271)), c_Groups_Ozero__class_Ozero(_1007267))))], (12799 ^ _777081) ^ [_1007522, _1007524, _1007526, _1007528] : [class_Groups_Oordered__comm__monoid__add(_1007522), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007522), c_Groups_Ozero__class_Ozero(_1007522)), _1007524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007522), _1007526), _1007528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007522), _1007526), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007522), _1007524), _1007528))))], (12813 ^ _777081) ^ [_1007775, _1007777, _1007779, _1007781] : [class_Groups_Oordered__comm__monoid__add(_1007775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007775), c_Groups_Ozero__class_Ozero(_1007775)), _1007777)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007775), _1007779), _1007781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007775), _1007779), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1007775), _1007777), _1007781))))], (12827 ^ _777081) ^ [_1008028, _1008030, _1008032] : [class_Groups_Oordered__comm__monoid__add(_1008028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008028), c_Groups_Ozero__class_Ozero(_1008028)), _1008030)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008028), c_Groups_Ozero__class_Ozero(_1008028)), _1008032)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008028), c_Groups_Ozero__class_Ozero(_1008028)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008028), _1008030), _1008032))))], (12841 ^ _777081) ^ [_1008283, _1008285, _1008287] : [class_Groups_Oordered__comm__monoid__add(_1008283), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008283), c_Groups_Ozero__class_Ozero(_1008283)), _1008285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008283), c_Groups_Ozero__class_Ozero(_1008283)), _1008287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008283), c_Groups_Ozero__class_Ozero(_1008283)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1008283), _1008285), _1008287))))], (12855 ^ _777081) ^ [_1008538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1008538)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1008538), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1008538)], (12861 ^ _777081) ^ [_1008635, _1008637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1008635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1008635), hAPP(c_Nat_OSuc, _1008637))), _1008635)))], (12883 ^ _777081) ^ [_1009054, _1009056, _1009058] : [-(hBOOL(hAPP(_1009054, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1009056), _1009058)))), 12886 ^ _777081 : [(12887 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1009056), _1009058)))], (12889 ^ _777081) ^ [] : [hBOOL(hAPP(_1009054, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 12891 ^ _777081 : [(12892 ^ _777081) ^ [] : [-(_1009056 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1009058), 12890 ^ [_1009054, _1009056, _1009058]))], (12894 ^ _777081) ^ [] : [hBOOL(hAPP(_1009054, 12890 ^ [_1009054, _1009056, _1009058]))]]], (12867 ^ _777081) ^ [_1008762, _1008764, _1008766] : [hBOOL(hAPP(_1008762, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1008764), _1008766))), 12870 ^ _777081 : [(12871 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1008764), _1008766)), -(hBOOL(hAPP(_1008762, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (12877 ^ _777081) ^ [_1008953] : [_1008764 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1008766), _1008953), -(hBOOL(hAPP(_1008762, _1008953)))]]], (12914 ^ _777081) ^ [_1009649, _1009651, _1009653] : [-(hBOOL(hAPP(_1009649, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1009651), _1009653)))), 12917 ^ _777081 : [(12918 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1009651), _1009653)))], (12920 ^ _777081) ^ [] : [hBOOL(hAPP(_1009649, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 12922 ^ _777081 : [(12923 ^ _777081) ^ [] : [-(_1009651 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1009653), 12921 ^ [_1009649, _1009651, _1009653]))], (12925 ^ _777081) ^ [] : [hBOOL(hAPP(_1009649, 12921 ^ [_1009649, _1009651, _1009653]))]]], (12898 ^ _777081) ^ [_1009365, _1009367, _1009369] : [hBOOL(hAPP(_1009365, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1009367), _1009369))), 12901 ^ _777081 : [(12902 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1009367), _1009369)), -(hBOOL(hAPP(_1009365, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (12908 ^ _777081) ^ [_1009550] : [_1009367 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1009369), _1009550), -(hBOOL(hAPP(_1009365, _1009550)))]]], (12929 ^ _777081) ^ [_1009934, _1009936, _1009938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1009934), _1009936)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1009938), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1009936), _1009934))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1009938), _1009934)), hAPP(c_Nat_OSuc, _1009936)))], (12935 ^ _777081) ^ [_1010083, _1010085, _1010087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1010083), _1010085)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1010085), _1010083))), _1010087) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1010085)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1010083), _1010087)))], (12941 ^ _777081) ^ [_1010232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1010232)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1010232), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1010232)], (12947 ^ _777081) ^ [_1010329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1010329)), -(_1010329 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1010329), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (12979 ^ _777081) ^ [_1010974, _1010976, _1010978, _1010980] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1010974, tc_HOL_Obool)), _1010976), hAPP(hAPP(c_Set_Oinsert(_1010974), _1010978), _1010980)))), 12982 ^ _777081 : [(12983 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1010974), _1010978), _1010980)))], (12985 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1010974, tc_HOL_Obool)), _1010976), _1010980))]], 12986 ^ _777081 : [(12987 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1010974), _1010978), _1010980))], (12989 ^ _777081) ^ [] : [12990 ^ _777081 : [(12991 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1010974), _1010978), _1010976)))], (12993 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1010974, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010974, tc_HOL_Obool)), _1010976), hAPP(hAPP(c_Set_Oinsert(_1010974), _1010978), c_Orderings_Obot__class_Obot(tc_fun(_1010974, tc_HOL_Obool))))), _1010980))]], 12994 ^ _777081 : [(12995 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1010974), _1010978), _1010976))], (12997 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1010974, tc_HOL_Obool)), _1010976), _1010980))]]]]], (12953 ^ _777081) ^ [_1010447, _1010449, _1010451, _1010453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1010447, tc_HOL_Obool)), _1010449), hAPP(hAPP(c_Set_Oinsert(_1010447), _1010451), _1010453))), 12956 ^ _777081 : [(12957 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1010447), _1010451), _1010453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1010447, tc_HOL_Obool)), _1010449), _1010453)))], (12963 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1010447), _1010451), _1010453))), 12966 ^ _777081 : [(12967 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1010447), _1010451), _1010449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1010447, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1010447, tc_HOL_Obool)), _1010449), hAPP(hAPP(c_Set_Oinsert(_1010447), _1010451), c_Orderings_Obot__class_Obot(tc_fun(_1010447, tc_HOL_Obool))))), _1010453)))], (12973 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1010447), _1010451), _1010449))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1010447, tc_HOL_Obool)), _1010449), _1010453)))]]]]], (13001 ^ _777081) ^ [_1011513, _1011515] : [class_Rings_Olinordered__idom(_1011513), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011513), _1011515), c_Groups_Ozero__class_Ozero(_1011513))), -(c_Groups_Osgn__class_Osgn(_1011513, _1011515) = hAPP(c_Groups_Ouminus__class_Ouminus(_1011513), c_Groups_Oone__class_Oone(_1011513)))], (13011 ^ _777081) ^ [_1011678, _1011680] : [class_Rings_Olinordered__idom(_1011678), 13014 ^ _777081 : [(13015 ^ _777081) ^ [] : [c_Groups_Osgn__class_Osgn(_1011678, _1011680) = hAPP(c_Groups_Ouminus__class_Ouminus(_1011678), c_Groups_Oone__class_Oone(_1011678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011678), _1011680), c_Groups_Ozero__class_Ozero(_1011678))))], (13021 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011678), _1011680), c_Groups_Ozero__class_Ozero(_1011678))), -(c_Groups_Osgn__class_Osgn(_1011678, _1011680) = hAPP(c_Groups_Ouminus__class_Ouminus(_1011678), c_Groups_Oone__class_Oone(_1011678)))]]], (13027 ^ _777081) ^ [_1011940, _1011942] : [class_Groups_Osgn__if(_1011940), 13030 ^ _777081 : [(13031 ^ _777081) ^ [] : [_1011942 = c_Groups_Ozero__class_Ozero(_1011940), -(c_Groups_Osgn__class_Osgn(_1011940, _1011942) = c_Groups_Ozero__class_Ozero(_1011940))], (13037 ^ _777081) ^ [] : [-(_1011942 = c_Groups_Ozero__class_Ozero(_1011940)), 13040 ^ _777081 : [(13041 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011940), c_Groups_Ozero__class_Ozero(_1011940)), _1011942)), -(c_Groups_Osgn__class_Osgn(_1011940, _1011942) = c_Groups_Oone__class_Oone(_1011940))], (13047 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1011940), c_Groups_Ozero__class_Ozero(_1011940)), _1011942))), -(c_Groups_Osgn__class_Osgn(_1011940, _1011942) = hAPP(c_Groups_Ouminus__class_Ouminus(_1011940), c_Groups_Oone__class_Oone(_1011940)))]]]]], (13053 ^ _777081) ^ [_1012337, _1012339] : [class_Rings_Osemiring__1(_1012337), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1012337), _1012339) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1012337, hAPP(hAPP(c_COMBC(_1012337, _1012337, _1012337), c_Groups_Oplus__class_Oplus(_1012337)), c_Groups_Oone__class_Oone(_1012337)), _1012339, c_Groups_Ozero__class_Ozero(_1012337)))], (13059 ^ _777081) ^ [_1012464, _1012466, _1012468, _1012470, _1012472, _1012474] : [class_Rings_Olinordered__semiring__1__strict(_1012464), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012464), _1012466), _1012468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012464), _1012470), _1012468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012464), c_Groups_Ozero__class_Ozero(_1012464)), _1012472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012464), c_Groups_Ozero__class_Ozero(_1012464)), _1012474)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012464), _1012472), _1012474) = c_Groups_Oone__class_Oone(_1012464), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012464), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1012464), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012464), _1012472), _1012466)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012464), _1012474), _1012470))), _1012468)))], (13085 ^ _777081) ^ [_1012993, _1012995] : [class_Rings_Olinordered__idom(_1012993), 13088 ^ _777081 : [(13089 ^ _777081) ^ [] : [c_Groups_Osgn__class_Osgn(_1012993, _1012995) = c_Groups_Oone__class_Oone(_1012993), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012993), c_Groups_Ozero__class_Ozero(_1012993)), _1012995)))], (13095 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1012993), c_Groups_Ozero__class_Ozero(_1012993)), _1012995)), -(c_Groups_Osgn__class_Osgn(_1012993, _1012995) = c_Groups_Oone__class_Oone(_1012993))]]], (13101 ^ _777081) ^ [_1013240, _1013242] : [class_Rings_Olinordered__idom(_1013240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1013240), c_Groups_Ozero__class_Ozero(_1013240)), _1013242)), -(c_Groups_Osgn__class_Osgn(_1013240, _1013242) = c_Groups_Oone__class_Oone(_1013240))], (13111 ^ _777081) ^ [_1013419, _1013421, _1013423, _1013425, _1013427] : [c_Fun_Oinj__on(_1013419, _1013421, _1013423, hAPP(hAPP(c_Set_Oinsert(_1013419), _1013425), _1013427)), 13114 ^ _777081 : [(13115 ^ _777081) ^ [] : [-(c_Fun_Oinj__on(_1013419, _1013421, _1013423, _1013427))], (13117 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1013421), hAPP(_1013423, _1013425)), hAPP(c_Set_Oimage(_1013419, _1013421, _1013423), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013419, tc_HOL_Obool)), _1013427), hAPP(hAPP(c_Set_Oinsert(_1013419), _1013425), c_Orderings_Obot__class_Obot(tc_fun(_1013419, tc_HOL_Obool)))))))]]], (13119 ^ _777081) ^ [_1013638, _1013640, _1013642, _1013644, _1013646] : [-(c_Fun_Oinj__on(_1013638, _1013640, _1013642, hAPP(hAPP(c_Set_Oinsert(_1013638), _1013644), _1013646))), c_Fun_Oinj__on(_1013638, _1013640, _1013642, _1013646), -(hBOOL(hAPP(hAPP(c_member(_1013640), hAPP(_1013642, _1013644)), hAPP(c_Set_Oimage(_1013638, _1013640, _1013642), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013638, tc_HOL_Obool)), _1013646), hAPP(hAPP(c_Set_Oinsert(_1013638), _1013644), c_Orderings_Obot__class_Obot(tc_fun(_1013638, tc_HOL_Obool))))))))], (13129 ^ _777081) ^ [_1013899, _1013901] : [_1013899 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013899), _1013901) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13135 ^ _777081) ^ [_1013982, _1013984] : [-(_1013982 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1013982), _1013984) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1013984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1013982), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1013984)))], (13141 ^ _777081) ^ [_1014044, _1014046] : [-(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, _1014044)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1014046))))], (13143 ^ _777081) ^ [_1014086, _1014088, _1014090] : [-(c_Fun_Oinj__on(_1014086, _1014088, _1014090, c_Orderings_Obot__class_Obot(tc_fun(_1014086, tc_HOL_Obool))))], (13145 ^ _777081) ^ [_1014120, _1014122] : [class_Groups_Oordered__ab__group__add(_1014120), -(c_Fun_Oinj__on(_1014120, _1014120, c_Groups_Ouminus__class_Ouminus(_1014120), _1014122))], (13151 ^ _777081) ^ [_1014203] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014203), _1014203)))], (13153 ^ _777081) ^ [_1014231] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014231), _1014231))))], (13155 ^ _777081) ^ [_1014265] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1014265), _1014265)))))], (13157 ^ _777081) ^ [_1014301, _1014303] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014301), _1014303))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014303), _1014301)))], (13163 ^ _777081) ^ [_1014362, _1014364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1014362), _1014364)), 13166 ^ _777081 : [(13167 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014362), _1014364)))], (13169 ^ _777081) ^ [] : [_1014362 = _1014364]]], (13171 ^ _777081) ^ [_1014489, _1014491] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1014489), _1014491))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014489), _1014491)), -(_1014489 = _1014491)], (13191 ^ _777081) ^ [_1014764, _1014766] : [13192 ^ _777081 : [(13193 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1014764), _1014766))], (13195 ^ _777081) ^ [] : [_1014764 = _1014766]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014764), _1014766)))], (13181 ^ _777081) ^ [_1014658, _1014660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014658), _1014660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1014658), _1014660))), -(_1014658 = _1014660)], (13199 ^ _777081) ^ [_1014901, _1014903] : [_1014901 = _1014903, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014901), _1014903)))], (13205 ^ _777081) ^ [_1014988, _1014990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1014988), _1014990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1014988), _1014990)))], (13211 ^ _777081) ^ [_1015085, _1015087, _1015089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015085), _1015087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015085), _1015089)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015087), _1015089))))], (13217 ^ _777081) ^ [_1015208, _1015210, _1015212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015208), _1015210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015212), _1015208)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015212), _1015210))))], (13223 ^ _777081) ^ [_1015331, _1015333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015331), _1015333)), -(_1015331 = _1015333), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015331), _1015333)))], (13233 ^ _777081) ^ [_1015443, _1015445, _1015447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015443), _1015445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015445), _1015447)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015443), _1015447)))], (13243 ^ _777081) ^ [_1015606, _1015608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015606), _1015608)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015608), _1015606)), -(_1015606 = _1015608)], (13253 ^ _777081) ^ [_1015755, _1015757, _1015759, _1015761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015755), _1015757)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015759), _1015761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015755), _1015759)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1015757), _1015761))))], (13263 ^ _777081) ^ [_1015946, _1015948] : [13264 ^ _777081 : [(13265 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1015946), _1015948))], (13267 ^ _777081) ^ [] : [_1015946 = _1015948]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1015946), _1015948)))], (13271 ^ _777081) ^ [_1016096, _1016098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016096)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016096), _1016098)))], (13277 ^ _777081) ^ [_1016201, _1016203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1016201), _1016203)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016201)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016203))))], (13283 ^ _777081) ^ [_1016312, _1016314, _1016316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1016312), _1016314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1016316)), -(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), _1016316)), _1016312)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016316)), _1016314))))], (13293 ^ _777081) ^ [_1016520, _1016522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016520)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016522))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1016520), _1016522)))], (13299 ^ _777081) ^ [_1016625, _1016627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1016625), _1016627)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016625)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1016627))))], (13305 ^ _777081) ^ [_1016736, _1016738, _1016740] : [13306 ^ _777081 : [(13307 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1016736), _1016738)))], (13309 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1016740, _1016738), _1016736))]], 13312 ^ _777081 : [(13313 ^ _777081) ^ [] : [-(_1016736 = _1016738)], (13315 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1016740, _1016738), _1016736))]], 13318 ^ _777081 : [(13319 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1016738), _1016736)))], (13321 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1016740, _1016738), _1016736))]], -(hBOOL(hAPP(hAPP(_1016740, _1016738), _1016736)))], (13325 ^ _777081) ^ [_1017082, _1017084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017082), _1017084)), _1017082 = _1017084], (13331 ^ _777081) ^ [_1017170, _1017172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017170), _1017172)), _1017172 = _1017170], (13337 ^ _777081) ^ [_1017267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017267), _1017267))], (13339 ^ _777081) ^ [_1017291, _1017293] : [-(_1017291 = _1017293), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017291), _1017293))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017293), _1017291)))], (13359 ^ _777081) ^ [_1017402, _1017404] : [13360 ^ _777081 : [(13361 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017402), _1017404))], (13363 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017404), _1017402))]], _1017402 = _1017404], (13349 ^ _777081) ^ [_1017353, _1017355] : [-(_1017353 = _1017355), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017353), _1017355))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017355), _1017353)))], (13367 ^ _777081) ^ [_1017549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017549), _1017549))], (13369 ^ _777081) ^ [_1017577, _1017579] : [class_Rings_Olinordered__idom(_1017577), -(c_Groups_Osgn__class_Osgn(_1017577, c_Groups_Osgn__class_Osgn(_1017577, _1017579)) = c_Groups_Osgn__class_Osgn(_1017577, _1017579))], (13375 ^ _777081) ^ [_1017670, _1017672, _1017674] : [class_Rings_Olinordered__idom(_1017670), -(c_Groups_Osgn__class_Osgn(_1017670, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017670), _1017672), _1017674)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017670), c_Groups_Osgn__class_Osgn(_1017670, _1017672)), c_Groups_Osgn__class_Osgn(_1017670, _1017674)))], (13381 ^ _777081) ^ [_1017797, _1017799, _1017801, _1017803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1017797, tc_HOL_Obool)), _1017799), _1017801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1017797, tc_HOL_Obool)), _1017801), _1017803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1017797, tc_HOL_Obool)), _1017799), _1017803)))], (13391 ^ _777081) ^ [_1017994, _1017996] : [-(c_Fun_Oinj__on(_1017994, _1017994, c_COMBI(_1017994), _1017996))], (13393 ^ _777081) ^ [_1018023, _1018025, _1018027, _1018029] : [class_Groups_Oab__semigroup__mult(_1018023), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018023), _1018025), _1018027)), _1018029) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018023), _1018025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018023), _1018027), _1018029)))], (13417 ^ _777081) ^ [_1018572, _1018574, _1018576, _1018578] : [13419 ^ _777081 : [(13420 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1018572), 13418 ^ [_1018572, _1018574, _1018576, _1018578]), _1018578)))], (13423 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1018572), 13421 ^ [_1018572, _1018574, _1018576, _1018578]), _1018578)))], (13425 ^ _777081) ^ [] : [-(hAPP(_1018576, 13418 ^ [_1018572, _1018574, _1018576, _1018578]) = hAPP(_1018576, 13421 ^ [_1018572, _1018574, _1018576, _1018578]))], (13427 ^ _777081) ^ [] : [13418 ^ [_1018572, _1018574, _1018576, _1018578] = 13421 ^ [_1018572, _1018574, _1018576, _1018578]]], -(c_Fun_Oinj__on(_1018572, _1018574, _1018576, _1018578))], (13399 ^ _777081) ^ [_1018187, _1018189, _1018191, _1018193] : [c_Fun_Oinj__on(_1018187, _1018189, _1018191, _1018193), 13402 ^ _777081 : [(13403 ^ _777081) ^ [_1018295] : [hBOOL(hAPP(hAPP(c_member(_1018187), _1018295), _1018193)), 13406 ^ _777081 : [(13407 ^ _777081) ^ [_1018397] : [hBOOL(hAPP(hAPP(c_member(_1018187), _1018397), _1018193)), hAPP(_1018191, _1018295) = hAPP(_1018191, _1018397), -(_1018295 = _1018397)]]]]], (13431 ^ _777081) ^ [_1018964, _1018966, _1018968] : [class_Rings_Osemiring__1(_1018964), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1018964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1018966), _1018968)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018964), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1018964), _1018966)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1018964), _1018968)))], (13437 ^ _777081) ^ [_1019099, _1019101] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1019099), _1019101) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1019101), _1019099))], (13439 ^ _777081) ^ [_1019136, _1019138, _1019140] : [class_Nat_Osemiring__char__0(_1019136), 13442 ^ _777081 : [(13443 ^ _777081) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1019136), _1019138) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1019136), _1019140), -(_1019138 = _1019140)], (13449 ^ _777081) ^ [] : [_1019138 = _1019140, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1019136), _1019138) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1019136), _1019140))]]], (13455 ^ _777081) ^ [_1019377, _1019379, _1019381] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1019377), _1019379)), _1019381) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1019377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1019379), _1019381)))], (13457 ^ _777081) ^ [_1019428, _1019430] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1019428), _1019430)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019428)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019430)))], (13459 ^ _777081) ^ [_1019474, _1019476, _1019478] : [class_Rings_Ocomm__semiring__1(_1019474), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019474), _1019476), _1019478) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019474), _1019478), _1019476))], (13465 ^ _777081) ^ [_1019583, _1019585, _1019587, _1019589] : [class_Rings_Ocomm__semiring__1(_1019583), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019583), _1019585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019583), _1019587), _1019589)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019583), _1019587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019583), _1019585), _1019589)))], (13471 ^ _777081) ^ [_1019726, _1019728, _1019730, _1019732] : [class_Rings_Ocomm__semiring__1(_1019726), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019726), _1019728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019726), _1019730), _1019732)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019726), _1019728), _1019730)), _1019732))], (13477 ^ _777081) ^ [_1019869, _1019871] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019869)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1019871)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1019869), _1019871)))], (13479 ^ _777081) ^ [_1019915, _1019917, _1019919, _1019921] : [class_Rings_Ocomm__semiring__1(_1019915), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019915), _1019917), _1019919)), _1019921) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019915), _1019917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019915), _1019919), _1019921)))], (13485 ^ _777081) ^ [_1020058, _1020060, _1020062, _1020064] : [class_Rings_Ocomm__semiring__1(_1020058), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020058), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020058), _1020060), _1020062)), _1020064) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020058), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020058), _1020060), _1020064)), _1020062))], (13491 ^ _777081) ^ [_1020201, _1020203, _1020205, _1020207, _1020209] : [class_Rings_Ocomm__semiring__1(_1020201), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020201), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020201), _1020203), _1020205)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020201), _1020207), _1020209)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020201), _1020203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020201), _1020205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020201), _1020207), _1020209))))], (13497 ^ _777081) ^ [_1020378, _1020380, _1020382, _1020384, _1020386] : [class_Rings_Ocomm__semiring__1(_1020378), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020378), _1020380), _1020382)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020378), _1020384), _1020386)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020378), _1020384), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020378), _1020380), _1020382)), _1020386)))], (13503 ^ _777081) ^ [_1020555, _1020557, _1020559, _1020561, _1020563] : [class_Rings_Ocomm__semiring__1(_1020555), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020555), _1020557), _1020559)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020555), _1020561), _1020563)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020555), _1020557), _1020561)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020555), _1020559), _1020563)))], (13509 ^ _777081) ^ [_1020732, _1020734] : [class_Lattices_Oab__semigroup__idem__mult(_1020732), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020732), _1020734), _1020734) = _1020734)], (13515 ^ _777081) ^ [_1020823, _1020825] : [class_Lattices_Oab__semigroup__idem__mult(_1020823), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020823), _1020825), _1020825) = _1020825)], (13521 ^ _777081) ^ [_1020914, _1020916, _1020918] : [class_Lattices_Oab__semigroup__idem__mult(_1020914), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020914), _1020916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020914), _1020916), _1020918)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020914), _1020916), _1020918))], (13527 ^ _777081) ^ [_1021039, _1021041, _1021043, _1021045, _1021047, _1021049] : [c_Fun_Oinj__on(_1021039, _1021041, _1021043, _1021045), -(_1021047 = _1021049), hBOOL(hAPP(hAPP(c_member(_1021039), _1021047), _1021045)), hBOOL(hAPP(hAPP(c_member(_1021039), _1021049), _1021045)), hAPP(_1021043, _1021047) = hAPP(_1021043, _1021049)], (13545 ^ _777081) ^ [_1021352, _1021354, _1021356, _1021358, _1021360, _1021362] : [c_Fun_Oinj__on(_1021352, _1021354, _1021356, _1021358), hBOOL(hAPP(hAPP(c_member(_1021352), _1021360), _1021358)), hBOOL(hAPP(hAPP(c_member(_1021352), _1021362), _1021358)), 13556 ^ _777081 : [(13557 ^ _777081) ^ [] : [hAPP(_1021356, _1021360) = hAPP(_1021356, _1021362), -(_1021360 = _1021362)], (13563 ^ _777081) ^ [] : [_1021360 = _1021362, -(hAPP(_1021356, _1021360) = hAPP(_1021356, _1021362))]]], (13569 ^ _777081) ^ [_1021753, _1021755, _1021757, _1021759, _1021761, _1021763] : [c_Fun_Oinj__on(_1021753, _1021755, _1021757, _1021759), hAPP(_1021757, _1021761) = hAPP(_1021757, _1021763), hBOOL(hAPP(hAPP(c_member(_1021753), _1021761), _1021759)), hBOOL(hAPP(hAPP(c_member(_1021753), _1021763), _1021759)), -(_1021761 = _1021763)], (13587 ^ _777081) ^ [_1022062] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1022062))], (13589 ^ _777081) ^ [_1022087, _1022089, _1022091, _1022093, _1022095] : [c_Fun_Oinj__on(_1022087, _1022089, _1022091, _1022093), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022087, tc_HOL_Obool)), _1022095), _1022093)), -(c_Fun_Oinj__on(_1022087, _1022089, _1022091, _1022095))], (13599 ^ _777081) ^ [_1022256, _1022258, _1022260, _1022262, _1022264] : [c_Fun_Oinj__on(_1022256, _1022258, _1022260, _1022262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1022256, tc_HOL_Obool)), _1022264), _1022262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1022258, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1022256, _1022258, _1022260), _1022264)), hAPP(c_Set_Oimage(_1022256, _1022258, _1022260), _1022262))))], (13609 ^ _777081) ^ [_1022469, _1022471, _1022473, _1022475, _1022477] : [c_Fun_Oinj__on(_1022469, _1022471, _1022473, _1022475), -(c_Fun_Oinj__on(_1022469, _1022471, _1022473, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022469, tc_HOL_Obool)), _1022475), _1022477)))], (13615 ^ _777081) ^ [_1022582, _1022584] : [-(c_Fun_Oinj__on(_1022582, tc_Option_Ooption(_1022582), c_Option_Ooption_OSome(_1022582), _1022584))], (13617 ^ _777081) ^ [_1022628, _1022630] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1022628)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1022630), 13620 ^ _777081 : [(13621 ^ _777081) ^ [] : [-(_1022628 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13623 ^ _777081) ^ [] : [-(_1022630 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (13625 ^ _777081) ^ [_1022745, _1022747] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1022745)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1022747)), _1022745 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1022747 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13635 ^ _777081) ^ [] : [-(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))], (13637 ^ _777081) ^ [_1022924] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1022924) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1022924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13643 ^ _777081) ^ [_1023001] : [_1023001 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1023001) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13649 ^ _777081) ^ [_1023096] : [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), _1023096))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1023096)))], (13655 ^ _777081) ^ [_1023181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1023181)), -(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), _1023181))))], (13661 ^ _777081) ^ [_1023284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1023284)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1023284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13667 ^ _777081) ^ [_1023371] : [_1023371 = 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), _1023371)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13673 ^ _777081) ^ [_1023479, _1023481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1023479)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1023481)))), 13676 ^ _777081 : [(13677 ^ _777081) ^ [] : [-(_1023479 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13679 ^ _777081) ^ [] : [-(_1023481 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (13681 ^ _777081) ^ [_1023606, _1023608] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1023606)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1023608))))), _1023606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1023608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13691 ^ _777081) ^ [_1023780, _1023782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023780), _1023782)), -(_1023782 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023780), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 13694 ^ [_1023780, _1023782]))))], (13698 ^ _777081) ^ [_1023899, _1023901] : [13699 ^ _777081 : [(13700 ^ _777081) ^ [_1023955] : [_1023901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1023899), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1023955)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1023899), _1023901)))], (13704 ^ _777081) ^ [_1024025] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1024025)) = 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), _1024025)))], (13706 ^ _777081) ^ [_1024060] : [-(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, _1024060)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13708 ^ _777081) ^ [_1024106] : [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, _1024106)))))], (13710 ^ _777081) ^ [_1024140, _1024142] : [class_Rings_Ocomm__semiring__1(_1024140), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024140), _1024142), c_Groups_Ozero__class_Ozero(_1024140)) = c_Groups_Ozero__class_Ozero(_1024140))], (13716 ^ _777081) ^ [_1024239, _1024241] : [class_Rings_Ocomm__semiring__1(_1024239), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024239), c_Groups_Ozero__class_Ozero(_1024239)), _1024241) = c_Groups_Ozero__class_Ozero(_1024239))], (13722 ^ _777081) ^ [_1024338, _1024340] : [class_Rings_Omult__zero(_1024338), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024338), c_Groups_Ozero__class_Ozero(_1024338)), _1024340) = c_Groups_Ozero__class_Ozero(_1024338))], (13728 ^ _777081) ^ [_1024437, _1024439] : [class_Rings_Omult__zero(_1024437), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024437), _1024439), c_Groups_Ozero__class_Ozero(_1024437)) = c_Groups_Ozero__class_Ozero(_1024437))], (13734 ^ _777081) ^ [_1024536, _1024538, _1024540] : [class_Rings_Oring__no__zero__divisors(_1024536), 13737 ^ _777081 : [(13748 ^ _777081) ^ [] : [13749 ^ _777081 : [(13750 ^ _777081) ^ [] : [_1024538 = c_Groups_Ozero__class_Ozero(_1024536)], (13752 ^ _777081) ^ [] : [_1024540 = c_Groups_Ozero__class_Ozero(_1024536)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024536), _1024538), _1024540) = c_Groups_Ozero__class_Ozero(_1024536))], (13738 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024536), _1024538), _1024540) = c_Groups_Ozero__class_Ozero(_1024536), -(_1024538 = c_Groups_Ozero__class_Ozero(_1024536)), -(_1024540 = c_Groups_Ozero__class_Ozero(_1024536))]]], (13756 ^ _777081) ^ [_1024834, _1024836, _1024838] : [class_Rings_Ono__zero__divisors(_1024834), -(_1024836 = c_Groups_Ozero__class_Ozero(_1024834)), -(_1024838 = c_Groups_Ozero__class_Ozero(_1024834)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1024834), _1024836), _1024838) = c_Groups_Ozero__class_Ozero(_1024834)], (13770 ^ _777081) ^ [_1025054, _1025056, _1025058] : [class_Rings_Ono__zero__divisors(_1025054), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025054), _1025056), _1025058) = c_Groups_Ozero__class_Ozero(_1025054), -(_1025056 = c_Groups_Ozero__class_Ozero(_1025054)), -(_1025058 = c_Groups_Ozero__class_Ozero(_1025054))], (13784 ^ _777081) ^ [_1025226, _1025228] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1025226)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1025228)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1025226), _1025228)))], (13786 ^ _777081) ^ [_1025272, _1025274, _1025276] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1025272)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1025274)), _1025276)) = 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), _1025272), _1025274))), _1025276))], (13788 ^ _777081) ^ [_1025332, _1025334, _1025336, _1025338, _1025340] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1025332), 13791 ^ _777081 : [(13802 ^ _777081) ^ [] : [13803 ^ _777081 : [(13804 ^ _777081) ^ [] : [_1025334 = _1025338], (13806 ^ _777081) ^ [] : [_1025336 = _1025340]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025332), _1025334), _1025336)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025332), _1025338), _1025340)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025332), _1025334), _1025340)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025332), _1025338), _1025336)))], (13792 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025332), _1025334), _1025336)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025332), _1025338), _1025340)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025332), _1025334), _1025340)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025332), _1025338), _1025336)), -(_1025334 = _1025338), -(_1025336 = _1025340)]]], (13810 ^ _777081) ^ [_1025744, _1025746, _1025748, _1025750] : [class_Rings_Ocomm__semiring__1(_1025744), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025744), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025744), _1025746), _1025748)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025744), _1025750), _1025748)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025744), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025744), _1025746), _1025750)), _1025748))], (13816 ^ _777081) ^ [_1025903, _1025905, _1025907, _1025909] : [class_Rings_Ocomm__semiring__1(_1025903), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025903), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025903), _1025905), _1025907)), _1025909) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1025903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025903), _1025905), _1025909)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025903), _1025907), _1025909)))], (13822 ^ _777081) ^ [_1026062, _1026064, _1026066, _1026068, _1026070] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1026062), 13825 ^ _777081 : [(13836 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026062), _1026064), _1026068)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026062), _1026066), _1026070)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026062), _1026064), _1026070)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026062), _1026066), _1026068))), 13839 ^ _777081 : [(13840 ^ _777081) ^ [] : [_1026064 = _1026066], (13842 ^ _777081) ^ [] : [_1026068 = _1026070]]], (13826 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026062), _1026064), _1026068)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026062), _1026066), _1026070)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026062), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026062), _1026064), _1026070)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026062), _1026066), _1026068)), -(_1026064 = _1026066), -(_1026068 = _1026070)]]], (13844 ^ _777081) ^ [_1026480, _1026482, _1026484, _1026486] : [class_Rings_Ocomm__semiring__1(_1026480), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026480), _1026482), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026480), _1026484), _1026486)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026480), _1026482), _1026484)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026480), _1026482), _1026486)))], (13850 ^ _777081) ^ [_1026639, _1026641, _1026643, _1026645, _1026647] : [class_Rings_Osemiring(_1026639), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026639), _1026641), _1026643)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026639), _1026645), _1026643)), _1026647)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026639), _1026641), _1026645)), _1026643)), _1026647))], (13856 ^ _777081) ^ [_1026832, _1026834, _1026836, _1026838] : [class_Rings_Ocomm__semiring(_1026832), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026832), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026832), _1026834), _1026836)), _1026838) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1026832), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026832), _1026834), _1026838)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026832), _1026836), _1026838)))], (13862 ^ _777081) ^ [_1026991, _1026993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1026991), _1026993)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1026993)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1026991)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1026993), _1026991)))], (13868 ^ _777081) ^ [_1027120, _1027122, _1027124] : [class_Rings_Olinordered__semidom(_1027120), 13871 ^ _777081 : [(13872 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027120), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027120), _1027122)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027120), _1027124))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027122), _1027124)))], (13878 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027122), _1027124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027120), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027120), _1027122)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027120), _1027124))))]]], (13884 ^ _777081) ^ [_1027397, _1027399, _1027401] : [class_Rings_Olinordered__semidom(_1027397), 13887 ^ _777081 : [(13888 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027397), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027397), _1027399)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027397), _1027401))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027399), _1027401)))], (13894 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027399), _1027401)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027397), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027397), _1027399)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027397), _1027401))))]]], (13900 ^ _777081) ^ [_1027674, _1027676, _1027678] : [class_Rings_Olinordered__semidom(_1027674), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027676), _1027678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027674), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027674), _1027676)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027674), _1027678))))], (13910 ^ _777081) ^ [_1027849, _1027851, _1027853] : [class_Rings_Olinordered__semidom(_1027849), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027849), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027849), _1027851)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1027849), _1027853))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027851), _1027853)))], (13920 ^ _777081) ^ [_1028024, _1028026] : [class_Groups_Omonoid__mult(_1028024), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028024), c_Groups_Oone__class_Oone(_1028024)), _1028026) = _1028026)], (13926 ^ _777081) ^ [_1028119, _1028121] : [class_Groups_Ocomm__monoid__mult(_1028119), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028119), c_Groups_Oone__class_Oone(_1028119)), _1028121) = _1028121)], (13932 ^ _777081) ^ [_1028214, _1028216] : [class_Groups_Omonoid__mult(_1028214), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028214), _1028216), c_Groups_Oone__class_Oone(_1028214)) = _1028216)], (13938 ^ _777081) ^ [_1028309, _1028311] : [class_Groups_Ocomm__monoid__mult(_1028309), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028309), _1028311), c_Groups_Oone__class_Oone(_1028309)) = _1028311)], (13944 ^ _777081) ^ [_1028404, _1028406] : [class_Rings_Ocomm__semiring__1(_1028404), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028404), c_Groups_Oone__class_Oone(_1028404)), _1028406) = _1028406)], (13950 ^ _777081) ^ [_1028499, _1028501] : [class_Rings_Ocomm__semiring__1(_1028499), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1028499), _1028501), c_Groups_Oone__class_Oone(_1028499)) = _1028501)], (13956 ^ _777081) ^ [_1028594, _1028596, _1028598] : [-(c_Fun_Oinj__on(_1028594, tc_sum(_1028596, _1028594), c_Sum__Type_OInr(_1028594, _1028596), _1028598))], (13958 ^ _777081) ^ [_1028629] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1028629) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13960 ^ _777081) ^ [_1028655] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028655), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13972 ^ _777081) ^ [_1028797, _1028799] : [13973 ^ _777081 : [(13974 ^ _777081) ^ [] : [_1028797 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13976 ^ _777081) ^ [] : [_1028799 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028797), _1028799) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13962 ^ _777081) ^ [_1028699, _1028701] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028699), _1028701) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1028699 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1028701 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13990 ^ _777081) ^ [_1029056, _1029058, _1029060] : [13991 ^ _777081 : [(13992 ^ _777081) ^ [] : [_1029058 = _1029060], (13994 ^ _777081) ^ [] : [_1029056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029056), _1029058) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029056), _1029060))], (13980 ^ _777081) ^ [_1028944, _1028946, _1028948] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028944), _1028946) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1028944), _1028948), -(_1028946 = _1028948), -(_1028944 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14008 ^ _777081) ^ [_1029329, _1029331, _1029333] : [14009 ^ _777081 : [(14010 ^ _777081) ^ [] : [_1029329 = _1029333], (14012 ^ _777081) ^ [] : [_1029331 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029329), _1029331) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029333), _1029331))], (13998 ^ _777081) ^ [_1029217, _1029219, _1029221] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029217), _1029219) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029221), _1029219), -(_1029217 = _1029221), -(_1029219 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14016 ^ _777081) ^ [_1029472, _1029474, _1029476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029472), _1029474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1029476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029476), _1029472)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029476), _1029474))))], (14026 ^ _777081) ^ [_1029653, _1029655, _1029657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029653), _1029655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1029657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029653), _1029657)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029655), _1029657))))], (14036 ^ _777081) ^ [_1029852, _1029854, _1029856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029852), _1029854)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1029856), _1029854))), 14039 ^ _777081 : [(14040 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1029854)))], (14042 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1029852), _1029856)))]]], (14044 ^ _777081) ^ [_1030001, _1030003, _1030005] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030001), _1030003)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030005), _1030003)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1030003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030001), _1030005))], (14054 ^ _777081) ^ [_1030202, _1030204, _1030206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030202), _1030204)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030202), _1030206))), 14057 ^ _777081 : [(14058 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1030202)))], (14060 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030204), _1030206)))]]], (14062 ^ _777081) ^ [_1030351, _1030353, _1030355] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030351), _1030353)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030351), _1030355)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1030351)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1030353), _1030355))], (14072 ^ _777081) ^ [_1030549, _1030551] : [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), _1030549), _1030551))), 14075 ^ _777081 : [(14076 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1030549)))], (14078 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1030551)))]]], (14080 ^ _777081) ^ [_1030672, _1030674] : [-(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), _1030672), _1030674)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1030672)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1030674))], (14100 ^ _777081) ^ [_1031022, _1031024, _1031026] : [14101 ^ _777081 : [(14102 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1031024)))], (14104 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031022), _1031026))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031022), _1031024)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031026), _1031024))))], (14090 ^ _777081) ^ [_1030845, _1030847, _1030849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030845), _1030847)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1030849), _1030847))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1030847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030845), _1030849)))], (14118 ^ _777081) ^ [_1031379, _1031381, _1031383] : [14119 ^ _777081 : [(14120 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1031379)))], (14122 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031381), _1031383))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031379), _1031381)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031379), _1031383))))], (14108 ^ _777081) ^ [_1031202, _1031204, _1031206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031202), _1031204)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031202), _1031206))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1031202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1031204), _1031206)))], (14126 ^ _777081) ^ [_1031541, _1031543, _1031545] : [class_Rings_Oidom(_1031541), 14129 ^ _777081 : [(14140 ^ _777081) ^ [] : [14141 ^ _777081 : [(14142 ^ _777081) ^ [] : [_1031543 = _1031545], (14144 ^ _777081) ^ [] : [_1031543 = hAPP(c_Groups_Ouminus__class_Ouminus(_1031541), _1031545)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031541), _1031543), _1031543) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031541), _1031545), _1031545))], (14130 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031541), _1031543), _1031543) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031541), _1031545), _1031545), -(_1031543 = _1031545), -(_1031543 = hAPP(c_Groups_Ouminus__class_Ouminus(_1031541), _1031545))]]], (14148 ^ _777081) ^ [_1031860, _1031862, _1031864] : [class_Rings_Oring(_1031860), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031860), hAPP(c_Groups_Ouminus__class_Ouminus(_1031860), _1031862)), hAPP(c_Groups_Ouminus__class_Ouminus(_1031860), _1031864)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031860), _1031862), _1031864))], (14154 ^ _777081) ^ [_1031989, _1031991, _1031993] : [class_Rings_Oring(_1031989), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031989), hAPP(c_Groups_Ouminus__class_Ouminus(_1031989), _1031991)), _1031993) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031989), _1031991), hAPP(c_Groups_Ouminus__class_Ouminus(_1031989), _1031993)))], (14160 ^ _777081) ^ [_1032118, _1032120, _1032122] : [class_Rings_Oring(_1032118), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1032118), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032118), _1032120), _1032122)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032118), hAPP(c_Groups_Ouminus__class_Ouminus(_1032118), _1032120)), _1032122))], (14166 ^ _777081) ^ [_1032247, _1032249, _1032251] : [class_Rings_Oring(_1032247), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1032247), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032247), _1032249), _1032251)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032247), _1032249), hAPP(c_Groups_Ouminus__class_Ouminus(_1032247), _1032251)))], (14172 ^ _777081) ^ [_1032394, _1032396, _1032398] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1032394)), _1032396) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1032394)), _1032398), -(_1032396 = _1032398)], (14178 ^ _777081) ^ [_1032505, _1032507, _1032509] : [_1032507 = _1032509, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1032505)), _1032507) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1032505)), _1032509))], (14184 ^ _777081) ^ [_1032640, _1032642, _1032644] : [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, _1032640)), _1032642)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1032640)), _1032644))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1032642), _1032644)))], (14190 ^ _777081) ^ [_1032771, _1032773, _1032775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1032773), _1032775)), -(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, _1032771)), _1032773)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1032771)), _1032775))))], (14196 ^ _777081) ^ [_1032926, _1032928, _1032930] : [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, _1032926)), _1032928)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1032926)), _1032930))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032928), _1032930)))], (14202 ^ _777081) ^ [_1033057, _1033059, _1033061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1033059), _1033061)), -(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, _1033057)), _1033059)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1033057)), _1033061))))], (14208 ^ _777081) ^ [] : [-(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))], (14210 ^ _777081) ^ [_1033212, _1033214, _1033216] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033212), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1033214), _1033216)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033212), _1033214)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033212), _1033216)))], (14212 ^ _777081) ^ [_1033269, _1033271, _1033273] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1033269), _1033271)), _1033273) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033269), _1033273)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033271), _1033273)))], (14214 ^ _777081) ^ [_1033326, _1033328, _1033330] : [-(c_Fun_Oinj__on(_1033326, tc_sum(_1033326, _1033328), c_Sum__Type_OInl(_1033326, _1033328), _1033330))], (14216 ^ _777081) ^ [_1033361, _1033363, _1033365] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033361), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033363), _1033365)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033361), _1033363)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033361), _1033365)))], (14218 ^ _777081) ^ [_1033418, _1033420, _1033422] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1033418), _1033420)), _1033422) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033418), _1033422)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033420), _1033422)))], (14220 ^ _777081) ^ [_1033475] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1033475) = _1033475)], (14222 ^ _777081) ^ [_1033516, _1033518] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033516), _1033518), 14225 ^ _777081 : [(14226 ^ _777081) ^ [] : [-(_1033516 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (14228 ^ _777081) ^ [] : [-(_1033518 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (14230 ^ _777081) ^ [_1033627, _1033629] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033627), _1033629)), _1033627 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1033629 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (14240 ^ _777081) ^ [_1033770] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033770), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1033770)], (14242 ^ _777081) ^ [_1033814, _1033816] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033814), _1033816) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 14245 ^ _777081 : [(14246 ^ _777081) ^ [] : [-(_1033814 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (14248 ^ _777081) ^ [] : [-(_1033816 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (14250 ^ _777081) ^ [_1033925, _1033927] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1033925), _1033927) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1033925 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1033927 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (14260 ^ _777081) ^ [_1034068, _1034070] : [-(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)), _1034068), _1034070))], (14262 ^ _777081) ^ [_1034098] : [class_Groups_Osgn__if(_1034098), -(c_Groups_Osgn__class_Osgn(_1034098, c_Groups_Ozero__class_Ozero(_1034098)) = c_Groups_Ozero__class_Ozero(_1034098))], (14268 ^ _777081) ^ [_1034185, _1034187] : [class_Rings_Olinordered__idom(_1034185), 14271 ^ _777081 : [(14272 ^ _777081) ^ [] : [c_Groups_Osgn__class_Osgn(_1034185, _1034187) = c_Groups_Ozero__class_Ozero(_1034185), -(_1034187 = c_Groups_Ozero__class_Ozero(_1034185))], (14278 ^ _777081) ^ [] : [_1034187 = c_Groups_Ozero__class_Ozero(_1034185), -(c_Groups_Osgn__class_Osgn(_1034185, _1034187) = c_Groups_Ozero__class_Ozero(_1034185))]]], (14284 ^ _777081) ^ [_1034411, _1034413, _1034415, _1034417, _1034419] : [c_Fun_Oinj__on(_1034411, _1034413, _1034415, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1034411, tc_HOL_Obool)), _1034417), _1034419)), 14287 ^ _777081 : [(14288 ^ _777081) ^ [] : [hAPP(c_Set_Oimage(_1034411, _1034413, _1034415), _1034417) = hAPP(c_Set_Oimage(_1034411, _1034413, _1034415), _1034419), -(_1034417 = _1034419)], (14294 ^ _777081) ^ [] : [_1034417 = _1034419, -(hAPP(c_Set_Oimage(_1034411, _1034413, _1034415), _1034417) = hAPP(c_Set_Oimage(_1034411, _1034413, _1034415), _1034419))]]], (14300 ^ _777081) ^ [] : [-(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))], (14302 ^ _777081) ^ [_1034722, _1034724, _1034726] : [class_Rings_Oordered__cancel__semiring(_1034722), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1034722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034722), _1034724), _1034726)), c_Groups_Ozero__class_Ozero(_1034722)))), 14307 ^ _777081 : [(14308 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1034722), c_Groups_Ozero__class_Ozero(_1034722)), _1034724)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1034722), _1034726), c_Groups_Ozero__class_Ozero(_1034722)))], (14314 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1034722), _1034724), c_Groups_Ozero__class_Ozero(_1034722))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1034722), c_Groups_Ozero__class_Ozero(_1034722)), _1034726))]]], (14322 ^ _777081) ^ [_1035098, _1035100, _1035102] : [class_Rings_Oordered__ring(_1035098), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035098), c_Groups_Ozero__class_Ozero(_1035098)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035098), _1035100), _1035102)))), 14327 ^ _777081 : [(14328 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035098), c_Groups_Ozero__class_Ozero(_1035098)), _1035100)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035098), c_Groups_Ozero__class_Ozero(_1035098)), _1035102))], (14334 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035098), _1035100), c_Groups_Ozero__class_Ozero(_1035098))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035098), _1035102), c_Groups_Ozero__class_Ozero(_1035098)))]]], (14342 ^ _777081) ^ [_1035474, _1035476, _1035478, _1035480, _1035482] : [class_Rings_Oordered__semiring(_1035474), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035474), _1035476), _1035478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035474), _1035480), _1035482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035474), c_Groups_Ozero__class_Ozero(_1035474)), _1035478)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035474), c_Groups_Ozero__class_Ozero(_1035474)), _1035480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035474), _1035476), _1035480)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035474), _1035478), _1035482))))], (14364 ^ _777081) ^ [_1035897, _1035899, _1035901, _1035903, _1035905] : [class_Rings_Oordered__semiring(_1035897), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035897), _1035899), _1035901)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035897), _1035903), _1035905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035897), c_Groups_Ozero__class_Ozero(_1035897)), _1035899)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035897), c_Groups_Ozero__class_Ozero(_1035897)), _1035903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1035897), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035897), _1035899), _1035903)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035897), _1035901), _1035905))))], (14386 ^ _777081) ^ [_1036320, _1036322, _1036324, _1036326] : [class_Rings_Oordered__ring(_1036320), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036320), _1036322), _1036324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036320), _1036326), c_Groups_Ozero__class_Ozero(_1036320))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036320), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036320), _1036326), _1036324)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036320), _1036326), _1036322))))], (14400 ^ _777081) ^ [_1036589, _1036591, _1036593, _1036595] : [class_Rings_Oordered__ring(_1036589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036589), _1036591), _1036593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036589), _1036595), c_Groups_Ozero__class_Ozero(_1036589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036589), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036589), _1036593), _1036595)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036589), _1036591), _1036595))))], (14414 ^ _777081) ^ [_1036858, _1036860, _1036862, _1036864] : [class_Rings_Oordered__comm__semiring(_1036858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036858), _1036860), _1036862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036858), c_Groups_Ozero__class_Ozero(_1036858)), _1036864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036858), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036858), _1036864), _1036860)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036858), _1036864), _1036862))))], (14428 ^ _777081) ^ [_1037127, _1037129, _1037131, _1037133] : [class_Rings_Oordered__semiring(_1037127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037127), _1037129), _1037131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037127), c_Groups_Ozero__class_Ozero(_1037127)), _1037133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037127), _1037133), _1037129)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037127), _1037133), _1037131))))], (14442 ^ _777081) ^ [_1037396, _1037398, _1037400, _1037402] : [class_Rings_Oordered__semiring(_1037396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037396), _1037398), _1037400)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037396), c_Groups_Ozero__class_Ozero(_1037396)), _1037402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037396), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037396), _1037398), _1037402)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037396), _1037400), _1037402))))], (14456 ^ _777081) ^ [_1037665, _1037667, _1037669] : [class_Rings_Oordered__ring(_1037665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037665), _1037667), c_Groups_Ozero__class_Ozero(_1037665))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037665), _1037669), c_Groups_Ozero__class_Ozero(_1037665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037665), c_Groups_Ozero__class_Ozero(_1037665)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037665), _1037667), _1037669))))], (14470 ^ _777081) ^ [_1037920, _1037922, _1037924] : [class_Rings_Oordered__cancel__semiring(_1037920), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037920), _1037922), c_Groups_Ozero__class_Ozero(_1037920))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037920), c_Groups_Ozero__class_Ozero(_1037920)), _1037924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1037920), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037920), _1037922), _1037924)), c_Groups_Ozero__class_Ozero(_1037920))))], (14484 ^ _777081) ^ [_1038175, _1038177, _1038179] : [class_Rings_Oordered__cancel__semiring(_1038175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038175), c_Groups_Ozero__class_Ozero(_1038175)), _1038177)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038175), _1038179), c_Groups_Ozero__class_Ozero(_1038175))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038175), _1038179), _1038177)), c_Groups_Ozero__class_Ozero(_1038175))))], (14498 ^ _777081) ^ [_1038430, _1038432, _1038434] : [class_Rings_Oordered__cancel__semiring(_1038430), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038430), c_Groups_Ozero__class_Ozero(_1038430)), _1038432)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038430), _1038434), c_Groups_Ozero__class_Ozero(_1038430))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038430), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038430), _1038432), _1038434)), c_Groups_Ozero__class_Ozero(_1038430))))], (14512 ^ _777081) ^ [_1038685, _1038687, _1038689] : [class_Rings_Oordered__cancel__semiring(_1038685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038685), c_Groups_Ozero__class_Ozero(_1038685)), _1038687)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038685), c_Groups_Ozero__class_Ozero(_1038685)), _1038689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038685), c_Groups_Ozero__class_Ozero(_1038685)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038685), _1038687), _1038689))))], (14526 ^ _777081) ^ [_1038940, _1038942, _1038944] : [class_Rings_Olinordered__ring__strict(_1038940), 14529 ^ _777081 : [(14530 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038940), _1038942), _1038944)), c_Groups_Ozero__class_Ozero(_1038940))), 14535 ^ _777081 : [(14536 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038940), c_Groups_Ozero__class_Ozero(_1038940)), _1038942)))], (14538 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038940), _1038944), c_Groups_Ozero__class_Ozero(_1038940))))]], 14539 ^ _777081 : [(14540 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038940), _1038942), c_Groups_Ozero__class_Ozero(_1038940))))], (14542 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038940), c_Groups_Ozero__class_Ozero(_1038940)), _1038944)))]]], (14544 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1038940), _1038942), _1038944)), c_Groups_Ozero__class_Ozero(_1038940)))), 14545 ^ _777081 : [(14546 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038940), c_Groups_Ozero__class_Ozero(_1038940)), _1038942)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038940), _1038944), c_Groups_Ozero__class_Ozero(_1038940)))], (14552 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038940), _1038942), c_Groups_Ozero__class_Ozero(_1038940))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1038940), c_Groups_Ozero__class_Ozero(_1038940)), _1038944))]]]]], (14560 ^ _777081) ^ [_1039530, _1039532, _1039534] : [class_Rings_Olinordered__ring__strict(_1039530), 14563 ^ _777081 : [(14564 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039530), c_Groups_Ozero__class_Ozero(_1039530)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039530), _1039532), _1039534))), 14569 ^ _777081 : [(14570 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039530), c_Groups_Ozero__class_Ozero(_1039530)), _1039532)))], (14572 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039530), c_Groups_Ozero__class_Ozero(_1039530)), _1039534)))]], 14573 ^ _777081 : [(14574 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039530), _1039532), c_Groups_Ozero__class_Ozero(_1039530))))], (14576 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039530), _1039534), c_Groups_Ozero__class_Ozero(_1039530))))]]], (14578 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039530), c_Groups_Ozero__class_Ozero(_1039530)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1039530), _1039532), _1039534)))), 14579 ^ _777081 : [(14580 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039530), c_Groups_Ozero__class_Ozero(_1039530)), _1039532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039530), c_Groups_Ozero__class_Ozero(_1039530)), _1039534))], (14586 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039530), _1039532), c_Groups_Ozero__class_Ozero(_1039530))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1039530), _1039534), c_Groups_Ozero__class_Ozero(_1039530)))]]]]], (14594 ^ _777081) ^ [_1040120, _1040122] : [class_Rings_Olinordered__ring(_1040120), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040120), c_Groups_Ozero__class_Ozero(_1040120)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040120), _1040122), _1040122))))], (14600 ^ _777081) ^ [_1040229, _1040231, _1040233, _1040235] : [class_Rings_Olinordered__ring__strict(_1040229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040229), _1040231), _1040233)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040229), _1040235), c_Groups_Ozero__class_Ozero(_1040229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040229), _1040235), _1040233)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040229), _1040235), _1040231))))], (14614 ^ _777081) ^ [_1040498, _1040500, _1040502, _1040504] : [class_Rings_Olinordered__ring__strict(_1040498), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040498), _1040500), _1040502)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040498), _1040504), c_Groups_Ozero__class_Ozero(_1040498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040498), _1040502), _1040504)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040498), _1040500), _1040504))))], (14628 ^ _777081) ^ [_1040767, _1040769, _1040771, _1040773] : [class_Rings_Olinordered__comm__semiring__strict(_1040767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040767), _1040769), _1040771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040767), c_Groups_Ozero__class_Ozero(_1040767)), _1040773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040767), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040767), _1040773), _1040769)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040767), _1040773), _1040771))))], (14642 ^ _777081) ^ [_1041036, _1041038, _1041040, _1041042] : [class_Rings_Olinordered__semiring__strict(_1041036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041036), _1041038), _1041040)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041036), 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hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041574), _1041578), c_Groups_Ozero__class_Ozero(_1041574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041574), c_Groups_Ozero__class_Ozero(_1041574)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041574), _1041576), _1041578))))], (14684 ^ _777081) ^ [_1041829, _1041831, _1041833] : [class_Rings_Olinordered__semiring__strict(_1041829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041829), _1041831), c_Groups_Ozero__class_Ozero(_1041829))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041829), c_Groups_Ozero__class_Ozero(_1041829)), _1041833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1041829), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1041829), _1041831), _1041833)), c_Groups_Ozero__class_Ozero(_1041829))))], (14698 ^ _777081) ^ [_1042084, _1042086, _1042088, _1042090] : [class_Rings_Olinordered__ring__strict(_1042084), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042084), _1042086), 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hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042465), c_Groups_Ozero__class_Ozero(_1042465)), _1042469)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042465), c_Groups_Ozero__class_Ozero(_1042465)), _1042467)))], (14732 ^ _777081) ^ [_1042720, _1042722, _1042724] : [class_Rings_Olinordered__semiring__strict(_1042720), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042720), c_Groups_Ozero__class_Ozero(_1042720)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042720), _1042722), _1042724))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042720), c_Groups_Ozero__class_Ozero(_1042720)), _1042722)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042720), c_Groups_Ozero__class_Ozero(_1042720)), _1042724)))], (14746 ^ _777081) ^ [_1042975, _1042977, _1042979] : [class_Rings_Olinordered__semiring__strict(_1042975), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042975), c_Groups_Ozero__class_Ozero(_1042975)), _1042977)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1042975), 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: [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044727), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044727), _1044729), _1044731)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044727), _1044733), _1044731))), 14851 ^ _777081 : [(14852 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044727), c_Groups_Ozero__class_Ozero(_1044727)), _1044731)))], (14854 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044727), _1044729), _1044733)))]], 14855 ^ _777081 : [(14856 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044727), _1044731), c_Groups_Ozero__class_Ozero(_1044727))))], (14858 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044727), _1044733), _1044729)))]]], (14860 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1044727), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044727), _1044729), _1044731)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1044727), _1044733), _1044731)))), 14861 ^ _777081 : 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1045781), _1045785), _1045785)) = c_Groups_Ozero__class_Ozero(_1045781)), _1045783 = c_Groups_Ozero__class_Ozero(_1045781), _1045785 = c_Groups_Ozero__class_Ozero(_1045781)]]], (14922 ^ _777081) ^ [_1046156, _1046158, _1046160] : [class_Rings_Olinordered__semidom(_1046156), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046156), c_Groups_Oone__class_Oone(_1046156)), _1046158)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046156), c_Groups_Oone__class_Oone(_1046156)), _1046160)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1046156), c_Groups_Oone__class_Oone(_1046156)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046156), _1046158), _1046160))))], (14936 ^ _777081) ^ [_1046411, _1046413, _1046415, _1046417, _1046419, _1046421] : [class_Rings_Oring(_1046411), 14939 ^ _777081 : [(14940 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1046411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1046411), _1046413), _1046415)), _1046417) = 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_1046818))]]], (14968 ^ _777081) ^ [_1047205, _1047207] : [class_Rings_Olinordered__semidom(_1047205), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047205), c_Groups_Ozero__class_Ozero(_1047205)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1047205), _1047207))))], (14974 ^ _777081) ^ [_1047308, _1047310] : [class_Rings_Olinordered__semidom(_1047308), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1047308), c_Groups_Ozero__class_Ozero(_1047308)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1047308), _1047310))))], (14980 ^ _777081) ^ [_1047411, _1047413, _1047415] : [class_Rings_Ocomm__semiring__1(_1047411), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047411), _1047413), _1047415)), _1047415) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047411), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047411), _1047413), c_Groups_Oone__class_Oone(_1047411))), _1047415))], (14986 ^ _777081) ^ [_1047556, _1047558, _1047560] : [class_Rings_Ocomm__semiring__1(_1047556), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047556), _1047558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047556), _1047560), _1047558)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047556), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047556), _1047560), c_Groups_Oone__class_Oone(_1047556))), _1047558))], (14992 ^ _777081) ^ [_1047701, _1047703] : [class_Rings_Ocomm__semiring__1(_1047701), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047701), _1047703), _1047703) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1047701), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1047701), c_Groups_Oone__class_Oone(_1047701)), c_Groups_Oone__class_Oone(_1047701))), _1047703))], (14998 ^ _777081) ^ [_1047832, _1047834] : [class_Rings_Olinordered__semidom(_1047832), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1047832), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1047832), _1047834)), c_Groups_Ozero__class_Ozero(_1047832)))], (15004 ^ _777081) ^ [_1047936] : [class_Rings_Osemiring__1(_1047936), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1047936), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1047936))], (15010 ^ _777081) ^ [_1048023, _1048025] : [class_Rings_Ocomm__ring__1(_1048023), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1048023), _1048025) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048023), hAPP(c_Groups_Ouminus__class_Ouminus(_1048023), c_Groups_Oone__class_Oone(_1048023))), _1048025))], (15016 ^ _777081) ^ [_1048138, _1048140] : [class_Rings_Oring__1__no__zero__divisors(_1048138), 15019 ^ _777081 : [(15030 ^ _777081) ^ [] : [15031 ^ _777081 : [(15032 ^ _777081) ^ [] : [_1048140 = c_Groups_Oone__class_Oone(_1048138)], (15034 ^ _777081) ^ [] : [_1048140 = hAPP(c_Groups_Ouminus__class_Ouminus(_1048138), c_Groups_Oone__class_Oone(_1048138))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048138), _1048140), _1048140) = c_Groups_Oone__class_Oone(_1048138))], (15020 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1048138), _1048140), _1048140) = c_Groups_Oone__class_Oone(_1048138), -(_1048140 = c_Groups_Oone__class_Oone(_1048138)), -(_1048140 = hAPP(c_Groups_Ouminus__class_Ouminus(_1048138), c_Groups_Oone__class_Oone(_1048138)))]]], (15038 ^ _777081) ^ [_1048460, _1048462] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048460), _1048462) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 15041 ^ _777081 : [(15042 ^ _777081) ^ [] : [-(_1048460 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15044 ^ _777081) ^ [] : [-(_1048462 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (15046 ^ _777081) ^ [_1048571, _1048573] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1048571), _1048573) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1048571 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1048573 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15056 ^ _777081) ^ [_1048729, _1048731] : [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), _1048729), _1048731))), 15059 ^ _777081 : [(15060 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1048729)))], (15062 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1048731)))]]], (15064 ^ _777081) ^ [_1048852, _1048854] : [-(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), _1048852), _1048854)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1048852)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1048854))], (15074 ^ _777081) ^ [_1049007, _1049009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1049007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1049009)), -(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), _1049009), _1049007))))], (15084 ^ _777081) ^ [_1049160, _1049162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1049160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1049162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049160), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049160), _1049162))))], (15094 ^ _777081) ^ [_1049319, _1049321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1049319)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1049321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1049319), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1049321), _1049319))))], (15104 ^ _777081) ^ [_1049478, _1049480, _1049482, _1049484, _1049486] : [c_Fun_Oinj__on(_1049478, _1049480, _1049482, _1049484), hBOOL(hAPP(hAPP(c_member(_1049478), _1049486), _1049484)), -(hAPP(c_Fun_Othe__inv__into(_1049478, _1049480, _1049484, _1049482), hAPP(_1049482, _1049486)) = _1049486)], (15114 ^ _777081) ^ [_1049659, _1049661, _1049663, _1049665, _1049667, _1049669] : [c_Fun_Oinj__on(_1049659, _1049661, _1049663, _1049665), hAPP(_1049663, _1049667) = _1049669, hBOOL(hAPP(hAPP(c_member(_1049659), _1049667), _1049665)), -(hAPP(c_Fun_Othe__inv__into(_1049659, _1049661, _1049665, _1049663), _1049669) = _1049667)], (15128 ^ _777081) ^ [_1049925, _1049927, _1049929, _1049931] : [c_Fun_Oinj__on(_1049925, tc_Option_Ooption(_1049927), c_Map_Omap__add(_1049925, _1049927, _1049929, _1049931), c_Map_Odom(_1049925, _1049927, _1049931)), -(c_Fun_Oinj__on(_1049925, tc_Option_Ooption(_1049927), _1049931, c_Map_Odom(_1049925, _1049927, _1049931)))], (15134 ^ _777081) ^ [_1050044, _1050046, _1050048, _1050050] : [c_Fun_Oinj__on(_1050044, tc_Option_Ooption(_1050046), _1050050, c_Map_Odom(_1050044, _1050046, _1050050)), -(c_Fun_Oinj__on(_1050044, tc_Option_Ooption(_1050046), c_Map_Omap__add(_1050044, _1050046, _1050048, _1050050), c_Map_Odom(_1050044, _1050046, _1050050)))], (15140 ^ _777081) ^ [_1050169, _1050171] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050169), hAPP(c_Nat_OSuc, _1050171)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050169), _1050171)))], (15142 ^ _777081) ^ [_1050215, _1050217] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1050215)), _1050217) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050217), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050215), _1050217)))], (15144 ^ _777081) ^ [_1050261, _1050263, _1050265] : [class_Rings_Osemiring__1(_1050261), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1050261), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050263), _1050265)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1050261), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1050261), _1050263)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1050261), _1050265)))], (15150 ^ _777081) ^ [_1050396, _1050398, _1050400, _1050402] : [c_Fun_Oinj__on(_1050396, _1050398, _1050400, _1050402), -(c_Fun_Oinj__on(_1050398, _1050396, c_Fun_Othe__inv__into(_1050396, _1050398, _1050402, _1050400), hAPP(c_Set_Oimage(_1050396, _1050398, _1050400), _1050402)))], (15156 ^ _777081) ^ [_1050509, _1050511, _1050513, _1050515] : [c_Fun_Oinj__on(_1050509, _1050511, _1050513, _1050515), -(hAPP(c_Set_Oimage(_1050511, _1050509, c_Fun_Othe__inv__into(_1050509, _1050511, _1050515, _1050513)), hAPP(c_Set_Oimage(_1050509, _1050511, _1050513), _1050515)) = _1050515)], (15162 ^ _777081) ^ [_1050632, _1050634, _1050636] : [class_Rings_Oring__1(_1050632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050634), _1050636)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1050632), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1050636), _1050634)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1050632), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1050632), _1050636)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1050632), _1050634)))], (15172 ^ _777081) ^ [_1050831, _1050833] : [_1050831 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1050831), _1050833), -(_1050833 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1050831 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15182 ^ _777081) ^ [_1050933] : [class_Rings_Osemiring__1(_1050933), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1050933), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1050933))], (15188 ^ _777081) ^ [_1051020, _1051022, _1051024] : [class_Rings_Oring__1(_1051020), hBOOL(hAPP(hAPP(c_member(_1051020), _1051022), c_Int_Oring__1__class_OInts(_1051020))), hBOOL(hAPP(hAPP(c_member(_1051020), _1051024), c_Int_Oring__1__class_OInts(_1051020))), -(hBOOL(hAPP(hAPP(c_member(_1051020), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051020), _1051022), _1051024)), c_Int_Oring__1__class_OInts(_1051020))))], (15202 ^ _777081) ^ [_1051275, _1051277] : [class_Rings_Oring__1(_1051275), -(hBOOL(hAPP(hAPP(c_member(_1051275), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1051275), _1051277)), c_Int_Oring__1__class_OInts(_1051275))))], (15208 ^ _777081) ^ [_1051378, _1051380, _1051382, _1051384, _1051386, _1051388] : [c_Fun_Oinj__on(_1051378, _1051380, _1051382, _1051384), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1051378, tc_HOL_Obool)), _1051386), _1051384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1051378, tc_HOL_Obool)), _1051388), _1051384)), -(hAPP(c_Set_Oimage(_1051378, _1051380, _1051382), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1051378, tc_HOL_Obool)), _1051386), _1051388)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1051380, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1051378, _1051380, _1051382), _1051386)), hAPP(c_Set_Oimage(_1051378, _1051380, _1051382), _1051388)))], (15222 ^ _777081) ^ [_1051713, _1051715, _1051717, _1051719, _1051721, _1051723] : [c_Fun_Oinj__on(_1051713, _1051715, _1051717, _1051719), -(hBOOL(hAPP(hAPP(c_member(_1051715), _1051721), hAPP(c_Set_Oimage(_1051713, _1051715, _1051717), _1051719)))), -(c_Fun_Oinj__on(_1051713, _1051715, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1051713, _1051715), _1051717), _1051723), _1051721), _1051719))], (15232 ^ _777081) ^ [_1051873, _1051875, _1051877, _1051879] : [class_Rings_Olinordered__semiring__strict(_1051873), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051873), _1051875), _1051877)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1051873), _1051875), _1051879))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051873), c_Groups_Ozero__class_Ozero(_1051873)), _1051875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051873), _1051877), _1051879)))], (15246 ^ _777081) ^ [_1052142, _1052144, _1052146, _1052148] : [class_Rings_Olinordered__semiring__strict(_1052142), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052142), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052142), _1052144), _1052146)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052142), _1052148), _1052146))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052142), c_Groups_Ozero__class_Ozero(_1052142)), _1052146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052142), _1052144), _1052148)))], (15260 ^ _777081) ^ [_1052411, _1052413, _1052415, _1052417] : [class_Rings_Olinordered__semiring__strict(_1052411), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052411), _1052413), _1052415)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052411), _1052413), _1052417))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052411), c_Groups_Ozero__class_Ozero(_1052411)), _1052413)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052411), _1052415), _1052417)))], (15274 ^ _777081) ^ [_1052680, _1052682, _1052684, _1052686] : [class_Rings_Olinordered__semiring(_1052680), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052680), _1052682), _1052684)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052680), _1052682), _1052686))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052680), c_Groups_Ozero__class_Ozero(_1052680)), _1052682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052680), _1052684), _1052686)))], (15288 ^ _777081) ^ [_1052949, _1052951, _1052953, _1052955] : [class_Rings_Olinordered__semiring__strict(_1052949), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052949), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052949), _1052951), _1052953)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052949), _1052955), _1052953))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052949), c_Groups_Ozero__class_Ozero(_1052949)), _1052953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1052949), _1052951), _1052955)))], (15302 ^ _777081) ^ [_1053218, _1053220, _1053222, _1053224] : [class_Rings_Olinordered__semiring(_1053218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053218), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053218), _1053220), _1053222)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053218), _1053224), _1053222))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053218), c_Groups_Ozero__class_Ozero(_1053218)), _1053222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053218), _1053220), _1053224)))], (15316 ^ _777081) ^ [_1053487, _1053489, _1053491, _1053493, _1053495] : [class_Rings_Olinordered__semiring__strict(_1053487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053487), _1053489), _1053491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053487), _1053493), _1053495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053487), c_Groups_Ozero__class_Ozero(_1053487)), _1053489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053487), c_Groups_Ozero__class_Ozero(_1053487)), _1053493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053487), _1053489), _1053493)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053487), _1053491), _1053495))))], (15338 ^ _777081) ^ [_1053910, _1053912, _1053914, _1053916, _1053918] : [class_Rings_Olinordered__semiring__strict(_1053910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053910), _1053912), _1053914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053910), _1053916), _1053918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053910), c_Groups_Ozero__class_Ozero(_1053910)), _1053912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053910), c_Groups_Ozero__class_Ozero(_1053910)), _1053916)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053910), _1053912), _1053916)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1053910), _1053914), _1053918))))], (15360 ^ _777081) ^ [_1054333, _1054335, _1054337, _1054339, _1054341] : [class_Rings_Olinordered__semiring__strict(_1054333), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054333), _1054335), _1054337)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054333), _1054339), _1054341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054333), c_Groups_Ozero__class_Ozero(_1054333)), _1054335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054333), c_Groups_Ozero__class_Ozero(_1054333)), _1054339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054333), _1054335), _1054339)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054333), _1054337), _1054341))))], (15382 ^ _777081) ^ [_1054756, _1054758, _1054760, _1054762, _1054764] : [class_Rings_Olinordered__semiring__strict(_1054756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054756), _1054758), _1054760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054756), _1054762), _1054764)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054756), c_Groups_Ozero__class_Ozero(_1054756)), _1054760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054756), c_Groups_Ozero__class_Ozero(_1054756)), _1054762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1054756), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054756), _1054758), _1054762)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1054756), _1054760), _1054764))))], (15404 ^ _777081) ^ [_1055179, _1055181, _1055183, _1055185] : [class_Rings_Olinordered__ring__strict(_1055179), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055179), _1055181), c_Groups_Ozero__class_Ozero(_1055179))), 15411 ^ _777081 : [(15412 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055179), _1055181), _1055183)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055179), _1055181), _1055185))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055179), _1055185), _1055183)))], (15418 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055179), _1055185), _1055183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055179), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055179), _1055181), _1055183)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055179), _1055181), _1055185))))]]], (15424 ^ _777081) ^ [_1055560, _1055562, _1055564, _1055566] : [class_Rings_Olinordered__ring__strict(_1055560), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055560), c_Groups_Ozero__class_Ozero(_1055560)), _1055562)), 15431 ^ _777081 : [(15432 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055560), _1055562), _1055564)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055560), _1055562), _1055566))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055560), _1055564), _1055566)))], (15438 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055560), _1055564), _1055566)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055560), _1055562), _1055564)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055560), _1055562), _1055566))))]]], (15444 ^ _777081) ^ [_1055941, _1055943, _1055945] : [class_Rings_Olinordered__ring__strict(_1055941), 15447 ^ _777081 : [(15448 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055941), _1055943), _1055943)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055941), _1055945), _1055945))), c_Groups_Ozero__class_Ozero(_1055941))), 15451 ^ _777081 : [(15452 ^ _777081) ^ [] : [-(_1055943 = c_Groups_Ozero__class_Ozero(_1055941))], (15454 ^ _777081) ^ [] : [-(_1055945 = c_Groups_Ozero__class_Ozero(_1055941))]]], (15456 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055941), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1055941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055941), _1055943), _1055943)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055941), _1055945), _1055945))), c_Groups_Ozero__class_Ozero(_1055941)))), _1055943 = c_Groups_Ozero__class_Ozero(_1055941), _1055945 = c_Groups_Ozero__class_Ozero(_1055941)]]], (15466 ^ _777081) ^ [_1056337, _1056339, _1056341] : [class_Rings_Olinordered__ring(_1056337), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056337), c_Groups_Ozero__class_Ozero(_1056337)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056337), _1056339), _1056339)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056337), _1056341), _1056341)))))], (15472 ^ _777081) ^ [_1056480, _1056482, _1056484] : [class_Rings_Olinordered__ring__strict(_1056480), 15475 ^ _777081 : [(15486 ^ _777081) ^ [] : [15487 ^ _777081 : [(15488 ^ _777081) ^ [] : [-(_1056482 = c_Groups_Ozero__class_Ozero(_1056480))], (15490 ^ _777081) ^ [] : [-(_1056484 = c_Groups_Ozero__class_Ozero(_1056480))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056480), c_Groups_Ozero__class_Ozero(_1056480)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056480), _1056482), _1056482)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056480), _1056484), _1056484)))))], (15476 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056480), c_Groups_Ozero__class_Ozero(_1056480)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056480), _1056482), _1056482)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056480), _1056484), _1056484)))), _1056482 = c_Groups_Ozero__class_Ozero(_1056480), _1056484 = c_Groups_Ozero__class_Ozero(_1056480)]]], (15494 ^ _777081) ^ [_1056855, _1056857, _1056859] : [class_Rings_Olinordered__ring(_1056855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1056855), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056855), _1056857), _1056857)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056855), _1056859), _1056859))), c_Groups_Ozero__class_Ozero(_1056855)))], (15500 ^ _777081) ^ [_1056999, _1057001, _1057003] : [class_Rings_Olinordered__idom(_1056999), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056999), c_Groups_Ozero__class_Ozero(_1056999)), _1057001)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056999), c_Groups_Ozero__class_Ozero(_1056999)), _1057003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056999), _1057003), c_Groups_Oone__class_Oone(_1056999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1056999), _1057003), _1057001)), _1057001)))], (15518 ^ _777081) ^ [_1057322, _1057324, _1057326] : [class_Rings_Olinordered__idom(_1057322), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057322), c_Groups_Ozero__class_Ozero(_1057322)), _1057324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057322), c_Groups_Ozero__class_Ozero(_1057322)), _1057326)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057322), _1057326), c_Groups_Oone__class_Oone(_1057322))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057322), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057322), _1057324), _1057326)), _1057324)))], (15536 ^ _777081) ^ [_1057645, _1057647, _1057649, _1057651, _1057653, _1057655] : [class_Rings_Oordered__ring(_1057645), 15539 ^ _777081 : [(15540 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057645), _1057647), _1057649)), _1057651)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057645), _1057653), _1057649)), _1057655))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057645), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057645), _1057647), _1057653)), _1057649)), _1057651)), _1057655)))], (15546 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057645), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1057645), _1057647), _1057653)), _1057649)), _1057651)), _1057655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057645), _1057647), _1057649)), _1057651)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057645), _1057653), _1057649)), _1057655))))]]], (15552 ^ _777081) ^ [_1058084, _1058086, _1058088, _1058090, _1058092, _1058094] : [class_Rings_Oordered__ring(_1058084), 15555 ^ _777081 : [(15556 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058084), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058084), _1058086), _1058088)), _1058090)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058084), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058084), _1058092), _1058088)), _1058094))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058084), _1058090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058084), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058084), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058084), _1058092), _1058086)), _1058088)), _1058094))))], (15562 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058084), _1058090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058084), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058084), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058084), _1058092), _1058086)), _1058088)), _1058094))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058084), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058084), 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058718), _1058726), _1058722)), _1058728))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058718), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058718), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058718), _1058720), _1058726)), _1058722)), _1058724)), _1058728)))], (15588 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058718), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058718), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058718), _1058720), _1058726)), _1058722)), _1058724)), _1058728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058718), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058718), _1058720), _1058722)), _1058724)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058718), _1058726), _1058722)), _1058728))))]]], (15594 ^ _777081) ^ [_1059157, _1059159, _1059161, _1059163, _1059165, _1059167] : [class_Rings_Oordered__ring(_1059157), 15597 ^ _777081 : [(15598 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059157), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059157), _1059159), _1059161)), _1059163)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059157), _1059165), _1059161)), _1059167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059157), _1059163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059157), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1059157), _1059165), _1059159)), _1059161)), _1059167))))], (15604 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059157), _1059163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059157), 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-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059596), c_Groups_Osgn__class_Osgn(_1059596, _1059598)), c_Groups_Ozero__class_Ozero(_1059596))))]]], (15626 ^ _777081) ^ [_1059864, _1059866] : [class_Rings_Olinordered__idom(_1059864), 15629 ^ _777081 : [(15630 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059864), c_Groups_Ozero__class_Ozero(_1059864)), c_Groups_Osgn__class_Osgn(_1059864, _1059866))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059864), c_Groups_Ozero__class_Ozero(_1059864)), _1059866)))], (15636 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059864), c_Groups_Ozero__class_Ozero(_1059864)), _1059866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1059864), c_Groups_Ozero__class_Ozero(_1059864)), c_Groups_Osgn__class_Osgn(_1059864, _1059866))))]]], (15642 ^ _777081) ^ [_1060132, _1060134] : [class_Rings_Olinordered__semidom(_1060132), 15645 ^ _777081 : [(15646 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060132), c_Groups_Ozero__class_Ozero(_1060132)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1060132), _1060134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060134)))], (15652 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1060134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060132), c_Groups_Ozero__class_Ozero(_1060132)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1060132), _1060134))))]]], (15658 ^ _777081) ^ [_1060385, _1060387] : [class_Rings_Osemiring__1(_1060385), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1060385), hAPP(c_Nat_OSuc, _1060387)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060385), c_Groups_Oone__class_Oone(_1060385)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1060385), _1060387)))], (15664 ^ _777081) ^ [_1060506, _1060508, _1060510, _1060512] : [-(c_Sum__Type_OPlus(_1060506, _1060508, _1060510, _1060512) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_sum(_1060506, _1060508), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1060506, tc_sum(_1060506, _1060508), c_Sum__Type_OInl(_1060506, _1060508)), _1060510)), hAPP(c_Set_Oimage(_1060508, tc_sum(_1060506, _1060508), c_Sum__Type_OInr(_1060508, _1060506)), _1060512)))], (15666 ^ _777081) ^ [_1060580, _1060582, _1060584, _1060586, _1060588, _1060590] : [c_Fun_Oinj__on(_1060580, _1060582, _1060584, _1060586), hBOOL(hAPP(hAPP(c_member(_1060582), _1060588), hAPP(c_Set_Oimage(_1060580, _1060582, _1060584), _1060586))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1060580, tc_HOL_Obool)), _1060586), _1060590)), -(hBOOL(hAPP(hAPP(c_member(_1060580), hAPP(c_Fun_Othe__inv__into(_1060580, _1060582, _1060586, _1060584), _1060588)), _1060590)))], (15680 ^ _777081) ^ [_1060867, _1060869, _1060871, _1060873, _1060875, _1060877] : [class_Rings_Olinordered__semiring__1(_1060867), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060867), _1060869), _1060871)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060867), _1060873), _1060871)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060867), c_Groups_Ozero__class_Ozero(_1060867)), _1060875)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060867), c_Groups_Ozero__class_Ozero(_1060867)), _1060877)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060867), _1060875), _1060877) = c_Groups_Oone__class_Oone(_1060867), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060867), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060867), _1060875), _1060869)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060867), _1060877), _1060873))), _1060871)))], (15706 ^ _777081) ^ [_1061396, _1061398, _1061400, _1061402, _1061404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061396), _1061398)), 15709 ^ _777081 : [(15710 ^ _777081) ^ [] : [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), _1061398), _1061400)), _1061402)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061396), _1061400)), _1061404))), -(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), _1061398), _1061396)), _1061400)), _1061402)), _1061404)))], (15716 ^ _777081) ^ [] : [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), _1061398), _1061396)), _1061400)), _1061402)), _1061404)), -(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), _1061398), _1061400)), _1061402)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061396), _1061400)), _1061404))))]]], (15722 ^ _777081) ^ [_1061787, _1061789, _1061791, _1061793, _1061795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1061787), _1061789)), 15725 ^ _777081 : [(15726 ^ _777081) ^ [] : [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), _1061787), _1061791)), _1061793)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061789), _1061791)), _1061795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1061793), 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), _1061789), _1061787)), _1061791)), _1061795))))], (15732 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1061793), 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), _1061789), _1061787)), _1061791)), _1061795))), -(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), _1061787), _1061791)), _1061793)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1061789), _1061791)), _1061795))))]]], (15738 ^ _777081) ^ [_1062178, _1062180, _1062182, _1062184, _1062186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1062178), _1062180)), 15741 ^ _777081 : [(15742 ^ _777081) ^ [] : [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), _1062180), _1062182)), _1062184)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062178), _1062182)), _1062186))), -(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), _1062180), _1062178)), _1062182)), _1062184)), _1062186)))], (15748 ^ _777081) ^ [] : [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), _1062180), _1062178)), _1062182)), _1062184)), _1062186)), -(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), _1062180), _1062182)), _1062184)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062178), _1062182)), _1062186))))]]], (15754 ^ _777081) ^ [_1062569, _1062571, _1062573, _1062575, _1062577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1062569), _1062571)), -(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), _1062571), _1062573)), _1062575)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062569), _1062573)), _1062577)) = 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), _1062571), _1062569)), _1062573)), _1062575)), _1062577))], (15760 ^ _777081) ^ [_1062770, _1062772, _1062774, _1062776, _1062778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1062770), _1062772)), 15763 ^ _777081 : [(15764 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062772), _1062774)), _1062776) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062770), _1062774)), _1062778), -(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), _1062772), _1062770)), _1062774)), _1062776) = _1062778)], (15770 ^ _777081) ^ [] : [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), _1062772), _1062770)), _1062774)), _1062776) = _1062778, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062772), _1062774)), _1062776) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1062770), _1062774)), _1062778))]]], (15776 ^ _777081) ^ [_1063131, _1063133, _1063135, _1063137, _1063139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1063131), _1063133)), 15779 ^ _777081 : [(15780 ^ _777081) ^ [] : [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), _1063131), _1063135)), _1063137)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063133), _1063135)), _1063139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1063137), 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), _1063133), _1063131)), _1063135)), _1063139))))], (15786 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1063137), 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), _1063133), _1063131)), _1063135)), _1063139))), -(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), _1063131), _1063135)), _1063137)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063133), _1063135)), _1063139))))]]], (15792 ^ _777081) ^ [_1063522, _1063524, _1063526, _1063528, _1063530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1063522), _1063524)), -(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), _1063522), _1063526)), _1063528)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063524), _1063526)), _1063530)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1063528), 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), _1063524), _1063522)), _1063526)), _1063530)))], (15798 ^ _777081) ^ [_1063723, _1063725, _1063727, _1063729, _1063731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1063723), _1063725)), 15801 ^ _777081 : [(15802 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063723), _1063727)), _1063729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063725), _1063727)), _1063731), -(_1063729 = 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), _1063725), _1063723)), _1063727)), _1063731))], (15808 ^ _777081) ^ [] : [_1063729 = 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), _1063725), _1063723)), _1063727)), _1063731), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063723), _1063727)), _1063729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1063725), _1063727)), _1063731))]]], (15814 ^ _777081) ^ [_1064084, _1064086] : [-(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), _1064084))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1064086))))], (15816 ^ _777081) ^ [_1064138, _1064140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1064138), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1064140), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1064138), _1064140)))], (15822 ^ _777081) ^ [_1064243, _1064245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1064243), _1064245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1064243), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1064245), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (15828 ^ _777081) ^ [_1064354] : [-(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), _1064354))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15830 ^ _777081) ^ [_1064394] : [_1064394 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1064394) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15836 ^ _777081) ^ [_1064470] : [-(_1064470 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 15839 ^ _777081 : [(15840 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1064470)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1064470) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (15846 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1064470))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1064470) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (15852 ^ _777081) ^ [_1064674, _1064676] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1064674)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1064676))))], (15854 ^ _777081) ^ [_1064713] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1064713), _1064713)))], (15856 ^ _777081) ^ [_1064741] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1064741) = _1064741)], (15858 ^ _777081) ^ [_1064767] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1064767), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1064767)], (15860 ^ _777081) ^ [_1064792, _1064794] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1064792), _1064794))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1064794), _1064792)))], (15866 ^ _777081) ^ [_1064853, _1064855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1064853), _1064855)), 15869 ^ _777081 : [(15870 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1064853), _1064855)))], (15872 ^ _777081) ^ [] : [_1064853 = _1064855]]], (15874 ^ _777081) ^ [_1064980, _1064982] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1064980), _1064982))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1064980), _1064982)), -(_1064980 = _1064982)], (15884 ^ _777081) ^ [_1065134, _1065136, _1065138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1065134), _1065136)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1065136), _1065138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1065134), _1065138)))], (15894 ^ _777081) ^ [_1065297, _1065299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1065297), _1065299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1065299), _1065297)), -(_1065297 = _1065299)], (15904 ^ _777081) ^ [] : [-(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))))], (15906 ^ _777081) ^ [_1065464] : [-(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), _1065464))))], (15908 ^ _777081) ^ [_1065504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1065504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1065504)))], (15914 ^ _777081) ^ [_1065583] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1065583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1065583)))], (15920 ^ _777081) ^ [_1065680] : [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)), _1065680)), _1065680)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1065680), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15926 ^ _777081) ^ [_1065789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1065789), 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)), _1065789)), _1065789)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15932 ^ _777081) ^ [_1065904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1065904)), -(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)), _1065904))))], (15938 ^ _777081) ^ [_1065993, _1065995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1065993)), 15941 ^ _777081 : [(15942 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1065993), _1065995) = c_Groups_Oone__class_Oone(tc_Int_Oint), 15945 ^ _777081 : [(15946 ^ _777081) ^ [] : [-(_1065993 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (15948 ^ _777081) ^ [] : [-(_1065995 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (15950 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1065993), _1065995) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1065993 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1065995 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (15960 ^ _777081) ^ [_1066294, _1066296, _1066298, _1066300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1066294), _1066296)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1066298), _1066300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1066294), _1066298)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1066296), _1066300))))], (15970 ^ _777081) ^ [_1066485, _1066487, _1066489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1066485), _1066487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1066489), _1066485)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1066489), _1066487))))], (15976 ^ _777081) ^ [_1066608, _1066610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1066608), _1066610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1066608), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1066610)))], (15982 ^ _777081) ^ [_1066732, _1066734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1066732), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1066734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1066732), _1066734)))], (15988 ^ _777081) ^ [_1066837, _1066839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1066837), _1066839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1066837), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1066839)))], (16004 ^ _777081) ^ [_1067081, _1067083] : [16005 ^ _777081 : [(16006 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067081), _1067083))], (16008 ^ _777081) ^ [] : [_1067081 = _1067083]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067081), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067083), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (15994 ^ _777081) ^ [_1066963, _1066965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1066963), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1066965), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1066963), _1066965))), -(_1066963 = _1066965)], (16012 ^ _777081) ^ [_1067245, _1067247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067245), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067247), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067245), _1067247)))], (16018 ^ _777081) ^ [_1067350, _1067352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067350), _1067352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067350), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067352), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (16024 ^ _777081) ^ [_1067476, _1067478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067476), _1067478)), -(_1067478 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067476), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 16027 ^ [_1067476, _1067478])))], (16031 ^ _777081) ^ [_1067589, _1067591] : [16032 ^ _777081 : [(16033 ^ _777081) ^ [_1067642] : [_1067591 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067589), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1067642))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1067589), _1067591)))], (16037 ^ _777081) ^ [_1067709, _1067711, _1067713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067709), _1067711)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067709), _1067713)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1067711), _1067713))))], (16043 ^ _777081) ^ [_1067832, _1067834, _1067836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1067832), _1067834)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1067836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1067836), _1067832)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1067836), _1067834))))], (16053 ^ _777081) ^ [_1068022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1068022)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (16055 ^ _777081) ^ [_1068049, _1068051] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068049), _1068051))), -(_1068049 = _1068051), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068051), _1068049)))], (16065 ^ _777081) ^ [_1068117, _1068119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068117), _1068119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1068117), _1068119)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16071 ^ _777081) ^ [_1068222, _1068224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1068222), _1068224)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1068222), _1068224)))], (16077 ^ _777081) ^ [_1068333, _1068335, _1068337] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1068333), _1068335)), _1068337) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068333), _1068337)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068335), _1068337)))], (16079 ^ _777081) ^ [_1068390, _1068392, _1068394] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068390), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1068392), _1068394)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068390), _1068392)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068390), _1068394)))], (16081 ^ _777081) ^ [_1068447, _1068449] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068447), _1068449) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068449), _1068447))], (16083 ^ _777081) ^ [_1068499, _1068501] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1068499) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1068501), -(_1068499 = _1068501)], (16089 ^ _777081) ^ [_1068584, _1068586] : [_1068584 = _1068586, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1068584) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1068586))], (16095 ^ _777081) ^ [_1068675, _1068677, _1068679] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068675), _1068677)), _1068679) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068677), _1068679)))], (16097 ^ _777081) ^ [_1068726, _1068728, _1068730] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1068726), _1068728)), _1068730) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068726), _1068730)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068728), _1068730)))], (16099 ^ _777081) ^ [_1068783, _1068785, _1068787] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1068785), _1068787)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068783), _1068785)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068783), _1068787)))], (16101 ^ _777081) ^ [_1068840, _1068842] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068840)), _1068842) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1068840), _1068842)))], (16103 ^ _777081) ^ [_1068883, _1068885] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1068883), _1068885) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1068883), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068885)))], (16105 ^ _777081) ^ [_1068923, _1068925] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1068923), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1068923), _1068925))], (16107 ^ _777081) ^ [_1068963, _1068965] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1068963), _1068965)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068963)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1068965)))], (16109 ^ _777081) ^ [_1069009] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1069009)), _1069009) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16111 ^ _777081) ^ [] : [-(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))], (16113 ^ _777081) ^ [_1069059] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1069059)) = _1069059)], (16115 ^ _777081) ^ [_1069088, _1069090] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069088), _1069090) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069090), _1069088))], (16117 ^ _777081) ^ [_1069125, _1069127, _1069129] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069125), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069127), _1069129)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069127), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069125), _1069129)))], (16119 ^ _777081) ^ [_1069176, _1069178, _1069180] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069176), _1069178)), _1069180) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069176), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069178), _1069180)))], (16121 ^ _777081) ^ [_1069227] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1069227), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1069227)], (16123 ^ _777081) ^ [_1069256] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1069256) = _1069256)], (16125 ^ _777081) ^ [_1069291] : [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)), _1069291)), _1069291) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (16127 ^ _777081) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (16139 ^ _777081) ^ [_1069477, _1069479, _1069481] : [16140 ^ _777081 : [(16141 ^ _777081) ^ [] : [_1069477 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (16143 ^ _777081) ^ [] : [_1069479 = _1069481]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069477), _1069479) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069477), _1069481))], (16129 ^ _777081) ^ [_1069365, _1069367, _1069369] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069365), _1069367) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069365), _1069369), -(_1069365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1069367 = _1069369)], (16147 ^ _777081) ^ [_1069620, _1069622, _1069624, _1069626] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069620), _1069622)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069624), _1069622)), _1069626)) = 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), _1069620), _1069624)), _1069622)), _1069626))], (16149 ^ _777081) ^ [_1069691, _1069693, _1069695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069691)), 16152 ^ _777081 : [(16153 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069691), _1069693)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069691), _1069695))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069693), _1069695)))], (16159 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069693), _1069695)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069691), _1069693)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069691), _1069695))))]]], (16165 ^ _777081) ^ [_1069974, _1069976, _1069978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1069974)), 16168 ^ _777081 : [(16169 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069974), _1069976) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069974), _1069978), -(_1069976 = _1069978)], (16175 ^ _777081) ^ [] : [_1069976 = _1069978, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069974), _1069976) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1069974), _1069978))]]], (16181 ^ _777081) ^ [_1070227, _1070229, _1070231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1070227)), 16184 ^ _777081 : [(16185 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070227), _1070229)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070227), _1070231))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070229), _1070231)))], (16191 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070229), _1070231)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070227), _1070229)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1070227), _1070231))))]]], (16213 ^ _777081) ^ [_1070817, _1070819, _1070821] : [-(hBOOL(hAPP(_1070817, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1070819), _1070821))))), 16216 ^ _777081 : [(16217 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070821), _1070819)))], (16219 ^ _777081) ^ [] : [hBOOL(hAPP(_1070817, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1070819)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1070821))))]], 16220 ^ _777081 : [(16221 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070819), _1070821)))], (16223 ^ _777081) ^ [] : [hBOOL(hAPP(_1070817, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (16197 ^ _777081) ^ [_1070528, _1070530, _1070532] : [hBOOL(hAPP(_1070528, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1070530), _1070532)))), 16200 ^ _777081 : [(16201 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1070532), _1070530)), -(hBOOL(hAPP(_1070528, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1070530)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1070532)))))], (16207 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1070530), _1070532)), -(hBOOL(hAPP(_1070528, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (16227 ^ _777081) ^ [_1071092, _1071094, _1071096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1071092)), _1071092 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071094), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1071092), _1071096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1071094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071096), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (16241 ^ _777081) ^ [_1071321, _1071323, _1071325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1071321)), _1071321 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1071323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1071321), _1071325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071323), _1071321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1071325)))], (16255 ^ _777081) ^ [_1071550, _1071552, _1071554] : [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), _1071550), _1071552)), _1071554))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1071554), _1071550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1071550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1071552)))], (16269 ^ _777081) ^ [_1071783, _1071785, _1071787] : [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), _1071783), _1071785)), _1071787)), 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)), _1071787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1071783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1071785), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16283 ^ _777081) ^ [_1072022, _1072024, _1072026, _1072028, _1072030] : [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), _1072022), _1072024)), _1072026)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1072022), _1072028)), _1072030))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1072026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072026), _1072022)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072030), _1072022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1072024), _1072028)))], (16301 ^ _777081) ^ [_1072371, _1072373, _1072375, _1072377, _1072379, _1072381] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1072371), _1072373)), _1072375) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1072377), _1072379)), _1072381), 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), _1072377), _1072379)), _1072381))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072381), _1072377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1072375)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1072377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1072377), _1072371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1072373), _1072379)))], (16327 ^ _777081) ^ [_1072870, _1072872, _1072874, _1072876, _1072878, _1072880] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1072870), _1072872)), _1072874) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1072876), _1072878)), _1072880), 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), _1072876), _1072878)), _1072880)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1072874), _1072870)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1072880)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1072876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1072876), _1072870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1072878), _1072872)))], (16353 ^ _777081) ^ [_1073375, _1073377, _1073379, _1073381, _1073383] : [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), _1073375), _1073377)), _1073379)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1073375), _1073381)), _1073383))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1073383), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1073375), _1073383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1073375), _1073379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1073381), _1073377)))], (16371 ^ _777081) ^ [_1073729, _1073731, _1073733, _1073735] : [-(_1073729 = c_Orderings_Obot__class_Obot(tc_fun(_1073731, tc_HOL_Obool))), 16374 ^ _777081 : [(16386 ^ _777081) ^ [] : [16387 ^ _777081 : [(16388 ^ _777081) ^ [_1074062] : [hAPP(c_Set_Oimage(_1073733, _1073731, _1074062), _1073735) = _1073729]], 16390 ^ _777081 : [(16391 ^ _777081) ^ [] : [-(c_Fun_Oinj__on(_1073731, _1073733, 16389 ^ [_1073729, _1073731, _1073733, _1073735], _1073729))], (16393 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073733, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1073731, _1073733, 16389 ^ [_1073729, _1073731, _1073733, _1073735]), _1073729)), _1073735)))]]], (16375 ^ _777081) ^ [] : [-(hAPP(c_Set_Oimage(_1073733, _1073731, 16382 ^ [_1073729, _1073731, _1073733, _1073735]), _1073735) = _1073729), 16376 ^ _777081 : [(16377 ^ _777081) ^ [_1073870] : [c_Fun_Oinj__on(_1073731, _1073733, _1073870, _1073729), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073733, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1073731, _1073733, _1073870), _1073729)), _1073735))]]]]], (16395 ^ _777081) ^ [] : [-(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)))], (16397 ^ _777081) ^ [_1074205, _1074207] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074205)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074207)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1074205), _1074207)))], (16399 ^ _777081) ^ [_1074251, _1074253] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074251)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074253)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1074251), _1074253)))], (16401 ^ _777081) ^ [_1074312, _1074314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074312)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074314))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074312), _1074314)))], (16407 ^ _777081) ^ [_1074417, _1074419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1074417), _1074419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074417)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074419))))], (16413 ^ _777081) ^ [_1074543, _1074545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074543)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074545))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1074543), _1074545)))], (16419 ^ _777081) ^ [_1074648, _1074650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1074648), _1074650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074648)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074650))))], (16425 ^ _777081) ^ [_1074759, _1074761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1074759)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1074761)), -(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), _1074759), _1074761))))], (16435 ^ _777081) ^ [_1074927, _1074929] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1074927), _1074929)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1074927)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1074929))))], (16441 ^ _777081) ^ [_1075032, _1075034] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1075032)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1075034))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1075032), _1075034)))], (16447 ^ _777081) ^ [] : [-(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))))], (16449 ^ _777081) ^ [_1075176, _1075178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1075176), _1075178)), -(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)), _1075176)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1075178))))], (16455 ^ _777081) ^ [_1075281, _1075283] : [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)), _1075281)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1075283))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1075281), _1075283)))], (16461 ^ _777081) ^ [_1075407, _1075409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1075407), _1075409)), -(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)), _1075407)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1075409))))], (16467 ^ _777081) ^ [_1075512, _1075514] : [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)), _1075512)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1075514))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1075512), _1075514)))], (16473 ^ _777081) ^ [_1075638, _1075640] : [_1075638 = _1075640, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1075638) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1075640))], (16479 ^ _777081) ^ [_1075723, _1075725] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1075723) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1075725), -(_1075723 = _1075725)], (16485 ^ _777081) ^ [_1075829, _1075831] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1075829) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1075831), -(_1075829 = _1075831)], (16491 ^ _777081) ^ [_1075914, _1075916] : [_1075914 = _1075916, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1075914) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1075916))], (16497 ^ _777081) ^ [] : [-(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))))], (16499 ^ _777081) ^ [] : [-(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)))], (16501 ^ _777081) ^ [_1076041, _1076043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1076041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1076043)), -(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), _1076041), _1076043))))], (16511 ^ _777081) ^ [_1076206] : [16513 ^ _777081 : [(16514 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 16512 ^ [_1076206])))], (16516 ^ _777081) ^ [] : [hBOOL(hAPP(_1076206, 16512 ^ [_1076206]))]], 16517 ^ _777081 : [(16518 ^ _777081) ^ [_1076333] : [-(hBOOL(hAPP(_1076206, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1076333))))]]], (16520 ^ _777081) ^ [_1076363] : [hBOOL(hAPP(_1076363, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 16521 ^ [_1076363]))), 16524 ^ _777081 : [(16525 ^ _777081) ^ [_1076463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1076463)), -(hBOOL(hAPP(_1076363, _1076463)))]]], (16542 ^ _777081) ^ [_1076736] : [16543 ^ _777081 : [(16544 ^ _777081) ^ [_1076793] : [hBOOL(hAPP(_1076736, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1076793)))]], 16546 ^ _777081 : [(16547 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 16545 ^ [_1076736])))], (16549 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1076736, 16545 ^ [_1076736])))]]], (16531 ^ _777081) ^ [_1076566] : [-(hBOOL(hAPP(_1076566, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 16538 ^ [_1076566])))), 16532 ^ _777081 : [(16533 ^ _777081) ^ [_1076618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1076618)), hBOOL(hAPP(_1076566, _1076618))]]], (16551 ^ _777081) ^ [_1076885] : [-(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), _1076885))))], (16553 ^ _777081) ^ [] : [-(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))))], (16555 ^ _777081) ^ [_1076943, _1076945, _1076947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1076943), _1076945)), -(c_Smallcheck_Osmall_H(_1076947, _1076943, _1076945) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (16561 ^ _777081) ^ [_1077034, _1077036, _1077038] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1077034), _1077036))), -(c_Smallcheck_Osmall_H(_1077038, _1077034, _1077036) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1077038, _1077034, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1077036), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1077038, _1077036)))], (16567 ^ _777081) ^ [_1077113, _1077115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1077113), _1077115)), -(c_Nat__Transfer_Otsub(_1077115, _1077113) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1077115), _1077113))], (16573 ^ _777081) ^ [_1077212, _1077214] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1077212), _1077214))), -(c_Nat__Transfer_Otsub(_1077214, _1077212) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (16579 ^ _777081) ^ [_1077258, _1077260, _1077262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077258), _1077260)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077258), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1077260), _1077262))))], (16585 ^ _777081) ^ [_1077369, _1077371, _1077373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077369), _1077371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077369), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1077373), _1077371))))], (16591 ^ _777081) ^ [_1077480, _1077482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077480), _1077482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077480), _1077482)))], (16597 ^ _777081) ^ [_1077577, _1077579, _1077581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077577), _1077579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077577), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1077579), _1077581))))], (16603 ^ _777081) ^ [_1077688, _1077690, _1077692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077688), _1077690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077688), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1077692), _1077690))))], (16609 ^ _777081) ^ [_1077799, _1077801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1077799)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1077801)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1077799, _1077801))))], (16619 ^ _777081) ^ [_1077946, _1077948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1077946), _1077948)), -(c_Nat__Transfer_Otsub(_1077948, _1077946) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1077948), _1077946))], (16625 ^ _777081) ^ [_1078051, _1078053] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1078051), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1078053)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1078051), _1078053)))], (16627 ^ _777081) ^ [_1078094, _1078096, _1078098] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078094)), 16633 ^ _777081 : [(16634 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1078096, 16632 ^ [_1078094, _1078096, _1078098])))], (16636 ^ _777081) ^ [] : [hBOOL(hAPP(_1078096, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 16632 ^ [_1078094, _1078096, _1078098]), _1078094)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078098)), 16641 ^ _777081 : [(16642 ^ _777081) ^ [_1078383] : [hBOOL(hAPP(_1078096, _1078383)), -(hBOOL(hAPP(_1078096, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1078383), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1078098), _1078094)))))]]], (16648 ^ _777081) ^ [_1078506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1078506), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1078506 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 16651 ^ [_1078506]))))], (16655 ^ _777081) ^ [_1078619, _1078621, _1078623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078619)), 16661 ^ _777081 : [(16662 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1078621, 16660 ^ [_1078619, _1078621, _1078623])))], (16664 ^ _777081) ^ [] : [hBOOL(hAPP(_1078621, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 16660 ^ [_1078619, _1078621, _1078623]), _1078619)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1078623)), 16669 ^ _777081 : [(16670 ^ _777081) ^ [_1078908] : [hBOOL(hAPP(_1078621, _1078908)), -(hBOOL(hAPP(_1078621, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1078908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1078623), _1078619)))))]]], (16676 ^ _777081) ^ [_1079030, _1079032] : [-(hBOOL(hAPP(_1079030, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1079030, _1079032)), 16684 ^ _777081 : [(16685 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 16683 ^ [_1079030, _1079032]), _1079032)))], (16693 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1079030, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 16683 ^ [_1079030, _1079032]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (16687 ^ _777081) ^ [_1079268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1079268), 16683 ^ [_1079030, _1079032])), hBOOL(hAPP(_1079030, _1079268))]]], (16695 ^ _777081) ^ [_1079420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1079420)), 16699 ^ _777081 : [(16700 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 16698 ^ [_1079420])))], (16702 ^ _777081) ^ [] : [-(_1079420 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 16698 ^ [_1079420]))]]], (16704 ^ _777081) ^ [_1079550, _1079552, _1079554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1079550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1079552), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1079554), 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), _1079554), _1079552))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1079550)))))], (16710 ^ _777081) ^ [_1079697, _1079699, _1079701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1079697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1079699), 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), _1079699), _1079701))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1079697))), _1079701)))], (16716 ^ _777081) ^ [_1079844, _1079846] : [class_Groups_Oordered__ab__group__add__abs(_1079844), -(hAPP(c_Groups_Oabs__class_Oabs(_1079844), hAPP(c_Groups_Oabs__class_Oabs(_1079844), _1079846)) = hAPP(c_Groups_Oabs__class_Oabs(_1079844), _1079846))], (16722 ^ _777081) ^ [_1079949, _1079951, _1079953] : [class_Groups_Oordered__ab__group__add__abs(_1079949), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079949), hAPP(c_Groups_Oabs__class_Oabs(_1079949), _1079951)), _1079953)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079949), _1079951), _1079953)))], (16732 ^ _777081) ^ [_1080118, _1080120] : [class_Groups_Oordered__ab__group__add__abs(_1080118), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080118), _1080120), hAPP(c_Groups_Oabs__class_Oabs(_1080118), _1080120))))], (16738 ^ _777081) ^ [_1080217] : [class_Groups_Oordered__ab__group__add__abs(_1080217), -(hAPP(c_Groups_Oabs__class_Oabs(_1080217), c_Groups_Ozero__class_Ozero(_1080217)) = c_Groups_Ozero__class_Ozero(_1080217))], (16744 ^ _777081) ^ [_1080308, _1080310] : [class_Groups_Oordered__ab__group__add__abs(_1080308), 16747 ^ _777081 : [(16748 ^ _777081) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1080308), _1080310) = c_Groups_Ozero__class_Ozero(_1080308), -(_1080310 = c_Groups_Ozero__class_Ozero(_1080308))], (16754 ^ _777081) ^ [] : [_1080310 = c_Groups_Ozero__class_Ozero(_1080308), -(hAPP(c_Groups_Oabs__class_Oabs(_1080308), _1080310) = c_Groups_Ozero__class_Ozero(_1080308))]]], (16760 ^ _777081) ^ [_1080540, _1080542, _1080544] : [class_Groups_Oordered__ab__group__add__abs(_1080540), -(hAPP(c_Groups_Oabs__class_Oabs(_1080540), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080540), hAPP(c_Groups_Oabs__class_Oabs(_1080540), _1080542)), hAPP(c_Groups_Oabs__class_Oabs(_1080540), _1080544))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080540), hAPP(c_Groups_Oabs__class_Oabs(_1080540), _1080542)), hAPP(c_Groups_Oabs__class_Oabs(_1080540), _1080544)))], (16766 ^ _777081) ^ [_1080699, _1080701] : [class_Rings_Olinordered__idom(_1080699), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080699), hAPP(c_Groups_Oabs__class_Oabs(_1080699), _1080701)), hAPP(c_Groups_Oabs__class_Oabs(_1080699), _1080701)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080699), _1080701), _1080701))], (16772 ^ _777081) ^ [_1080826, _1080828, _1080830] : [class_Rings_Olinordered__idom(_1080826), -(hAPP(c_Groups_Oabs__class_Oabs(_1080826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080826), _1080828), _1080830)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080826), hAPP(c_Groups_Oabs__class_Oabs(_1080826), _1080828)), hAPP(c_Groups_Oabs__class_Oabs(_1080826), _1080830)))], (16778 ^ _777081) ^ [_1080965, _1080967, _1080969] : [class_Groups_Oordered__ab__group__add__abs(_1080965), -(hAPP(c_Groups_Oabs__class_Oabs(_1080965), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080965), _1080967), _1080969)) = hAPP(c_Groups_Oabs__class_Oabs(_1080965), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080965), _1080969), _1080967)))], (16784 ^ _777081) ^ [_1081094] : [class_Rings_Olinordered__idom(_1081094), -(hAPP(c_Groups_Oabs__class_Oabs(_1081094), c_Groups_Oone__class_Oone(_1081094)) = c_Groups_Oone__class_Oone(_1081094))], (16790 ^ _777081) ^ [_1081185, _1081187] : [class_Groups_Oordered__ab__group__add__abs(_1081185), -(hAPP(c_Groups_Oabs__class_Oabs(_1081185), hAPP(c_Groups_Ouminus__class_Ouminus(_1081185), _1081187)) = hAPP(c_Groups_Oabs__class_Oabs(_1081185), _1081187))], (16796 ^ _777081) ^ [_1081290, _1081292] : [class_Rings_Olinordered__idom(_1081290), -(hAPP(c_Groups_Oabs__class_Oabs(_1081290), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1081290), _1081292)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1081290), _1081292))], (16802 ^ _777081) ^ [_1081395] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1081395)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1081395))], (16804 ^ _777081) ^ [_1081427, _1081429] : [class_Groups_Oordered__ab__group__add__abs(_1081427), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081427), c_Groups_Ozero__class_Ozero(_1081427)), hAPP(c_Groups_Oabs__class_Oabs(_1081427), _1081429))))], (16810 ^ _777081) ^ [_1081530, _1081532] : [class_Groups_Oordered__ab__group__add__abs(_1081530), 16813 ^ _777081 : [(16814 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081530), hAPP(c_Groups_Oabs__class_Oabs(_1081530), _1081532)), c_Groups_Ozero__class_Ozero(_1081530))), -(_1081532 = c_Groups_Ozero__class_Ozero(_1081530))], (16820 ^ _777081) ^ [] : [_1081532 = c_Groups_Ozero__class_Ozero(_1081530), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081530), hAPP(c_Groups_Oabs__class_Oabs(_1081530), _1081532)), c_Groups_Ozero__class_Ozero(_1081530))))]]], (16826 ^ _777081) ^ [_1081783, _1081785] : [class_Groups_Oordered__ab__group__add__abs(_1081783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081783), c_Groups_Ozero__class_Ozero(_1081783)), _1081785)), -(hAPP(c_Groups_Oabs__class_Oabs(_1081783), _1081785) = _1081785)], (16836 ^ _777081) ^ [_1081938, _1081940] : [class_Groups_Oordered__ab__group__add__abs(_1081938), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1081938), hAPP(c_Groups_Oabs__class_Oabs(_1081938), _1081940)), c_Groups_Ozero__class_Ozero(_1081938)))], (16842 ^ _777081) ^ [_1082042, _1082044] : [class_Groups_Oordered__ab__group__add__abs(_1082042), 16845 ^ _777081 : [(16846 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082042), c_Groups_Ozero__class_Ozero(_1082042)), hAPP(c_Groups_Oabs__class_Oabs(_1082042), _1082044))), _1082044 = c_Groups_Ozero__class_Ozero(_1082042)], (16852 ^ _777081) ^ [] : [-(_1082044 = c_Groups_Ozero__class_Ozero(_1082042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082042), c_Groups_Ozero__class_Ozero(_1082042)), hAPP(c_Groups_Oabs__class_Oabs(_1082042), _1082044))))]]], (16858 ^ _777081) ^ [_1082257, _1082259] : [class_Groups_Oordered__ab__group__add__abs(_1082257), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082257), c_Groups_Ozero__class_Ozero(_1082257)), _1082259)), -(hAPP(c_Groups_Oabs__class_Oabs(_1082257), _1082259) = _1082259)], (16868 ^ _777081) ^ [_1082412, _1082414, _1082416] : [class_Groups_Oordered__ab__group__add__abs(_1082412), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082412), hAPP(c_Groups_Oabs__class_Oabs(_1082412), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082412), _1082414), _1082416))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1082412), hAPP(c_Groups_Oabs__class_Oabs(_1082412), _1082414)), hAPP(c_Groups_Oabs__class_Oabs(_1082412), _1082416)))))], (16874 ^ _777081) ^ [_1082565, _1082567, _1082569, _1082571, _1082573] : [class_Rings_Olinordered__idom(_1082565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082565), hAPP(c_Groups_Oabs__class_Oabs(_1082565), _1082567)), _1082569)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082565), hAPP(c_Groups_Oabs__class_Oabs(_1082565), _1082571)), _1082573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1082565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082565), hAPP(c_Groups_Oabs__class_Oabs(_1082565), _1082567)), hAPP(c_Groups_Oabs__class_Oabs(_1082565), _1082571))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082565), _1082569), _1082573))))], (16888 ^ _777081) ^ [_1082876, _1082878, _1082880] : [class_Groups_Oordered__ab__group__add__abs(_1082876), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1082876), hAPP(c_Groups_Oabs__class_Oabs(_1082876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082876), hAPP(c_Groups_Oabs__class_Oabs(_1082876), _1082878)), hAPP(c_Groups_Oabs__class_Oabs(_1082876), _1082880)))), hAPP(c_Groups_Oabs__class_Oabs(_1082876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082876), _1082878), _1082880)))))], (16894 ^ _777081) ^ [_1083039, _1083041, _1083043] : [class_Groups_Oordered__ab__group__add__abs(_1083039), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083039), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1083039), hAPP(c_Groups_Oabs__class_Oabs(_1083039), _1083041)), hAPP(c_Groups_Oabs__class_Oabs(_1083039), _1083043))), hAPP(c_Groups_Oabs__class_Oabs(_1083039), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1083039), _1083041), _1083043)))))], (16900 ^ _777081) ^ [_1083192, _1083194, _1083196] : [class_Groups_Oordered__ab__group__add__abs(_1083192), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083192), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1083192), hAPP(c_Groups_Oabs__class_Oabs(_1083192), _1083194)), hAPP(c_Groups_Oabs__class_Oabs(_1083192), _1083196))), hAPP(c_Groups_Oabs__class_Oabs(_1083192), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1083192), _1083196), _1083194)))))], (16906 ^ _777081) ^ [_1083345, _1083347] : [class_Groups_Oordered__ab__group__add__abs(_1083345), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083345), hAPP(c_Groups_Ouminus__class_Ouminus(_1083345), _1083347)), hAPP(c_Groups_Oabs__class_Oabs(_1083345), _1083347))))], (16912 ^ _777081) ^ [_1083454, _1083456, _1083458] : [class_Groups_Oordered__ab__group__add__abs(_1083454), 16915 ^ _777081 : [(16916 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083454), hAPP(c_Groups_Oabs__class_Oabs(_1083454), _1083456)), _1083458)), 16919 ^ _777081 : [(16920 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083454), _1083456), _1083458)))], (16922 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083454), hAPP(c_Groups_Ouminus__class_Ouminus(_1083454), _1083456)), _1083458)))]]], (16924 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083454), hAPP(c_Groups_Oabs__class_Oabs(_1083454), _1083456)), _1083458))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083454), _1083456), _1083458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083454), hAPP(c_Groups_Ouminus__class_Ouminus(_1083454), _1083456)), _1083458))]]], (16934 ^ _777081) ^ [_1083832, _1083834, _1083836] : [class_Groups_Oordered__ab__group__add__abs(_1083832), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083832), _1083834), _1083836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083832), hAPP(c_Groups_Ouminus__class_Ouminus(_1083832), _1083834)), _1083836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083832), hAPP(c_Groups_Oabs__class_Oabs(_1083832), _1083834)), _1083836)))], (16948 ^ _777081) ^ [_1084079, _1084081, _1084083] : [class_Groups_Oordered__ab__group__add__abs(_1084079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084079), hAPP(c_Groups_Oabs__class_Oabs(_1084079), _1084081)), _1084083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084079), hAPP(c_Groups_Ouminus__class_Ouminus(_1084079), _1084081)), _1084083)))], (16958 ^ _777081) ^ [_1084258, _1084260, _1084262] : [class_Rings_Olinordered__idom(_1084258), 16961 ^ _777081 : [(16962 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084258), hAPP(c_Groups_Oabs__class_Oabs(_1084258), _1084260)), _1084262)), 16965 ^ _777081 : [(16966 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084258), _1084260), _1084262)))], (16968 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084258), hAPP(c_Groups_Ouminus__class_Ouminus(_1084258), _1084260)), _1084262)))]]], (16970 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084258), hAPP(c_Groups_Oabs__class_Oabs(_1084258), _1084260)), _1084262))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084258), _1084260), _1084262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1084258), hAPP(c_Groups_Ouminus__class_Ouminus(_1084258), _1084260)), _1084262))]]], (16980 ^ _777081) ^ [_1084636, _1084638] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1084636), _1084638)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1084636) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (16986 ^ _777081) ^ [_1084737, _1084739] : [class_Rings_Olinordered__idom(_1084737), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084737), c_Groups_Osgn__class_Osgn(_1084737, _1084739)), hAPP(c_Groups_Oabs__class_Oabs(_1084737), _1084739)) = _1084739)], (16992 ^ _777081) ^ [_1084844, _1084846] : [class_Rings_Olinordered__idom(_1084844), -(hAPP(c_Groups_Oabs__class_Oabs(_1084844), _1084846) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084844), _1084846), c_Groups_Osgn__class_Osgn(_1084844, _1084846)))], (16998 ^ _777081) ^ [_1084951, _1084953, _1084955] : [class_Rings_Olinordered__idom(_1084951), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084951), c_Groups_Ozero__class_Ozero(_1084951)), _1084953)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084951), hAPP(c_Groups_Oabs__class_Oabs(_1084951), _1084955)), _1084953) = hAPP(c_Groups_Oabs__class_Oabs(_1084951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084951), _1084955), _1084953)))], (17008 ^ _777081) ^ [_1085152, _1085154, _1085156] : [class_Rings_Oordered__ring__abs(_1085152), -(hAPP(c_Groups_Oabs__class_Oabs(_1085152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085152), _1085154), _1085156)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085152), hAPP(c_Groups_Oabs__class_Oabs(_1085152), _1085154)), hAPP(c_Groups_Oabs__class_Oabs(_1085152), _1085156))), 17015 ^ _777081 : [(17016 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085152), c_Groups_Ozero__class_Ozero(_1085152)), _1085154))], (17018 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085152), _1085154), c_Groups_Ozero__class_Ozero(_1085152)))]], 17019 ^ _777081 : [(17020 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085152), c_Groups_Ozero__class_Ozero(_1085152)), _1085156))], (17022 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085152), _1085156), c_Groups_Ozero__class_Ozero(_1085152)))]]], (17026 ^ _777081) ^ [_1085547, _1085549, _1085551] : [class_Groups_Oordered__ab__group__add__abs(_1085547), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085547), hAPP(c_Groups_Oabs__class_Oabs(_1085547), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1085547), _1085549), _1085551))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085547), hAPP(c_Groups_Oabs__class_Oabs(_1085547), _1085549)), hAPP(c_Groups_Oabs__class_Oabs(_1085547), _1085551)))))], (17032 ^ _777081) ^ [_1085700, _1085702, _1085704, _1085706, _1085708] : [class_Groups_Oordered__ab__group__add__abs(_1085700), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085700), hAPP(c_Groups_Oabs__class_Oabs(_1085700), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1085700), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085700), _1085702), _1085704)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085700), _1085706), _1085708)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1085700), hAPP(c_Groups_Oabs__class_Oabs(_1085700), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1085700), _1085702), _1085706))), hAPP(c_Groups_Oabs__class_Oabs(_1085700), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1085700), _1085704), _1085708))))))], (17038 ^ _777081) ^ [_1085921, _1085923] : [class_Groups_Oordered__ab__group__add__abs(_1085921), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1085921), hAPP(c_Groups_Ouminus__class_Ouminus(_1085921), hAPP(c_Groups_Oabs__class_Oabs(_1085921), _1085923))), c_Groups_Ozero__class_Ozero(_1085921))))], (17044 ^ _777081) ^ [_1086034, _1086036] : [class_Groups_Oordered__ab__group__add__abs(_1086034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1086034), _1086036), c_Groups_Ozero__class_Ozero(_1086034))), -(hAPP(c_Groups_Oabs__class_Oabs(_1086034), _1086036) = hAPP(c_Groups_Ouminus__class_Ouminus(_1086034), _1086036))], (17054 ^ _777081) ^ [_1086199, _1086201] : [class_Groups_Oabs__if(_1086199), 17057 ^ _777081 : [(17058 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086199), _1086201), c_Groups_Ozero__class_Ozero(_1086199))), -(hAPP(c_Groups_Oabs__class_Oabs(_1086199), _1086201) = hAPP(c_Groups_Ouminus__class_Ouminus(_1086199), _1086201))], (17064 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086199), _1086201), c_Groups_Ozero__class_Ozero(_1086199)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1086199), _1086201) = _1086201)]]], (17070 ^ _777081) ^ [_1086439, _1086441] : [class_Groups_Oordered__ab__group__add__abs(_1086439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1086439), _1086441), c_Groups_Ozero__class_Ozero(_1086439))), -(hAPP(c_Groups_Oabs__class_Oabs(_1086439), _1086441) = hAPP(c_Groups_Ouminus__class_Ouminus(_1086439), _1086441))], (17080 ^ _777081) ^ [_1086616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1086616)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1086616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17086 ^ _777081) ^ [_1086703] : [_1086703 = 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), _1086703)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (17092 ^ _777081) ^ [_1086802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086802), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1086802) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1086802))], (17098 ^ _777081) ^ [_1086893] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086893), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1086893) = _1086893)], (17104 ^ _777081) ^ [_1086937, _1086939, _1086941] : [17106 ^ _777081 : [(17107 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17105 ^ [_1086937, _1086939, _1086941]), _1086937)))], (17109 ^ _777081) ^ [] : [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(_1086939, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 17105 ^ [_1086937, _1086939, _1086941]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1086939, 17105 ^ [_1086937, _1086939, _1086941])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1086939, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1086941)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086941), hAPP(_1086939, _1086937))), 17119 ^ _777081 : [(17120 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 17118 ^ [_1086937, _1086939, _1086941]), _1086937)))], (17122 ^ _777081) ^ [] : [-(hAPP(_1086939, 17118 ^ [_1086937, _1086939, _1086941]) = _1086941)]]], (17124 ^ _777081) ^ [_1087387, _1087389, _1087391] : [17126 ^ _777081 : [(17127 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17125 ^ [_1087387, _1087389, _1087391]), _1087387)))], (17129 ^ _777081) ^ [] : [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(_1087389, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 17125 ^ [_1087387, _1087389, _1087391]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1087389, 17125 ^ [_1087387, _1087389, _1087391])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1087389, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1087391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1087391), hAPP(_1087389, _1087387))), 17139 ^ _777081 : [(17140 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 17138 ^ [_1087387, _1087389, _1087391]), _1087387)))], (17142 ^ _777081) ^ [] : [-(hAPP(_1087389, 17138 ^ [_1087387, _1087389, _1087391]) = _1087391)]]], (17144 ^ _777081) ^ [_1087837, _1087839] : [17146 ^ _777081 : [(17147 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 17145 ^ [_1087837, _1087839]), _1087837)))], (17149 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1087839), 17145 ^ [_1087837, _1087839]))]], -(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)), _1087839), _1087837))], (17153 ^ _777081) ^ [_1088012] : [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), _1088012))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088012) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1088012)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (17159 ^ _777081) ^ [_1088151, _1088153, _1088155, _1088157, _1088159] : [c_Fun_Oinj__on(_1088151, _1088153, _1088155, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088151, tc_HOL_Obool)), _1088157), _1088159)), 17162 ^ _777081 : [(17163 ^ _777081) ^ [] : [-(c_Fun_Oinj__on(_1088151, _1088153, _1088155, _1088157))], (17165 ^ _777081) ^ [] : [-(c_Fun_Oinj__on(_1088151, _1088153, _1088155, _1088159))], (17167 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088153, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1088151, _1088153, _1088155), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1088151, tc_HOL_Obool)), _1088157), _1088159))), hAPP(c_Set_Oimage(_1088151, _1088153, _1088155), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1088151, tc_HOL_Obool)), _1088159), _1088157))) = c_Orderings_Obot__class_Obot(tc_fun(_1088153, tc_HOL_Obool)))]]], (17169 ^ _777081) ^ [_1088418, _1088420, _1088422, _1088424, _1088426] : [-(c_Fun_Oinj__on(_1088418, _1088420, _1088422, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088418, tc_HOL_Obool)), _1088424), _1088426))), c_Fun_Oinj__on(_1088418, _1088420, _1088422, _1088424), c_Fun_Oinj__on(_1088418, _1088420, _1088422, _1088426), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088420, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1088418, _1088420, _1088422), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1088418, tc_HOL_Obool)), _1088424), _1088426))), hAPP(c_Set_Oimage(_1088418, _1088420, _1088422), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1088418, tc_HOL_Obool)), _1088426), _1088424))) = c_Orderings_Obot__class_Obot(tc_fun(_1088420, tc_HOL_Obool))], (17183 ^ _777081) ^ [_1088757, _1088759, _1088761, _1088763] : [17185 ^ _777081 : [(17186 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1088757), 17184 ^ [_1088757, _1088759, _1088761, _1088763])))], (17188 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17184 ^ [_1088757, _1088759, _1088761, _1088763]), _1088759)))], (17190 ^ _777081) ^ [] : [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(_1088761, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 17184 ^ [_1088757, _1088759, _1088761, _1088763]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1088761, 17184 ^ [_1088757, _1088759, _1088761, _1088763])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1088757), _1088759)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1088761, _1088757)), _1088763)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1088763), hAPP(_1088761, _1088759))), 17204 ^ _777081 : [(17205 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1088757), 17203 ^ [_1088757, _1088759, _1088761, _1088763])))], (17207 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 17203 ^ [_1088757, _1088759, _1088761, _1088763]), _1088759)))], (17209 ^ _777081) ^ [] : [-(hAPP(_1088761, 17203 ^ [_1088757, _1088759, _1088761, _1088763]) = _1088763)]]], (17211 ^ _777081) ^ [_1089383, _1089385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1089383), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1089383), _1089385)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1089383))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1089385))))], (17217 ^ _777081) ^ [_1089524, _1089526, _1089528, _1089530] : [hBOOL(hAPP(_1089524, _1089526)), hBOOL(hAPP(_1089528, _1089526)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1089530, tc_HOL_Obool)), _1089524), _1089528), _1089526)))], (17227 ^ _777081) ^ [_1089695, _1089697, _1089699, _1089701] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1089695, tc_HOL_Obool)), _1089697), _1089699), _1089701)), 17230 ^ _777081 : [(17231 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1089697, _1089701)))], (17233 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1089699, _1089701)))]]], (17235 ^ _777081) ^ [_1089840, _1089842, _1089844, _1089846] : [hBOOL(hAPP(hAPP(c_member(_1089840), _1089842), _1089844)), hBOOL(hAPP(hAPP(c_member(_1089840), _1089842), _1089846)), -(hBOOL(hAPP(hAPP(c_member(_1089840), _1089842), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1089840, tc_HOL_Obool)), _1089844), _1089846))))], (17245 ^ _777081) ^ [_1090041, _1090043, _1090045, _1090047] : [hBOOL(hAPP(hAPP(c_member(_1090041), _1090043), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090041, tc_HOL_Obool)), _1090045), _1090047))), 17248 ^ _777081 : [(17249 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1090041), _1090043), _1090045)))], (17251 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1090041), _1090043), _1090047)))]]], (17253 ^ _777081) ^ [_1090216, _1090218, _1090220, _1090222, _1090224] : [class_Lattices_Olattice(_1090216), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090218, _1090216)), _1090220), _1090222), _1090224) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1090216), hAPP(_1090220, _1090224)), hAPP(_1090222, _1090224)))], (17259 ^ _777081) ^ [_1090353, _1090355] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090353, tc_HOL_Obool)), _1090355), _1090355) = _1090355)], (17261 ^ _777081) ^ [_1090389, _1090391, _1090393] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090389, tc_HOL_Obool)), _1090391), _1090393) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090389, tc_HOL_Obool)), _1090393), _1090391))], (17263 ^ _777081) ^ [_1090438, _1090440, _1090442] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090438, tc_HOL_Obool)), _1090440), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090438, tc_HOL_Obool)), _1090440), _1090442)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090438, tc_HOL_Obool)), _1090440), _1090442))], (17265 ^ _777081) ^ [_1090498, _1090500, _1090502, _1090504] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090498, tc_HOL_Obool)), _1090500), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090498, tc_HOL_Obool)), _1090502), _1090504)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090498, tc_HOL_Obool)), _1090502), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090498, tc_HOL_Obool)), _1090500), _1090504)))], (17267 ^ _777081) ^ [_1090571, _1090573, _1090575, _1090577] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090571, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090571, tc_HOL_Obool)), _1090573), _1090575)), _1090577) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090571, tc_HOL_Obool)), _1090573), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090571, tc_HOL_Obool)), _1090575), _1090577)))], (17269 ^ _777081) ^ [_1090644, _1090646, _1090648] : [class_Int_Onumber(_1090644), 17272 ^ _777081 : [(17273 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1090644), _1090646) = _1090648, -(_1090648 = hAPP(c_Int_Onumber__class_Onumber__of(_1090644), _1090646))], (17279 ^ _777081) ^ [] : [_1090648 = hAPP(c_Int_Onumber__class_Onumber__of(_1090644), _1090646), -(hAPP(c_Int_Onumber__class_Onumber__of(_1090644), _1090646) = _1090648)]]], (17285 ^ _777081) ^ [_1090885, _1090887, _1090889] : [class_Int_Onumber__ring(_1090885), class_Int_Oring__char__0(_1090885), 17292 ^ _777081 : [(17293 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1090885), _1090887) = hAPP(c_Int_Onumber__class_Onumber__of(_1090885), _1090889), -(_1090887 = _1090889)], (17299 ^ _777081) ^ [] : [_1090887 = _1090889, -(hAPP(c_Int_Onumber__class_Onumber__of(_1090885), _1090887) = hAPP(c_Int_Onumber__class_Onumber__of(_1090885), _1090889))]]], (17305 ^ _777081) ^ [_1091180, _1091182, _1091184, _1091186] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1091180, tc_HOL_Obool)), _1091182), _1091184), _1091186)), -(hBOOL(hAPP(_1091182, _1091186)))], (17311 ^ _777081) ^ [_1091291, _1091293, _1091295, _1091297] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1091291, tc_HOL_Obool)), _1091293), _1091295), _1091297)), -(hBOOL(hAPP(_1091295, _1091297)))], (17317 ^ _777081) ^ [_1091402, _1091404] : [class_Lattices_Osemilattice__inf(_1091402), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091402), _1091404), _1091404) = _1091404)], (17323 ^ _777081) ^ [_1091493, _1091495] : [class_Lattices_Osemilattice__inf(_1091493), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091493), _1091495), _1091495) = _1091495)], (17329 ^ _777081) ^ [_1091584, _1091586, _1091588] : [class_Lattices_Osemilattice__inf(_1091584), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091584), _1091586), _1091588) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091584), _1091588), _1091586))], (17335 ^ _777081) ^ [_1091693, _1091695, _1091697] : [class_Lattices_Olattice(_1091693), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091693), _1091695), _1091697) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091693), _1091697), _1091695))], (17341 ^ _777081) ^ [_1091802, _1091804, _1091806] : [class_Lattices_Osemilattice__inf(_1091802), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091802), _1091804), _1091806) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091802), _1091806), _1091804))], (17347 ^ _777081) ^ [_1091911, _1091913, _1091915] : [class_Lattices_Osemilattice__inf(_1091911), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091911), _1091913), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091911), _1091913), _1091915)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1091911), _1091913), _1091915))], (17353 ^ _777081) ^ [_1092036, _1092038, _1092040] : [class_Lattices_Olattice(_1092036), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092036), _1092038), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092036), _1092038), _1092040)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092036), _1092038), _1092040))], (17359 ^ _777081) ^ [_1092161, _1092163, _1092165] : [class_Lattices_Osemilattice__inf(_1092161), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092161), _1092163), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092161), _1092163), _1092165)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092161), _1092163), _1092165))], (17365 ^ _777081) ^ [_1092286, _1092288, _1092290, _1092292] : [class_Lattices_Osemilattice__inf(_1092286), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092286), _1092288), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092286), _1092290), _1092292)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092286), _1092290), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092286), _1092288), _1092292)))], (17371 ^ _777081) ^ [_1092429, _1092431, _1092433, _1092435] : [class_Lattices_Olattice(_1092429), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092429), _1092431), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092429), _1092433), _1092435)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092429), _1092433), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092429), _1092431), _1092435)))], (17377 ^ _777081) ^ [_1092572, _1092574, _1092576, _1092578] : [class_Lattices_Osemilattice__inf(_1092572), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092572), _1092574), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092572), _1092576), _1092578)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092572), _1092576), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092572), _1092574), _1092578)))], (17383 ^ _777081) ^ [_1092715, _1092717, _1092719, _1092721] : [class_Lattices_Osemilattice__inf(_1092715), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092715), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092715), _1092717), _1092719)), _1092721) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092715), _1092717), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092715), _1092719), _1092721)))], (17389 ^ _777081) ^ [_1092858, _1092860, _1092862, _1092864] : [class_Lattices_Olattice(_1092858), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092858), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092858), _1092860), _1092862)), _1092864) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092858), _1092860), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1092858), _1092862), _1092864)))], (17395 ^ _777081) ^ [_1093001, _1093003, _1093005, _1093007] : [class_Lattices_Osemilattice__inf(_1093001), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1093001), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1093001), _1093003), _1093005)), _1093007) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1093001), _1093003), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1093001), _1093005), _1093007)))], (17401 ^ _777081) ^ [_1093144, _1093146, _1093148, _1093150, _1093152] : [class_Lattices_Olattice(_1093144), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1093146, _1093144)), _1093148), _1093150), _1093152) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1093144), hAPP(_1093148, _1093152)), hAPP(_1093150, _1093152)))], (17407 ^ _777081) ^ [_1093281, _1093283] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1093281), _1093283) = 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)), _1093281)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1093283))))], (17409 ^ _777081) ^ [_1093327, _1093329, _1093331] : [class_Lattices_Olattice(_1093327), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093327), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1093327), _1093329), _1093331)), _1093329)))], (17415 ^ _777081) ^ [_1093434, _1093436, _1093438] : [class_Lattices_Osemilattice__inf(_1093434), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093434), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1093434), _1093436), _1093438)), _1093436)))], (17421 ^ _777081) ^ [_1093541, _1093543, _1093545] : [class_Lattices_Olattice(_1093541), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093541), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1093541), _1093543), _1093545)), _1093545)))], (17427 ^ _777081) ^ [_1093648, _1093650, _1093652] : [class_Lattices_Osemilattice__inf(_1093648), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093648), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1093648), _1093650), _1093652)), _1093652)))], (17433 ^ _777081) ^ [_1093755, _1093757, _1093759] : [class_Lattices_Osemilattice__inf(_1093755), 17436 ^ _777081 : [(17437 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093755), _1093757), _1093759)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1093755), _1093757), _1093759) = _1093757)], (17443 ^ _777081) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1093755), _1093757), _1093759) = _1093757, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093755), _1093757), _1093759)))]]], (17449 ^ _777081) ^ [_1094011, _1094013, _1094015, _1094017] : [class_Lattices_Osemilattice__inf(_1094011), 17452 ^ _777081 : [(17453 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094011), _1094013), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1094011), _1094015), _1094017))), 17456 ^ _777081 : [(17457 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094011), _1094013), _1094015)))], (17459 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094011), _1094013), _1094017)))]]], (17461 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094011), _1094013), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1094011), _1094015), _1094017)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094011), _1094013), _1094015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094011), _1094013), _1094017))]]], (17471 ^ _777081) ^ [_1094391, _1094393, _1094395, _1094397] : [class_Lattices_Osemilattice__inf(_1094391), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094391), _1094393), _1094395)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094391), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1094391), _1094393), _1094397)), _1094395)))], (17481 ^ _777081) ^ [_1094570, _1094572, _1094574, _1094576] : [class_Lattices_Osemilattice__inf(_1094570), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094570), _1094572), _1094574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094570), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1094570), _1094576), _1094572)), _1094574)))], (17491 ^ _777081) ^ [_1094749, _1094751, _1094753] : [class_Lattices_Osemilattice__inf(_1094749), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094749), _1094751), _1094753)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1094749), _1094751), _1094753) = _1094751)], (17501 ^ _777081) ^ [_1094910, _1094912, _1094914] : [class_Lattices_Osemilattice__inf(_1094910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094910), _1094912), _1094914)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1094910), _1094914), _1094912) = _1094912)], (17511 ^ _777081) ^ [_1095071, _1095073, _1095075, _1095077] : [class_Lattices_Osemilattice__inf(_1095071), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095071), _1095073), _1095075)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095071), _1095073), _1095077)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095071), _1095073), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1095071), _1095075), _1095077))))], (17525 ^ _777081) ^ [_1095320, _1095322, _1095324, _1095326] : [class_Lattices_Osemilattice__inf(_1095320), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095320), _1095322), _1095324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095320), _1095322), _1095326)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095320), _1095322), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1095320), _1095324), _1095326))))], (17539 ^ _777081) ^ [_1095569, _1095571, _1095573, _1095575, _1095577] : [class_Lattices_Osemilattice__inf(_1095569), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095569), _1095571), _1095573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095569), _1095575), _1095577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095569), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1095569), _1095571), _1095575)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1095569), _1095573), _1095577))))], (17553 ^ _777081) ^ [_1095840, _1095842, _1095844, _1095846] : [class_Lattices_Osemilattice__inf(_1095840), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095840), _1095842), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1095840), _1095844), _1095846))), 17560 ^ _777081 : [(17561 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095840), _1095842), _1095844)))], (17563 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095840), _1095842), _1095846)))]]], (17565 ^ _777081) ^ [_1096063, _1096065, _1096067, _1096069] : [class_Lattices_Osemilattice__inf(_1096063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096063), _1096065), _1096067)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096063), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096063), _1096065), _1096069)), _1096067)))], (17575 ^ _777081) ^ [_1096242, _1096244, _1096246, _1096248] : [class_Lattices_Osemilattice__inf(_1096242), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096242), _1096244), _1096246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096242), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096242), _1096248), _1096244)), _1096246)))], (17585 ^ _777081) ^ [_1096421, _1096423] : [class_Lattices_Obounded__lattice__bot(_1096421), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096421), _1096423), c_Orderings_Obot__class_Obot(_1096421)) = c_Orderings_Obot__class_Obot(_1096421))], (17591 ^ _777081) ^ [_1096520, _1096522] : [class_Lattices_Obounded__lattice__bot(_1096520), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096520), c_Orderings_Obot__class_Obot(_1096520)), _1096522) = c_Orderings_Obot__class_Obot(_1096520))], (17597 ^ _777081) ^ [_1096619, _1096621, _1096623] : [class_Lattices_Olattice(_1096619), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096619), _1096621), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1096619), _1096621), _1096623)) = _1096621)], (17603 ^ _777081) ^ [_1096728, _1096730, _1096732] : [class_Lattices_Olattice(_1096728), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1096728), _1096730), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096728), _1096730), _1096732)) = _1096730)], (17609 ^ _777081) ^ [_1096837, _1096839, _1096841, _1096843] : [class_Lattices_Odistrib__lattice(_1096837), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096837), _1096839), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1096837), _1096841), _1096843)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1096837), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096837), _1096839), _1096841)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096837), _1096839), _1096843)))], (17615 ^ _777081) ^ [_1096996, _1096998, _1097000, _1097002] : [class_Lattices_Odistrib__lattice(_1096996), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1096996), _1096998), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096996), _1097000), _1097002)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1096996), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1096996), _1096998), _1097000)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1096996), _1096998), _1097002)))], (17621 ^ _777081) ^ [_1097155, _1097157, _1097159, _1097161] : [class_Lattices_Odistrib__lattice(_1097155), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1097155), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1097155), _1097157), _1097159)), _1097161) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1097155), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1097155), _1097157), _1097161)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1097155), _1097159), _1097161)))], (17627 ^ _777081) ^ [_1097314, _1097316, _1097318, _1097320] : [class_Lattices_Odistrib__lattice(_1097314), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1097314), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1097314), _1097316), _1097318)), _1097320) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1097314), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1097314), _1097316), _1097320)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1097314), _1097318), _1097320)))], (17633 ^ _777081) ^ [_1097494, _1097496, _1097498, _1097500] : [hBOOL(hAPP(hAPP(c_member(_1097494), _1097496), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1097494, tc_HOL_Obool)), _1097498), _1097500))), 17636 ^ _777081 : [(17637 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1097494), _1097496), _1097498)))], (17639 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1097494), _1097496), _1097500)))]]], (17641 ^ _777081) ^ [_1097661, _1097663, _1097665, _1097667] : [-(hBOOL(hAPP(hAPP(c_member(_1097661), _1097663), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1097661, tc_HOL_Obool)), _1097665), _1097667)))), hBOOL(hAPP(hAPP(c_member(_1097661), _1097663), _1097665)), hBOOL(hAPP(hAPP(c_member(_1097661), _1097663), _1097667))], (17651 ^ _777081) ^ [_1097864, _1097866, _1097868, _1097870] : [hBOOL(hAPP(hAPP(c_member(_1097864), _1097866), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1097864, tc_HOL_Obool)), _1097868), _1097870))), -(hBOOL(hAPP(hAPP(c_member(_1097864), _1097866), _1097868)))], (17657 ^ _777081) ^ [_1097995, _1097997, _1097999, _1098001] : [hBOOL(hAPP(hAPP(c_member(_1097995), _1097997), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1097995, tc_HOL_Obool)), _1097999), _1098001))), -(hBOOL(hAPP(hAPP(c_member(_1097995), _1097997), _1098001)))], (17663 ^ _777081) ^ [_1098126, _1098128] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1098126, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1098126, tc_HOL_Obool))), _1098128) = c_Orderings_Obot__class_Obot(tc_fun(_1098126, tc_HOL_Obool)))], (17665 ^ _777081) ^ [_1098172, _1098174] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1098172, tc_HOL_Obool)), _1098174), c_Orderings_Obot__class_Obot(tc_fun(_1098172, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1098172, tc_HOL_Obool)))], (17681 ^ _777081) ^ [_1098550, _1098552, _1098554] : [17683 ^ _777081 : [(17684 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098550), 17682 ^ [_1098550, _1098552, _1098554]), _1098552)))], (17687 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098550), 17685 ^ [_1098550, _1098552, _1098554]), _1098554)))], (17689 ^ _777081) ^ [] : [-(17682 ^ [_1098550, _1098552, _1098554] = 17685 ^ [_1098550, _1098552, _1098554])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1098550, tc_HOL_Obool)), _1098552), _1098554) = c_Orderings_Obot__class_Obot(tc_fun(_1098550, tc_HOL_Obool)))], (17667 ^ _777081) ^ [_1098236, _1098238, _1098240] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1098236, tc_HOL_Obool)), _1098238), _1098240) = c_Orderings_Obot__class_Obot(tc_fun(_1098236, tc_HOL_Obool)), 17670 ^ _777081 : [(17671 ^ _777081) ^ [_1098360] : [hBOOL(hAPP(hAPP(c_member(_1098236), _1098360), _1098238)), 17674 ^ _777081 : [(17675 ^ _777081) ^ [_1098450] : [hBOOL(hAPP(hAPP(c_member(_1098236), _1098450), _1098240)), _1098360 = _1098450]]]]], (17693 ^ _777081) ^ [_1098711] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 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_1099159))))], (17723 ^ _777081) ^ [_1099372, _1099374, _1099376, _1099378, _1099380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1099372, tc_HOL_Obool)), _1099374), _1099376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1099372, tc_HOL_Obool)), _1099378), _1099380)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1099372, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099372, tc_HOL_Obool)), _1099374), _1099378)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099372, tc_HOL_Obool)), _1099376), _1099380))))], (17733 ^ _777081) ^ [_1099617, _1099619, _1099621, _1099623] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099617, tc_HOL_Obool)), _1099619), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1099617, tc_HOL_Obool)), _1099621), _1099623)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1099617, tc_HOL_Obool)), 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hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1099785, tc_HOL_Obool)), _1099787), _1099789)), _1099791) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1099785, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099785, tc_HOL_Obool)), _1099787), _1099791)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099785, tc_HOL_Obool)), _1099789), _1099791)))], (17739 ^ _777081) ^ [_1099869, _1099871, _1099873, _1099875] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1099869, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099869, tc_HOL_Obool)), _1099871), _1099873)), _1099875) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1099869, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1099869, tc_HOL_Obool)), _1099871), _1099875)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1099869, tc_HOL_Obool)), _1099873), _1099875)))], (17741 ^ 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tc_HOL_Obool)), _1099959), _1099955)))], (17743 ^ _777081) ^ [_1100092, _1100094, _1100096, _1100098] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100092, tc_HOL_Obool)), _1100094), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100092, tc_HOL_Obool)), _1100096), _1100098)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100092, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100092, tc_HOL_Obool)), _1100094), _1100096)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100092, tc_HOL_Obool)), _1100094), _1100098)))], (17745 ^ _777081) ^ [_1100176, _1100178, _1100180, _1100182] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100176, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100176, tc_HOL_Obool)), _1100178), _1100180)), _1100182) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100176, tc_HOL_Obool)), _1100178), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100176, tc_HOL_Obool)), _1100180), _1100182)))], (17747 ^ _777081) ^ [_1100249, _1100251, _1100253, _1100255] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100249, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100249, tc_HOL_Obool)), _1100251), _1100253)), _1100255) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100249, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100249, tc_HOL_Obool)), _1100251), _1100255)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100249, tc_HOL_Obool)), _1100253), _1100255)))], (17749 ^ _777081) ^ [_1100333, _1100335, _1100337, _1100339] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100333, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100333, tc_HOL_Obool)), _1100335), _1100337)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100333, tc_HOL_Obool)), _1100339), _1100337)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1100333, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100333, tc_HOL_Obool)), _1100335), _1100337)), _1100339))], (17751 ^ _777081) ^ [_1100417, _1100419, _1100421, _1100423, _1100425] : [c_Fun_Oinj__on(_1100417, _1100419, _1100421, _1100423), c_Fun_Oinj__on(_1100417, _1100419, _1100421, _1100425), -(c_Fun_Oinj__on(_1100417, _1100419, _1100421, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100417, tc_HOL_Obool)), _1100423), _1100425)))], (17761 ^ _777081) ^ [_1100592, _1100594] : [class_Int_Onumber__ring(_1100592), 17764 ^ _777081 : [(17765 ^ _777081) ^ [] : [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), _1100594))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1100592), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100594)) = hAPP(c_Int_Onumber__class_Onumber__of(_1100592), _1100594))], (17771 ^ _777081) ^ [] : [-(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), _1100594)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1100592), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1100594)) = c_Groups_Ozero__class_Ozero(_1100592))]]], (17777 ^ _777081) ^ [_1100832, _1100834, _1100836, _1100838, _1100840] : [-(c_Map_Orestrict__map(_1100832, _1100834, c_Map_Orestrict__map(_1100832, _1100834, _1100836, _1100838), _1100840) = c_Map_Orestrict__map(_1100832, _1100834, _1100836, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100832, tc_HOL_Obool)), _1100838), _1100840)))], (17779 ^ _777081) ^ [_1100910, _1100912, _1100914, _1100916] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1100910, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1100910, tc_fun(_1100910, tc_HOL_Obool), tc_HOL_Obool), c_member(_1100910)), _1100912)), hAPP(hAPP(c_COMBC(_1100910, tc_fun(_1100910, 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_1101664] : [class_Int_Onumber(_1101660), class_Orderings_Olinorder(_1101660), 17810 ^ _777081 : [(17811 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101660), hAPP(c_Int_Onumber__class_Onumber__of(_1101660), _1101662)), hAPP(c_Int_Onumber__class_Onumber__of(_1101660), _1101664))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101660), hAPP(c_Int_Onumber__class_Onumber__of(_1101660), _1101664)), hAPP(c_Int_Onumber__class_Onumber__of(_1101660), _1101662)))], (17817 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101660), hAPP(c_Int_Onumber__class_Onumber__of(_1101660), _1101664)), hAPP(c_Int_Onumber__class_Onumber__of(_1101660), _1101662)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101660), hAPP(c_Int_Onumber__class_Onumber__of(_1101660), _1101662)), hAPP(c_Int_Onumber__class_Onumber__of(_1101660), _1101664))))]]], (17823 ^ _777081) ^ [_1101987, _1101989] : [class_Lattices_Oboolean__algebra(_1101987), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1101987), hAPP(c_Groups_Ouminus__class_Ouminus(_1101987), _1101989)), _1101989) = c_Orderings_Obot__class_Obot(_1101987))], (17829 ^ _777081) ^ [_1102092, _1102094] : [class_Lattices_Oboolean__algebra(_1102092), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1102092), _1102094), hAPP(c_Groups_Ouminus__class_Ouminus(_1102092), _1102094)) = c_Orderings_Obot__class_Obot(_1102092))], (17835 ^ _777081) ^ [_1102197, _1102199, _1102201] : [class_Lattices_Oboolean__algebra(_1102197), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1102197), _1102199), _1102201) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1102197), _1102199), hAPP(c_Groups_Ouminus__class_Ouminus(_1102197), _1102201)))], (17841 ^ _777081) ^ [_1102316, _1102318, _1102320, _1102322] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102316), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102316), _1102318), _1102320)), hAPP(c_Int_Onumber__class_Onumber__of(_1102316), _1102322)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102316), _1102318), hAPP(c_Int_Onumber__class_Onumber__of(_1102316), _1102322))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102316), _1102320), hAPP(c_Int_Onumber__class_Onumber__of(_1102316), _1102322)))), class_Int_Onumber(_1102316), class_Rings_Osemiring(_1102316)], (17851 ^ _777081) ^ [_1102559, _1102561, _1102563, _1102565] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102559), hAPP(c_Int_Onumber__class_Onumber__of(_1102559), _1102561)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102559), _1102563), _1102565)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102559), hAPP(c_Int_Onumber__class_Onumber__of(_1102559), _1102561)), _1102563)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102559), hAPP(c_Int_Onumber__class_Onumber__of(_1102559), _1102561)), _1102565))), class_Int_Onumber(_1102559), class_Rings_Osemiring(_1102559)], (17861 ^ _777081) ^ [_1102802, _1102804, _1102806] : [class_Lattices_Oboolean__algebra(_1102802), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1102802), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1102802), _1102804), _1102806)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1102802), hAPP(c_Groups_Ouminus__class_Ouminus(_1102802), _1102804)), hAPP(c_Groups_Ouminus__class_Ouminus(_1102802), _1102806)))], (17867 ^ _777081) ^ [_1102941, _1102943, _1102945] : [class_Lattices_Oboolean__algebra(_1102941), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1102941), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1102941), _1102943), _1102945)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1102941), hAPP(c_Groups_Ouminus__class_Ouminus(_1102941), _1102943)), hAPP(c_Groups_Ouminus__class_Ouminus(_1102941), _1102945)))], (17873 ^ _777081) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17875 ^ _777081) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (17877 ^ _777081) ^ [_1103116, _1103118, _1103120, _1103122] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103116), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1103116), _1103118), _1103120)), hAPP(c_Int_Onumber__class_Onumber__of(_1103116), _1103122)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1103116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103116), _1103118), hAPP(c_Int_Onumber__class_Onumber__of(_1103116), _1103122))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103116), _1103120), hAPP(c_Int_Onumber__class_Onumber__of(_1103116), _1103122)))), class_Int_Onumber(_1103116), class_Rings_Oring(_1103116)], (17887 ^ _777081) ^ [_1103359, _1103361, _1103363, _1103365] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103359), hAPP(c_Int_Onumber__class_Onumber__of(_1103359), _1103361)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1103359), _1103363), _1103365)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1103359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103359), hAPP(c_Int_Onumber__class_Onumber__of(_1103359), _1103361)), _1103363)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103359), hAPP(c_Int_Onumber__class_Onumber__of(_1103359), _1103361)), _1103365))), class_Int_Onumber(_1103359), class_Rings_Oring(_1103359)], (17897 ^ _777081) ^ [_1103602, _1103604, _1103606] : [class_Int_Onumber__ring(_1103602), class_Rings_Olinordered__idom(_1103602), 17904 ^ _777081 : [(17905 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103602), hAPP(c_Int_Onumber__class_Onumber__of(_1103602), _1103604)), hAPP(c_Int_Onumber__class_Onumber__of(_1103602), _1103606))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103604), _1103606)))], (17911 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1103604), _1103606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1103602), hAPP(c_Int_Onumber__class_Onumber__of(_1103602), _1103604)), hAPP(c_Int_Onumber__class_Onumber__of(_1103602), _1103606))))]]], (17917 ^ _777081) ^ [_1103933, _1103935, _1103937] : [class_Int_Onumber__ring(_1103933), class_Rings_Olinordered__idom(_1103933), 17924 ^ _777081 : [(17925 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103933), hAPP(c_Int_Onumber__class_Onumber__of(_1103933), _1103935)), hAPP(c_Int_Onumber__class_Onumber__of(_1103933), _1103937))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103935), _1103937)))], (17931 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1103935), _1103937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103933), hAPP(c_Int_Onumber__class_Onumber__of(_1103933), _1103935)), hAPP(c_Int_Onumber__class_Onumber__of(_1103933), _1103937))))]]], (17937 ^ _777081) ^ [_1104264, _1104266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1104264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1104266)), 17944 ^ _777081 : [(17945 ^ _777081) ^ [] : [hAPP(c_Int_Onat, _1104264) = hAPP(c_Int_Onat, _1104266), -(_1104264 = _1104266)], (17951 ^ _777081) ^ [] : [_1104264 = _1104266, -(hAPP(c_Int_Onat, _1104264) = hAPP(c_Int_Onat, _1104266))]]], (17957 ^ _777081) ^ [_1104561] : [17958 ^ _777081 : [(17959 ^ _777081) ^ [_1104618] : [hBOOL(hAPP(_1104561, _1104618))]], 17961 ^ _777081 : [(17962 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 17960 ^ [_1104561])))], (17964 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1104561, hAPP(c_Int_Onat, 17960 ^ [_1104561]))))]]], (17966 ^ _777081) ^ [_1104704] : [-(hBOOL(hAPP(_1104704, 17973 ^ [_1104704]))), 17967 ^ _777081 : [(17968 ^ _777081) ^ [_1104756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1104756)), hBOOL(hAPP(_1104704, hAPP(c_Int_Onat, _1104756)))]]], (17988 ^ _777081) ^ [_1105080] : [17990 ^ _777081 : [(17991 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 17989 ^ [_1105080])))], (17993 ^ _777081) ^ [] : [hBOOL(hAPP(_1105080, hAPP(c_Int_Onat, 17989 ^ [_1105080])))]], 17994 ^ _777081 : [(17995 ^ _777081) ^ [_1105213] : [-(hBOOL(hAPP(_1105080, _1105213)))]]], (17977 ^ _777081) ^ [_1104895] : [hBOOL(hAPP(_1104895, 17978 ^ [_1104895])), 17981 ^ _777081 : [(17982 ^ _777081) ^ [_1104989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1104989)), -(hBOOL(hAPP(_1104895, hAPP(c_Int_Onat, _1104989))))]]], (17997 ^ _777081) ^ [_1105246, _1105248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1105246)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1105248)), 18004 ^ _777081 : [(18005 ^ _777081) ^ [] : [hAPP(c_Int_Onat, _1105246) = hAPP(c_Int_Onat, _1105248), -(_1105246 = _1105248)], (18011 ^ _777081) ^ [] : [_1105246 = _1105248, -(hAPP(c_Int_Onat, _1105246) = hAPP(c_Int_Onat, _1105248))]]], (18017 ^ _777081) ^ [_1105531, _1105533, _1105535, _1105537] : [class_Int_Onumber__ring(_1105531), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105531), hAPP(c_Int_Onumber__class_Onumber__of(_1105531), _1105533)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105531), hAPP(c_Int_Onumber__class_Onumber__of(_1105531), _1105535)), _1105537)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105531), hAPP(c_Int_Onumber__class_Onumber__of(_1105531), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105533), _1105535))), _1105537))], (18023 ^ _777081) ^ [_1105700, _1105702, _1105704] : [class_Int_Onumber__ring(_1105700), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105700), hAPP(c_Int_Onumber__class_Onumber__of(_1105700), _1105702)), hAPP(c_Int_Onumber__class_Onumber__of(_1105700), _1105704)) = hAPP(c_Int_Onumber__class_Onumber__of(_1105700), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105702), _1105704)))], (18029 ^ _777081) ^ [_1105835, _1105837, _1105839] : [class_Int_Onumber__ring(_1105835), -(hAPP(c_Int_Onumber__class_Onumber__of(_1105835), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105837), _1105839)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105835), hAPP(c_Int_Onumber__class_Onumber__of(_1105835), _1105837)), hAPP(c_Int_Onumber__class_Onumber__of(_1105835), _1105839)))], (18035 ^ _777081) ^ [_1105985, _1105987, _1105989, _1105991] : [hBOOL(hAPP(hAPP(c_member(_1105985), _1105987), _1105989)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1105985, tc_HOL_Obool)), _1105989), hAPP(hAPP(c_Set_Oinsert(_1105985), _1105987), _1105991)) = hAPP(hAPP(c_Set_Oinsert(_1105985), _1105987), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1105985, tc_HOL_Obool)), _1105989), _1105991)))], (18041 ^ _777081) ^ [_1106150, _1106152, _1106154, _1106156] : [-(hBOOL(hAPP(hAPP(c_member(_1106150), _1106152), _1106154))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106150, tc_HOL_Obool)), _1106154), hAPP(hAPP(c_Set_Oinsert(_1106150), _1106152), _1106156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106150, tc_HOL_Obool)), _1106154), _1106156))], (18047 ^ _777081) ^ [_1106244, _1106246, _1106248, _1106250] : [hBOOL(hAPP(hAPP(c_member(_1106244), _1106246), _1106248)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106244, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1106244), _1106246), _1106250)), _1106248) = hAPP(hAPP(c_Set_Oinsert(_1106244), _1106246), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106244, tc_HOL_Obool)), _1106250), _1106248)))], (18053 ^ _777081) ^ [_1106409, _1106411, _1106413, _1106415] : [-(hBOOL(hAPP(hAPP(c_member(_1106409), _1106411), _1106413))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106409, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1106409), _1106411), _1106415)), _1106413) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106409, tc_HOL_Obool)), _1106415), _1106413))], (18059 ^ _777081) ^ [_1106484, _1106486, _1106488, _1106490] : [-(hBOOL(hAPP(hAPP(c_member(_1106484), _1106486), _1106488))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106484, tc_HOL_Obool)), _1106488), hAPP(hAPP(c_Set_Oinsert(_1106484), _1106486), _1106490)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106484, tc_HOL_Obool)), _1106488), _1106490))], (18065 ^ _777081) ^ [_1106557, _1106559, _1106561, _1106563] : [-(hBOOL(hAPP(hAPP(c_member(_1106557), _1106559), _1106561))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106557, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1106557), _1106559), _1106563)), _1106561) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106557, tc_HOL_Obool)), _1106563), _1106561))], (18071 ^ _777081) ^ [_1106634, _1106636, _1106638, _1106640] : [hBOOL(hAPP(hAPP(c_member(_1106634), _1106636), _1106638)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106634, tc_HOL_Obool)), _1106638), hAPP(hAPP(c_Set_Oinsert(_1106634), _1106636), _1106640)) = hAPP(hAPP(c_Set_Oinsert(_1106634), _1106636), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106634, tc_HOL_Obool)), _1106638), _1106640)))], (18077 ^ _777081) ^ [_1106805, _1106807, _1106809, _1106811] : [hBOOL(hAPP(hAPP(c_member(_1106805), _1106807), _1106809)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106805, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1106805), _1106807), _1106811)), _1106809) = hAPP(hAPP(c_Set_Oinsert(_1106805), _1106807), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1106805, tc_HOL_Obool)), _1106811), _1106809)))], (18083 ^ _777081) ^ [_1106976, _1106978, _1106980] : [class_Int_Onumber__ring(_1106976), -(hAPP(c_Int_Onumber__class_Onumber__of(_1106976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1106978), _1106980)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1106976), hAPP(c_Int_Onumber__class_Onumber__of(_1106976), _1106978)), hAPP(c_Int_Onumber__class_Onumber__of(_1106976), _1106980)))], (18089 ^ _777081) ^ [_1107111, _1107113, _1107115] : [class_Int_Onumber__ring(_1107111), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107111), hAPP(c_Int_Onumber__class_Onumber__of(_1107111), _1107113)), hAPP(c_Int_Onumber__class_Onumber__of(_1107111), _1107115)) = hAPP(c_Int_Onumber__class_Onumber__of(_1107111), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1107113), _1107115)))], (18095 ^ _777081) ^ [_1107246, _1107248, _1107250, _1107252] : [class_Int_Onumber__ring(_1107246), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107246), hAPP(c_Int_Onumber__class_Onumber__of(_1107246), _1107248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107246), hAPP(c_Int_Onumber__class_Onumber__of(_1107246), _1107250)), _1107252)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107246), hAPP(c_Int_Onumber__class_Onumber__of(_1107246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1107248), _1107250))), _1107252))], (18101 ^ _777081) ^ [_1107415, _1107417, _1107419] : [class_Int_Onumber__ring(_1107415), -(hAPP(c_Int_Onumber__class_Onumber__of(_1107415), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1107417), _1107419)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1107415), hAPP(c_Int_Onumber__class_Onumber__of(_1107415), _1107417)), hAPP(c_Int_Onumber__class_Onumber__of(_1107415), _1107419)))], (18107 ^ _777081) ^ [_1107550, _1107552] : [class_Int_Onumber__ring(_1107550), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1107550), hAPP(c_Int_Onumber__class_Onumber__of(_1107550), _1107552)) = hAPP(c_Int_Onumber__class_Onumber__of(_1107550), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1107552)))], (18113 ^ _777081) ^ [_1107661, _1107663] : [class_Int_Onumber__ring(_1107661), -(hAPP(c_Int_Onumber__class_Onumber__of(_1107661), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1107663)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1107661), hAPP(c_Int_Onumber__class_Onumber__of(_1107661), _1107663)))], (18119 ^ _777081) ^ [_1107772, _1107774, _1107776, _1107778, _1107780] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1107772, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1107774, _1107772, _1107776), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1107774, tc_HOL_Obool)), _1107778), _1107780))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1107772, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1107774, _1107772, _1107776), _1107778)), hAPP(c_Set_Oimage(_1107774, _1107772, _1107776), _1107780)))))], (18121 ^ _777081) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18123 ^ _777081) ^ [_1107874, _1107876, _1107878] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1107874, tc_HOL_Obool)), _1107876), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1107874, tc_HOL_Obool)), _1107878), _1107876)) = c_Orderings_Obot__class_Obot(tc_fun(_1107874, tc_HOL_Obool)))], (18125 ^ _777081) ^ [_1107928, _1107930, _1107932] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1107928, tc_HOL_Obool)), _1107930), _1107932) = c_Orderings_Obot__class_Obot(tc_fun(_1107928, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1107928, tc_HOL_Obool)), _1107930), _1107932) = _1107930)], (18131 ^ _777081) ^ [_1108082, _1108084, _1108086, _1108088] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1108082, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108082, tc_HOL_Obool)), _1108084), _1108086)), _1108088) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108082, tc_HOL_Obool)), _1108084), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1108082, tc_HOL_Obool)), _1108086), _1108088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1108082, tc_HOL_Obool)), _1108088), _1108084)))], (18137 ^ _777081) ^ [_1108267, _1108269, _1108271, _1108273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1108267, tc_HOL_Obool)), _1108273), _1108269)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1108267, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108267, tc_HOL_Obool)), _1108269), _1108271)), _1108273) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108267, tc_HOL_Obool)), _1108269), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1108267, tc_HOL_Obool)), _1108271), _1108273)))], (18143 ^ _777081) ^ [_1108458, _1108460, _1108462] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1108458, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108458, tc_HOL_Obool)), _1108460), _1108462)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108458, tc_HOL_Obool)), _1108460), _1108462)) = _1108460)], (18145 ^ _777081) ^ [_1108518, _1108520, _1108522, _1108524] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108518, tc_HOL_Obool)), _1108520), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1108518, tc_HOL_Obool)), _1108522), _1108524)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108518, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108518, tc_HOL_Obool)), _1108520), _1108522)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108518, tc_HOL_Obool)), _1108520), _1108524)))], (18147 ^ _777081) ^ [_1108602, _1108604, _1108606, _1108608] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108602, tc_HOL_Obool)), _1108604), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108602, tc_HOL_Obool)), _1108606), _1108608)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1108602, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108602, tc_HOL_Obool)), _1108604), _1108606)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108602, tc_HOL_Obool)), _1108604), _1108608)))], (18149 ^ _777081) ^ [_1108686, _1108688] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108686, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1108686, tc_HOL_Obool)), _1108688)), _1108688) = c_Orderings_Obot__class_Obot(tc_fun(_1108686, tc_HOL_Obool)))], (18151 ^ _777081) ^ [_1108735, _1108737] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108735, tc_HOL_Obool)), _1108737), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1108735, tc_HOL_Obool)), _1108737)) = c_Orderings_Obot__class_Obot(tc_fun(_1108735, tc_HOL_Obool)))], (18153 ^ _777081) ^ [_1108784, _1108786] : [class_Int_Onumber__ring(_1108784), -(hBOOL(hAPP(hAPP(c_member(_1108784), hAPP(c_Int_Onumber__class_Onumber__of(_1108784), _1108786)), c_Int_Oring__1__class_OInts(_1108784))))], (18159 ^ _777081) ^ [_1108887, _1108889, _1108891] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1108887, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108887, tc_HOL_Obool)), _1108889), _1108891)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1108887, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1108887, tc_HOL_Obool)), _1108889)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1108887, tc_HOL_Obool)), _1108891)))], (18161 ^ _777081) ^ [_1108960, _1108962, _1108964] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1108960, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1108960, tc_HOL_Obool)), _1108962), _1108964)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108960, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1108960, tc_HOL_Obool)), _1108962)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1108960, tc_HOL_Obool)), _1108964)))], (18163 ^ _777081) ^ [_1109033, _1109035, _1109037] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1109033, tc_HOL_Obool)), _1109035), _1109037) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1109033, tc_HOL_Obool)), _1109035), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1109033, tc_HOL_Obool)), _1109037)))], (18165 ^ _777081) ^ [_1109090, _1109092, _1109094] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1109090, tc_HOL_Obool)), _1109092), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1109090, tc_HOL_Obool)), _1109094)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1109090, tc_HOL_Obool)), _1109092), _1109094))], (18167 ^ _777081) ^ [_1109147, _1109149] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1109147), _1109149) = 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)), _1109147)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1109149))))], (18169 ^ _777081) ^ [_1109193] : [-(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)), _1109193)) = _1109193)], (18171 ^ _777081) ^ [_1109222, _1109224, _1109226, _1109228] : [-(c_Map_Odom(_1109222, _1109224, c_Map_Orestrict__map(_1109222, _1109224, _1109226, _1109228)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1109222, tc_HOL_Obool)), c_Map_Odom(_1109222, _1109224, _1109226)), _1109228))], (18173 ^ _777081) ^ [] : [-(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))))], (18175 ^ _777081) ^ [_1109293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109293), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1109293) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18181 ^ _777081) ^ [_1109396] : [hAPP(c_Int_Onat, _1109396) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109396), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18187 ^ _777081) ^ [_1109483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109483), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1109483) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18193 ^ _777081) ^ [_1109576, _1109578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109576)), 18196 ^ _777081 : [(18197 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1109578)), hAPP(c_Int_Onat, _1109576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109578), _1109576)))], (18203 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109578), _1109576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1109578)), hAPP(c_Int_Onat, _1109576))))]]], (18209 ^ _777081) ^ [_1109850, _1109852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1109850)), hAPP(c_Int_Onat, _1109852))), 18212 ^ _777081 : [(18213 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109852)))], (18215 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109850), _1109852)))]]], (18217 ^ _777081) ^ [_1109985, _1109987] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1109985)), hAPP(c_Int_Onat, _1109987)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109985), _1109987))], (18227 ^ _777081) ^ [_1110152, _1110154, _1110156, _1110158] : [class_Int_Onumber__ring(_1110152), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1110152), hAPP(c_Int_Onumber__class_Onumber__of(_1110152), _1110154)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1110152), hAPP(c_Int_Onumber__class_Onumber__of(_1110152), _1110156)), _1110158)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1110152), hAPP(c_Int_Onumber__class_Onumber__of(_1110152), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1110154), _1110156))), _1110158))], (18233 ^ _777081) ^ [_1110321, _1110323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110323)), 18240 ^ _777081 : [(18241 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1110321)), hAPP(c_Int_Onat, _1110323))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110321), _1110323)))], (18247 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110321), _1110323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1110321)), hAPP(c_Int_Onat, _1110323))))]]], (18253 ^ _777081) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18255 ^ _777081) ^ [_1110654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110654)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1110654)) = _1110654)], (18261 ^ _777081) ^ [_1110760, _1110762] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1110760) = _1110762, 18264 ^ _777081 : [(18265 ^ _777081) ^ [] : [-(_1110760 = hAPP(c_Int_Onat, _1110762))], (18267 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110762)))]]], (18269 ^ _777081) ^ [_1110875, _1110877] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1110875) = _1110877), _1110875 = hAPP(c_Int_Onat, _1110877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1110877))], (18279 ^ _777081) ^ [_1111028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1111028)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1111028)) = _1111028)], (18285 ^ _777081) ^ [_1111113] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1111113))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1111113)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18291 ^ _777081) ^ [_1111172, _1111174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111172), hAPP(c_Int_Onat, _1111174))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1111172)), _1111174)))], (18297 ^ _777081) ^ [_1111277, _1111279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1111277)), _1111279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111277), hAPP(c_Int_Onat, _1111279))))], (18303 ^ _777081) ^ [_1111388, _1111390, _1111392] : [class_Int_Onumber__ring(_1111388), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1111388), hAPP(c_Groups_Ouminus__class_Ouminus(_1111388), hAPP(c_Int_Onumber__class_Onumber__of(_1111388), _1111390))), _1111392) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1111388), hAPP(c_Int_Onumber__class_Onumber__of(_1111388), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1111390))), _1111392))], (18309 ^ _777081) ^ [_1111533] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1111533))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18311 ^ _777081) ^ [_1111565, _1111567, _1111569] : [class_Int_Onumber__ring(_1111565), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1111565), hAPP(c_Int_Onumber__class_Onumber__of(_1111565), _1111567)), hAPP(c_Int_Onumber__class_Onumber__of(_1111565), _1111569)) = hAPP(c_Int_Onumber__class_Onumber__of(_1111565), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1111567), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1111569))))], (18317 ^ _777081) ^ [_1111706, _1111708, _1111710, _1111712, _1111714, _1111716] : [c_Fun_Oinj__on(_1111706, _1111708, _1111710, _1111712), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1111706, tc_HOL_Obool)), _1111714), _1111712)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1111706, tc_HOL_Obool)), _1111716), _1111712)), -(hAPP(c_Set_Oimage(_1111706, _1111708, _1111710), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1111706, tc_HOL_Obool)), _1111714), _1111716)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1111708, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1111706, _1111708, _1111710), _1111714)), hAPP(c_Set_Oimage(_1111706, _1111708, _1111710), _1111716)))], (18331 ^ _777081) ^ [_1112041, _1112043] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1112041), _1112043))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1112041))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1112043))))], (18333 ^ _777081) ^ [_1112114, _1112116, _1112118] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1112114, tc_HOL_Obool)), _1112116), _1112118) = c_Orderings_Obot__class_Obot(tc_fun(_1112114, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1112114, tc_HOL_Obool)), _1112116), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1112114, tc_HOL_Obool)), _1112118))))], (18339 ^ _777081) ^ [_1112257, _1112259, _1112261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1112257, tc_HOL_Obool)), _1112259), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1112257, tc_HOL_Obool)), _1112261))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1112257, tc_HOL_Obool)), _1112259), _1112261) = c_Orderings_Obot__class_Obot(tc_fun(_1112257, tc_HOL_Obool)))], (18345 ^ _777081) ^ [_1112406, _1112408, _1112410, _1112412] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1112406, tc_HOL_Obool)), c_Map_Odom(_1112406, _1112408, _1112410)), c_Map_Odom(_1112406, _1112408, _1112412)) = c_Orderings_Obot__class_Obot(tc_fun(_1112406, tc_HOL_Obool)), -(c_Map_Omap__add(_1112406, _1112408, _1112410, _1112412) = c_Map_Omap__add(_1112406, _1112408, _1112412, _1112410))], (18351 ^ _777081) ^ [_1112567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1112567))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1112567)))], (18357 ^ _777081) ^ [_1112652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1112652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1112652))))], (18363 ^ _777081) ^ [_1112743, _1112745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1112743)), 18366 ^ _777081 : [(18367 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1112743)), hAPP(c_Int_Onat, _1112745))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112743), _1112745)))], (18373 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1112743), _1112745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1112743)), hAPP(c_Int_Onat, _1112745))))]]], (18379 ^ _777081) ^ [_1113002, _1113004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1113002)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1113004)), 18386 ^ _777081 : [(18387 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1113002)), hAPP(c_Int_Onat, _1113004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1113002), _1113004)))], (18393 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1113002), _1113004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1113002)), hAPP(c_Int_Onat, _1113004))))]]], (18399 ^ _777081) ^ [_1113317, _1113319] : [class_Int_Onumber__ring(_1113317), class_Rings_Olinordered__idom(_1113317), 18406 ^ _777081 : [(18407 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113317), hAPP(c_Int_Onumber__class_Onumber__of(_1113317), _1113319)), c_Groups_Ozero__class_Ozero(_1113317))), -(hAPP(c_Groups_Oabs__class_Oabs(_1113317), hAPP(c_Int_Onumber__class_Onumber__of(_1113317), _1113319)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1113317), hAPP(c_Int_Onumber__class_Onumber__of(_1113317), _1113319)))], (18413 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1113317), hAPP(c_Int_Onumber__class_Onumber__of(_1113317), _1113319)), c_Groups_Ozero__class_Ozero(_1113317)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1113317), hAPP(c_Int_Onumber__class_Onumber__of(_1113317), _1113319)) = hAPP(c_Int_Onumber__class_Onumber__of(_1113317), _1113319))]]], (18435 ^ _777081) ^ [_1113876, _1113878] : [-(_1113876 = hAPP(c_Int_Onat, _1113878)), 18438 ^ _777081 : [(18439 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1113878)))], (18441 ^ _777081) ^ [] : [_1113878 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1113876)]], 18442 ^ _777081 : [(18443 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1113878))], (18445 ^ _777081) ^ [] : [_1113876 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (18419 ^ _777081) ^ [_1113684, _1113686] : [_1113684 = hAPP(c_Int_Onat, _1113686), 18422 ^ _777081 : [(18423 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1113686)), -(_1113686 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1113684))], (18429 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1113686))), -(_1113684 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18465 ^ _777081) ^ [_1114307, _1114309] : [-(hAPP(c_Int_Onat, _1114307) = _1114309), 18468 ^ _777081 : [(18469 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114307)))], (18471 ^ _777081) ^ [] : [_1114307 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1114309)]], 18472 ^ _777081 : [(18473 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114307))], (18475 ^ _777081) ^ [] : [_1114309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (18449 ^ _777081) ^ [_1114115, _1114117] : [hAPP(c_Int_Onat, _1114115) = _1114117, 18452 ^ _777081 : [(18453 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114115)), -(_1114115 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1114117))], (18459 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114115))), -(_1114117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18479 ^ _777081) ^ [_1114531, _1114533] : [18480 ^ _777081 : [(18481 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114531))], (18483 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114533))]], 18484 ^ _777081 : [(18485 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1114531)), hAPP(c_Int_Onat, _1114533))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114531), _1114533)))], (18491 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1114531), _1114533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1114531)), hAPP(c_Int_Onat, _1114533))))]]], (18513 ^ _777081) ^ [_1115110, _1115112] : [-(hBOOL(hAPP(_1115110, hAPP(c_Int_Onat, _1115112)))), 18517 ^ _777081 : [(18518 ^ _777081) ^ [] : [-(_1115112 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 18516 ^ [_1115110, _1115112]))], (18520 ^ _777081) ^ [] : [hBOOL(hAPP(_1115110, 18516 ^ [_1115110, _1115112]))]], 18521 ^ _777081 : [(18522 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1115112), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18524 ^ _777081) ^ [] : [hBOOL(hAPP(_1115110, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (18497 ^ _777081) ^ [_1114847, _1114849] : [hBOOL(hAPP(_1114847, hAPP(c_Int_Onat, _1114849))), 18500 ^ _777081 : [(18501 ^ _777081) ^ [_1114947] : [_1114849 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1114947), -(hBOOL(hAPP(_1114847, _1114947)))], (18507 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1114849), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1114847, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (18528 ^ _777081) ^ [_1115373, _1115375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115375)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1115373), _1115375)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1115373)), hAPP(c_Int_Onat, _1115375)))], (18538 ^ _777081) ^ [_1115552, _1115554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115552)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115554)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1115552)), hAPP(c_Int_Onat, _1115554)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1115552), _1115554)))], (18548 ^ _777081) ^ [_1115731, _1115733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115731)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1115731), _1115733)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1115731)), hAPP(c_Int_Onat, _1115733)))], (18554 ^ _777081) ^ [_1115854, _1115856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115856)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1115854)), hAPP(c_Int_Onat, _1115856)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1115854), _1115856)))], (18564 ^ _777081) ^ [_1116033, _1116035, _1116037, _1116039] : [class_Int_Onumber__ring(_1116033), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116033), hAPP(c_Int_Onumber__class_Onumber__of(_1116033), _1116035)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1116033), _1116037), hAPP(c_Int_Onumber__class_Onumber__of(_1116033), _1116039))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116033), hAPP(c_Int_Onumber__class_Onumber__of(_1116033), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1116035), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1116039)))), _1116037))], (18570 ^ _777081) ^ [_1116208, _1116210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1116208), _1116210)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1116210), _1116208)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1116210)), hAPP(c_Int_Onat, _1116208)))], (18580 ^ _777081) ^ [_1116393, _1116395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116393)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116395)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1116393)), hAPP(c_Int_Onat, _1116395)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1116393, _1116395)))], (18590 ^ _777081) ^ [_1116578] : [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, _1116578))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1116578)))], (18596 ^ _777081) ^ [_1116663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1116663)), -(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, _1116663))))], (18602 ^ _777081) ^ [_1116754, _1116756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1116754)), 18605 ^ _777081 : [(18606 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1116754)), _1116756)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116754), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1116756))))], (18612 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1116754), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1116756))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1116754)), _1116756)))]]], (18618 ^ _777081) ^ [_1117013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1117013)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1117013)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1117013)))], (18624 ^ _777081) ^ [_1117116, _1117118] : [-(c_Int_Onat__aux(_1117116, _1117118) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1117116)), _1117118))], (18626 ^ _777081) ^ [] : [-(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))))], (18628 ^ _777081) ^ [_1117171, _1117173] : [class_Rings_Oring__1(_1117171), 18631 ^ _777081 : [(18632 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1117173), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1117171), _1117173) = hAPP(c_Groups_Ouminus__class_Ouminus(_1117171), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1117171), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1117173)))))], (18638 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1117173), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1117171), _1117173) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1117171), hAPP(c_Int_Onat, _1117173)))]]], (18644 ^ _777081) ^ [_1117433, _1117435] : [-(c_Nitpick_Oint__lcm(_1117433, _1117435) = 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), _1117433)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1117435)))))], (18646 ^ _777081) ^ [_1117479, _1117481] : [c_Nat__Transfer_Onat__set(_1117479), c_Nat__Transfer_Onat__set(_1117481), 18653 ^ _777081 : [(18654 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1117479), _1117481)), -(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), _1117479)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1117481))))], (18660 ^ _777081) ^ [] : [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), _1117479)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1117481))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1117479), _1117481)))]]], (18666 ^ _777081) ^ [_1117782, _1117784] : [c_Nat__Transfer_Onat__set(_1117782), c_Nat__Transfer_Onat__set(_1117784), 18673 ^ _777081 : [(18674 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1117782), _1117784)), -(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), _1117782)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1117784))))], (18680 ^ _777081) ^ [] : [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), _1117782)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1117784))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1117782), _1117784)))]]], (18686 ^ _777081) ^ [_1118085, _1118087] : [c_Nat__Transfer_Onat__set(_1118085), c_Nat__Transfer_Onat__set(_1118087), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1118085), _1118087)))], (18696 ^ _777081) ^ [_1118220] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1118220) = _1118220)], (18698 ^ _777081) ^ [_1118246] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1118246) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1118246))], (18700 ^ _777081) ^ [_1118275, _1118277, _1118279] : [class_Int_Oring__char__0(_1118275), 18703 ^ _777081 : [(18704 ^ _777081) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1118275), _1118277) = hAPP(c_Int_Oring__1__class_Oof__int(_1118275), _1118279), -(_1118277 = _1118279)], (18710 ^ _777081) ^ [] : [_1118277 = _1118279, -(hAPP(c_Int_Oring__1__class_Oof__int(_1118275), _1118277) = hAPP(c_Int_Oring__1__class_Oof__int(_1118275), _1118279))]]], (18716 ^ _777081) ^ [_1118516, _1118518] : [c_Nat__Transfer_Onat__set(_1118516), c_Nat__Transfer_Onat__set(_1118518), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1118516), _1118518)))], (18726 ^ _777081) ^ [_1118666, _1118668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1118666)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1118668))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118666), _1118668)))], (18732 ^ _777081) ^ [_1118771, _1118773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1118771), _1118773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1118771)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1118773))))], (18738 ^ _777081) ^ [_1118897, _1118899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1118897)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1118899))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1118897), _1118899)))], (18744 ^ _777081) ^ [_1119002, _1119004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1119002), _1119004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119002)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119004))))], (18750 ^ _777081) ^ [_1119113, _1119115] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119113)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119115)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1119113), _1119115)))], (18752 ^ _777081) ^ [_1119159, _1119161] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119159)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119161)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1119159), _1119161)))], (18754 ^ _777081) ^ [_1119205] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119205)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1119205)))], (18756 ^ _777081) ^ [_1119240, _1119242] : [class_Int_Onumber__ring(_1119240), -(hAPP(c_Int_Oring__1__class_Oof__int(_1119240), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119242)) = hAPP(c_Int_Onumber__class_Onumber__of(_1119240), _1119242))], (18762 ^ _777081) ^ [_1119341, _1119343] : [class_Int_Onumber__ring(_1119341), -(hAPP(c_Int_Onumber__class_Onumber__of(_1119341), _1119343) = hAPP(c_Int_Oring__1__class_Oof__int(_1119341), _1119343))], (18768 ^ _777081) ^ [_1119436] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1119436)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1119436))], (18770 ^ _777081) ^ [_1119468, _1119470] : [c_Nat__Transfer_Onat__set(_1119468), c_Nat__Transfer_Onat__set(_1119470), 18777 ^ _777081 : [(18778 ^ _777081) ^ [] : [_1119468 = _1119470, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1119468) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1119470))], (18784 ^ _777081) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1119468) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1119470), -(_1119468 = _1119470)]]], (18790 ^ _777081) ^ [_1119741] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119741)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1119741))], (18792 ^ _777081) ^ [_1119773] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1119773) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1119773)))], (18794 ^ _777081) ^ [_1119805] : [class_Rings_Oring__1(_1119805), -(hAPP(c_Int_Oring__1__class_Oof__int(_1119805), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1119805))], (18800 ^ _777081) ^ [_1119892, _1119894] : [class_Int_Oring__char__0(_1119892), 18803 ^ _777081 : [(18804 ^ _777081) ^ [] : [c_Groups_Ozero__class_Ozero(_1119892) = hAPP(c_Int_Oring__1__class_Oof__int(_1119892), _1119894), -(_1119894 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (18810 ^ _777081) ^ [] : [_1119894 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1119892) = hAPP(c_Int_Oring__1__class_Oof__int(_1119892), _1119894))]]], (18816 ^ _777081) ^ [_1120118, _1120120] : [class_Int_Oring__char__0(_1120118), 18819 ^ _777081 : [(18820 ^ _777081) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1120118), _1120120) = c_Groups_Ozero__class_Ozero(_1120118), -(_1120120 = 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hAPP(c_Int_Oring__1__class_Oof__int(_1120362), _1120366))))]]], (18850 ^ _777081) ^ [_1120639, _1120641, _1120643] : [class_Rings_Olinordered__idom(_1120639), 18853 ^ _777081 : [(18854 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120639), hAPP(c_Int_Oring__1__class_Oof__int(_1120639), _1120641)), hAPP(c_Int_Oring__1__class_Oof__int(_1120639), _1120643))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120641), _1120643)))], (18860 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120641), _1120643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1120639), hAPP(c_Int_Oring__1__class_Oof__int(_1120639), _1120641)), hAPP(c_Int_Oring__1__class_Oof__int(_1120639), _1120643))))]]], (18866 ^ _777081) ^ [_1120916, _1120918, _1120920] : [class_Rings_Oring__1(_1120916), -(hAPP(c_Int_Oring__1__class_Oof__int(_1120916), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1120918), _1120920)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120916), hAPP(c_Int_Oring__1__class_Oof__int(_1120916), _1120918)), hAPP(c_Int_Oring__1__class_Oof__int(_1120916), _1120920)))], (18872 ^ _777081) ^ [_1121051, _1121053, _1121055] : [class_Rings_Oring__1(_1121051), -(hAPP(c_Int_Oring__1__class_Oof__int(_1121051), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1121053), _1121055)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121051), hAPP(c_Int_Oring__1__class_Oof__int(_1121051), _1121053)), hAPP(c_Int_Oring__1__class_Oof__int(_1121051), _1121055)))], (18878 ^ _777081) ^ [_1121186] : [class_Rings_Oring__1(_1121186), -(hAPP(c_Int_Oring__1__class_Oof__int(_1121186), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1121186))], (18884 ^ _777081) ^ [_1121273, _1121275, _1121277] : [class_Rings_Oring__1(_1121273), -(hAPP(c_Int_Oring__1__class_Oof__int(_1121273), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1121275), _1121277)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1121273), hAPP(c_Int_Oring__1__class_Oof__int(_1121273), _1121275)), hAPP(c_Int_Oring__1__class_Oof__int(_1121273), _1121277)))], (18890 ^ _777081) ^ [_1121408, _1121410] : [class_Rings_Oring__1(_1121408), -(hAPP(c_Int_Oring__1__class_Oof__int(_1121408), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1121410)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1121408), _1121410))], (18896 ^ _777081) ^ [_1121509, _1121511] : [class_Rings_Oring__1(_1121509), -(hAPP(c_Int_Oring__1__class_Oof__int(_1121509), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1121511)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1121509), hAPP(c_Int_Oring__1__class_Oof__int(_1121509), _1121511)))], (18902 ^ _777081) ^ [_1121620, _1121622] : [class_Rings_Oring__1(_1121620), -(hBOOL(hAPP(hAPP(c_member(_1121620), hAPP(c_Int_Oring__1__class_Oof__int(_1121620), _1121622)), c_Int_Oring__1__class_OInts(_1121620))))], (18918 ^ _777081) ^ [_1121892] : [18920 ^ _777081 : [(18921 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 18919 ^ [_1121892]), _1121892)))], (18923 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 18919 ^ [_1121892]))]], -(c_Nat__Transfer_Onat__set(_1121892))], (18908 ^ _777081) ^ [_1121735] : [c_Nat__Transfer_Onat__set(_1121735), 18911 ^ _777081 : [(18912 ^ _777081) ^ [_1121801] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1121801), _1121735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1121801)))]]], (18927 ^ _777081) ^ [_1122040] : [-(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)), _1122040)))], (18929 ^ _777081) ^ [_1122065, _1122067] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122065)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122067)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1122065), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1122067))))], (18931 ^ _777081) ^ [_1122129, _1122131] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1122129) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122131), 18934 ^ _777081 : [(18935 ^ _777081) ^ [] : [-(_1122129 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122131)))], (18937 ^ _777081) ^ [] : [-(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), _1122131))))]]], (18939 ^ _777081) ^ [_1122262, _1122264] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1122262) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122264)), _1122262 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122264)), 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), _1122264)))], (18949 ^ _777081) ^ [_1122427, _1122429] : [c_Nat__Transfer_Onat__set(_1122427), c_Nat__Transfer_Onat__set(_1122429), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1122427), _1122429) = 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), _1122427)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1122429))))], (18959 ^ _777081) ^ [_1122594] : [c_Nat__Transfer_Onat__set(_1122594), -(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), _1122594)) = _1122594)], (18965 ^ _777081) ^ [_1122679, _1122681] : [c_Nat__Transfer_Onat__set(_1122679), c_Nat__Transfer_Onat__set(_1122681), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1122679), _1122681) = 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), _1122679)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1122681))))], (18975 ^ _777081) ^ [_1122846, _1122848] : [c_Nat__Transfer_Onat__set(_1122846), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1122848), _1122846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1122848)))], (18985 ^ _777081) ^ [_1122987, _1122989] : [class_Rings_Olinordered__idom(_1122987), 18988 ^ _777081 : [(18989 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122987), 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[c_Nat__Transfer_Ois__nat(_1127150), c_Nat__Transfer_Ois__nat(_1127152), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1127150), _1127152)))], (19257 ^ _777081) ^ [_1127285, _1127287, _1127289, _1127291] : [c_Fun_Oinj__on(_1127285, _1127287, _1127289, c_Orderings_Otop__class_Otop(tc_fun(_1127285, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1127285, tc_fun(_1127291, _1127287), hAPP(hAPP(c_COMBB(_1127287, tc_fun(_1127291, _1127287), _1127285), c_COMBK(_1127287, _1127291)), _1127289), c_Orderings_Otop__class_Otop(tc_fun(_1127285, tc_HOL_Obool))))], (19263 ^ _777081) ^ [_1127432, _1127434] : [class_Orderings_Otop(_1127432), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127432), _1127434), c_Orderings_Otop__class_Otop(_1127432))))], (19269 ^ _777081) ^ [_1127525, _1127527] : [class_Lattices_Obounded__lattice__top(_1127525), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1127525), c_Orderings_Otop__class_Otop(_1127525)), _1127527) = c_Orderings_Otop__class_Otop(_1127525))], (19275 ^ _777081) ^ [_1127624, _1127626] : [class_Lattices_Obounded__lattice__top(_1127624), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1127624), _1127626), c_Orderings_Otop__class_Otop(_1127624)) = c_Orderings_Otop__class_Otop(_1127624))], (19281 ^ _777081) ^ [_1127723, _1127725] : [class_Lattices_Obounded__lattice__top(_1127723), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1127723), c_Orderings_Otop__class_Otop(_1127723)), _1127725) = _1127725)], (19287 ^ _777081) ^ [_1127818, _1127820] : [class_Lattices_Obounded__lattice__top(_1127818), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1127818), _1127820), c_Orderings_Otop__class_Otop(_1127818)) = _1127820)], (19293 ^ _777081) ^ [_1127913, _1127915, _1127917] : [class_Lattices_Obounded__lattice__top(_1127913), 19296 ^ _777081 : [(19297 ^ _777081) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1127913), _1127915), _1127917) = c_Orderings_Otop__class_Otop(_1127913), 19300 ^ _777081 : [(19301 ^ _777081) ^ [] : [-(_1127915 = c_Orderings_Otop__class_Otop(_1127913))], (19303 ^ _777081) ^ [] : [-(_1127917 = c_Orderings_Otop__class_Otop(_1127913))]]], (19305 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1127913), _1127915), _1127917) = c_Orderings_Otop__class_Otop(_1127913)), _1127915 = c_Orderings_Otop__class_Otop(_1127913), _1127917 = c_Orderings_Otop__class_Otop(_1127913)]]], (19315 ^ _777081) ^ [_1128240] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1128240), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1128240)), c_Option_Ooption_ONone(_1128240)), hAPP(c_Set_Oimage(_1128240, tc_Option_Ooption(_1128240), c_Option_Ooption_OSome(_1128240)), c_Orderings_Otop__class_Otop(tc_fun(_1128240, tc_HOL_Obool)))))], (19317 ^ _777081) ^ [_1128298, _1128300] : [class_Rings_Osemiring__1(_1128298), 19320 ^ _777081 : [(19321 ^ _777081) ^ [] : [c_Int_Oiszero(_1128298, _1128300), -(_1128300 = c_Groups_Ozero__class_Ozero(_1128298))], (19327 ^ _777081) ^ [] : [_1128300 = c_Groups_Ozero__class_Ozero(_1128298), -(c_Int_Oiszero(_1128298, _1128300))]]], (19333 ^ _777081) ^ [_1128509] : [class_Rings_Osemiring__1(_1128509), -(c_Int_Oiszero(_1128509, c_Groups_Ozero__class_Ozero(_1128509)))], (19339 ^ _777081) ^ [_1128586] : [class_Rings_Osemiring__1(_1128586), c_Int_Oiszero(_1128586, c_Groups_Oone__class_Oone(_1128586))], (19345 ^ _777081) ^ [_1128664] : [class_Int_Onumber__ring(_1128664), -(hAPP(c_Int_Onumber__class_Onumber__of(_1128664), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1128664))], (19351 ^ _777081) ^ [_1128751] : [class_Int_Onumber__ring(_1128751), -(c_Groups_Ozero__class_Ozero(_1128751) = hAPP(c_Int_Onumber__class_Onumber__of(_1128751), c_Int_OPls))], (19357 ^ _777081) ^ [_1128838, _1128840] : [class_Int_Onumber__ring(_1128838), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128838), _1128840), hAPP(c_Int_Onumber__class_Onumber__of(_1128838), c_Int_OPls)) = _1128840)], (19363 ^ _777081) ^ [_1128939, _1128941] : [class_Int_Onumber__ring(_1128939), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1128939), hAPP(c_Int_Onumber__class_Onumber__of(_1128939), c_Int_OPls)), _1128941) = _1128941)], (19369 ^ _777081) ^ [_1129040, _1129042, _1129044, _1129046] : [-(hBOOL(hAPP(hAPP(c_member(_1129040), hAPP(_1129042, _1129044)), hAPP(c_Set_Oimage(_1129046, _1129040, _1129042), c_Orderings_Otop__class_Otop(tc_fun(_1129046, tc_HOL_Obool))))))], (19371 ^ _777081) ^ [_1129091, _1129093, _1129095, _1129097, _1129099] : [_1129091 = hAPP(_1129093, _1129095), -(hBOOL(hAPP(hAPP(c_member(_1129097), _1129091), hAPP(c_Set_Oimage(_1129099, _1129097, _1129093), c_Orderings_Otop__class_Otop(tc_fun(_1129099, tc_HOL_Obool))))))], (19377 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (19379 ^ _777081) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (19381 ^ _777081) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19383 ^ _777081) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (19385 ^ _777081) ^ [_1129296, _1129298] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1129296, tc_HOL_Obool)), _1129298), c_Orderings_Otop__class_Otop(tc_fun(_1129296, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1129296, tc_HOL_Obool)))], (19387 ^ _777081) ^ [_1129342, _1129344] : [c_Nat__Transfer_Ois__nat(_1129342), c_Nat__Transfer_Ois__nat(_1129344), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1129342, _1129344)))], (19397 ^ _777081) ^ [_1129471, _1129473, _1129475, _1129477, _1129479] : [c_Fun_Oinj__on(_1129471, _1129473, _1129475, c_Orderings_Otop__class_Otop(tc_fun(_1129471, tc_HOL_Obool))), 19400 ^ _777081 : [(19401 ^ _777081) ^ [] : [hAPP(c_Set_Oimage(_1129471, _1129473, _1129475), _1129477) = hAPP(c_Set_Oimage(_1129471, _1129473, _1129475), _1129479), -(_1129477 = _1129479)], (19407 ^ _777081) ^ [] : [_1129477 = _1129479, -(hAPP(c_Set_Oimage(_1129471, _1129473, _1129475), _1129477) = hAPP(c_Set_Oimage(_1129471, _1129473, _1129475), _1129479))]]], (19413 ^ _777081) ^ [_1129752] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1129752, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1129752, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1129752, tc_HOL_Obool)))], (19415 ^ _777081) ^ [_1129793] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1129793, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1129793, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1129793, tc_HOL_Obool)))], (19417 ^ _777081) ^ [_1129834, _1129836] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1129834, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1129834, tc_HOL_Obool)), _1129836)), _1129836) = c_Orderings_Otop__class_Otop(tc_fun(_1129834, tc_HOL_Obool)))], (19419 ^ _777081) ^ [_1129883, _1129885] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1129883, tc_HOL_Obool)), _1129885), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1129883, tc_HOL_Obool)), _1129885)) = c_Orderings_Otop__class_Otop(tc_fun(_1129883, tc_HOL_Obool)))], (19421 ^ _777081) ^ [_1129932, _1129934] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1129932, tc_HOL_Obool)), _1129934) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1129932, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1129932, tc_HOL_Obool))), _1129934))], (19423 ^ _777081) ^ [_1129987] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1129987))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1129987)))], (19429 ^ _777081) ^ [_1130021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1130021)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1130021))], (19435 ^ _777081) ^ [_1130119] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1130119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130119), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19441 ^ _777081) ^ [_1130204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1130204), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1130204)))], (19447 ^ _777081) ^ [_1130295] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1130295)), -(hAPP(c_Int_Onat, _1130295) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19453 ^ _777081) ^ [_1130380, _1130382] : [class_Int_Onumber__ring(_1130380), 19456 ^ _777081 : [(19457 ^ _777081) ^ [] : [c_Groups_Ozero__class_Ozero(_1130380) = hAPP(c_Int_Onumber__class_Onumber__of(_1130380), _1130382), -(c_Int_Oiszero(_1130380, hAPP(c_Int_Onumber__class_Onumber__of(_1130380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1130382)))))], (19463 ^ _777081) ^ [] : [c_Int_Oiszero(_1130380, hAPP(c_Int_Onumber__class_Onumber__of(_1130380), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1130382)))), -(c_Groups_Ozero__class_Ozero(_1130380) = hAPP(c_Int_Onumber__class_Onumber__of(_1130380), _1130382))]]], (19469 ^ _777081) ^ [_1130639, _1130641] : [class_Int_Onumber__ring(_1130639), 19472 ^ _777081 : [(19473 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1130639), _1130641) = c_Groups_Ozero__class_Ozero(_1130639), -(c_Int_Oiszero(_1130639, hAPP(c_Int_Onumber__class_Onumber__of(_1130639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1130641), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (19479 ^ _777081) ^ [] : [c_Int_Oiszero(_1130639, hAPP(c_Int_Onumber__class_Onumber__of(_1130639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1130641), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1130639), _1130641) = c_Groups_Ozero__class_Ozero(_1130639))]]], (19485 ^ _777081) ^ [_1130898] : [-(c_Fun_Oinj__on(_1130898, tc_fun(_1130898, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1130898, tc_fun(_1130898, tc_HOL_Obool), tc_fun(_1130898, tc_HOL_Obool)), c_Set_Oinsert(_1130898)), c_Orderings_Obot__class_Obot(tc_fun(_1130898, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1130898, tc_HOL_Obool))))], (19487 ^ _777081) ^ [_1130950] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1130950))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1130950)) = _1130950)], (19493 ^ _777081) ^ [_1130992, _1130994, _1130996, _1130998] : [c_Fun_Oinj__on(_1130992, _1130994, _1130996, c_Orderings_Otop__class_Otop(tc_fun(_1130992, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1130992, _1130994, c_Orderings_Otop__class_Otop(tc_fun(_1130992, tc_HOL_Obool)), _1130996), hAPP(_1130996, _1130998)) = _1130998)], (19499 ^ _777081) ^ [_1131119] : [class_Nat_Osemiring__char__0(_1131119), -(c_Fun_Oinj__on(tc_Nat_Onat, _1131119, c_Nat_Osemiring__1__class_Oof__nat(_1131119), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (19505 ^ _777081) ^ [_1131200, _1131202, _1131204] : [-(c_Map_Odom(_1131200, _1131202, hAPP(hAPP(c_COMBB(_1131202, tc_Option_Ooption(_1131202), _1131200), c_Option_Ooption_OSome(_1131202)), _1131204)) = c_Orderings_Otop__class_Otop(tc_fun(_1131200, tc_HOL_Obool)))], (19507 ^ _777081) ^ [_1131262] : [c_Nat__Transfer_Ois__nat(_1131262), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131262)))], (19513 ^ _777081) ^ [_1131335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1131335)), -(c_Nat__Transfer_Ois__nat(_1131335))], (19519 ^ _777081) ^ [_1131414] : [class_Lattices_Oboolean__algebra(_1131414), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1131414), c_Orderings_Obot__class_Obot(_1131414)) = c_Orderings_Otop__class_Otop(_1131414))], (19525 ^ _777081) ^ [_1131505] : [class_Lattices_Oboolean__algebra(_1131505), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1131505), c_Orderings_Otop__class_Otop(_1131505)) = c_Orderings_Obot__class_Obot(_1131505))], (19531 ^ _777081) ^ [_1131596, _1131598] : [class_Lattices_Oboolean__algebra(_1131596), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1131596), _1131598), hAPP(c_Groups_Ouminus__class_Ouminus(_1131596), _1131598)) = c_Orderings_Otop__class_Otop(_1131596))], (19537 ^ _777081) ^ [_1131701, _1131703] : [class_Lattices_Oboolean__algebra(_1131701), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1131701), hAPP(c_Groups_Ouminus__class_Ouminus(_1131701), _1131703)), _1131703) = c_Orderings_Otop__class_Otop(_1131701))], (19543 ^ _777081) ^ [_1131806, _1131808, _1131810, _1131812] : [c_Fun_Oinj__on(_1131806, _1131808, _1131810, c_Orderings_Otop__class_Otop(tc_fun(_1131806, tc_HOL_Obool))), 19546 ^ _777081 : [(19547 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1131808), _1131812), hAPP(c_Set_Oimage(_1131806, _1131808, _1131810), c_Orderings_Otop__class_Otop(tc_fun(_1131806, tc_HOL_Obool))))), 19551 ^ _777081 : [(19552 ^ _777081) ^ [] : [-(_1131812 = hAPP(_1131810, 19550 ^ [_1131806, _1131808, _1131810, _1131812]))], (19554 ^ _777081) ^ [_1132071] : [_1131812 = hAPP(_1131810, _1132071), -(_1132071 = 19550 ^ [_1131806, _1131808, _1131810, _1131812])]]], (19560 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1131808), _1131812), hAPP(c_Set_Oimage(_1131806, _1131808, _1131810), c_Orderings_Otop__class_Otop(tc_fun(_1131806, tc_HOL_Obool)))))), 19561 ^ _777081 : [(19562 ^ _777081) ^ [_1132209] : [_1131812 = hAPP(_1131810, _1132209), 19566 ^ _777081 : [(19567 ^ _777081) ^ [] : [-(_1131812 = hAPP(_1131810, 19565 ^ [_1131806, _1131808, _1131810, _1131812, _1132209]))], (19569 ^ _777081) ^ [] : [19565 ^ [_1131806, _1131808, _1131810, _1131812, _1132209] = _1132209]]]]]]], (19573 ^ _777081) ^ [_1132437, _1132439, _1132441, _1132443, _1132445] : [c_Fun_Oinj__on(_1132437, _1132439, _1132441, c_Orderings_Otop__class_Otop(tc_fun(_1132437, tc_HOL_Obool))), 19576 ^ _777081 : [(19577 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1132439), hAPP(_1132441, _1132443)), hAPP(c_Set_Oimage(_1132437, _1132439, _1132441), _1132445))), -(hBOOL(hAPP(hAPP(c_member(_1132437), _1132443), _1132445)))], (19583 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1132437), _1132443), _1132445)), -(hBOOL(hAPP(hAPP(c_member(_1132439), hAPP(_1132441, _1132443)), hAPP(c_Set_Oimage(_1132437, _1132439, _1132441), _1132445))))]]], (19589 ^ _777081) ^ [_1132760] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1132760) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132760), c_Int_OPls)))], (19595 ^ _777081) ^ [_1132847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132847), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1132847) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19601 ^ _777081) ^ [_1132952] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1132952), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1132952), c_Int_OPls)))], (19607 ^ _777081) ^ [_1133039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1133039), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1133039))], (19613 ^ _777081) ^ [] : [-(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))))], (19615 ^ _777081) ^ [_1133165, _1133167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1133165)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1133167))), 19618 ^ _777081 : [(19625 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133165), _1133167)))], (19619 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133165), _1133167)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1133167)))]]], (19627 ^ _777081) ^ [_1133368, _1133370] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1133368)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1133370)))), 19630 ^ _777081 : [(19631 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133368), _1133370)))], (19633 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1133370))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1133368), _1133370))], (19649 ^ _777081) ^ [_1133723, _1133725] : [19650 ^ _777081 : [(19651 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1133723), _1133725))], (19653 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1133723), 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), _1133723)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1133725))))], (19639 ^ _777081) ^ [_1133593, _1133595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1133593)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1133595))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1133593), _1133595))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1133593), c_Int_OPls)))], (19657 ^ _777081) ^ [_1133884, _1133886, _1133888, _1133890, _1133892] : [c_Fun_Oinj__on(_1133884, _1133886, _1133888, c_Orderings_Otop__class_Otop(tc_fun(_1133884, tc_HOL_Obool))), 19660 ^ _777081 : [(19661 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133886, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1133884, _1133886, _1133888), _1133890)), hAPP(c_Set_Oimage(_1133884, _1133886, _1133888), _1133892))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133884, tc_HOL_Obool)), _1133890), _1133892)))], (19667 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133884, tc_HOL_Obool)), _1133890), _1133892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133886, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1133884, _1133886, _1133888), _1133890)), hAPP(c_Set_Oimage(_1133884, _1133886, _1133888), _1133892))))]]], (19673 ^ _777081) ^ [_1134225, _1134227, _1134229, _1134231, _1134233] : [c_Fun_Oinj__on(_1134225, _1134227, _1134229, c_Orderings_Otop__class_Otop(tc_fun(_1134225, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1134225, _1134227, _1134229), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1134225, tc_HOL_Obool)), _1134231), _1134233)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1134227, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1134225, _1134227, _1134229), _1134231)), hAPP(c_Set_Oimage(_1134225, _1134227, _1134229), _1134233)))], (19679 ^ _777081) ^ [_1134408, _1134410, _1134412, _1134414, _1134416] : [c_Fun_Oinj__on(_1134408, _1134410, _1134412, c_Orderings_Otop__class_Otop(tc_fun(_1134408, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1134408, _1134410, _1134412), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1134408, tc_HOL_Obool)), _1134414), _1134416)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1134410, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1134408, _1134410, _1134412), _1134414)), hAPP(c_Set_Oimage(_1134408, _1134410, _1134412), _1134416)))], (19685 ^ _777081) ^ [_1134591, _1134593, _1134595, _1134597] : [hAPP(c_Set_Oimage(_1134591, _1134593, _1134595), c_Orderings_Otop__class_Otop(tc_fun(_1134591, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1134593, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1134593, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1134593, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1134591, _1134593, _1134595), _1134597))), hAPP(c_Set_Oimage(_1134591, _1134593, _1134595), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1134591, tc_HOL_Obool)), _1134597)))))], (19691 ^ _777081) ^ [_1134786, _1134788] : [c_Nat__Transfer_Onat__set(_1134786), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1134788), _1134786)), -(c_Nat__Transfer_Ois__nat(_1134788))], (19701 ^ _777081) ^ [_1134921] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134921))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1134921) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19707 ^ _777081) ^ [_1135012] : [-(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, _1135012))))))], (19709 ^ _777081) ^ [_1135046, _1135048] : [class_Int_Onumber__ring(_1135046), class_Rings_Olinordered__idom(_1135046), 19716 ^ _777081 : [(19717 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135046), c_Groups_Ozero__class_Ozero(_1135046)), hAPP(c_Int_Onumber__class_Onumber__of(_1135046), _1135048))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1135048)))], (19723 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1135048)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135046), c_Groups_Ozero__class_Ozero(_1135046)), hAPP(c_Int_Onumber__class_Onumber__of(_1135046), _1135048))))]]], (19729 ^ _777081) ^ [_1135351, _1135353] : [class_Int_Onumber__ring(_1135351), class_Rings_Olinordered__idom(_1135351), 19736 ^ _777081 : [(19737 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135351), hAPP(c_Int_Onumber__class_Onumber__of(_1135351), _1135353)), c_Groups_Ozero__class_Ozero(_1135351))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1135353), c_Int_OPls)))], (19743 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1135353), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135351), hAPP(c_Int_Onumber__class_Onumber__of(_1135351), _1135353)), c_Groups_Ozero__class_Ozero(_1135351))))]]], (19749 ^ _777081) ^ [_1135665, _1135667] : [class_Int_Onumber__ring(_1135665), class_Rings_Olinordered__idom(_1135665), 19756 ^ _777081 : [(19757 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135665), c_Groups_Ozero__class_Ozero(_1135665)), hAPP(c_Int_Onumber__class_Onumber__of(_1135665), _1135667))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1135667)))], (19763 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1135667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135665), c_Groups_Ozero__class_Ozero(_1135665)), hAPP(c_Int_Onumber__class_Onumber__of(_1135665), _1135667))))]]], (19769 ^ _777081) ^ [_1135970, _1135972] : [class_Int_Onumber__ring(_1135970), class_Rings_Olinordered__idom(_1135970), 19776 ^ _777081 : [(19777 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135970), hAPP(c_Int_Onumber__class_Onumber__of(_1135970), _1135972)), c_Groups_Ozero__class_Ozero(_1135970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1135972), c_Int_OPls)))], (19783 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1135972), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135970), hAPP(c_Int_Onumber__class_Onumber__of(_1135970), _1135972)), c_Groups_Ozero__class_Ozero(_1135970))))]]], (19789 ^ _777081) ^ [_1136296] : [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), _1136296))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1136296)))], (19795 ^ _777081) ^ [_1136381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1136381)), -(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), _1136381))))], (19801 ^ _777081) ^ [_1136481, _1136483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1136481), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1136481)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1136483)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1136483))], (19807 ^ _777081) ^ [_1136593, _1136595] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1136593), c_Int_OPls))), 19810 ^ _777081 : [(19811 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1136595), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1136593)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1136595)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1136593))], (19817 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1136595), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1136593)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1136595)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1136593), _1136595)))]]], (19823 ^ _777081) ^ [_1136866, _1136868, _1136870, _1136872] : [c_Fun_Oinj__on(_1136866, _1136868, _1136870, c_Orderings_Otop__class_Otop(tc_fun(_1136866, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1136868, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1136866, _1136868, _1136870), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1136866, tc_HOL_Obool)), _1136872))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1136868, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1136866, _1136868, _1136870), _1136872)))))], (19829 ^ _777081) ^ [_1137050, _1137052] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137050), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1137052)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1137050)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1137052))], (19835 ^ _777081) ^ [_1137161, _1137163] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1137161), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1137163)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1137161)) = 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), _1137163), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1137161)))), 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)))], (19867 ^ _777081) ^ [_1137634, _1137636] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1137634) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1137636)), 19870 ^ _777081 : [(19871 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137634))))], (19873 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137636)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 19874 ^ _777081 : [(19875 ^ _777081) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137634)))], (19877 ^ _777081) ^ [] : [19878 ^ _777081 : [(19879 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137636))))], (19881 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137634) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 19882 ^ _777081 : [(19883 ^ _777081) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137636)))], (19885 ^ _777081) ^ [] : [_1137634 = _1137636]]]]], (19841 ^ _777081) ^ [_1137249, _1137251] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1137249) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1137251), 19844 ^ _777081 : [(19845 ^ _777081) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137249))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137251)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (19851 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137249)))), 19854 ^ _777081 : [(19855 ^ _777081) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137251))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137249) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19861 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1137251)))), -(_1137249 = _1137251)]]]]], (19889 ^ _777081) ^ [_1138047, _1138049, _1138051] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138047))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138047)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138049)), _1138051)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138049)), _1138051))], (19895 ^ _777081) ^ [_1138185, _1138187, _1138189] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138185)))), 19898 ^ _777081 : [(19899 ^ _777081) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138187))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138185)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138187)), _1138189)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138185)), _1138189))], (19905 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138187)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138185)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138187)), _1138189)) = 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), _1138185), _1138187))), _1138189))]]], (19911 ^ _777081) ^ [_1138516] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138516))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138516)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (19917 ^ _777081) ^ [_1138607] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138607)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138607)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138607))], (19923 ^ _777081) ^ [_1138666, _1138668] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1138666)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1138668)), hAPP(c_Int_Onat, _1138666)) = hAPP(c_Int_Onat, _1138668))], (19929 ^ _777081) ^ [_1138771, _1138773] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1138771))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1138773)), hAPP(c_Int_Onat, _1138771)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1138773), _1138771)), 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)))], (19935 ^ _777081) ^ [_1138844, _1138846] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138844))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138844)), _1138846)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1138846))], (19941 ^ _777081) ^ [_1138955, _1138957] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1138955)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1138955)), _1138957)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1138955))), _1138957))], (19947 ^ _777081) ^ [_1139021, _1139023, _1139025, _1139027, _1139029] : [-(c_Nat_Onat_Onat__case(_1139021, _1139023, _1139025, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139027)), _1139029)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1139021), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1139027))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1139021, _1139021), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1139021, tc_fun(_1139021, _1139021)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1139021, tc_fun(_1139021, _1139021)), tc_Int_Oint), c_If(_1139021)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1139021, _1139023, _1139025, _1139029))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1139021, tc_Int_Oint), _1139025), 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)), _1139029)))))], (19949 ^ _777081) ^ [_1139145] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1139145))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139145)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (19955 ^ _777081) ^ [_1139236] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1139236)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139236)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1139236)))], (19961 ^ _777081) ^ [_1139303, _1139305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1139303)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139305))), -(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(_1139305))), 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), _1139303)), c_Int_Onat))))))], (19967 ^ _777081) ^ [_1139448, _1139450] : [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(_1139450))), 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), _1139448)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1139448)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139450))))], (19973 ^ _777081) ^ [_1139614, _1139616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139614)), hAPP(c_Nat_OSuc, _1139616))), -(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(_1139614))), 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)), _1139616)))))], (19979 ^ _777081) ^ [_1139741, _1139743] : [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(_1139741))), 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)), _1139743)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139741)), hAPP(c_Nat_OSuc, _1139743))))], (19985 ^ _777081) ^ [_1139880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139880), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139880)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (19991 ^ _777081) ^ [_1139977] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1139977), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1139977)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1139977)))], (19997 ^ _777081) ^ [_1140032, _1140034] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1140032, tc_HOL_Obool)), _1140034)))], (19999 ^ _777081) ^ [_1140064] : [-(c_Int_Osucc(c_Int_Opred(_1140064)) = _1140064)], (20001 ^ _777081) ^ [_1140106, _1140108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1140106), _1140108)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1140106)), _1140108)))], (20007 ^ _777081) ^ [_1140203, _1140205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1140203)), _1140205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1140203), _1140205)))], (20013 ^ _777081) ^ [_1140306] : [-(c_Int_Opred(_1140306) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1140306), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20015 ^ _777081) ^ [_1140337] : [-(c_Int_Osucc(_1140337) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140337), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (20017 ^ _777081) ^ [_1140368, _1140370] : [class_Int_Onumber__ring(_1140368), -(hAPP(c_Int_Onumber__class_Onumber__of(_1140368), c_Int_Osucc(_1140370)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140368), c_Groups_Oone__class_Oone(_1140368)), hAPP(c_Int_Onumber__class_Onumber__of(_1140368), _1140370)))], (20023 ^ _777081) ^ [_1140487, _1140489] : [class_Int_Onumber__ring(_1140487), -(hAPP(c_Int_Onumber__class_Onumber__of(_1140487), c_Int_Opred(_1140489)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140487), hAPP(c_Groups_Ouminus__class_Ouminus(_1140487), c_Groups_Oone__class_Oone(_1140487))), hAPP(c_Int_Onumber__class_Onumber__of(_1140487), _1140489)))], (20029 ^ _777081) ^ [_1140628] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1140628)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1140628) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20035 ^ _777081) ^ [_1140719] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1140719) = 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(_1140719)))))], (20041 ^ _777081) ^ [_1140816, _1140818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1140816)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1140818)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1140816)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1140818), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1140816))))], (20047 ^ _777081) ^ [_1140958, _1140960] : [hAPP(c_Nat_OSuc, _1140958) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1140960), -(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(_1140960))), 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)), _1140958))))))], (20053 ^ _777081) ^ [_1141081, _1141083] : [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(_1141083))), 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)), _1141081))))), -(hAPP(c_Nat_OSuc, _1141081) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141083))], (20059 ^ _777081) ^ [_1141225, _1141227] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141225) = hAPP(c_Nat_OSuc, _1141227), -(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(_1141225))), 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)), _1141227))))))], (20065 ^ _777081) ^ [_1141348, _1141350] : [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(_1141348))), 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)), _1141350))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141348) = hAPP(c_Nat_OSuc, _1141350))], (20071 ^ _777081) ^ [_1141477, _1141479, _1141481, _1141483] : [-(c_Nat_Onat_Onat__case(_1141477, _1141479, _1141481, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141483)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1141477), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1141483))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1141477, _1141477), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1141477, tc_fun(_1141477, _1141477)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1141477, tc_fun(_1141477, _1141477)), tc_Int_Oint), c_If(_1141477)), c_Nat__Numeral_Oneg)), _1141479)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1141477, tc_Int_Oint), _1141481), c_Int_Onat))))], (20073 ^ _777081) ^ [_1141585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141585), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141585)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20079 ^ _777081) ^ [_1141682] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1141682), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141682)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1141682)))], (20085 ^ _777081) ^ [_1141752, _1141754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1141752)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141754))), -(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(_1141754))), 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), _1141752)), c_Int_Onat))))))], (20091 ^ _777081) ^ [_1141897, _1141899] : [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(_1141899))), 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), _1141897)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1141897)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1141899))))], (20097 ^ _777081) ^ [_1142063, _1142065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1142063)), hAPP(c_Nat_OSuc, _1142065))), -(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(_1142063))), 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)), _1142065)))))], (20103 ^ _777081) ^ [_1142190, _1142192] : [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(_1142190))), 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)), _1142192)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1142190)), hAPP(c_Nat_OSuc, _1142192))))], (20109 ^ _777081) ^ [_1142329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142329), 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), _1142329)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20115 ^ _777081) ^ [_1142420] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142420), 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), _1142420)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1142420)))], (20121 ^ _777081) ^ [_1142472, _1142474, _1142476, _1142478, _1142480] : [-(hAPP(c_Nat_Onat_Onat__rec(_1142472, _1142474, _1142476), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1142478)), _1142480)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1142472), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1142478))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1142472, _1142472), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1142472, tc_fun(_1142472, _1142472)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1142472, tc_fun(_1142472, _1142472)), tc_Int_Oint), c_If(_1142472)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1142472, _1142474, _1142476), _1142480))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1142472, _1142472), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1142472, _1142472), tc_Int_Oint), _1142476), 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)), _1142480))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1142472, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1142472, _1142474, _1142476)), 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)), _1142480))))))], (20123 ^ _777081) ^ [_1142624, _1142626, _1142628, _1142630] : [-(hAPP(c_Nat_Onat_Onat__rec(_1142624, _1142626, _1142628), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1142630)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1142624), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1142630))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1142624, _1142624), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1142624, tc_fun(_1142624, _1142624)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1142624, tc_fun(_1142624, _1142624)), tc_Int_Oint), c_If(_1142624)), c_Nat__Numeral_Oneg)), _1142626)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1142624, _1142624), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1142624, _1142624), tc_Int_Oint), _1142628), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1142624, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1142624, _1142626, _1142628)), c_Int_Onat)))))], (20125 ^ _777081) ^ [_1142755, _1142757] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1142755)), hAPP(c_Nat_OSuc, _1142757)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1142755))), 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)), _1142757)))))], (20127 ^ _777081) ^ [_1142812, _1142814] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1142812)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1142814)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1142814))), 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), _1142812)), c_Int_Onat)))))], (20129 ^ _777081) ^ [_1142875, _1142877] : [class_Int_Onumber__ring(_1142875), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1142877)), -(hBOOL(hAPP(hAPP(c_member(_1142875), hAPP(c_Int_Onumber__class_Onumber__of(_1142875), _1142877)), c_Nat_Osemiring__1__class_ONats(_1142875))))], (20139 ^ _777081) ^ [_1143034, _1143036] : [-(hBOOL(hAPP(hAPP(c_member(_1143034), _1143036), c_Orderings_Otop__class_Otop(tc_fun(_1143034, tc_HOL_Obool)))))], (20141 ^ _777081) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (20143 ^ _777081) ^ [_1143089, _1143091] : [class_Orderings_Olinorder(_1143089), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143089), _1143091), _1143091) = _1143091)], (20149 ^ _777081) ^ [_1143180, _1143182, _1143184] : [class_Orderings_Olinorder(_1143180), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143180), _1143182), _1143184) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143180), _1143184), _1143182))], (20155 ^ _777081) ^ [_1143289, _1143291, _1143293] : [class_Orderings_Olinorder(_1143289), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143289), _1143291), _1143293) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143289), _1143293), _1143291))], (20161 ^ _777081) ^ [_1143398, _1143400, _1143402] : [class_Orderings_Olinorder(_1143398), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143398), _1143400), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143398), _1143400), _1143402)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143398), _1143400), _1143402))], (20167 ^ _777081) ^ [_1143523, _1143525, _1143527] : [class_Orderings_Olinorder(_1143523), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143523), _1143525), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143523), _1143525), _1143527)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143523), _1143525), _1143527))], (20173 ^ _777081) ^ [_1143648, _1143650, _1143652, _1143654] : [class_Orderings_Olinorder(_1143648), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143648), _1143650), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143648), _1143652), _1143654)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143648), _1143652), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143648), _1143650), _1143654)))], (20179 ^ _777081) ^ [_1143791, _1143793, _1143795, _1143797] : [class_Orderings_Olinorder(_1143791), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143791), _1143793), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143791), _1143795), _1143797)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143791), _1143795), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143791), _1143793), _1143797)))], (20185 ^ _777081) ^ [_1143934, _1143936, _1143938, _1143940] : [class_Orderings_Olinorder(_1143934), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143934), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143934), _1143936), _1143938)), _1143940) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143934), _1143936), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1143934), _1143938), _1143940)))], (20191 ^ _777081) ^ [_1144077, _1144079, _1144081, _1144083] : [class_Orderings_Olinorder(_1144077), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1144077), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1144077), _1144079), _1144081)), _1144083) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1144077), _1144079), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1144077), _1144081), _1144083)))], (20197 ^ _777081) ^ [_1144220, _1144222, _1144224, _1144226] : [class_Orderings_Olinorder(_1144220), 20200 ^ _777081 : [(20211 ^ _777081) ^ [] : [20212 ^ _777081 : [(20213 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144220), _1144222), _1144226))], (20215 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144220), _1144224), _1144226))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144220), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1144220), _1144222), _1144224)), _1144226)))], (20201 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144220), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1144220), _1144222), _1144224)), _1144226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144220), _1144222), _1144226))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144220), _1144224), _1144226)))]]], (20219 ^ _777081) ^ [_1144569, _1144571, _1144573] : [class_Orderings_Olinorder(_1144569), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144569), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1144569), _1144571), _1144573)), _1144571)))], (20225 ^ _777081) ^ [_1144676, _1144678, _1144680] : [class_Orderings_Olinorder(_1144676), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144676), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1144676), _1144678), _1144680)), _1144680)))], (20231 ^ _777081) ^ [_1144783, _1144785, _1144787] : [class_Orderings_Olinorder(_1144783), 20234 ^ _777081 : [(20235 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144783), _1144785), _1144787)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1144783), _1144785), _1144787) = _1144785)], (20241 ^ _777081) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1144783), _1144785), _1144787) = _1144785, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1144783), _1144785), _1144787)))]]], (20247 ^ _777081) ^ [_1145039, _1145041, _1145043, _1145045] : [class_Orderings_Olinorder(_1145039), 20250 ^ _777081 : [(20251 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145039), _1145041), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1145039), _1145043), _1145045))), 20254 ^ _777081 : [(20255 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145039), _1145041), _1145043)))], (20257 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145039), _1145041), _1145045)))]]], (20259 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145039), _1145041), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1145039), _1145043), _1145045)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145039), _1145041), _1145043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145039), _1145041), _1145045))]]], (20269 ^ _777081) ^ [_1145419, _1145421, _1145423, _1145425] : [class_Orderings_Olinorder(_1145419), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145419), _1145421), _1145423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145419), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1145419), _1145421), _1145425)), _1145423)))], (20279 ^ _777081) ^ [_1145598, _1145600, _1145602, _1145604] : [class_Orderings_Olinorder(_1145598), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145598), _1145600), _1145602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145598), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1145598), _1145604), _1145600)), _1145602)))], (20289 ^ _777081) ^ [_1145777, _1145779, _1145781] : [class_Orderings_Olinorder(_1145777), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145777), _1145779), _1145781)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1145777), _1145779), _1145781) = _1145779)], (20299 ^ _777081) ^ [_1145938, _1145940, _1145942] : [class_Orderings_Olinorder(_1145938), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145938), _1145940), _1145942)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1145938), _1145942), _1145940) = _1145940)], (20309 ^ _777081) ^ [_1146099, _1146101, _1146103, _1146105] : [class_Orderings_Olinorder(_1146099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146099), _1146101), _1146103)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146099), _1146101), _1146105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146099), _1146101), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1146099), _1146103), _1146105))))], (20323 ^ _777081) ^ [_1146348, _1146350, _1146352, _1146354] : [class_Orderings_Olinorder(_1146348), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146348), _1146350), _1146352)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146348), _1146350), _1146354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146348), _1146350), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1146348), _1146352), _1146354))))], (20337 ^ _777081) ^ [_1146597, _1146599, _1146601, _1146603, _1146605] : [class_Orderings_Olinorder(_1146597), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146597), _1146599), _1146601)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146597), _1146603), _1146605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146597), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1146597), _1146599), _1146603)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1146597), _1146601), _1146605))))], (20351 ^ _777081) ^ [_1146868, _1146870, _1146872, _1146874] : [class_Orderings_Olinorder(_1146868), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146868), _1146870), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1146868), _1146872), _1146874))), 20358 ^ _777081 : [(20359 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146868), _1146870), _1146872)))], (20361 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146868), _1146870), _1146874)))]]], (20363 ^ _777081) ^ [_1147091, _1147093, _1147095, _1147097] : [class_Orderings_Olinorder(_1147091), 20366 ^ _777081 : [(20367 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147091), _1147093), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1147091), _1147095), _1147097))), 20370 ^ _777081 : [(20371 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147091), _1147093), _1147095)))], (20373 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147091), _1147093), _1147097)))]]], (20375 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147091), _1147093), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1147091), _1147095), _1147097)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147091), _1147093), _1147095)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147091), _1147093), _1147097))]]], (20385 ^ _777081) ^ [_1147471, _1147473, _1147475, _1147477] : [class_Orderings_Olinorder(_1147471), 20388 ^ _777081 : [(20399 ^ _777081) ^ [] : [20400 ^ _777081 : [(20401 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147471), _1147473), _1147477))], (20403 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147471), _1147475), _1147477))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147471), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1147471), _1147473), _1147475)), _1147477)))], (20389 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147471), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1147471), _1147473), _1147475)), _1147477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147471), _1147473), _1147477))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147471), _1147475), _1147477)))]]], (20407 ^ _777081) ^ [_1147820, _1147822, _1147824, _1147826] : [class_Orderings_Olinorder(_1147820), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147820), _1147822), _1147824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147820), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1147820), _1147822), _1147826)), _1147824)))], (20417 ^ _777081) ^ [_1147999, _1148001, _1148003, _1148005] : [class_Orderings_Olinorder(_1147999), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147999), _1148001), _1148003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147999), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1147999), _1148005), _1148001)), _1148003)))], (20427 ^ _777081) ^ [_1148178, _1148180, _1148182, _1148184] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1148178), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148178), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1148178), _1148180), _1148182)), _1148184) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1148178), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148178), _1148180), _1148184)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148178), _1148182), _1148184)))], (20433 ^ _777081) ^ [_1148337, _1148339, _1148341, _1148343] : [class_Groups_Oordered__ab__group__add(_1148337), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1148337), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1148337), _1148339), _1148341)), _1148343) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1148337), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1148337), _1148339), _1148343)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1148337), _1148341), _1148343)))], (20439 ^ _777081) ^ [_1148496] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1148496) = c_Orderings_Oord__class_Omin(_1148496)), class_Lattices_Osemilattice__inf(_1148496), class_Orderings_Olinorder(_1148496)], (20449 ^ _777081) ^ [_1148625] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1148625) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20451 ^ _777081) ^ [_1148651] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1148651), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20453 ^ _777081) ^ [_1148680, _1148682] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1148680)), hAPP(c_Nat_OSuc, _1148682)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1148680), _1148682)))], (20455 ^ _777081) ^ [_1148726, _1148728, _1148730] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1148726), _1148728)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1148730), _1148728)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1148726), _1148730)), _1148728))], (20457 ^ _777081) ^ [_1148783, _1148785, _1148787] : [class_Int_Onumber(_1148783), class_Orderings_Oord(_1148783), 20464 ^ _777081 : [(20465 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148783), hAPP(c_Int_Onumber__class_Onumber__of(_1148783), _1148785)), hAPP(c_Int_Onumber__class_Onumber__of(_1148783), _1148787))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1148783), hAPP(c_Int_Onumber__class_Onumber__of(_1148783), _1148785)), hAPP(c_Int_Onumber__class_Onumber__of(_1148783), _1148787)) = hAPP(c_Int_Onumber__class_Onumber__of(_1148783), _1148785))], (20471 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148783), hAPP(c_Int_Onumber__class_Onumber__of(_1148783), _1148785)), hAPP(c_Int_Onumber__class_Onumber__of(_1148783), _1148787)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1148783), hAPP(c_Int_Onumber__class_Onumber__of(_1148783), _1148785)), hAPP(c_Int_Onumber__class_Onumber__of(_1148783), _1148787)) = hAPP(c_Int_Onumber__class_Onumber__of(_1148783), _1148787))]]], (20477 ^ _777081) ^ [_1149175, _1149177, _1149179] : [-(hAPP(c_Nat_Onat_Onat__rec(_1149175, _1149177, _1149179), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1149177)], (20479 ^ _777081) ^ [_1149209, _1149211, _1149213, _1149215] : [-(hAPP(c_Nat_Onat_Onat__rec(_1149209, _1149211, _1149213), hAPP(c_Nat_OSuc, _1149215)) = hAPP(hAPP(_1149213, _1149215), hAPP(c_Nat_Onat_Onat__rec(_1149209, _1149211, _1149213), _1149215)))], (20481 ^ _777081) ^ [_1149261] : [class_Rings_Osemiring__1(_1149261), -(hBOOL(hAPP(hAPP(c_member(_1149261), c_Groups_Ozero__class_Ozero(_1149261)), c_Nat_Osemiring__1__class_ONats(_1149261))))], (20487 ^ _777081) ^ [_1149356, _1149358, _1149360] : [class_Rings_Osemiring__1(_1149356), hBOOL(hAPP(hAPP(c_member(_1149356), _1149358), c_Nat_Osemiring__1__class_ONats(_1149356))), hBOOL(hAPP(hAPP(c_member(_1149356), _1149360), c_Nat_Osemiring__1__class_ONats(_1149356))), -(hBOOL(hAPP(hAPP(c_member(_1149356), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149356), _1149358), _1149360)), c_Nat_Osemiring__1__class_ONats(_1149356))))], (20501 ^ _777081) ^ [_1149611, _1149613, _1149615] : [class_Rings_Osemiring__1(_1149611), hBOOL(hAPP(hAPP(c_member(_1149611), _1149613), c_Nat_Osemiring__1__class_ONats(_1149611))), hBOOL(hAPP(hAPP(c_member(_1149611), _1149615), c_Nat_Osemiring__1__class_ONats(_1149611))), -(hBOOL(hAPP(hAPP(c_member(_1149611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149611), _1149613), _1149615)), c_Nat_Osemiring__1__class_ONats(_1149611))))], (20515 ^ _777081) ^ [_1149866] : [class_Rings_Osemiring__1(_1149866), -(hBOOL(hAPP(hAPP(c_member(_1149866), c_Groups_Oone__class_Oone(_1149866)), c_Nat_Osemiring__1__class_ONats(_1149866))))], (20521 ^ _777081) ^ [_1149961, _1149963] : [class_Rings_Osemiring__1(_1149961), -(hBOOL(hAPP(hAPP(c_member(_1149961), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1149961), _1149963)), c_Nat_Osemiring__1__class_ONats(_1149961))))], (20527 ^ _777081) ^ [_1150064, _1150066] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1150064)), _1150066) = 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), _1150064)), _1150066))], (20529 ^ _777081) ^ [_1150109, _1150111] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1150109), hAPP(c_Nat_OSuc, _1150111)) = 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)), _1150111)), _1150109))], (20531 ^ _777081) ^ [_1150154] : [class_Orderings_Oord(_1150154), -(c_Orderings_Oord__class_Omin(_1150154) = c_Orderings_Oord_Omin(_1150154, c_Orderings_Oord__class_Oless__eq(_1150154)))], (20537 ^ _777081) ^ [_1150241, _1150243] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1150241)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150243)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1150243))), 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, _1150241))), 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), _1150241)), c_Int_Onat)))))], (20539 ^ _777081) ^ [_1150313, _1150315] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150313)), hAPP(c_Nat_OSuc, _1150315)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1150313))), 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, _1150315))), 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)), _1150315)))))], (20541 ^ _777081) ^ [_1150379, _1150381, _1150383, _1150385] : [c_Fun_Oinj__on(_1150379, _1150381, _1150383, c_Orderings_Otop__class_Otop(tc_fun(_1150379, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1150379, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1150379, _1150381, _1150383), hAPP(hAPP(c_Set_Oinsert(_1150381), _1150385), c_Orderings_Obot__class_Obot(tc_fun(_1150381, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1150379), c_HOL_OThe(_1150379, hAPP(hAPP(c_COMBC(_1150379, _1150381, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1150381, tc_fun(_1150381, tc_HOL_Obool), _1150379), c_fequal), _1150383)), _1150385))), c_Orderings_Obot__class_Obot(tc_fun(_1150379, tc_HOL_Obool))))))], (20547 ^ _777081) ^ [_1150618] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150618))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1150618)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20553 ^ _777081) ^ [_1150707] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1150707)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1150707)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1150707)), 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)))))], (20559 ^ _777081) ^ [_1150762, _1150764] : [class_Int_Onumber__ring(_1150762), 20562 ^ _777081 : [(20563 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1150762), _1150764) = c_Groups_Oone__class_Oone(_1150762), -(c_Int_Oiszero(_1150762, hAPP(c_Int_Onumber__class_Onumber__of(_1150762), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1150764), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (20569 ^ _777081) ^ [] : [c_Int_Oiszero(_1150762, hAPP(c_Int_Onumber__class_Onumber__of(_1150762), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1150764), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1150762), _1150764) = c_Groups_Oone__class_Oone(_1150762))]]], (20575 ^ _777081) ^ [_1151021, _1151023, _1151025, _1151027, _1151029, _1151031] : [hAPP(_1151021, _1151023) = _1151025, hBOOL(hAPP(hAPP(c_member(_1151027), _1151025), _1151029)), -(hBOOL(hAPP(hAPP(c_member(_1151031), _1151023), hAPP(c_Set_Ovimage(_1151031, _1151027, _1151021), _1151029))))], (20585 ^ _777081) ^ [_1151214, _1151216] : [-(hAPP(c_Set_Ovimage(_1151214, _1151214, c_COMBI(_1151214)), _1151216) = _1151216)], (20587 ^ _777081) ^ [_1151248, _1151250, _1151252, _1151254] : [class_Orderings_Olinorder(_1151248), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151248), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151248), _1151250), _1151252)), _1151254) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151248), _1151250), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151248), _1151252), _1151254)))], (20593 ^ _777081) ^ [_1151391, _1151393, _1151395, _1151397] : [class_Orderings_Olinorder(_1151391), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151391), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151391), _1151393), _1151395)), _1151397) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151391), _1151393), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151391), _1151395), _1151397)))], (20599 ^ _777081) ^ [_1151534, _1151536, _1151538, _1151540] : [class_Orderings_Olinorder(_1151534), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151534), _1151536), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151534), _1151538), _1151540)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151534), _1151538), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151534), _1151536), _1151540)))], (20605 ^ _777081) ^ [_1151677, _1151679, _1151681, _1151683] : [class_Orderings_Olinorder(_1151677), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151677), _1151679), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151677), _1151681), _1151683)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151677), _1151681), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151677), _1151679), _1151683)))], (20611 ^ _777081) ^ [_1151820, _1151822, _1151824] : [class_Orderings_Olinorder(_1151820), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151820), _1151822), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151820), _1151822), _1151824)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151820), _1151822), _1151824))], (20617 ^ _777081) ^ [_1151945, _1151947, _1151949] : [class_Orderings_Olinorder(_1151945), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151945), _1151947), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151945), _1151947), _1151949)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1151945), _1151947), _1151949))], (20623 ^ _777081) ^ [_1152070, _1152072, _1152074] : [class_Orderings_Olinorder(_1152070), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1152070), _1152072), _1152074) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1152070), _1152074), _1152072))], (20629 ^ _777081) ^ [_1152179, _1152181, _1152183] : [class_Orderings_Olinorder(_1152179), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1152179), _1152181), _1152183) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1152179), _1152183), _1152181))], (20635 ^ _777081) ^ [_1152288, _1152290] : [class_Orderings_Olinorder(_1152288), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1152288), _1152290), _1152290) = _1152290)], (20641 ^ _777081) ^ [_1152394, _1152396] : [c_Int_OBit1(_1152394) = c_Int_OBit1(_1152396), -(_1152394 = _1152396)], (20647 ^ _777081) ^ [_1152475, _1152477] : [_1152475 = _1152477, -(c_Int_OBit1(_1152475) = c_Int_OBit1(_1152477))], (20653 ^ _777081) ^ [_1152586, _1152588, _1152590, _1152592, _1152594] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1152586, _1152588, _1152590), _1152592), _1152594)), -(hBOOL(hAPP(_1152592, hAPP(_1152590, _1152594))))], (20659 ^ _777081) ^ [_1152693, _1152695, _1152697, _1152699, _1152701] : [hBOOL(hAPP(_1152699, hAPP(_1152697, _1152701))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1152693, _1152695, _1152697), _1152699), _1152701)))], (20665 ^ _777081) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (20667 ^ _777081) ^ [_1152824, _1152826, _1152828, _1152830] : [class_Orderings_Olinorder(_1152824), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152824), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1152824), _1152826), _1152828)), _1152830)), 20674 ^ _777081 : [(20675 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152824), _1152826), _1152830)))], (20677 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152824), _1152828), _1152830)))]]], (20679 ^ _777081) ^ [_1153047, _1153049, _1153051, _1153053, _1153055] : [class_Orderings_Olinorder(_1153047), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153047), _1153049), _1153051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153047), _1153053), _1153055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153047), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1153047), _1153049), _1153053)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1153047), _1153051), _1153055))))], (20693 ^ _777081) ^ [_1153318, _1153320, _1153322, _1153324] : [class_Orderings_Olinorder(_1153318), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153318), _1153320), _1153322)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153318), _1153324), _1153322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153318), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1153318), _1153320), _1153324)), _1153322)))], (20707 ^ _777081) ^ [_1153567, _1153569, _1153571, _1153573] : [class_Orderings_Olinorder(_1153567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153567), _1153569), _1153571)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153567), _1153573), _1153571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153567), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1153567), _1153569), _1153573)), _1153571)))], (20721 ^ _777081) ^ [_1153816, _1153818, _1153820] : [class_Orderings_Olinorder(_1153816), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153816), _1153818), _1153820)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1153816), _1153820), _1153818) = _1153820)], (20731 ^ _777081) ^ [_1153977, _1153979, _1153981] : [class_Orderings_Olinorder(_1153977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153977), _1153979), _1153981)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1153977), _1153979), _1153981) = _1153981)], (20741 ^ _777081) ^ [_1154138, _1154140, _1154142, _1154144] : [class_Orderings_Olinorder(_1154138), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154138), _1154140), _1154142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154138), _1154140), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1154138), _1154144), _1154142))))], (20751 ^ _777081) ^ [_1154317, _1154319, _1154321, _1154323] : [class_Orderings_Olinorder(_1154317), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154317), _1154319), _1154321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154317), _1154319), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1154317), _1154321), _1154323))))], (20761 ^ _777081) ^ [_1154496, _1154498, _1154500, _1154502] : [class_Orderings_Olinorder(_1154496), 20764 ^ _777081 : [(20765 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154496), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1154496), _1154498), _1154500)), _1154502)), 20768 ^ _777081 : [(20769 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154496), _1154498), _1154502)))], (20771 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154496), _1154500), _1154502)))]]], (20773 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154496), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1154496), _1154498), _1154500)), _1154502))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154496), _1154498), _1154502)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154496), _1154500), _1154502))]]], (20783 ^ _777081) ^ [_1154876, _1154878, _1154880] : [class_Orderings_Olinorder(_1154876), 20786 ^ _777081 : [(20787 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154876), _1154878), _1154880)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1154876), _1154878), _1154880) = _1154880)], (20793 ^ _777081) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1154876), _1154878), _1154880) = _1154880, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154876), _1154878), _1154880)))]]], (20799 ^ _777081) ^ [_1155132, _1155134, _1155136] : [class_Orderings_Olinorder(_1155132), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155132), _1155134), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1155132), _1155136), _1155134))))], (20805 ^ _777081) ^ [_1155239, _1155241, _1155243] : [class_Orderings_Olinorder(_1155239), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155239), _1155241), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1155239), _1155241), _1155243))))], (20811 ^ _777081) ^ [_1155346, _1155348, _1155350, _1155352] : [class_Orderings_Olinorder(_1155346), 20814 ^ _777081 : [(20825 ^ _777081) ^ [] : [20826 ^ _777081 : [(20827 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155346), _1155348), _1155350))], (20829 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155346), _1155348), _1155352))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155346), _1155348), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1155346), _1155350), _1155352))))], (20815 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155346), _1155348), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1155346), _1155350), _1155352))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155346), _1155348), _1155350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155346), _1155348), _1155352)))]]], (20833 ^ _777081) ^ [_1155695, _1155697, _1155699, _1155701] : [class_Orderings_Olinorder(_1155695), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155695), _1155697), _1155699)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155695), _1155697), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1155695), _1155701), _1155699))))], (20843 ^ _777081) ^ [_1155874, _1155876, _1155878, _1155880] : [class_Orderings_Olinorder(_1155874), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155874), _1155876), _1155878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155874), _1155876), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1155874), _1155878), _1155880))))], (20853 ^ _777081) ^ [_1156053, _1156055, _1156057, _1156059] : [class_Orderings_Olinorder(_1156053), 20856 ^ _777081 : [(20857 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156053), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1156053), _1156055), _1156057)), _1156059)), 20860 ^ _777081 : [(20861 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156053), _1156055), _1156059)))], (20863 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156053), _1156057), _1156059)))]]], (20865 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156053), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1156053), _1156055), _1156057)), _1156059))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156053), _1156055), _1156059)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156053), _1156057), _1156059))]]], (20875 ^ _777081) ^ [_1156433, _1156435, _1156437, _1156439] : [class_Orderings_Olinorder(_1156433), 20878 ^ _777081 : [(20889 ^ _777081) ^ [] : [20890 ^ _777081 : [(20891 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156433), _1156435), _1156437))], (20893 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156433), _1156435), _1156439))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156433), _1156435), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1156433), _1156437), _1156439))))], (20879 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156433), _1156435), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1156433), _1156437), _1156439))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156433), _1156435), _1156437))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156433), _1156435), _1156439)))]]], (20897 ^ _777081) ^ [_1156782, _1156784, _1156786, _1156788] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1156782), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156782), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1156782), _1156784), _1156786)), _1156788) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1156782), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156782), _1156784), _1156788)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156782), _1156786), _1156788)))], (20903 ^ _777081) ^ [_1156941, _1156943, _1156945, _1156947] : [class_Groups_Oordered__ab__group__add(_1156941), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1156941), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1156941), _1156943), _1156945)), _1156947) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1156941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1156941), _1156943), _1156947)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1156941), _1156945), _1156947)))], (20909 ^ _777081) ^ [_1157100, _1157102, _1157104, _1157106, _1157108] : [hBOOL(hAPP(hAPP(c_member(_1157100), hAPP(_1157102, _1157104)), _1157106)), -(hBOOL(hAPP(hAPP(c_member(_1157108), _1157104), hAPP(c_Set_Ovimage(_1157108, _1157100, _1157102), _1157106))))], (20915 ^ _777081) ^ [_1157231, _1157233, _1157235, _1157237, _1157239] : [hBOOL(hAPP(hAPP(c_member(_1157231), _1157233), hAPP(c_Set_Ovimage(_1157231, _1157235, _1157237), _1157239))), -(hBOOL(hAPP(hAPP(c_member(_1157235), hAPP(_1157237, _1157233)), _1157239)))], (20921 ^ _777081) ^ [_1157386, _1157388, _1157390, _1157392, _1157394] : [hBOOL(hAPP(hAPP(c_member(_1157386), _1157388), hAPP(c_Set_Ovimage(_1157386, _1157390, _1157392), _1157394))), -(hBOOL(hAPP(hAPP(c_member(_1157390), hAPP(_1157392, _1157388)), _1157394)))], (20927 ^ _777081) ^ [_1157513, _1157515, _1157517, _1157519, _1157521] : [hBOOL(hAPP(hAPP(c_member(_1157517), hAPP(_1157519, _1157515)), _1157521)), -(hBOOL(hAPP(hAPP(c_member(_1157513), _1157515), hAPP(c_Set_Ovimage(_1157513, _1157517, _1157519), _1157521))))], (20933 ^ _777081) ^ [_1157646] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1157646) = c_Orderings_Oord__class_Omax(_1157646)), class_Lattices_Osemilattice__sup(_1157646), class_Orderings_Olinorder(_1157646)], (20943 ^ _777081) ^ [_1157775] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1157775), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1157775)], (20945 ^ _777081) ^ [_1157804] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1157804) = _1157804)], (20947 ^ _777081) ^ [_1157830, _1157832] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1157830)), hAPP(c_Nat_OSuc, _1157832)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1157830), _1157832)))], (20949 ^ _777081) ^ [_1157876, _1157878, _1157880] : [-(hAPP(c_Set_Ovimage(_1157876, _1157878, _1157880), c_Orderings_Obot__class_Obot(tc_fun(_1157878, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1157876, tc_HOL_Obool)))], (20951 ^ _777081) ^ [_1157920, _1157922, _1157924, _1157926] : [class_Orderings_Olinorder(_1157920), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1157920), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1157920), _1157922), _1157924)), _1157926) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1157920), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1157920), _1157922), _1157926)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1157920), _1157924), _1157926)))], (20957 ^ _777081) ^ [_1158079, _1158081, _1158083, _1158085] : [class_Orderings_Olinorder(_1158079), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1158079), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158079), _1158081), _1158083)), _1158085) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158079), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1158079), _1158081), _1158085)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1158079), _1158083), _1158085)))], (20963 ^ _777081) ^ [_1158238, _1158240, _1158242, _1158244] : [class_Orderings_Olinorder(_1158238), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158238), _1158240), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1158238), _1158242), _1158244)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1158238), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158238), _1158240), _1158242)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158238), _1158240), _1158244)))], (20969 ^ _777081) ^ [_1158397, _1158399, _1158401, _1158403] : [class_Orderings_Olinorder(_1158397), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1158397), _1158399), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158397), _1158401), _1158403)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158397), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1158397), _1158399), _1158401)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1158397), _1158399), _1158403)))], (20975 ^ _777081) ^ [_1158556, _1158558, _1158560] : [class_Orderings_Olinorder(_1158556), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158556), _1158558), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1158556), _1158558), _1158560)) = _1158558)], (20981 ^ _777081) ^ [_1158665, _1158667, _1158669] : [class_Orderings_Olinorder(_1158665), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1158665), _1158667), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1158665), _1158667), _1158669)) = _1158667)], (20987 ^ _777081) ^ [_1158789, _1158791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1158789)), c_Int_OBit1(_1158791))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158789), _1158791)))], (20993 ^ _777081) ^ [_1158890, _1158892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1158890), _1158892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1158890)), c_Int_OBit1(_1158892))))], (20999 ^ _777081) ^ [_1159012, _1159014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1159012)), c_Int_OBit1(_1159014))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159012), _1159014)))], (21005 ^ _777081) ^ [_1159113, _1159115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159113), _1159115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1159113)), c_Int_OBit1(_1159115))))], (21011 ^ _777081) ^ [_1159235, _1159237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1159235)), c_Int_OBit1(_1159237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159235), _1159237)))], (21017 ^ _777081) ^ [_1159336, _1159338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159336), _1159338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1159336)), c_Int_OBit1(_1159338))))], (21023 ^ _777081) ^ [_1159458, _1159460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1159458)), c_Int_OBit1(_1159460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159458), _1159460)))], (21029 ^ _777081) ^ [_1159559, _1159561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159559), _1159561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1159559)), c_Int_OBit1(_1159561))))], (21035 ^ _777081) ^ [_1159666, _1159668, _1159670, _1159672, _1159674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1159666, tc_HOL_Obool)), _1159668), _1159670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1159672, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1159672, _1159666, _1159674), _1159668)), hAPP(c_Set_Ovimage(_1159672, _1159666, _1159674), _1159670))))], (21041 ^ _777081) ^ [_1159826] : [c_Int_OBit1(_1159826) = c_Int_OPls], (21043 ^ _777081) ^ [_1159860] : [c_Int_OPls = c_Int_OBit1(_1159860)], (21045 ^ _777081) ^ [_1159885, _1159887, _1159889] : [-(hAPP(c_Set_Ovimage(_1159885, _1159887, _1159889), c_Orderings_Otop__class_Otop(tc_fun(_1159887, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1159885, tc_HOL_Obool)))], (21047 ^ _777081) ^ [_1159929, _1159931, _1159933, _1159935, _1159937] : [-(hAPP(c_Set_Ovimage(_1159929, _1159931, _1159933), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1159931, tc_HOL_Obool)), _1159935), _1159937)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1159929, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1159929, _1159931, _1159933), _1159935)), hAPP(c_Set_Ovimage(_1159929, _1159931, _1159933), _1159937)))], (21049 ^ _777081) ^ [_1160003, _1160005, _1160007, _1160009, _1160011] : [-(hAPP(c_Set_Ovimage(_1160003, _1160005, _1160007), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1160005, tc_HOL_Obool)), _1160009), _1160011)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1160003, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1160003, _1160005, _1160007), _1160009)), hAPP(c_Set_Ovimage(_1160003, _1160005, _1160007), _1160011)))], (21051 ^ _777081) ^ [_1160077, _1160079, _1160081, _1160083, _1160085] : [-(hAPP(c_Set_Ovimage(_1160077, _1160079, _1160081), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1160079, tc_HOL_Obool)), _1160083), _1160085)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1160077, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1160077, _1160079, _1160081), _1160083)), hAPP(c_Set_Ovimage(_1160077, _1160079, _1160081), _1160085)))], (21053 ^ _777081) ^ [_1160151, _1160153, _1160155, _1160157] : [-(hAPP(c_Set_Ovimage(_1160151, _1160153, _1160155), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1160153, tc_HOL_Obool)), _1160157)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1160151, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1160151, _1160153, _1160155), _1160157)))], (21055 ^ _777081) ^ [_1160210, _1160212, _1160214] : [class_Int_Onumber(_1160210), class_Orderings_Oord(_1160210), 21062 ^ _777081 : [(21063 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160210), hAPP(c_Int_Onumber__class_Onumber__of(_1160210), _1160212)), hAPP(c_Int_Onumber__class_Onumber__of(_1160210), _1160214))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1160210), hAPP(c_Int_Onumber__class_Onumber__of(_1160210), _1160212)), hAPP(c_Int_Onumber__class_Onumber__of(_1160210), _1160214)) = hAPP(c_Int_Onumber__class_Onumber__of(_1160210), _1160214))], (21069 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160210), hAPP(c_Int_Onumber__class_Onumber__of(_1160210), _1160212)), hAPP(c_Int_Onumber__class_Onumber__of(_1160210), _1160214)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1160210), hAPP(c_Int_Onumber__class_Onumber__of(_1160210), _1160212)), hAPP(c_Int_Onumber__class_Onumber__of(_1160210), _1160214)) = hAPP(c_Int_Onumber__class_Onumber__of(_1160210), _1160212))]]], (21075 ^ _777081) ^ [_1160602, _1160604, _1160606, _1160608] : [class_Orderings_Olinorder(_1160602), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160602), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1160602), _1160604), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160602), _1160606), _1160608))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160602), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1160602), _1160604), _1160606)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1160602), _1160604), _1160608)))))], (21081 ^ _777081) ^ [_1160775, _1160777, _1160779, _1160781] : [class_Orderings_Olinorder(_1160775), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160775), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1160775), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160775), _1160777), _1160779)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160775), _1160777), _1160781))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160775), _1160777), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1160775), _1160779), _1160781)))))], (21087 ^ _777081) ^ [_1160948, _1160950, _1160952] : [class_Groups_Olinordered__ab__group__add(_1160948), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1160948), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1160948), _1160950), _1160952)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1160948), hAPP(c_Groups_Ouminus__class_Ouminus(_1160948), _1160950)), hAPP(c_Groups_Ouminus__class_Ouminus(_1160948), _1160952)))], (21093 ^ _777081) ^ [_1161087, _1161089, _1161091] : [class_Groups_Olinordered__ab__group__add(_1161087), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1161087), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1161087), _1161089), _1161091)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1161087), hAPP(c_Groups_Ouminus__class_Ouminus(_1161087), _1161089)), hAPP(c_Groups_Ouminus__class_Ouminus(_1161087), _1161091)))], (21099 ^ _777081) ^ [_1161238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1161238)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161238), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21105 ^ _777081) ^ [_1161333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161333), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1161333)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21111 ^ _777081) ^ [_1161434, _1161436] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1161434), _1161436)), _1161436) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1161434), _1161436))], (21113 ^ _777081) ^ [_1161489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1161489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1161489)))], (21119 ^ _777081) ^ [_1161572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1161572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1161572))))], (21125 ^ _777081) ^ [_1161673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1161673)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161673), c_Int_OPls)))], (21131 ^ _777081) ^ [_1161768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161768), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1161768)), c_Int_OPls)))], (21137 ^ _777081) ^ [_1161869, _1161871, _1161873, _1161875] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1161869, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1161871, _1161869, _1161873), hAPP(c_Set_Ovimage(_1161871, _1161869, _1161873), _1161875))), _1161875)))], (21139 ^ _777081) ^ [_1161922, _1161924, _1161926, _1161928] : [hAPP(c_Set_Oimage(_1161922, _1161924, _1161926), c_Orderings_Otop__class_Otop(tc_fun(_1161922, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1161924, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1161922, _1161924, _1161926), hAPP(c_Set_Ovimage(_1161922, _1161924, _1161926), _1161928)) = _1161928)], (21145 ^ _777081) ^ [_1162065] : [-(c_Int_OBit1(_1162065) = 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)), _1162065)), _1162065))], (21147 ^ _777081) ^ [_1162111] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1162111)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1162111))))], (21153 ^ _777081) ^ [_1162206] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1162206))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1162206)))))], (21159 ^ _777081) ^ [_1162307] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1162307)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1162307))))], (21161 ^ _777081) ^ [_1162342, _1162344] : [c_Int_Oiszero(_1162342, hAPP(c_Int_Onumber__class_Onumber__of(_1162342), c_Int_OBit1(_1162344))), class_Int_Onumber__ring(_1162342), class_Int_Oring__char__0(_1162342)], (21171 ^ _777081) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (21173 ^ _777081) ^ [_1162500, _1162502] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1162500), hAPP(c_Nat_OSuc, _1162502)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1162502), 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)), _1162502)), _1162500))], (21175 ^ _777081) ^ [_1162548, _1162550] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1162548)), _1162550) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1162548), 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), _1162548)), _1162550))], (21177 ^ _777081) ^ [_1162596, _1162598] : [class_Int_Onumber__ring(_1162596), -(hAPP(c_Int_Onumber__class_Onumber__of(_1162596), c_Int_OBit1(_1162598)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162596), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162596), c_Groups_Oone__class_Oone(_1162596)), hAPP(c_Int_Onumber__class_Onumber__of(_1162596), _1162598))), hAPP(c_Int_Onumber__class_Onumber__of(_1162596), _1162598)))], (21183 ^ _777081) ^ [_1162765, _1162767, _1162769, _1162771, _1162773] : [hBOOL(hAPP(hAPP(c_member(_1162765), _1162767), hAPP(c_Set_Ovimage(_1162765, _1162769, _1162771), hAPP(hAPP(c_Set_Oinsert(_1162769), _1162773), c_Orderings_Obot__class_Obot(tc_fun(_1162769, tc_HOL_Obool)))))), -(hAPP(_1162771, _1162767) = _1162773)], (21189 ^ _777081) ^ [_1162904, _1162906, _1162908, _1162910, _1162912] : [hAPP(_1162910, _1162906) = _1162912, -(hBOOL(hAPP(hAPP(c_member(_1162904), _1162906), hAPP(c_Set_Ovimage(_1162904, _1162908, _1162910), hAPP(hAPP(c_Set_Oinsert(_1162908), _1162912), c_Orderings_Obot__class_Obot(tc_fun(_1162908, tc_HOL_Obool)))))))], (21195 ^ _777081) ^ [_1163049, _1163051] : [class_Int_Onumber__ring(_1163049), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163049), _1163051), hAPP(c_Int_Onumber__class_Onumber__of(_1163049), c_Int_OBit1(c_Int_OPls))) = _1163051)], (21201 ^ _777081) ^ [_1163150, _1163152] : [class_Int_Onumber__ring(_1163150), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163150), hAPP(c_Int_Onumber__class_Onumber__of(_1163150), c_Int_OBit1(c_Int_OPls))), _1163152) = _1163152)], (21207 ^ _777081) ^ [_1163251] : [class_Int_Onumber__ring(_1163251), -(hAPP(c_Int_Onumber__class_Onumber__of(_1163251), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1163251))], (21213 ^ _777081) ^ [_1163338] : [class_Int_Onumber__ring(_1163338), -(c_Groups_Oone__class_Oone(_1163338) = hAPP(c_Int_Onumber__class_Onumber__of(_1163338), c_Int_OBit1(c_Int_OPls)))], (21219 ^ _777081) ^ [_1163425, _1163427, _1163429, _1163431, _1163433] : [-(hAPP(c_Set_Ovimage(_1163425, _1163427, _1163429), hAPP(hAPP(c_Set_Oinsert(_1163427), _1163431), _1163433)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1163425, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1163425, _1163427, _1163429), hAPP(hAPP(c_Set_Oinsert(_1163427), _1163431), c_Orderings_Obot__class_Obot(tc_fun(_1163427, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1163425, _1163427, _1163429), _1163433)))], (21221 ^ _777081) ^ [_1163521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1163521))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1163521)))], (21227 ^ _777081) ^ [_1163604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1163604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1163604))))], (21233 ^ _777081) ^ [_1163705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1163705)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1163705), c_Int_OPls)))], (21239 ^ _777081) ^ [_1163800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1163800), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1163800)), c_Int_OPls)))], (21245 ^ _777081) ^ [_1163901, _1163903, _1163905, _1163907, _1163909] : [hAPP(c_Set_Oimage(_1163901, _1163903, _1163905), c_Orderings_Otop__class_Otop(tc_fun(_1163901, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1163903, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1163901, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1163901, _1163903, _1163905), _1163907)), _1163909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1163903, tc_HOL_Obool)), _1163907), hAPP(c_Set_Oimage(_1163901, _1163903, _1163905), _1163909))))], (21255 ^ _777081) ^ [_1164144, _1164146, _1164148, _1164150] : [-(hAPP(c_Set_Oimage(_1164144, _1164146, _1164148), hAPP(c_Set_Ovimage(_1164144, _1164146, _1164148), _1164150)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1164146, tc_HOL_Obool)), _1164150), hAPP(c_Set_Oimage(_1164144, _1164146, _1164148), c_Orderings_Otop__class_Otop(tc_fun(_1164144, tc_HOL_Obool)))))], (21257 ^ _777081) ^ [_1164210, _1164212, _1164214, _1164216] : [c_Fun_Oinj__on(_1164210, _1164212, _1164214, c_Orderings_Otop__class_Otop(tc_fun(_1164210, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1164210, _1164212, _1164214), hAPP(c_Set_Oimage(_1164210, _1164212, _1164214), _1164216)) = _1164216)], (21263 ^ _777081) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (21265 ^ _777081) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (21267 ^ _777081) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (21269 ^ _777081) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (21271 ^ _777081) ^ [_1164405] : [class_Int_Onumber__ring(_1164405), c_Int_Oiszero(_1164405, hAPP(c_Int_Onumber__class_Onumber__of(_1164405), c_Int_OBit1(c_Int_OPls)))], (21277 ^ _777081) ^ [_1164504, _1164506, _1164508, _1164510] : [hBOOL(hAPP(hAPP(c_member(_1164504), _1164506), _1164508)), -(hAPP(c_Set_Ovimage(_1164510, _1164504, hAPP(c_COMBK(_1164504, _1164510), _1164506)), _1164508) = c_Orderings_Otop__class_Otop(tc_fun(_1164510, tc_HOL_Obool)))], (21283 ^ _777081) ^ [_1164629, _1164631, _1164633, _1164635] : [-(hBOOL(hAPP(hAPP(c_member(_1164629), _1164631), _1164633))), -(hAPP(c_Set_Ovimage(_1164635, _1164629, hAPP(c_COMBK(_1164629, _1164635), _1164631)), _1164633) = c_Orderings_Obot__class_Obot(tc_fun(_1164635, tc_HOL_Obool)))], (21289 ^ _777081) ^ [] : [-(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)))], (21291 ^ _777081) ^ [] : [-(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)))))], (21293 ^ _777081) ^ [] : [-(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))))))], (21295 ^ _777081) ^ [_1164750] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1164750))) = 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)))), _1164750))], (21297 ^ _777081) ^ [_1164785, _1164787, _1164789, _1164791, _1164793] : [c_Fun_Oinj__on(_1164785, _1164787, _1164789, c_Orderings_Otop__class_Otop(tc_fun(_1164785, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1164787, tc_HOL_Obool)), _1164791), hAPP(c_Set_Oimage(_1164785, _1164787, _1164789), _1164793))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1164785, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1164785, _1164787, _1164789), _1164791)), _1164793)))], (21307 ^ _777081) ^ [] : [-(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)))))], (21309 ^ _777081) ^ [] : [-(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)))))], (21311 ^ _777081) ^ [_1165065, _1165067, _1165069, _1165071, _1165073, _1165075] : [hBOOL(hAPP(hAPP(c_member(_1165065), _1165067), _1165069)), 21314 ^ _777081 : [(21315 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1165065), _1165071), _1165069)), -(hAPP(c_Set_Ovimage(_1165073, _1165065, hAPP(hAPP(c_COMBC(_1165073, _1165065, _1165065), hAPP(hAPP(c_COMBC(_1165073, _1165065, tc_fun(_1165065, _1165065)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1165065, tc_fun(_1165065, _1165065)), _1165073), c_If(_1165065)), hAPP(hAPP(c_COMBC(_1165073, tc_fun(_1165073, tc_HOL_Obool), tc_HOL_Obool), c_member(_1165073)), _1165075))), _1165067)), _1165071)), _1165069) = c_Orderings_Otop__class_Otop(tc_fun(_1165073, tc_HOL_Obool)))], (21321 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1165065), _1165071), _1165069))), -(hAPP(c_Set_Ovimage(_1165073, _1165065, hAPP(hAPP(c_COMBC(_1165073, _1165065, _1165065), hAPP(hAPP(c_COMBC(_1165073, _1165065, tc_fun(_1165065, _1165065)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1165065, tc_fun(_1165065, _1165065)), _1165073), c_If(_1165065)), hAPP(hAPP(c_COMBC(_1165073, tc_fun(_1165073, tc_HOL_Obool), tc_HOL_Obool), c_member(_1165073)), _1165075))), _1165067)), _1165071)), _1165069) = _1165075)]]], (21327 ^ _777081) ^ [_1165556, _1165558, _1165560, _1165562, _1165564, _1165566] : [-(hBOOL(hAPP(hAPP(c_member(_1165556), _1165558), _1165560))), 21330 ^ _777081 : [(21331 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1165556), _1165562), _1165560)), -(hAPP(c_Set_Ovimage(_1165564, _1165556, hAPP(hAPP(c_COMBC(_1165564, _1165556, _1165556), hAPP(hAPP(c_COMBC(_1165564, _1165556, tc_fun(_1165556, _1165556)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1165556, tc_fun(_1165556, _1165556)), _1165564), c_If(_1165556)), hAPP(hAPP(c_COMBC(_1165564, tc_fun(_1165564, tc_HOL_Obool), tc_HOL_Obool), c_member(_1165564)), _1165566))), _1165558)), _1165562)), _1165560) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1165564, tc_HOL_Obool)), _1165566))], (21337 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1165556), _1165562), _1165560))), -(hAPP(c_Set_Ovimage(_1165564, _1165556, hAPP(hAPP(c_COMBC(_1165564, _1165556, _1165556), hAPP(hAPP(c_COMBC(_1165564, _1165556, tc_fun(_1165556, _1165556)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1165556, tc_fun(_1165556, _1165556)), _1165564), c_If(_1165556)), hAPP(hAPP(c_COMBC(_1165564, tc_fun(_1165564, tc_HOL_Obool), tc_HOL_Obool), c_member(_1165564)), _1165566))), _1165558)), _1165562)), _1165560) = c_Orderings_Obot__class_Obot(tc_fun(_1165564, tc_HOL_Obool)))]]], (21343 ^ _777081) ^ [_1166061, _1166063] : [class_Int_Onumber__ring(_1166061), class_Rings_Olinordered__idom(_1166061), 21350 ^ _777081 : [(21351 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166061), hAPP(c_Int_Onumber__class_Onumber__of(_1166061), _1166063)), c_Groups_Oone__class_Oone(_1166061))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1166063), c_Int_OBit1(c_Int_OPls))))], (21357 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1166063), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166061), hAPP(c_Int_Onumber__class_Onumber__of(_1166061), _1166063)), c_Groups_Oone__class_Oone(_1166061))))]]], (21363 ^ _777081) ^ [_1166375, _1166377] : [class_Int_Onumber__ring(_1166375), class_Rings_Olinordered__idom(_1166375), 21370 ^ _777081 : [(21371 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166375), c_Groups_Oone__class_Oone(_1166375)), hAPP(c_Int_Onumber__class_Onumber__of(_1166375), _1166377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1166377)))], (21377 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1166377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1166375), c_Groups_Oone__class_Oone(_1166375)), hAPP(c_Int_Onumber__class_Onumber__of(_1166375), _1166377))))]]], (21383 ^ _777081) ^ [_1166680, _1166682] : [class_Int_Onumber__ring(_1166680), class_Rings_Olinordered__idom(_1166680), 21390 ^ _777081 : [(21391 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166680), c_Groups_Oone__class_Oone(_1166680)), hAPP(c_Int_Onumber__class_Onumber__of(_1166680), _1166682))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1166682)))], (21397 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1166682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166680), c_Groups_Oone__class_Oone(_1166680)), hAPP(c_Int_Onumber__class_Onumber__of(_1166680), _1166682))))]]], (21403 ^ _777081) ^ [_1166985, _1166987] : [class_Int_Onumber__ring(_1166985), class_Rings_Olinordered__idom(_1166985), 21410 ^ _777081 : [(21411 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166985), hAPP(c_Int_Onumber__class_Onumber__of(_1166985), _1166987)), c_Groups_Oone__class_Oone(_1166985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1166987), c_Int_OBit1(c_Int_OPls))))], (21417 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1166987), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166985), hAPP(c_Int_Onumber__class_Onumber__of(_1166985), _1166987)), c_Groups_Oone__class_Oone(_1166985))))]]], (21423 ^ _777081) ^ [_1167299, _1167301] : [class_Int_Onumber__ring(_1167299), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167299), hAPP(c_Int_Onumber__class_Onumber__of(_1167299), _1167301)), c_Groups_Oone__class_Oone(_1167299)) = hAPP(c_Int_Onumber__class_Onumber__of(_1167299), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1167301), c_Int_OBit1(c_Int_OPls))))], (21429 ^ _777081) ^ [_1167426, _1167428] : [class_Int_Onumber__ring(_1167426), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167426), c_Groups_Oone__class_Oone(_1167426)), hAPP(c_Int_Onumber__class_Onumber__of(_1167426), _1167428)) = hAPP(c_Int_Onumber__class_Onumber__of(_1167426), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1167428)))], (21435 ^ _777081) ^ [_1167547, _1167549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1167547)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1167549)), _1167547) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1167549), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1167547), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (21441 ^ _777081) ^ [_1167670, _1167672] : [class_Int_Onumber__ring(_1167670), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1167670), c_Groups_Oone__class_Oone(_1167670)), hAPP(c_Int_Onumber__class_Onumber__of(_1167670), _1167672)) = hAPP(c_Int_Onumber__class_Onumber__of(_1167670), 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), _1167672))))], (21447 ^ _777081) ^ [_1167797, _1167799] : [class_Int_Onumber__ring(_1167797), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1167797), hAPP(c_Int_Onumber__class_Onumber__of(_1167797), _1167799)), c_Groups_Oone__class_Oone(_1167797)) = hAPP(c_Int_Onumber__class_Onumber__of(_1167797), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1167799), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (21453 ^ _777081) ^ [_1167924, _1167926] : [class_Int_Onumber__ring(_1167924), 21456 ^ _777081 : [(21457 ^ _777081) ^ [] : [c_Groups_Oone__class_Oone(_1167924) = hAPP(c_Int_Onumber__class_Onumber__of(_1167924), _1167926), -(c_Int_Oiszero(_1167924, hAPP(c_Int_Onumber__class_Onumber__of(_1167924), 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), _1167926)))))], (21463 ^ _777081) ^ [] : [c_Int_Oiszero(_1167924, hAPP(c_Int_Onumber__class_Onumber__of(_1167924), 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), _1167926)))), -(c_Groups_Oone__class_Oone(_1167924) = hAPP(c_Int_Onumber__class_Onumber__of(_1167924), _1167926))]]], (21469 ^ _777081) ^ [_1168183] : [class_Orderings_Olinorder(_1168183), -(c_Orderings_Oord_Omin(_1168183, hAPP(c_COMBC(_1168183, _1168183, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1168183))) = c_Orderings_Oord__class_Omax(_1168183))], (21475 ^ _777081) ^ [_1168284, _1168286] : [class_Rings_Osemiring__1(_1168284), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1168286)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1168284), 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)))), _1168286))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1168284), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1168284), hAPP(c_Int_Onat, _1168286))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1168284), hAPP(c_Int_Onat, _1168286))))], (21485 ^ _777081) ^ [_1168485] : [class_Orderings_Oord(_1168485), -(c_Orderings_Oord__class_Omax(_1168485) = c_Orderings_Oord_Omax(_1168485, c_Orderings_Oord__class_Oless__eq(_1168485)))], (21491 ^ _777081) ^ [_1168572, _1168574, _1168576] : [class_Int_Onumber__ring(_1168572), 21494 ^ _777081 : [(21495 ^ _777081) ^ [] : [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), _1168574))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1168572), hAPP(c_Int_Onumber__class_Onumber__of(_1168572), _1168576)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1168574))) = hAPP(hAPP(c_HOL_OLet(_1168572, _1168572), hAPP(hAPP(c_Power_Opower__class_Opower(_1168572), hAPP(c_Int_Onumber__class_Onumber__of(_1168572), _1168576)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1168574))), hAPP(hAPP(c_COMBS(_1168572, _1168572, _1168572), hAPP(hAPP(c_COMBB(_1168572, tc_fun(_1168572, _1168572), _1168572), c_Groups_Otimes__class_Otimes(_1168572)), hAPP(c_Groups_Otimes__class_Otimes(_1168572), hAPP(c_Int_Onumber__class_Onumber__of(_1168572), _1168576)))), c_COMBI(_1168572))))], (21501 ^ _777081) ^ [] : [-(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), _1168574)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1168572), hAPP(c_Int_Onumber__class_Onumber__of(_1168572), _1168576)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1168574))) = c_Groups_Oone__class_Oone(_1168572))]]], (21507 ^ _777081) ^ [_1168979, _1168981] : [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), _1168979))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1168981), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1168979))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1168981), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1168979))), 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), _1168981))), c_COMBI(tc_Int_Oint))))], (21513 ^ _777081) ^ [_1169136, _1169138] : [-(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), _1169136)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1169138), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1169136))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (21519 ^ _777081) ^ [_1169190, _1169192] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169190)), _1169192) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1169190), _1169192)))], (21521 ^ _777081) ^ [_1169233, _1169235] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1169233), _1169235)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169233)), _1169235))], (21523 ^ _777081) ^ [_1169276, _1169278] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169276)), _1169278) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1169276), _1169278)))], (21525 ^ _777081) ^ [_1169334, _1169336] : [c_Int_OBit0(_1169334) = c_Int_OBit0(_1169336), -(_1169334 = _1169336)], (21531 ^ _777081) ^ [_1169415, _1169417] : [_1169415 = _1169417, -(c_Int_OBit0(_1169415) = c_Int_OBit0(_1169417))], (21537 ^ _777081) ^ [_1169502, _1169504, _1169506] : [class_Rings_Oring__1(_1169502), -(hAPP(c_Int_Oring__1__class_Oof__int(_1169502), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1169504), _1169506)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1169502), hAPP(c_Int_Oring__1__class_Oof__int(_1169502), _1169504)), _1169506))], (21543 ^ _777081) ^ [_1169627, _1169629, _1169631, _1169633] : [class_Rings_Ocomm__semiring__1(_1169627), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1169627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169627), _1169629), _1169631)), _1169633) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169627), hAPP(hAPP(c_Power_Opower__class_Opower(_1169627), _1169629), _1169633)), hAPP(hAPP(c_Power_Opower__class_Opower(_1169627), _1169631), _1169633)))], (21549 ^ _777081) ^ [_1169786, _1169788, _1169790] : [class_Int_Onumber__ring(_1169786), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1169786), _1169788), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1169790))) = hAPP(hAPP(c_HOL_OLet(_1169786, _1169786), hAPP(hAPP(c_Power_Opower__class_Opower(_1169786), _1169788), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1169790))), hAPP(hAPP(c_COMBS(_1169786, _1169786, _1169786), c_Groups_Otimes__class_Otimes(_1169786)), c_COMBI(_1169786))))], (21555 ^ _777081) ^ [_1169972, _1169974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1169972)), c_Int_OBit0(_1169974))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1169972), _1169974)))], (21561 ^ _777081) ^ [_1170073, _1170075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1170073), _1170075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1170073)), c_Int_OBit0(_1170075))))], (21567 ^ _777081) ^ [_1170195, _1170197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1170195)), c_Int_OBit0(_1170197))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1170195), _1170197)))], (21573 ^ _777081) ^ [_1170296, _1170298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1170296), _1170298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1170296)), c_Int_OBit0(_1170298))))], (21579 ^ _777081) ^ [_1170418, _1170420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1170418)), c_Int_OBit0(_1170420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170418), _1170420)))], (21585 ^ _777081) ^ [_1170519, _1170521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170519), _1170521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1170519)), c_Int_OBit0(_1170521))))], (21591 ^ _777081) ^ [_1170641, _1170643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1170641)), c_Int_OBit0(_1170643))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170641), _1170643)))], (21597 ^ _777081) ^ [_1170742, _1170744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170742), _1170744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1170742)), c_Int_OBit0(_1170744))))], (21603 ^ _777081) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (21605 ^ _777081) ^ [_1170879] : [c_Int_OPls = c_Int_OBit0(_1170879), -(c_Int_OPls = _1170879)], (21611 ^ _777081) ^ [_1170954] : [c_Int_OPls = _1170954, -(c_Int_OPls = c_Int_OBit0(_1170954))], (21617 ^ _777081) ^ [_1171047] : [c_Int_OBit0(_1171047) = c_Int_OPls, -(_1171047 = c_Int_OPls)], (21623 ^ _777081) ^ [_1171122] : [_1171122 = c_Int_OPls, -(c_Int_OBit0(_1171122) = c_Int_OPls)], (21629 ^ _777081) ^ [_1171215, _1171217] : [c_Int_OBit0(_1171215) = c_Int_OBit1(_1171217)], (21631 ^ _777081) ^ [_1171256, _1171258] : [c_Int_OBit1(_1171256) = c_Int_OBit0(_1171258)], (21633 ^ _777081) ^ [_1171285, _1171287] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1171285)), c_Int_OBit0(_1171287)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1171285), _1171287)))], (21635 ^ _777081) ^ [_1171328] : [-(c_Int_OBit0(_1171328) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1171328), _1171328))], (21637 ^ _777081) ^ [_1171359, _1171361, _1171363, _1171365] : [class_Rings_Ocomm__semiring__1(_1171359), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1171359), hAPP(hAPP(c_Power_Opower__class_Opower(_1171359), _1171361), _1171363)), _1171365) = hAPP(hAPP(c_Power_Opower__class_Opower(_1171359), _1171361), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1171363), _1171365)))], (21643 ^ _777081) ^ [_1171498, _1171500, _1171502] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1171498), _1171500)), _1171502) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1171498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1171500), _1171502)))], (21645 ^ _777081) ^ [_1171549, _1171551] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1171549), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1171551))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1171549), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1171551))), 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))))], (21647 ^ _777081) ^ [_1171600, _1171602] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1171600)), _1171602) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1171600), _1171602)))], (21649 ^ _777081) ^ [_1171641, _1171643] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1171641)), c_Int_OBit0(_1171643)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1171641), _1171643)))], (21651 ^ _777081) ^ [_1171684] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1171684)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1171684)))], (21653 ^ _777081) ^ [_1171717, _1171719] : [class_Rings_Ocomm__semiring__1(_1171717), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1171717), _1171719), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1171719)], (21659 ^ _777081) ^ [_1171808, _1171810] : [c_Nat__Transfer_Ois__nat(_1171808), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1171808), _1171810)))], (21665 ^ _777081) ^ [_1171893, _1171895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171893)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1171893), _1171895)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1171893)), _1171895))], (21671 ^ _777081) ^ [_1172010, _1172012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172010)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1172010)), _1172012) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1172010), _1172012)))], (21677 ^ _777081) ^ [_1172127, _1172129, _1172131] : [class_Int_Onumber__ring(_1172127), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1172127), hAPP(c_Int_Onumber__class_Onumber__of(_1172127), _1172129)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1172131))) = hAPP(hAPP(c_HOL_OLet(_1172127, _1172127), hAPP(hAPP(c_Power_Opower__class_Opower(_1172127), hAPP(c_Int_Onumber__class_Onumber__of(_1172127), _1172129)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1172131))), hAPP(hAPP(c_COMBS(_1172127, _1172127, _1172127), c_Groups_Otimes__class_Otimes(_1172127)), c_COMBI(_1172127))))], (21683 ^ _777081) ^ [_1172318] : [class_Rings_Osemiring__1(_1172318), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1172318), c_Groups_Ozero__class_Ozero(_1172318)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1172318))], (21689 ^ _777081) ^ [_1172415, _1172417] : [class_Rings_Oring__1__no__zero__divisors(_1172415), 21692 ^ _777081 : [(21693 ^ _777081) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1172415), _1172417), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1172415), -(_1172417 = c_Groups_Ozero__class_Ozero(_1172415))], (21699 ^ _777081) ^ [] : [_1172417 = c_Groups_Ozero__class_Ozero(_1172415), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1172415), _1172417), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1172415))]]], (21705 ^ _777081) ^ [_1172656, _1172658] : [class_Rings_Ocomm__semiring__1(_1172656), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1172656), _1172658), _1172658) = hAPP(hAPP(c_Power_Opower__class_Opower(_1172656), _1172658), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (21711 ^ _777081) ^ [_1172763, _1172765] : [class_Groups_Omonoid__mult(_1172763), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1172763), _1172765), 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(_1172763), _1172765), _1172765))], (21717 ^ _777081) ^ [_1172870] : [class_Rings_Osemiring__1(_1172870), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1172870), c_Groups_Oone__class_Oone(_1172870)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1172870))], (21723 ^ _777081) ^ [_1172967, _1172969] : [class_Rings_Oring__1(_1172967), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1172967), hAPP(c_Groups_Ouminus__class_Ouminus(_1172967), _1172969)), 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(_1172967), _1172969), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (21729 ^ _777081) ^ [_1173084, _1173086, _1173088] : [class_Groups_Omonoid__mult(_1173084), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1173084), _1173086), 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)))), _1173088)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1173084), hAPP(hAPP(c_Power_Opower__class_Opower(_1173084), _1173086), _1173088)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (21735 ^ _777081) ^ [_1173215, _1173217] : [class_Rings_Olinordered__idom(_1173215), -(hAPP(c_Groups_Oabs__class_Oabs(_1173215), hAPP(hAPP(c_Power_Opower__class_Opower(_1173215), _1173217), 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(_1173215), _1173217), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (21741 ^ _777081) ^ [_1173332, _1173334] : [class_Rings_Olinordered__idom(_1173332), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1173332), hAPP(c_Groups_Oabs__class_Oabs(_1173332), _1173334)), 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(_1173332), _1173334), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (21747 ^ _777081) ^ [_1173449, _1173451, _1173453] : [class_Rings_Ocomm__semiring__1(_1173449), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173449), hAPP(hAPP(c_Power_Opower__class_Opower(_1173449), _1173451), _1173453)), _1173451) = hAPP(hAPP(c_Power_Opower__class_Opower(_1173449), _1173451), hAPP(c_Nat_OSuc, _1173453)))], (21753 ^ _777081) ^ [_1173580, _1173582, _1173584] : [class_Rings_Ocomm__semiring__1(_1173580), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173580), _1173582), hAPP(hAPP(c_Power_Opower__class_Opower(_1173580), _1173582), _1173584)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1173580), _1173582), hAPP(c_Nat_OSuc, _1173584)))], (21759 ^ _777081) ^ [_1173711, _1173713, _1173715] : [class_Rings_Ocomm__semiring__1(_1173711), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1173711), _1173713), hAPP(c_Nat_OSuc, _1173715)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173711), _1173713), hAPP(hAPP(c_Power_Opower__class_Opower(_1173711), _1173713), _1173715)))], (21765 ^ _777081) ^ [_1173842, _1173844] : [class_Rings_Ocomm__semiring__1(_1173842), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1173842), _1173844), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1173842))], (21771 ^ _777081) ^ [_1173937, _1173939, _1173941, _1173943] : [class_Rings_Ocomm__semiring__1(_1173937), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1173937), hAPP(hAPP(c_Power_Opower__class_Opower(_1173937), _1173939), _1173941)), hAPP(hAPP(c_Power_Opower__class_Opower(_1173937), _1173939), _1173943)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1173937), _1173939), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1173941), _1173943)))], (21777 ^ _777081) ^ [_1174104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1174104)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1174104), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21783 ^ _777081) ^ [_1174199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1174199), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1174199)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21789 ^ _777081) ^ [_1174300, _1174302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174300)), -(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), _1174300), _1174302))))], (21795 ^ _777081) ^ [_1174409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1174409)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1174409), c_Int_OPls)))], (21801 ^ _777081) ^ [_1174504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1174504), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1174504)), c_Int_OPls)))], (21807 ^ _777081) ^ [_1174617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1174617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1174617)))], (21813 ^ _777081) ^ [_1174700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1174700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1174700))))], (21819 ^ _777081) ^ [_1174804, _1174806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1174804)), c_Int_OBit1(_1174806))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1174804), _1174806)))], (21825 ^ _777081) ^ [_1174905, _1174907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1174905), _1174907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1174905)), c_Int_OBit1(_1174907))))], (21831 ^ _777081) ^ [_1175027, _1175029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1175027)), c_Int_OBit1(_1175029))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1175027), _1175029)))], (21837 ^ _777081) ^ [_1175128, _1175130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1175128), _1175130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1175128)), c_Int_OBit1(_1175130))))], (21843 ^ _777081) ^ [_1175247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1175247))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1175247)))], (21849 ^ _777081) ^ [_1175330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1175330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1175330))))], (21855 ^ _777081) ^ [_1175431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1175431)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175431), c_Int_OPls)))], (21861 ^ _777081) ^ [_1175526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175526), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1175526)), c_Int_OPls)))], (21867 ^ _777081) ^ [_1175642, _1175644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1175642)), c_Int_OBit0(_1175644))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175642), _1175644)))], (21873 ^ _777081) ^ [_1175743, _1175745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175743), _1175745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1175743)), c_Int_OBit0(_1175745))))], (21879 ^ _777081) ^ [_1175865, _1175867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1175865)), c_Int_OBit0(_1175867))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175865), _1175867)))], (21885 ^ _777081) ^ [_1175966, _1175968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175966), _1175968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1175966)), c_Int_OBit0(_1175968))))], (21891 ^ _777081) ^ [_1176073, _1176075] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1176073)), c_Int_OBit1(_1176075)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176073), _1176075)))], (21893 ^ _777081) ^ [_1176116, _1176118] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1176116)), c_Int_OBit0(_1176118)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176116), _1176118)))], (21895 ^ _777081) ^ [_1176159, _1176161, _1176163] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1176159), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1176161), _1176163)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1176159), _1176161)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1176159), _1176163)))], (21897 ^ _777081) ^ [_1176216] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1176216)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1176216)))], (21899 ^ _777081) ^ [_1176249, _1176251] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1176249)), c_Int_OBit0(_1176251)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1176249), _1176251)))], (21901 ^ _777081) ^ [_1176292, _1176294] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1176292)), c_Int_OBit1(_1176294)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1176292), _1176294)))], (21903 ^ _777081) ^ [_1176335, _1176337, _1176339] : [class_Rings_Oring__1(_1176335), hBOOL(hAPP(hAPP(c_member(_1176335), _1176337), c_Int_Oring__1__class_OInts(_1176335))), -(hBOOL(hAPP(hAPP(c_member(_1176335), hAPP(hAPP(c_Power_Opower__class_Opower(_1176335), _1176337), _1176339)), c_Int_Oring__1__class_OInts(_1176335))))], (21913 ^ _777081) ^ [_1176530] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1176530)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1176530))))], (21919 ^ _777081) ^ [_1176625] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1176625))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1176625)))))], (21925 ^ _777081) ^ [_1176726] : [-(c_Int_Opred(c_Int_OBit0(_1176726)) = c_Int_OBit1(c_Int_Opred(_1176726)))], (21927 ^ _777081) ^ [_1176757] : [-(c_Int_Opred(c_Int_OBit1(_1176757)) = c_Int_OBit0(_1176757))], (21929 ^ _777081) ^ [_1176786, _1176788] : [class_Int_Onumber__ring(_1176786), class_Int_Oring__char__0(_1176786), 21936 ^ _777081 : [(21937 ^ _777081) ^ [] : [c_Int_Oiszero(_1176786, hAPP(c_Int_Onumber__class_Onumber__of(_1176786), c_Int_OBit0(_1176788))), -(c_Int_Oiszero(_1176786, hAPP(c_Int_Onumber__class_Onumber__of(_1176786), _1176788)))], (21943 ^ _777081) ^ [] : [c_Int_Oiszero(_1176786, hAPP(c_Int_Onumber__class_Onumber__of(_1176786), _1176788)), -(c_Int_Oiszero(_1176786, hAPP(c_Int_Onumber__class_Onumber__of(_1176786), c_Int_OBit0(_1176788))))]]], (21949 ^ _777081) ^ [_1177079, _1177081, _1177083] : [class_Rings_Olinordered__semidom(_1177079), hAPP(hAPP(c_Power_Opower__class_Opower(_1177079), _1177081), 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(_1177079), _1177083), 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(_1177079), c_Groups_Ozero__class_Ozero(_1177079)), _1177081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177079), c_Groups_Ozero__class_Ozero(_1177079)), _1177083)), -(_1177081 = _1177083)], (21967 ^ _777081) ^ [_1177386, _1177388, _1177390] : [class_Rings_Olinordered__semidom(_1177386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177386), hAPP(hAPP(c_Power_Opower__class_Opower(_1177386), _1177388), 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(_1177386), _1177390), 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(_1177386), c_Groups_Ozero__class_Ozero(_1177386)), _1177390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177386), _1177388), _1177390)))], (21981 ^ _777081) ^ [_1177649, _1177651] : [class_Rings_Olinordered__idom(_1177649), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177649), c_Groups_Ozero__class_Ozero(_1177649)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177649), _1177651), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21987 ^ _777081) ^ [_1177758, _1177760] : [class_Rings_Olinordered__idom(_1177758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177758), hAPP(hAPP(c_Power_Opower__class_Opower(_1177758), _1177760), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1177758)))], (21993 ^ _777081) ^ [_1177868, _1177870] : [class_Rings_Olinordered__idom(_1177868), 21996 ^ _777081 : [(21997 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177868), c_Groups_Ozero__class_Ozero(_1177868)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177868), _1177870), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1177870 = c_Groups_Ozero__class_Ozero(_1177868)], (22003 ^ _777081) ^ [] : [-(_1177870 = c_Groups_Ozero__class_Ozero(_1177868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177868), c_Groups_Ozero__class_Ozero(_1177868)), hAPP(hAPP(c_Power_Opower__class_Opower(_1177868), _1177870), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (22009 ^ _777081) ^ [_1178092, _1178094, _1178096] : [class_Rings_Olinordered__idom(_1178092), 22012 ^ _777081 : [(22013 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178092), hAPP(hAPP(c_Power_Opower__class_Opower(_1178092), _1178094), 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(_1178092), _1178096), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1178092), 22016 ^ _777081 : [(22017 ^ _777081) ^ [] : [-(_1178094 = c_Groups_Ozero__class_Ozero(_1178092))], (22019 ^ _777081) ^ [] : [-(_1178096 = c_Groups_Ozero__class_Ozero(_1178092))]]], (22021 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1178092), hAPP(hAPP(c_Power_Opower__class_Opower(_1178092), _1178094), 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(_1178092), _1178096), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1178092)), _1178094 = c_Groups_Ozero__class_Ozero(_1178092), _1178096 = c_Groups_Ozero__class_Ozero(_1178092)]]], (22031 ^ _777081) ^ [_1178467, _1178469] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1178467), hAPP(c_Int_Onumber__class_Onumber__of(_1178467), _1178469)), 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(_1178467), hAPP(c_Int_Onumber__class_Onumber__of(_1178467), _1178469)), hAPP(c_Int_Onumber__class_Onumber__of(_1178467), _1178469))), class_Groups_Omonoid__mult(_1178467), class_Int_Onumber(_1178467)], (22041 ^ _777081) ^ [_1178654] : [-(c_Int_Osucc(c_Int_OBit1(_1178654)) = c_Int_OBit0(c_Int_Osucc(_1178654)))], (22043 ^ _777081) ^ [_1178685] : [-(c_Int_Osucc(c_Int_OBit0(_1178685)) = c_Int_OBit1(_1178685))], (22045 ^ _777081) ^ [_1178714, _1178716] : [class_Rings_Oring__1__no__zero__divisors(_1178714), 22048 ^ _777081 : [(22059 ^ _777081) ^ [] : [22060 ^ _777081 : [(22061 ^ _777081) ^ [] : [_1178716 = c_Groups_Oone__class_Oone(_1178714)], (22063 ^ _777081) ^ [] : [_1178716 = hAPP(c_Groups_Ouminus__class_Ouminus(_1178714), c_Groups_Oone__class_Oone(_1178714))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1178714), _1178716), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1178714))], (22049 ^ _777081) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1178714), _1178716), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1178714), -(_1178716 = c_Groups_Oone__class_Oone(_1178714)), -(_1178716 = hAPP(c_Groups_Ouminus__class_Ouminus(_1178714), c_Groups_Oone__class_Oone(_1178714)))]]], (22067 ^ _777081) ^ [_1179021, _1179023, _1179025] : [class_Rings_Ocomm__semiring__1(_1179021), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1179021), _1179023), 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)))), _1179025)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179021), hAPP(hAPP(c_Power_Opower__class_Opower(_1179021), _1179023), _1179025)), hAPP(hAPP(c_Power_Opower__class_Opower(_1179021), _1179023), _1179025)))], (22073 ^ _777081) ^ [_1179168, _1179170, _1179172] : [class_Rings_Oring__1(_1179168), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1179168), hAPP(c_Groups_Ouminus__class_Ouminus(_1179168), _1179170)), 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)))), _1179172)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1179168), _1179170), 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)))), _1179172)))], (22079 ^ _777081) ^ [_1179299] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1179299)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179299)), 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))))], (22081 ^ _777081) ^ [_1179345, _1179347] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1179345))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179345)), _1179347) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1179347))], (22087 ^ _777081) ^ [_1179450, _1179452] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1179450)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179450)), _1179452) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1179450)), _1179452)))], (22093 ^ _777081) ^ [_1179523, _1179525] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1179523))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179523)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179525)) = 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), _1179525)))], (22099 ^ _777081) ^ [_1179640, _1179642] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1179640)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179640)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179642)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1179640)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1179642))))], (22105 ^ _777081) ^ [_1179710, _1179712, _1179714] : [class_Rings_Olinordered__semidom(_1179710), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179710), hAPP(hAPP(c_Power_Opower__class_Opower(_1179710), _1179712), 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(_1179710), _1179714), 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(_1179710), c_Groups_Ozero__class_Ozero(_1179710)), _1179714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179710), _1179712), _1179714)))], (22119 ^ _777081) ^ [_1179973, _1179975, _1179977] : [class_Rings_Olinordered__idom(_1179973), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179973), c_Groups_Ozero__class_Ozero(_1179973)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1179973), hAPP(hAPP(c_Power_Opower__class_Opower(_1179973), _1179975), 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(_1179973), _1179977), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (22125 ^ _777081) ^ [_1180116, _1180118, _1180120] : [class_Rings_Olinordered__idom(_1180116), 22128 ^ _777081 : [(22129 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180116), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180116), hAPP(hAPP(c_Power_Opower__class_Opower(_1180116), _1180118), 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(_1180116), _1180120), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1180116))), 22132 ^ _777081 : [(22133 ^ _777081) ^ [] : [-(_1180118 = c_Groups_Ozero__class_Ozero(_1180116))], (22135 ^ _777081) ^ [] : [-(_1180120 = c_Groups_Ozero__class_Ozero(_1180116))]]], (22137 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180116), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180116), hAPP(hAPP(c_Power_Opower__class_Opower(_1180116), _1180118), 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(_1180116), _1180120), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1180116)))), _1180118 = c_Groups_Ozero__class_Ozero(_1180116), _1180120 = c_Groups_Ozero__class_Ozero(_1180116)]]], (22147 ^ _777081) ^ [_1180512, _1180514, _1180516] : [class_Rings_Olinordered__idom(_1180512), 22150 ^ _777081 : [(22161 ^ _777081) ^ [] : [22162 ^ _777081 : [(22163 ^ _777081) ^ [] : [-(_1180514 = c_Groups_Ozero__class_Ozero(_1180512))], (22165 ^ _777081) ^ [] : [-(_1180516 = c_Groups_Ozero__class_Ozero(_1180512))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180512), c_Groups_Ozero__class_Ozero(_1180512)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180512), hAPP(hAPP(c_Power_Opower__class_Opower(_1180512), _1180514), 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(_1180512), _1180516), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (22151 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180512), c_Groups_Ozero__class_Ozero(_1180512)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180512), hAPP(hAPP(c_Power_Opower__class_Opower(_1180512), _1180514), 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(_1180512), _1180516), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1180514 = c_Groups_Ozero__class_Ozero(_1180512), _1180516 = c_Groups_Ozero__class_Ozero(_1180512)]]], (22169 ^ _777081) ^ [_1180887, _1180889, _1180891] : [class_Rings_Olinordered__idom(_1180887), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180887), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180887), hAPP(hAPP(c_Power_Opower__class_Opower(_1180887), _1180889), 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(_1180887), _1180891), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1180887)))], (22175 ^ _777081) ^ [_1181031, _1181033, _1181035] : [class_Int_Onumber__ring(_1181031), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1181031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181031), _1181033), _1181035)), 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(_1181031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181031), hAPP(hAPP(c_Power_Opower__class_Opower(_1181031), _1181033), 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(_1181031), _1181035), 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(_1181031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181031), hAPP(c_Int_Onumber__class_Onumber__of(_1181031), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1181033)), _1181035)))], (22181 ^ _777081) ^ [_1181246, _1181248, _1181250] : [class_Rings_Olinordered__idom(_1181246), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181246), c_Groups_Ozero__class_Ozero(_1181246)), hAPP(hAPP(c_Power_Opower__class_Opower(_1181246), _1181248), 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)))), _1181250)))))], (22187 ^ _777081) ^ [_1181363, _1181365, _1181367] : [class_Groups_Omonoid__mult(_1181363), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1181363), _1181365), 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)))), _1181367))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181363), _1181365), hAPP(hAPP(c_Power_Opower__class_Opower(_1181363), hAPP(hAPP(c_Power_Opower__class_Opower(_1181363), _1181365), _1181367)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (22193 ^ _777081) ^ [_1181516, _1181518, _1181520] : [class_Rings_Ocomm__semiring__1(_1181516), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1181516), _1181518), 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)))), _1181520))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181516), _1181518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181516), hAPP(hAPP(c_Power_Opower__class_Opower(_1181516), _1181518), _1181520)), hAPP(hAPP(c_Power_Opower__class_Opower(_1181516), _1181518), _1181520))))], (22199 ^ _777081) ^ [_1181685, _1181687] : [class_Rings_Oring__1(_1181685), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1181685), hAPP(c_Groups_Ouminus__class_Ouminus(_1181685), c_Groups_Oone__class_Oone(_1181685))), 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)))), _1181687)) = c_Groups_Oone__class_Oone(_1181685))], (22205 ^ _777081) ^ [_1181800, _1181802] : [class_Int_Onumber__ring(_1181800), -(hAPP(c_Int_Onumber__class_Onumber__of(_1181800), c_Int_OBit0(_1181802)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181800), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181800), c_Groups_Ozero__class_Ozero(_1181800)), hAPP(c_Int_Onumber__class_Onumber__of(_1181800), _1181802))), hAPP(c_Int_Onumber__class_Onumber__of(_1181800), _1181802)))], (22211 ^ _777081) ^ [_1181960, _1181962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1181960)), c_Int_OBit1(_1181962))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181960), _1181962)))], (22217 ^ _777081) ^ [_1182061, _1182063] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182061), _1182063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1182061)), c_Int_OBit1(_1182063))))], (22223 ^ _777081) ^ [_1182183, _1182185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1182183)), c_Int_OBit1(_1182185))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182183), _1182185)))], (22229 ^ _777081) ^ [_1182284, _1182286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182284), _1182286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1182284)), c_Int_OBit1(_1182286))))], (22235 ^ _777081) ^ [_1182406, _1182408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1182406)), c_Int_OBit0(_1182408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182406), _1182408)))], (22241 ^ _777081) ^ [_1182507, _1182509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182507), _1182509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1182507)), c_Int_OBit0(_1182509))))], (22247 ^ _777081) ^ [_1182629, _1182631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1182629)), c_Int_OBit0(_1182631))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182629), _1182631)))], (22253 ^ _777081) ^ [_1182730, _1182732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182730), _1182732)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1182730)), c_Int_OBit0(_1182732))))], (22259 ^ _777081) ^ [_1182837, _1182839] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1182837)), _1182839) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182837), _1182839))), _1182839))], (22261 ^ _777081) ^ [_1182884, _1182886] : [-(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), _1182884)), _1182886))))], (22263 ^ _777081) ^ [_1182920, _1182922] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1182920)), c_Int_OBit1(_1182922)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1182920)), _1182922)))], (22265 ^ _777081) ^ [_1182965, _1182967, _1182969] : [class_Int_Onumber__ring(_1182965), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1182965), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1182965), _1182967), _1182969)), 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(_1182965), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182965), hAPP(hAPP(c_Power_Opower__class_Opower(_1182965), _1182967), 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(_1182965), _1182969), 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(_1182965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182965), hAPP(c_Int_Onumber__class_Onumber__of(_1182965), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1182967)), _1182969)))], (22271 ^ _777081) ^ [_1183180, _1183182, _1183184] : [class_Rings_Olinordered__idom(_1183180), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183180), c_Groups_Ozero__class_Ozero(_1183180)), hAPP(hAPP(c_Power_Opower__class_Opower(_1183180), _1183182), 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)))), _1183184))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183180), c_Groups_Ozero__class_Ozero(_1183180)), _1183182)))], (22281 ^ _777081) ^ [_1183375, _1183377, _1183379] : [class_Rings_Olinordered__idom(_1183375), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183375), _1183377), c_Groups_Ozero__class_Ozero(_1183375))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183375), hAPP(hAPP(c_Power_Opower__class_Opower(_1183375), _1183377), 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)))), _1183379)))), c_Groups_Ozero__class_Ozero(_1183375))))], (22291 ^ _777081) ^ [_1183570, _1183572] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1183570)), c_Int_OBit1(_1183572)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1183570), c_Int_Osucc(_1183572))))], (22293 ^ _777081) ^ [_1183615, _1183617] : [class_Rings_Oring__1(_1183615), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1183615), hAPP(c_Groups_Ouminus__class_Ouminus(_1183615), c_Groups_Oone__class_Oone(_1183615))), 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)))), _1183617))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1183615), c_Groups_Oone__class_Oone(_1183615)))], (22299 ^ _777081) ^ [_1183746, _1183748] : [class_Lattices_Olattice(_1183746), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1183746), _1183748), _1183748) = _1183748)], (22305 ^ _777081) ^ [_1183837, _1183839] : [class_Lattices_Olattice(_1183837), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1183837), _1183839), _1183839) = _1183839)], (22311 ^ _777081) ^ [_1183928, _1183930] : [class_Orderings_Olinorder(_1183928), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1183928), _1183930), _1183930) = _1183930)], (22317 ^ _777081) ^ [_1184019, _1184021] : [class_Orderings_Olinorder(_1184019), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1184019), _1184021), _1184021) = _1184021)], (22323 ^ _777081) ^ [_1184110, _1184112] : [class_Int_Onumber__ring(_1184110), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184110), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184110), c_Groups_Oone__class_Oone(_1184110)), c_Groups_Oone__class_Oone(_1184110))), hAPP(c_Int_Onumber__class_Onumber__of(_1184110), _1184112)) = hAPP(c_Int_Onumber__class_Onumber__of(_1184110), c_Int_OBit0(_1184112)))], (22329 ^ _777081) ^ [_1184249, _1184251] : [class_Groups_Omonoid__mult(_1184249), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1184249), _1184251), 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(_1184249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184249), _1184251), _1184251)), _1184251))], (22335 ^ _777081) ^ [_1184372] : [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), _1184372))), 22338 ^ _777081 : [(22339 ^ _777081) ^ [] : [-(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(_1184372)))))], (22341 ^ _777081) ^ [] : [-(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(_1184372)))))]]], (22343 ^ _777081) ^ [_1184520, _1184522] : [_1184520 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1184522), _1184520) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (22349 ^ _777081) ^ [_1184603, _1184605] : [-(_1184603 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1184605), _1184603) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184605), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1184605), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1184603), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (22355 ^ _777081) ^ [_1184665] : [class_Orderings_Olinorder(_1184665), -(c_Orderings_Oord_Omax(_1184665, hAPP(c_COMBC(_1184665, _1184665, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1184665))) = c_Orderings_Oord__class_Omin(_1184665))], (22371 ^ _777081) ^ [_1184930, _1184932] : [22372 ^ _777081 : [(22373 ^ _777081) ^ [] : [-(_1184930 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22375 ^ _777081) ^ [] : [_1184932 = 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), _1184930)), _1184932))))], (22361 ^ _777081) ^ [_1184781, _1184783] : [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), _1184781)), _1184783))), _1184781 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1184783 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22379 ^ _777081) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (22381 ^ _777081) ^ [_1185084, _1185086] : [class_Int_Onumber__ring(_1185084), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185084), hAPP(c_Int_Onumber__class_Onumber__of(_1185084), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1185086) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185084), _1185086), _1185086))], (22387 ^ _777081) ^ [_1185201, _1185203] : [class_Int_Onumber__ring(_1185201), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185201), _1185203), hAPP(c_Int_Onumber__class_Onumber__of(_1185201), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185201), _1185203), _1185203))], (22393 ^ _777081) ^ [_1185318] : [class_Int_Onumber__ring(_1185318), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1185318), c_Groups_Oone__class_Oone(_1185318)), c_Groups_Oone__class_Oone(_1185318)) = hAPP(c_Int_Onumber__class_Onumber__of(_1185318), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (22399 ^ _777081) ^ [] : [-(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))))], (22401 ^ _777081) ^ [] : [-(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))))], (22403 ^ _777081) ^ [] : [-(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))))))], (22405 ^ _777081) ^ [_1185479] : [-(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)))), _1185479) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1185479)))], (22407 ^ _777081) ^ [_1185511] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1185511), 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, _1185511)))], (22409 ^ _777081) ^ [_1185546] : [-(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)))), _1185546) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1185546), _1185546))], (22411 ^ _777081) ^ [_1185578] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1185578), 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), _1185578), _1185578))], (22413 ^ _777081) ^ [] : [-(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)))))], (22415 ^ _777081) ^ [] : [-(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)))))], (22417 ^ _777081) ^ [] : [-(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))))], (22419 ^ _777081) ^ [_1185667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185667), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1185667 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1185667 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22429 ^ _777081) ^ [] : [-(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))))], (22431 ^ _777081) ^ [_1185783, _1185785, _1185787] : [class_Int_Onumber__ring(_1185783), 22434 ^ _777081 : [(22435 ^ _777081) ^ [] : [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), _1185785))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1185783), _1185787), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1185785))) = hAPP(hAPP(c_HOL_OLet(_1185783, _1185783), hAPP(hAPP(c_Power_Opower__class_Opower(_1185783), _1185787), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1185785))), hAPP(hAPP(c_COMBS(_1185783, _1185783, _1185783), hAPP(hAPP(c_COMBB(_1185783, tc_fun(_1185783, _1185783), _1185783), c_Groups_Otimes__class_Otimes(_1185783)), hAPP(c_Groups_Otimes__class_Otimes(_1185783), _1185787))), c_COMBI(_1185783))))], (22441 ^ _777081) ^ [] : [-(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), _1185785)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1185783), _1185787), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1185785))) = c_Groups_Oone__class_Oone(_1185783))]]], (22447 ^ _777081) ^ [_1186141, _1186143, _1186145, _1186147] : [class_Rings_Olinordered__semidom(_1186141), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186141), _1186143), _1186145)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186141), c_Groups_Ozero__class_Ozero(_1186141)), _1186143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186141), hAPP(hAPP(c_Power_Opower__class_Opower(_1186141), _1186143), _1186147)), hAPP(hAPP(c_Power_Opower__class_Opower(_1186141), _1186145), _1186147))))], (22465 ^ _777081) ^ [_1186470, _1186472, _1186474] : [class_Rings_Olinordered__semidom(_1186470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186470), c_Groups_Oone__class_Oone(_1186470)), _1186472)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186470), c_Groups_Oone__class_Oone(_1186470)), hAPP(hAPP(c_Power_Opower__class_Opower(_1186470), _1186472), _1186474))))], (22479 ^ _777081) ^ [_1186711, _1186713, _1186715, _1186717] : [class_Rings_Olinordered__semidom(_1186711), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186711), c_Groups_Oone__class_Oone(_1186711)), _1186713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186711), hAPP(hAPP(c_Power_Opower__class_Opower(_1186711), _1186713), _1186715)), hAPP(hAPP(c_Power_Opower__class_Opower(_1186711), _1186713), _1186717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186715), _1186717)))], (22493 ^ _777081) ^ [_1186976, _1186978, _1186980, _1186982] : [class_Rings_Olinordered__semidom(_1186976), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186976), c_Groups_Oone__class_Oone(_1186976)), _1186978)), 22500 ^ _777081 : [(22501 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186976), hAPP(hAPP(c_Power_Opower__class_Opower(_1186976), _1186978), _1186980)), hAPP(hAPP(c_Power_Opower__class_Opower(_1186976), _1186978), _1186982))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186980), _1186982)))], (22507 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186980), _1186982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186976), hAPP(hAPP(c_Power_Opower__class_Opower(_1186976), _1186978), _1186980)), hAPP(hAPP(c_Power_Opower__class_Opower(_1186976), _1186978), _1186982))))]]], (22513 ^ _777081) ^ [_1187351, _1187353, _1187355, _1187357] : [class_Rings_Olinordered__semidom(_1187351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1187353), _1187355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187351), c_Groups_Ozero__class_Ozero(_1187351)), _1187357)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187351), _1187357), c_Groups_Oone__class_Oone(_1187351))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187351), hAPP(hAPP(c_Power_Opower__class_Opower(_1187351), _1187357), _1187355)), hAPP(hAPP(c_Power_Opower__class_Opower(_1187351), _1187357), _1187353))))], (22531 ^ _777081) ^ [_1187690, _1187692, _1187694] : [class_Rings_Oring__1__no__zero__divisors(_1187690), -(_1187692 = c_Groups_Ozero__class_Ozero(_1187690)), hAPP(hAPP(c_Power_Opower__class_Opower(_1187690), _1187692), _1187694) = c_Groups_Ozero__class_Ozero(_1187690)], (22551 ^ _777081) ^ [_1187962, _1187964] : [22552 ^ _777081 : [(22553 ^ _777081) ^ [] : [_1187964 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22555 ^ _777081) ^ [] : [_1187962 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1187962), _1187964) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22541 ^ _777081) ^ [_1187864, _1187866] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1187864), _1187866) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1187866 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1187864 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22559 ^ _777081) ^ [_1188091] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1188091) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22561 ^ _777081) ^ [_1188117, _1188119, _1188121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188117)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1188117), _1188119)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1188117), _1188121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1188119), _1188121)))], (22581 ^ _777081) ^ [_1188419, _1188421] : [22582 ^ _777081 : [(22583 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188419))], (22585 ^ _777081) ^ [] : [_1188421 = 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), _1188419), _1188421))))], (22571 ^ _777081) ^ [_1188313, _1188315] : [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), _1188313), _1188315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188313))), -(_1188315 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22589 ^ _777081) ^ [_1188556, _1188558, _1188560] : [class_Groups_Omonoid__mult(_1188556), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188556), hAPP(hAPP(c_Power_Opower__class_Opower(_1188556), _1188558), _1188560)), _1188558) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188556), _1188558), hAPP(hAPP(c_Power_Opower__class_Opower(_1188556), _1188558), _1188560)))], (22595 ^ _777081) ^ [_1188697, _1188699, _1188701, _1188703] : [class_Groups_Ocomm__monoid__mult(_1188697), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1188697), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188697), _1188699), _1188701)), _1188703) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1188697), hAPP(hAPP(c_Power_Opower__class_Opower(_1188697), _1188699), _1188703)), hAPP(hAPP(c_Power_Opower__class_Opower(_1188697), _1188701), _1188703)))], (22601 ^ _777081) ^ [_1188856, _1188858] : [class_Groups_Omonoid__mult(_1188856), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1188856), c_Groups_Oone__class_Oone(_1188856)), _1188858) = c_Groups_Oone__class_Oone(_1188856))], (22607 ^ _777081) ^ [_1188955, _1188957, _1188959] : [class_Rings_Osemiring__1(_1188955), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188955), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1188957), _1188959)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1188955), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1188955), _1188957)), _1188959))], (22613 ^ _777081) ^ [_1189080, _1189082, _1189084, _1189086] : [class_Groups_Omonoid__mult(_1189080), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1189080), _1189082), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1189084), _1189086)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1189080), hAPP(hAPP(c_Power_Opower__class_Opower(_1189080), _1189082), _1189084)), _1189086))], (22619 ^ _777081) ^ [_1189219, _1189221, _1189223] : [class_Rings_Olinordered__idom(_1189219), -(hAPP(c_Groups_Oabs__class_Oabs(_1189219), hAPP(hAPP(c_Power_Opower__class_Opower(_1189219), _1189221), _1189223)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1189219), hAPP(c_Groups_Oabs__class_Oabs(_1189219), _1189221)), _1189223))], (22625 ^ _777081) ^ [_1189348, _1189350] : [class_Groups_Omonoid__mult(_1189348), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1189348), _1189350), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1189350)], (22631 ^ _777081) ^ [_1189439, _1189441, _1189443] : [class_Rings_Olinordered__semidom(_1189439), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189439), c_Groups_Ozero__class_Ozero(_1189439)), _1189441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189439), c_Groups_Ozero__class_Ozero(_1189439)), hAPP(hAPP(c_Power_Opower__class_Opower(_1189439), _1189441), _1189443))))], (22641 ^ _777081) ^ [_1189622, _1189624, _1189626, _1189628] : [class_Rings_Olinordered__semidom(_1189622), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189622), _1189624), _1189626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189622), c_Groups_Ozero__class_Ozero(_1189622)), _1189624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1189622), hAPP(hAPP(c_Power_Opower__class_Opower(_1189622), _1189624), _1189628)), hAPP(hAPP(c_Power_Opower__class_Opower(_1189622), _1189626), _1189628))))], (22655 ^ _777081) ^ [_1189891, _1189893, _1189895] : [class_Rings_Olinordered__semidom(_1189891), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189891), c_Groups_Ozero__class_Ozero(_1189891)), _1189893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1189891), c_Groups_Ozero__class_Ozero(_1189891)), hAPP(hAPP(c_Power_Opower__class_Opower(_1189891), _1189893), _1189895))))], (22665 ^ _777081) ^ [_1190074, _1190076, _1190078] : [class_Power_Opower(_1190074), class_Rings_Omult__zero(_1190074), class_Rings_Ono__zero__divisors(_1190074), class_Rings_Ozero__neq__one(_1190074), 22680 ^ _777081 : [(22681 ^ _777081) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1190074), _1190076), _1190078) = c_Groups_Ozero__class_Ozero(_1190074), 22684 ^ _777081 : [(22685 ^ _777081) ^ [] : [-(_1190076 = c_Groups_Ozero__class_Ozero(_1190074))], (22687 ^ _777081) ^ [] : [_1190078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (22689 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1190074), _1190076), _1190078) = c_Groups_Ozero__class_Ozero(_1190074)), _1190076 = c_Groups_Ozero__class_Ozero(_1190074), -(_1190078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22699 ^ _777081) ^ [_1190566, _1190568, _1190570] : [class_Rings_Olinordered__semidom(_1190566), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190566), c_Groups_Oone__class_Oone(_1190566)), _1190568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190566), c_Groups_Oone__class_Oone(_1190566)), hAPP(hAPP(c_Power_Opower__class_Opower(_1190566), _1190568), _1190570))))], (22709 ^ _777081) ^ [_1190749, _1190751] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1190749), c_Groups_Ozero__class_Ozero(_1190749)), hAPP(c_Nat_OSuc, _1190751)) = c_Groups_Ozero__class_Ozero(_1190749)), class_Power_Opower(_1190749), class_Rings_Osemiring__0(_1190749)], (22719 ^ _777081) ^ [_1190904, _1190906, _1190908, _1190910] : [class_Rings_Olinordered__semidom(_1190904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190904), c_Groups_Oone__class_Oone(_1190904)), _1190906)), 22726 ^ _777081 : [(22727 ^ _777081) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1190904), _1190906), _1190908) = hAPP(hAPP(c_Power_Opower__class_Opower(_1190904), _1190906), _1190910), -(_1190908 = _1190910)], (22733 ^ _777081) ^ [] : [_1190908 = _1190910, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1190904), _1190906), _1190908) = hAPP(hAPP(c_Power_Opower__class_Opower(_1190904), _1190906), _1190910))]]], (22739 ^ _777081) ^ [_1191243, _1191245, _1191247] : [class_Groups_Omonoid__mult(_1191243), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1191243), _1191245), hAPP(c_Nat_OSuc, _1191247)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191243), hAPP(hAPP(c_Power_Opower__class_Opower(_1191243), _1191245), _1191247)), _1191245))], (22745 ^ _777081) ^ [_1191374, _1191376, _1191378] : [class_Power_Opower(_1191374), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1191374), _1191376), hAPP(c_Nat_OSuc, _1191378)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191374), _1191376), hAPP(hAPP(c_Power_Opower__class_Opower(_1191374), _1191376), _1191378)))], (22751 ^ _777081) ^ [_1191505, _1191507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1191505)), -(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), _1191505), _1191507))))], (22757 ^ _777081) ^ [_1191602, _1191604] : [class_Power_Opower(_1191602), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1191602), _1191604), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1191602))], (22763 ^ _777081) ^ [_1191697, _1191699, _1191701, _1191703] : [class_Groups_Omonoid__mult(_1191697), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1191697), _1191699), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1191701), _1191703)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191697), hAPP(hAPP(c_Power_Opower__class_Opower(_1191697), _1191699), _1191701)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191697), _1191699), _1191703)))], (22769 ^ _777081) ^ [_1191852, _1191854, _1191856] : [class_Rings_Olinordered__idom(_1191852), -(hAPP(c_Groups_Oabs__class_Oabs(_1191852), hAPP(hAPP(c_Power_Opower__class_Opower(_1191852), hAPP(c_Groups_Ouminus__class_Ouminus(_1191852), _1191854)), _1191856)) = hAPP(c_Groups_Oabs__class_Oabs(_1191852), hAPP(hAPP(c_Power_Opower__class_Opower(_1191852), _1191854), _1191856)))], (22775 ^ _777081) ^ [_1191991, _1191993, _1191995, _1191997] : [class_Rings_Olinordered__semidom(_1191991), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191991), hAPP(hAPP(c_Power_Opower__class_Opower(_1191991), _1191993), _1191995)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191991), _1191997), _1191995))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191991), c_Groups_Ozero__class_Ozero(_1191991)), _1191997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191991), _1191993), _1191997)))], (22789 ^ _777081) ^ [_1192260, _1192262, _1192264, _1192266] : [class_Rings_Olinordered__semidom(_1192260), hAPP(hAPP(c_Power_Opower__class_Opower(_1192260), _1192262), hAPP(c_Nat_OSuc, _1192264)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1192260), _1192266), hAPP(c_Nat_OSuc, _1192264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192260), c_Groups_Ozero__class_Ozero(_1192260)), _1192262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192260), c_Groups_Ozero__class_Ozero(_1192260)), _1192266)), -(_1192262 = _1192266)], (22807 ^ _777081) ^ [_1192587, _1192589, _1192591, _1192593] : [class_Rings_Olinordered__semidom(_1192587), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192587), hAPP(hAPP(c_Power_Opower__class_Opower(_1192587), _1192589), hAPP(c_Nat_OSuc, _1192591))), hAPP(hAPP(c_Power_Opower__class_Opower(_1192587), _1192593), hAPP(c_Nat_OSuc, _1192591)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192587), c_Groups_Ozero__class_Ozero(_1192587)), _1192593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1192587), _1192589), _1192593)))], (22821 ^ _777081) ^ [_1192868, _1192870, _1192872] : [class_Rings_Olinordered__semidom(_1192868), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192868), c_Groups_Oone__class_Oone(_1192868)), _1192870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192868), hAPP(hAPP(c_Power_Opower__class_Opower(_1192868), _1192870), _1192872)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192868), _1192870), hAPP(hAPP(c_Power_Opower__class_Opower(_1192868), _1192870), _1192872)))))], (22831 ^ _777081) ^ [_1193079, _1193081, _1193083] : [class_Rings_Olinordered__semidom(_1193079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193079), c_Groups_Oone__class_Oone(_1193079)), _1193081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193079), c_Groups_Oone__class_Oone(_1193079)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193079), _1193081), hAPP(hAPP(c_Power_Opower__class_Opower(_1193079), _1193081), _1193083)))))], (22841 ^ _777081) ^ [_1193278, _1193280] : [class_Power_Opower(_1193278), class_Rings_Osemiring__0(_1193278), 22848 ^ _777081 : [(22849 ^ _777081) ^ [] : [_1193280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1193278), c_Groups_Ozero__class_Ozero(_1193278)), _1193280) = c_Groups_Oone__class_Oone(_1193278))], (22855 ^ _777081) ^ [] : [-(_1193280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1193278), c_Groups_Ozero__class_Ozero(_1193278)), _1193280) = c_Groups_Ozero__class_Ozero(_1193278))]]], (22861 ^ _777081) ^ [_1193552, _1193554, _1193556] : [class_Rings_Olinordered__semidom(_1193552), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193552), c_Groups_Oone__class_Oone(_1193552)), _1193554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193552), c_Groups_Oone__class_Oone(_1193552)), hAPP(hAPP(c_Power_Opower__class_Opower(_1193552), _1193554), hAPP(c_Nat_OSuc, _1193556)))))], (22871 ^ _777081) ^ [_1193741, _1193743, _1193745, _1193747] : [class_Rings_Olinordered__semidom(_1193741), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1193743), _1193745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193741), c_Groups_Oone__class_Oone(_1193741)), _1193747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1193741), hAPP(hAPP(c_Power_Opower__class_Opower(_1193741), _1193747), _1193743)), hAPP(hAPP(c_Power_Opower__class_Opower(_1193741), _1193747), _1193745))))], (22885 ^ _777081) ^ [_1194006, _1194008, _1194010, _1194012] : [class_Rings_Olinordered__semidom(_1194006), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194006), c_Groups_Oone__class_Oone(_1194006)), _1194008)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194006), hAPP(hAPP(c_Power_Opower__class_Opower(_1194006), _1194008), _1194010)), hAPP(hAPP(c_Power_Opower__class_Opower(_1194006), _1194008), _1194012))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1194010), _1194012)))], (22899 ^ _777081) ^ [_1194271, _1194273, _1194275, _1194277] : [class_Rings_Olinordered__semidom(_1194271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194271), c_Groups_Oone__class_Oone(_1194271)), _1194273)), 22906 ^ _777081 : [(22907 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194271), hAPP(hAPP(c_Power_Opower__class_Opower(_1194271), _1194273), _1194275)), hAPP(hAPP(c_Power_Opower__class_Opower(_1194271), _1194273), _1194277))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1194275), _1194277)))], (22913 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1194275), _1194277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194271), hAPP(hAPP(c_Power_Opower__class_Opower(_1194271), _1194273), _1194275)), hAPP(hAPP(c_Power_Opower__class_Opower(_1194271), _1194273), _1194277))))]]], (22919 ^ _777081) ^ [_1194646, _1194648, _1194650] : [class_Rings_Olinordered__idom(_1194646), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194646), c_Groups_Ozero__class_Ozero(_1194646)), hAPP(hAPP(c_Power_Opower__class_Opower(_1194646), hAPP(c_Groups_Oabs__class_Oabs(_1194646), _1194648)), _1194650))))], (22925 ^ _777081) ^ [_1194767, _1194769, _1194771, _1194773] : [class_Rings_Olinordered__semidom(_1194767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1194769), _1194771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194767), c_Groups_Oone__class_Oone(_1194767)), _1194773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194767), hAPP(hAPP(c_Power_Opower__class_Opower(_1194767), _1194773), _1194769)), hAPP(hAPP(c_Power_Opower__class_Opower(_1194767), _1194773), _1194771))))], (22939 ^ _777081) ^ [_1195032, _1195034, _1195036] : [class_Rings_Oring__1(_1195032), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1195032), hAPP(c_Groups_Ouminus__class_Ouminus(_1195032), _1195034)), _1195036) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195032), hAPP(hAPP(c_Power_Opower__class_Opower(_1195032), hAPP(c_Groups_Ouminus__class_Ouminus(_1195032), c_Groups_Oone__class_Oone(_1195032))), _1195036)), hAPP(hAPP(c_Power_Opower__class_Opower(_1195032), _1195034), _1195036)))], (22945 ^ _777081) ^ [_1195197, _1195199, _1195201] : [class_Rings_Olinordered__semidom(_1195197), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195197), c_Groups_Ozero__class_Ozero(_1195197)), _1195199)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195197), _1195199), c_Groups_Oone__class_Oone(_1195197))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195197), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1195197), _1195199), hAPP(hAPP(c_Power_Opower__class_Opower(_1195197), _1195199), _1195201))), hAPP(hAPP(c_Power_Opower__class_Opower(_1195197), _1195199), _1195201))))], (22959 ^ _777081) ^ [_1195480, _1195482, _1195484, _1195486] : [class_Rings_Olinordered__semidom(_1195480), hAPP(hAPP(c_Power_Opower__class_Opower(_1195480), _1195482), _1195484) = hAPP(hAPP(c_Power_Opower__class_Opower(_1195480), _1195486), _1195484), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195480), c_Groups_Ozero__class_Ozero(_1195480)), _1195482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195480), c_Groups_Ozero__class_Ozero(_1195480)), _1195486)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1195484)), -(_1195482 = _1195486)], (22981 ^ _777081) ^ [_1195855, _1195857, _1195859] : [class_Rings_Olinordered__semidom(_1195855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195855), c_Groups_Ozero__class_Ozero(_1195855)), _1195857)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195855), _1195857), c_Groups_Oone__class_Oone(_1195855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195855), hAPP(hAPP(c_Power_Opower__class_Opower(_1195855), _1195857), hAPP(c_Nat_OSuc, _1195859))), c_Groups_Oone__class_Oone(_1195855))))], (22995 ^ _777081) ^ [_1196116, _1196118, _1196120, _1196122] : [class_Rings_Olinordered__semidom(_1196116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1196118), _1196120)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196116), c_Groups_Ozero__class_Ozero(_1196116)), _1196122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196116), _1196122), c_Groups_Oone__class_Oone(_1196116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196116), hAPP(hAPP(c_Power_Opower__class_Opower(_1196116), _1196122), _1196120)), hAPP(hAPP(c_Power_Opower__class_Opower(_1196116), _1196122), _1196118))))], (23013 ^ _777081) ^ [_1196455, _1196457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1196455), 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)))), _1196457)), 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)))), _1196455)) = 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), _1196457), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1196455))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23019 ^ _777081) ^ [_1196615, _1196617] : [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), _1196615))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1196617)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1196615))) = 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), _1196617), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1196615)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23025 ^ _777081) ^ [_1196762, _1196764] : [-(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), _1196762)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1196764)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1196762))) = 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), _1196764)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1196762)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23031 ^ _777081) ^ [_1196844, _1196846] : [class_Rings_Oring__1(_1196844), 23034 ^ _777081 : [(23035 ^ _777081) ^ [] : [_1196846 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1196844), _1196846) = c_Groups_Ozero__class_Ozero(_1196844))], (23041 ^ _777081) ^ [] : [-(_1196846 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23044 ^ _777081 : [(23045 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196846), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1196844), _1196846) = hAPP(c_Groups_Ouminus__class_Ouminus(_1196844), hAPP(c_Int_Oring__1__class_Oof__int(_1196844), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1196846))))], (23051 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1196846), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1196844), _1196846) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1196844), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1196844, _1196844)), tc_fun(tc_Int_Oint, _1196844)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1196844, _1196844), _1196844), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1196844, _1196844)), tc_fun(tc_Int_Oint, _1196844)), tc_Int_Oint), c_COMBB(tc_fun(_1196844, _1196844), _1196844, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1196844, tc_fun(tc_fun(_1196844, _1196844), _1196844), tc_Int_Oint), c_HOL_OLet(_1196844, _1196844)), c_Int_Oring__1__class_Oof__int(_1196844)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1196844, _1196844), tc_fun(_1196844, _1196844)), hAPP(hAPP(c_COMBB(tc_fun(_1196844, tc_fun(_1196844, _1196844)), tc_fun(tc_fun(_1196844, _1196844), tc_fun(_1196844, _1196844)), tc_Int_Oint), c_COMBS(_1196844, _1196844, _1196844)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1196844, _1196844), tc_fun(_1196844, tc_fun(_1196844, _1196844))), hAPP(hAPP(c_COMBB(tc_fun(_1196844, tc_fun(_1196844, _1196844)), tc_fun(tc_fun(_1196844, _1196844), tc_fun(_1196844, tc_fun(_1196844, _1196844))), tc_Int_Oint), c_COMBB(_1196844, tc_fun(_1196844, _1196844), _1196844)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1196844, tc_fun(_1196844, _1196844)), tc_Int_Oint), c_If(_1196844)), 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(_1196844, _1196844, _1196844), c_Groups_Oplus__class_Oplus(_1196844)), c_COMBI(_1196844))))), hAPP(hAPP(c_COMBC(_1196844, _1196844, _1196844), hAPP(hAPP(c_COMBB(_1196844, tc_fun(_1196844, _1196844), _1196844), c_Groups_Oplus__class_Oplus(_1196844)), hAPP(hAPP(c_COMBS(_1196844, _1196844, _1196844), c_Groups_Oplus__class_Oplus(_1196844)), c_COMBI(_1196844)))), c_Groups_Oone__class_Oone(_1196844))))), c_Divides_Odivmod__int(_1196846, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (23057 ^ _777081) ^ [_1197757, _1197759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197757)), -(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)))), _1197759)), 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)))), _1197757)) = 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, _1197759, _1197757))))], (23063 ^ _777081) ^ [_1197884, _1197886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1197884)), -(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)))), _1197886))), 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)))), _1197884)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1197886), _1197884))], (23069 ^ _777081) ^ [_1198007, _1198009] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198007)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198009)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1198007), _1198009))], (23071 ^ _777081) ^ [_1198050, _1198052] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1198050), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198052)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198050)), _1198052))], (23073 ^ _777081) ^ [_1198093, _1198095, _1198097] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1198093), _1198095), _1198097) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1198093), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198095, _1198097)), _1198097))], (23075 ^ _777081) ^ [_1198144, _1198146, _1198148] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1198144), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198146, _1198148)), _1198148) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1198144), _1198146), _1198148))], (23077 ^ _777081) ^ [_1198195, _1198197, _1198199] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1198195), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198197, _1198199)), _1198199) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1198195), _1198197), _1198199))], (23079 ^ _777081) ^ [_1198246, _1198248, _1198250] : [-(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, _1198246, _1198248)), _1198250), _1198248) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1198246), _1198250), _1198248))], (23081 ^ _777081) ^ [_1198297, _1198299] : [-(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, _1198297, _1198299)), _1198299) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198297), _1198299))], (23083 ^ _777081) ^ [_1198340, _1198342] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198340), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198342)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198340, _1198342)))], (23085 ^ _777081) ^ [_1198382, _1198384] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1198382, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1198384)) = 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), _1198382), _1198384)))], (23087 ^ _777081) ^ [_1198424, _1198426, _1198428] : [class_Divides_Oring__div(_1198424), -(c_Divides_Odiv__class_Omod(_1198424, hAPP(c_Groups_Ouminus__class_Ouminus(_1198424), _1198426), _1198428) = c_Divides_Odiv__class_Omod(_1198424, hAPP(c_Groups_Ouminus__class_Ouminus(_1198424), c_Divides_Odiv__class_Omod(_1198424, _1198426, _1198428)), _1198428))], (23093 ^ _777081) ^ [_1198545, _1198547, _1198549, _1198551] : [class_Divides_Oring__div(_1198545), c_Divides_Odiv__class_Omod(_1198545, _1198547, _1198549) = c_Divides_Odiv__class_Omod(_1198545, _1198551, _1198549), -(c_Divides_Odiv__class_Omod(_1198545, hAPP(c_Groups_Ouminus__class_Ouminus(_1198545), _1198547), _1198549) = c_Divides_Odiv__class_Omod(_1198545, hAPP(c_Groups_Ouminus__class_Ouminus(_1198545), _1198551), _1198549))], (23103 ^ _777081) ^ [_1198732, _1198734] : [class_Divides_Osemiring__div(_1198732), -(c_Divides_Odiv__class_Omod(_1198732, c_Groups_Ozero__class_Ozero(_1198732), _1198734) = c_Groups_Ozero__class_Ozero(_1198732))], (23109 ^ _777081) ^ [_1198823, _1198825] : [class_Divides_Osemiring__div(_1198823), -(c_Divides_Odiv__class_Omod(_1198823, _1198825, c_Groups_Ozero__class_Ozero(_1198823)) = _1198825)], (23115 ^ _777081) ^ [_1198910, _1198912] : [class_Divides_Osemiring__div(_1198910), -(c_Divides_Odiv__class_Omod(_1198910, _1198912, _1198912) = c_Groups_Ozero__class_Ozero(_1198910))], (23121 ^ _777081) ^ [_1198997, _1198999, _1199001] : [class_Divides_Osemiring__div(_1198997), -(c_Divides_Odiv__class_Omod(_1198997, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198997), _1198999), _1199001), _1199001) = c_Divides_Odiv__class_Omod(_1198997, _1198999, _1199001))], (23127 ^ _777081) ^ [_1199106, _1199108, _1199110] : [class_Divides_Osemiring__div(_1199106), -(c_Divides_Odiv__class_Omod(_1199106, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199106), _1199108), _1199110), _1199108) = c_Divides_Odiv__class_Omod(_1199106, _1199110, _1199108))], (23133 ^ _777081) ^ [_1199215, _1199217, _1199219, _1199221] : [class_Divides_Osemiring__div(_1199215), -(c_Divides_Odiv__class_Omod(_1199215, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199215), _1199217), _1199219), _1199221) = c_Divides_Odiv__class_Omod(_1199215, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199215), _1199217), c_Divides_Odiv__class_Omod(_1199215, _1199219, _1199221)), _1199221))], (23139 ^ _777081) ^ [_1199350, _1199352, _1199354, _1199356] : [class_Divides_Osemiring__div(_1199350), -(c_Divides_Odiv__class_Omod(_1199350, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199350), _1199352), _1199354), _1199356) = c_Divides_Odiv__class_Omod(_1199350, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199350), c_Divides_Odiv__class_Omod(_1199350, _1199352, _1199356)), _1199354), _1199356))], (23145 ^ _777081) ^ [_1199485, _1199487, _1199489, _1199491] : [class_Divides_Osemiring__div(_1199485), -(c_Divides_Odiv__class_Omod(_1199485, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199485), _1199487), _1199489), _1199491) = c_Divides_Odiv__class_Omod(_1199485, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199485), c_Divides_Odiv__class_Omod(_1199485, _1199487, _1199491)), c_Divides_Odiv__class_Omod(_1199485, _1199489, _1199491)), _1199491))], (23151 ^ _777081) ^ [_1199628, _1199630, _1199632, _1199634] : [class_Divides_Osemiring__div(_1199628), -(c_Divides_Odiv__class_Omod(_1199628, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199628), _1199630), c_Divides_Odiv__class_Omod(_1199628, _1199632, _1199634)), _1199634) = c_Divides_Odiv__class_Omod(_1199628, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199628), _1199630), _1199632), _1199634))], (23157 ^ _777081) ^ [_1199763, _1199765, _1199767, _1199769] : [class_Divides_Osemiring__div(_1199763), -(c_Divides_Odiv__class_Omod(_1199763, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199763), c_Divides_Odiv__class_Omod(_1199763, _1199765, _1199767)), _1199769), _1199767) = c_Divides_Odiv__class_Omod(_1199763, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199763), _1199765), _1199769), _1199767))], (23163 ^ _777081) ^ [_1199898, _1199900, _1199902, _1199904, _1199906, _1199908] : [class_Divides_Osemiring__div(_1199898), c_Divides_Odiv__class_Omod(_1199898, _1199900, _1199902) = c_Divides_Odiv__class_Omod(_1199898, _1199904, _1199902), c_Divides_Odiv__class_Omod(_1199898, _1199906, _1199902) = c_Divides_Odiv__class_Omod(_1199898, _1199908, _1199902), -(c_Divides_Odiv__class_Omod(_1199898, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199898), _1199900), _1199906), _1199902) = c_Divides_Odiv__class_Omod(_1199898, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1199898), _1199904), _1199908), _1199902))], (23177 ^ _777081) ^ [_1200181, _1200183, _1200185, _1200187] : [class_Divides_Osemiring__div(_1200181), -(c_Divides_Odiv__class_Omod(_1200181, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200181), _1200183), _1200185), _1200187) = c_Divides_Odiv__class_Omod(_1200181, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200181), _1200183), c_Divides_Odiv__class_Omod(_1200181, _1200185, _1200187)), _1200187))], (23183 ^ _777081) ^ [_1200316, _1200318, _1200320, _1200322] : [class_Divides_Osemiring__div(_1200316), -(c_Divides_Odiv__class_Omod(_1200316, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200316), _1200318), _1200320), _1200322) = c_Divides_Odiv__class_Omod(_1200316, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200316), c_Divides_Odiv__class_Omod(_1200316, _1200318, _1200322)), _1200320), _1200322))], (23189 ^ _777081) ^ [_1200451, _1200453, _1200455, _1200457] : [class_Divides_Osemiring__div(_1200451), -(c_Divides_Odiv__class_Omod(_1200451, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200451), _1200453), _1200455), _1200457) = c_Divides_Odiv__class_Omod(_1200451, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200451), c_Divides_Odiv__class_Omod(_1200451, _1200453, _1200457)), c_Divides_Odiv__class_Omod(_1200451, _1200455, _1200457)), _1200457))], (23195 ^ _777081) ^ [_1200594, _1200596, _1200598, _1200600] : [class_Divides_Osemiring__div(_1200594), -(c_Divides_Odiv__class_Omod(_1200594, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200594), _1200596), _1200598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200594), _1200596), _1200600)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200594), _1200596), c_Divides_Odiv__class_Omod(_1200594, _1200598, _1200600)))], (23201 ^ _777081) ^ [_1200737, _1200739, _1200741, _1200743] : [class_Divides_Osemiring__div(_1200737), -(c_Divides_Odiv__class_Omod(_1200737, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200737), _1200739), _1200741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200737), _1200743), _1200741)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200737), c_Divides_Odiv__class_Omod(_1200737, _1200739, _1200743)), _1200741))], (23207 ^ _777081) ^ [_1200880, _1200882, _1200884, _1200886] : [class_Divides_Osemiring__div(_1200880), -(c_Divides_Odiv__class_Omod(_1200880, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200880), c_Divides_Odiv__class_Omod(_1200880, _1200882, _1200884)), _1200886), _1200884) = c_Divides_Odiv__class_Omod(_1200880, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200880), _1200882), _1200886), _1200884))], (23213 ^ _777081) ^ [_1201015, _1201017, _1201019, _1201021, _1201023, _1201025] : [class_Divides_Osemiring__div(_1201015), c_Divides_Odiv__class_Omod(_1201015, _1201017, _1201019) = c_Divides_Odiv__class_Omod(_1201015, _1201021, _1201019), c_Divides_Odiv__class_Omod(_1201015, _1201023, _1201019) = c_Divides_Odiv__class_Omod(_1201015, _1201025, _1201019), -(c_Divides_Odiv__class_Omod(_1201015, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201015), _1201017), _1201023), _1201019) = c_Divides_Odiv__class_Omod(_1201015, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201015), _1201021), _1201025), _1201019))], (23227 ^ _777081) ^ [_1201298, _1201300, _1201302] : [class_Divides_Osemiring__div(_1201298), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201298), c_Divides_Odiv__class_Omod(_1201298, _1201300, _1201302)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201298), hAPP(c_Divides_Odiv__class_Odiv(_1201298, _1201300), _1201302)), _1201302)) = _1201300)], (23233 ^ _777081) ^ [_1201427, _1201429, _1201431] : [class_Divides_Osemiring__div(_1201427), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201427), _1201429), hAPP(c_Divides_Odiv__class_Odiv(_1201427, _1201431), _1201429))), c_Divides_Odiv__class_Omod(_1201427, _1201431, _1201429)) = _1201431)], (23239 ^ _777081) ^ [_1201556, _1201558, _1201560] : [class_Divides_Osemiring__div(_1201556), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201556), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201556), hAPP(c_Divides_Odiv__class_Odiv(_1201556, _1201558), _1201560)), _1201560)), c_Divides_Odiv__class_Omod(_1201556, _1201558, _1201560)) = _1201558)], (23245 ^ _777081) ^ [_1201685, _1201687, _1201689, _1201691] : [class_Divides_Osemiring__div(_1201685), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201685), _1201687), hAPP(c_Divides_Odiv__class_Odiv(_1201685, _1201689), _1201687))), c_Divides_Odiv__class_Omod(_1201685, _1201689, _1201687))), _1201691) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201685), _1201689), _1201691))], (23251 ^ _777081) ^ [_1201848, _1201850, _1201852, _1201854] : [class_Divides_Osemiring__div(_1201848), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201848), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1201848), hAPP(c_Divides_Odiv__class_Odiv(_1201848, _1201850), _1201852)), _1201852)), c_Divides_Odiv__class_Omod(_1201848, _1201850, _1201852))), _1201854) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201848), _1201850), _1201854))], (23257 ^ _777081) ^ [_1202011, _1202013] : [-(_1202011 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202013), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1202011), _1202013))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202011, _1202013)))], (23259 ^ _777081) ^ [_1202058, _1202060, _1202062] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202058), _1202060)), _1202062) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202058), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1202060), _1202062))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202058), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202060, _1202062))), _1202062)))], (23261 ^ _777081) ^ [_1202131, _1202133, _1202135] : [-(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), _1202131), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1202133), _1202131))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202133, _1202131))), _1202135) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1202133), _1202135))], (23263 ^ _777081) ^ [_1202192, _1202194, _1202196] : [-(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(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1202192), _1202194)), _1202194)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202192, _1202194))), _1202196) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1202192), _1202196))], (23265 ^ _777081) ^ [_1202253, _1202255, _1202257] : [class_Divides_Osemiring__div(_1202253), -(c_Divides_Odiv__class_Omod(_1202253, c_Divides_Odiv__class_Omod(_1202253, _1202255, _1202257), _1202257) = c_Divides_Odiv__class_Omod(_1202253, _1202255, _1202257))], (23271 ^ _777081) ^ [_1202354, _1202356] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202354, _1202356)), _1202356) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23273 ^ _777081) ^ [_1202389, _1202391, _1202393] : [class_Divides_Osemiring__div(_1202389), -(hAPP(c_Divides_Odiv__class_Odiv(_1202389, c_Divides_Odiv__class_Omod(_1202389, _1202391, _1202393)), _1202393) = c_Groups_Ozero__class_Ozero(_1202389))], (23279 ^ _777081) ^ [_1202488] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1202488), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23281 ^ _777081) ^ [_1202514] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202514, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1202514)], (23283 ^ _777081) ^ [_1202543, _1202545, _1202547] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1202543), _1202545)), _1202547) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1202543), _1202547)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1202545), _1202547))), 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, _1202543, _1202547)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202545, _1202547))), _1202547)))], (23285 ^ _777081) ^ [_1202626, _1202628] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1202626), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1202628), _1202626)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1202628), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202628, _1202626)))], (23287 ^ _777081) ^ [_1202673, _1202675] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1202673, _1202675) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1202673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1202673), _1202675)), _1202675)))], (23289 ^ _777081) ^ [_1202720, _1202722, _1202724, _1202726, _1202728, _1202730] : [class_Divides_Oring__div(_1202720), c_Divides_Odiv__class_Omod(_1202720, _1202722, _1202724) = c_Divides_Odiv__class_Omod(_1202720, _1202726, _1202724), c_Divides_Odiv__class_Omod(_1202720, _1202728, _1202724) = c_Divides_Odiv__class_Omod(_1202720, _1202730, _1202724), -(c_Divides_Odiv__class_Omod(_1202720, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1202720), _1202722), _1202728), _1202724) = c_Divides_Odiv__class_Omod(_1202720, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1202720), _1202726), _1202730), _1202724))], (23303 ^ _777081) ^ [_1203003, _1203005, _1203007, _1203009] : [class_Divides_Oring__div(_1203003), -(c_Divides_Odiv__class_Omod(_1203003, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1203003), _1203005), _1203007), _1203009) = c_Divides_Odiv__class_Omod(_1203003, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1203003), c_Divides_Odiv__class_Omod(_1203003, _1203005, _1203009)), c_Divides_Odiv__class_Omod(_1203003, _1203007, _1203009)), _1203009))], (23309 ^ _777081) ^ [_1203146, _1203148, _1203150, _1203152] : [class_Divides_Oring__div(_1203146), -(c_Divides_Odiv__class_Omod(_1203146, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1203146), _1203148), _1203150), _1203152) = c_Divides_Odiv__class_Omod(_1203146, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1203146), c_Divides_Odiv__class_Omod(_1203146, _1203148, _1203152)), _1203150), _1203152))], (23315 ^ _777081) ^ [_1203281, _1203283, _1203285, _1203287] : [class_Divides_Oring__div(_1203281), -(c_Divides_Odiv__class_Omod(_1203281, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1203281), _1203283), _1203285), _1203287) = c_Divides_Odiv__class_Omod(_1203281, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1203281), _1203283), c_Divides_Odiv__class_Omod(_1203281, _1203285, _1203287)), _1203287))], (23321 ^ _777081) ^ [_1203416] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1203416, _1203416) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23323 ^ _777081) ^ [_1203443] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1203443) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23325 ^ _777081) ^ [_1203470] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1203470) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23327 ^ _777081) ^ [_1203496, _1203498] : [class_Divides_Osemiring__div(_1203496), -(hAPP(c_Divides_Odiv__class_Odiv(_1203496, _1203498), c_Groups_Ozero__class_Ozero(_1203496)) = c_Groups_Ozero__class_Ozero(_1203496))], (23333 ^ _777081) ^ [_1203591, _1203593] : [class_Divides_Osemiring__div(_1203591), -(hAPP(c_Divides_Odiv__class_Odiv(_1203591, c_Groups_Ozero__class_Ozero(_1203591)), _1203593) = c_Groups_Ozero__class_Ozero(_1203591))], (23339 ^ _777081) ^ [_1203686, _1203688] : [class_Divides_Osemiring__div(_1203686), -(hAPP(c_Divides_Odiv__class_Odiv(_1203686, _1203688), c_Groups_Oone__class_Oone(_1203686)) = _1203688)], (23345 ^ _777081) ^ [_1203777, _1203779] : [c_Nat__Transfer_Ois__nat(_1203777), c_Nat__Transfer_Ois__nat(_1203779), -(c_Nat__Transfer_Ois__nat(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1203777), _1203779)))], (23355 ^ _777081) ^ [_1203912, _1203914] : [c_Nat__Transfer_Ois__nat(_1203912), c_Nat__Transfer_Ois__nat(_1203914), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1203912, _1203914)))], (23365 ^ _777081) ^ [_1204043, _1204045, _1204047] : [-(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, _1204043, _1204045)), _1204047), _1204045) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1204043), _1204047), _1204045))], (23367 ^ _777081) ^ [_1204094, _1204096, _1204098] : [class_Divides_Osemiring__div(_1204094), -(c_Divides_Odiv__class_Omod(_1204094, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204094), _1204096), _1204098), _1204096) = c_Groups_Ozero__class_Ozero(_1204094))], (23373 ^ _777081) ^ [_1204199, _1204201, _1204203] : [class_Divides_Osemiring__div(_1204199), -(c_Divides_Odiv__class_Omod(_1204199, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204199), _1204201), _1204203), _1204203) = c_Groups_Ozero__class_Ozero(_1204199))], (23379 ^ _777081) ^ [_1204304, _1204306, _1204308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1204304)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1204306, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1204308), _1204304)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1204308), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1204306), _1204308), _1204304))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1204306, _1204308)))], (23385 ^ _777081) ^ [_1204459, _1204461, _1204463, _1204465] : [class_Divides_Osemiring__div(_1204459), -(c_Divides_Odiv__class_Omod(_1204459, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204459), _1204461), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204459), _1204463), _1204465)), _1204465) = c_Divides_Odiv__class_Omod(_1204459, _1204461, _1204465))], (23391 ^ _777081) ^ [_1204586, _1204588, _1204590, _1204592] : [class_Divides_Osemiring__div(_1204586), -(c_Divides_Odiv__class_Omod(_1204586, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204586), _1204588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1204586), _1204590), _1204592)), _1204590) = c_Divides_Odiv__class_Omod(_1204586, _1204588, _1204590))], (23397 ^ _777081) ^ [_1204713, _1204715] : [class_Divides_Osemiring__div(_1204713), -(c_Divides_Odiv__class_Omod(_1204713, _1204715, c_Groups_Oone__class_Oone(_1204713)) = c_Groups_Ozero__class_Ozero(_1204713))], (23403 ^ _777081) ^ [_1204803, _1204805] : [-(_1204803 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23406 ^ _777081 : [(23407 ^ _777081) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1204805, _1204803) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1204805), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204803)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1204805), _1204803)))], (23413 ^ _777081) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1204805, _1204803) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1204805), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1204803)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1204805), _1204803))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (23419 ^ _777081) ^ [_1205076, _1205078] : [-(_1205076 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23422 ^ _777081 : [(23423 ^ _777081) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1205078, _1205076) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205078)), _1205076) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1205078), _1205076)))], (23429 ^ _777081) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1205078, _1205076) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1205078)), _1205076) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1205078), _1205076))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (23435 ^ _777081) ^ [_1205350, _1205352] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205350)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1205350), _1205352))))], (23445 ^ _777081) ^ [_1205503, _1205505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205503), 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)), _1205505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1205503), _1205505)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23455 ^ _777081) ^ [_1205668, _1205670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205668), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23458 ^ _777081 : [(23459 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1205670), _1205668)), 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)), _1205670)))], (23465 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1205670), _1205668)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23471 ^ _777081) ^ [_1205924, _1205926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1205924)), 23474 ^ _777081 : [(23475 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1205926), _1205924)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205926), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23481 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1205926), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1205926), _1205924)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (23487 ^ _777081) ^ [_1206179] : [-(_1206179 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1206179), _1206179) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (23493 ^ _777081) ^ [_1206219, _1206221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206219)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206219, _1206221)), _1206219)))], (23499 ^ _777081) ^ [_1206318, _1206320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206320)), -(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, _1206318, _1206320))))], (23509 ^ _777081) ^ [_1206467, _1206469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206467), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1206467), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206469, _1206467))))], (23515 ^ _777081) ^ [_1206572, _1206574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206574, _1206572)), _1206572)))], (23521 ^ _777081) ^ [_1206671, _1206673] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1206671))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1206673))) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1206671)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1206673)))], (23523 ^ _777081) ^ [_1206739, _1206741] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206739, _1206741) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1206739 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1206741), 23526 ^ [_1206739, _1206741]))], (23530 ^ _777081) ^ [_1206844, _1206846] : [23531 ^ _777081 : [(23532 ^ _777081) ^ [_1206893] : [_1206844 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1206846), _1206893)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206844, _1206846) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23536 ^ _777081) ^ [_1206955, _1206957] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1206955), _1206957) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1206955, _1206957) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23542 ^ _777081) ^ [_1207045, _1207047] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1207045, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1207047)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1207045, _1207047) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23548 ^ _777081) ^ [_1207136, _1207138, _1207140, _1207142] : [class_Divides_Osemiring__div(_1207136), -(_1207138 = c_Groups_Ozero__class_Ozero(_1207136)), -(hAPP(c_Divides_Odiv__class_Odiv(_1207136, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207136), _1207138), _1207140)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207136), _1207138), _1207142)) = hAPP(c_Divides_Odiv__class_Odiv(_1207136, _1207140), _1207142))], (23558 ^ _777081) ^ [_1207290, _1207292, _1207294, _1207296] : [class_Divides_Osemiring__div(_1207290), -(_1207292 = c_Groups_Ozero__class_Ozero(_1207290)), -(hAPP(c_Divides_Odiv__class_Odiv(_1207290, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207290), _1207294), _1207292)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207290), _1207296), _1207292)) = hAPP(c_Divides_Odiv__class_Odiv(_1207290, _1207294), _1207296))], (23568 ^ _777081) ^ [_1207444, _1207446, _1207448] : [class_Divides_Osemiring__div(_1207444), -(_1207446 = c_Groups_Ozero__class_Ozero(_1207444)), -(hAPP(c_Divides_Odiv__class_Odiv(_1207444, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207444), _1207446), _1207448)), _1207446) = _1207448)], (23578 ^ _777081) ^ [_1207568, _1207570, _1207572] : [class_Divides_Osemiring__div(_1207568), -(_1207570 = c_Groups_Ozero__class_Ozero(_1207568)), -(hAPP(c_Divides_Odiv__class_Odiv(_1207568, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207568), _1207572), _1207570)), _1207570) = _1207572)], (23588 ^ _777081) ^ [_1207692, _1207694, _1207696, _1207698] : [class_Divides_Osemiring__div(_1207692), 23591 ^ _777081 : [(23592 ^ _777081) ^ [] : [_1207694 = c_Groups_Ozero__class_Ozero(_1207692), -(hAPP(c_Divides_Odiv__class_Odiv(_1207692, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207692), _1207694), _1207696)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207692), _1207694), _1207698)) = c_Groups_Ozero__class_Ozero(_1207692))], (23598 ^ _777081) ^ [] : [-(_1207694 = c_Groups_Ozero__class_Ozero(_1207692)), -(hAPP(c_Divides_Odiv__class_Odiv(_1207692, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207692), _1207694), _1207696)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207692), _1207694), _1207698)) = hAPP(c_Divides_Odiv__class_Odiv(_1207692, _1207696), _1207698))]]], (23604 ^ _777081) ^ [_1207986, _1207988] : [class_Divides_Osemiring__div(_1207986), -(_1207988 = c_Groups_Ozero__class_Ozero(_1207986)), -(hAPP(c_Divides_Odiv__class_Odiv(_1207986, _1207988), _1207988) = c_Groups_Oone__class_Oone(_1207986))], (23614 ^ _777081) ^ [_1208096, _1208098, _1208100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1208096), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23617 ^ _777081 : [(23636 ^ _777081) ^ [] : [23639 ^ _777081 : [(23640 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1208096), 23638 ^ [_1208096, _1208098, _1208100])))], (23642 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23638 ^ [_1208096, _1208098, _1208100]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23644 ^ _777081) ^ [] : [-(_1208100 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1208096), 23637 ^ [_1208096, _1208098, _1208100])), 23638 ^ [_1208096, _1208098, _1208100]))], (23646 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1208098, 23637 ^ [_1208096, _1208098, _1208100]), 23638 ^ [_1208096, _1208098, _1208100]))]], -(hBOOL(hAPP(hAPP(_1208098, hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1208100), _1208096)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208100, _1208096))))], (23618 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1208098, hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1208100), _1208096)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208100, _1208096))), 23621 ^ _777081 : [(23622 ^ _777081) ^ [_1208306, _1208308] : [-(hBOOL(hAPP(hAPP(_1208098, _1208308), _1208306))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1208096), _1208306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1208306), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1208100 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1208096), _1208308)), _1208306)]]]]], (23650 ^ _777081) ^ [_1208829, _1208831, _1208833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1208829)), 23653 ^ _777081 : [(23672 ^ _777081) ^ [] : [23675 ^ _777081 : [(23676 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23674 ^ [_1208829, _1208831, _1208833])))], (23678 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23674 ^ [_1208829, _1208831, _1208833]), _1208829)))], (23680 ^ _777081) ^ [] : [-(_1208833 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1208829), 23673 ^ [_1208829, _1208831, _1208833])), 23674 ^ [_1208829, _1208831, _1208833]))], (23682 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1208831, 23673 ^ [_1208829, _1208831, _1208833]), 23674 ^ [_1208829, _1208831, _1208833]))]], -(hBOOL(hAPP(hAPP(_1208831, hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1208833), _1208829)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208833, _1208829))))], (23654 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1208831, hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1208833), _1208829)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1208833, _1208829))), 23657 ^ _777081 : [(23658 ^ _777081) ^ [_1209030, _1209032] : [-(hBOOL(hAPP(hAPP(_1208831, _1209032), _1209030))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209030)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209030), _1208829)), _1208833 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1208829), _1209032)), _1209030)]]]]], (23686 ^ _777081) ^ [_1209559, _1209561] : [hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1209559), _1209561) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1209561 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23695 ^ _777081 : [(23696 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209559)))], (23698 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209559), _1209561)))]], 23699 ^ _777081 : [(23700 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1209559), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23702 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209561), _1209559)))]]], (23704 ^ _777081) ^ [_1209790, _1209792] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1209790), _1209792) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23705 ^ _777081 : [(23706 ^ _777081) ^ [] : [_1209792 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (23708 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209790), _1209792))], (23714 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1209790), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1209792), _1209790))]]], (23722 ^ _777081) ^ [_1210085, _1210087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210085)), 23725 ^ _777081 : [(23726 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1210087), _1210085))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210087)))], (23732 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1210087), _1210085))))]]], (23738 ^ _777081) ^ [_1210326, _1210328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210326)), 23741 ^ _777081 : [(23742 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1210328), _1210326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1210326), _1210328)))], (23748 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1210326), _1210328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1210328), _1210326))))]]], (23754 ^ _777081) ^ [_1210576, _1210578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210576)), 23757 ^ _777081 : [(23758 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1210576), _1210578))), 23761 ^ _777081 : [(23762 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1210578), _1210576)))], (23764 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210578)))]]], (23766 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1210576), _1210578)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1210578), _1210576)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210578))]]], (23776 ^ _777081) ^ [_1210904, _1210906, _1210908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1210906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1210906), _1210908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1210904), _1210908)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1210904), _1210906))))], (23790 ^ _777081) ^ [_1211143, _1211145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211145), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1211143), _1211145)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23800 ^ _777081) ^ [_1211308, _1211310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211308)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211308), _1211310)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1211308), _1211310) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23810 ^ _777081) ^ [_1211463, _1211465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211463), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23813 ^ _777081 : [(23814 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1211465), _1211463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211465), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23820 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211465), 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(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1211465), _1211463))))]]], (23826 ^ _777081) ^ [_1211719, _1211721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211719), 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)), _1211721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1211719), _1211721)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23836 ^ _777081) ^ [_1211884, _1211886, _1211888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211884), 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)), _1211886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211886), _1211888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1211884), _1211886)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1211884), _1211888))))], (23850 ^ _777081) ^ [_1212129, _1212131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212129), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212131), _1212129)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1212129), _1212131) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23860 ^ _777081) ^ [_1212290, _1212292, _1212294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212290), _1212292)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1212290), _1212294)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1212292), _1212294))))], (23870 ^ _777081) ^ [_1212471, _1212473, _1212475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1212471), _1212473)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212475), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1212473), _1212475)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1212471), _1212475))))], (23880 ^ _777081) ^ [_1212658, _1212660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1212660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1212658), _1212660)), _1212658)))], (23890 ^ _777081) ^ [_1212817, _1212819, _1212821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212817)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1212819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1212821), _1212817)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1212819), _1212821)), _1212817))], (23896 ^ _777081) ^ [_1212948, _1212950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212948)), -(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, _1212950, _1212948))))], (23902 ^ _777081) ^ [_1213041, _1213043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213041)), 23905 ^ _777081 : [(23906 ^ _777081) ^ [] : [-(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, _1213043, _1213041))))], (23908 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1213043, _1213041)), _1213041)))]]], (23910 ^ _777081) ^ [_1213178, _1213180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1213178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213178), _1213180)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1213178, _1213180) = _1213178)], (23920 ^ _777081) ^ [_1213329, _1213331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213329), 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, _1213331, _1213329)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23926 ^ _777081) ^ [_1213434, _1213436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213434), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23929 ^ _777081 : [(23930 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1213436, _1213434)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23932 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213434), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1213436, _1213434))))]]], (23934 ^ _777081) ^ [_1213583, _1213585] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1213583), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213585), _1213583)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1213583, _1213585) = _1213583)], (23944 ^ _777081) ^ [_1213749, _1213751] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1213749, _1213751) = 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), _1213749), _1213751) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23950 ^ _777081) ^ [_1213842, _1213844] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1213842, _1213844) = 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), _1213842), _1213844) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1213844), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1213842, _1213844)))], (23956 ^ _777081) ^ [_1213910, _1213912] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1213910, _1213912) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1213910, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1213912)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23962 ^ _777081) ^ [_1214003, _1214005] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1214003, _1214005) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1214003, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1214005)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1214003, _1214005)), _1214005))], (23968 ^ _777081) ^ [_1214062, _1214064, _1214066, _1214068] : [class_Divides_Osemiring__div(_1214062), -(_1214064 = c_Groups_Ozero__class_Ozero(_1214062)), -(hAPP(c_Divides_Odiv__class_Odiv(_1214062, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214062), _1214066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214062), _1214064), _1214068))), _1214064) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214062), _1214068), hAPP(c_Divides_Odiv__class_Odiv(_1214062, _1214066), _1214064)))], (23978 ^ _777081) ^ [_1214232, _1214234, _1214236, _1214238] : [class_Divides_Osemiring__div(_1214232), -(_1214234 = c_Groups_Ozero__class_Ozero(_1214232)), -(hAPP(c_Divides_Odiv__class_Odiv(_1214232, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214232), _1214236), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214232), _1214238), _1214234))), _1214234) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214232), _1214238), hAPP(c_Divides_Odiv__class_Odiv(_1214232, _1214236), _1214234)))], (23988 ^ _777081) ^ [_1214402, _1214404, _1214406] : [class_Divides_Osemiring__div(_1214402), -(_1214404 = c_Groups_Ozero__class_Ozero(_1214402)), -(hAPP(c_Divides_Odiv__class_Odiv(_1214402, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214402), _1214406), _1214404)), _1214404) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214402), hAPP(c_Divides_Odiv__class_Odiv(_1214402, _1214406), _1214404)), c_Groups_Oone__class_Oone(_1214402)))], (23998 ^ _777081) ^ [_1214558, _1214560, _1214562] : [class_Divides_Osemiring__div(_1214558), -(_1214560 = c_Groups_Ozero__class_Ozero(_1214558)), -(hAPP(c_Divides_Odiv__class_Odiv(_1214558, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214558), _1214560), _1214562)), _1214560) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214558), hAPP(c_Divides_Odiv__class_Odiv(_1214558, _1214562), _1214560)), c_Groups_Oone__class_Oone(_1214558)))], (24008 ^ _777081) ^ [_1214714, _1214716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214714), _1214716)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1214714, _1214716) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214714), _1214716))], (24018 ^ _777081) ^ [_1214889, _1214891, _1214893, _1214895] : [_1214889 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1214891), _1214893)), _1214895), -(_1214891 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1214889), _1214891) = _1214893), 24025 ^ _777081 : [(24026 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214891)))], (24028 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214895), _1214891))]], 24033 ^ _777081 : [(24034 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1214891))], (24036 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214891), _1214895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214895), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (24094 ^ _777081) ^ [_1216336, _1216338, _1216340] : [-(hBOOL(hAPP(_1216336, hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1216338), _1216340)))), 24097 ^ _777081 : [(24098 ^ _777081) ^ [] : [-(_1216340 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24100 ^ _777081) ^ [] : [hBOOL(hAPP(_1216336, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 24103 ^ _777081 : [(24104 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216340)))], (24108 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24106 ^ [_1216336, _1216338, _1216340])))], (24110 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24106 ^ [_1216336, _1216338, _1216340]), _1216340)))], (24112 ^ _777081) ^ [] : [-(_1216338 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1216340), 24105 ^ [_1216336, _1216338, _1216340])), 24106 ^ [_1216336, _1216338, _1216340]))], (24114 ^ _777081) ^ [] : [hBOOL(hAPP(_1216336, 24105 ^ [_1216336, _1216338, _1216340]))]], 24115 ^ _777081 : [(24116 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216340), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24120 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216340), 24118 ^ [_1216336, _1216338, _1216340])))], (24122 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24118 ^ [_1216336, _1216338, _1216340]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24124 ^ _777081) ^ [] : [-(_1216338 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1216340), 24117 ^ [_1216336, _1216338, _1216340])), 24118 ^ [_1216336, _1216338, _1216340]))], (24126 ^ _777081) ^ [] : [hBOOL(hAPP(_1216336, 24117 ^ [_1216336, _1216338, _1216340]))]]], (24048 ^ _777081) ^ [_1215376, _1215378, _1215380] : [hBOOL(hAPP(_1215376, hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1215378), _1215380))), 24051 ^ _777081 : [(24052 ^ _777081) ^ [] : [_1215380 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1215376, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24058 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215380)), 24061 ^ _777081 : [(24062 ^ _777081) ^ [_1215710] : [-(hBOOL(hAPP(_1215376, _1215710))), 24063 ^ _777081 : [(24064 ^ _777081) ^ [_1215781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215781), _1215380)), _1215378 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1215380), _1215710)), _1215781)]]]]], (24076 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215380), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24079 ^ _777081 : [(24080 ^ _777081) ^ [_1216040] : [-(hBOOL(hAPP(_1215376, _1216040))), 24081 ^ _777081 : [(24082 ^ _777081) ^ [_1216114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215380), _1216114)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216114), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1215378 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1215380), _1216040)), _1216114)]]]]]]], (24130 ^ _777081) ^ [_1217050, _1217052, _1217054, _1217056] : [_1217050 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1217052), _1217054)), _1217056), -(_1217052 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1217050, _1217052) = _1217056), 24137 ^ _777081 : [(24138 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217052)))], (24140 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217056), _1217052))]], 24145 ^ _777081 : [(24146 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217052))], (24148 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217052), _1217056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1217056), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (24160 ^ _777081) ^ [_1217515, _1217517, _1217519, _1217521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217515)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217517), _1217519)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1217519), 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), _1217517), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1217521, _1217515))), _1217519)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24174 ^ _777081) ^ [_1217774, _1217776, _1217778, _1217780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1217774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217776), _1217778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1217778), 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), _1217776), _1217774)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1217776), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1217780, _1217774))), _1217778))))], (24188 ^ _777081) ^ [_1218045, _1218047, _1218049, _1218051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218045)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218047)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218047), _1218049)), -(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), _1218049), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1218051, _1218045))), _1218047)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218049), _1218045))))], (24202 ^ _777081) ^ [_1218310, _1218312, _1218314, _1218316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218312)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218312), _1218314)), -(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), _1218314), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1218316, _1218310))), _1218312))))], (24262 ^ _777081) ^ [_1219452, _1219454, _1219456] : [-(hBOOL(hAPP(_1219452, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1219454, _1219456)))), 24265 ^ _777081 : [(24266 ^ _777081) ^ [] : [-(_1219456 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24268 ^ _777081) ^ [] : [hBOOL(hAPP(_1219452, _1219454))]], 24271 ^ _777081 : [(24272 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1219456)))], (24276 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24274 ^ [_1219452, _1219454, _1219456])))], (24278 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24274 ^ [_1219452, _1219454, _1219456]), _1219456)))], (24280 ^ _777081) ^ [] : [-(_1219454 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219456), 24273 ^ [_1219452, _1219454, _1219456])), 24274 ^ [_1219452, _1219454, _1219456]))], (24282 ^ _777081) ^ [] : [hBOOL(hAPP(_1219452, 24274 ^ [_1219452, _1219454, _1219456]))]], 24283 ^ _777081 : [(24284 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1219456), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24288 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1219456), 24286 ^ [_1219452, _1219454, _1219456])))], (24290 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24286 ^ [_1219452, _1219454, _1219456]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24292 ^ _777081) ^ [] : [-(_1219454 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1219456), 24285 ^ [_1219452, _1219454, _1219456])), 24286 ^ [_1219452, _1219454, _1219456]))], (24294 ^ _777081) ^ [] : [hBOOL(hAPP(_1219452, 24286 ^ [_1219452, _1219454, _1219456]))]]], (24216 ^ _777081) ^ [_1218575, _1218577, _1218579] : [hBOOL(hAPP(_1218575, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1218577, _1218579))), 24219 ^ _777081 : [(24220 ^ _777081) ^ [] : [_1218579 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1218575, _1218577)))], (24226 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218579)), 24229 ^ _777081 : [(24230 ^ _777081) ^ [_1218905, _1218907] : [-(hBOOL(hAPP(_1218575, _1218905))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1218905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218905), _1218579)), _1218577 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218579), _1218907)), _1218905)]]], (24244 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218579), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24247 ^ _777081 : [(24248 ^ _777081) ^ [_1219197, _1219199] : [-(hBOOL(hAPP(_1218575, _1219197))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1218579), _1219197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1219197), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1218577 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1218579), _1219199)), _1219197)]]]]], (24298 ^ _777081) ^ [_1220164, _1220166] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1220164)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1220166))) = 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), _1220164), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220166))))], (24300 ^ _777081) ^ [_1220225, _1220227] : [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), _1220225))), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1220227))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1220225))) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220227)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220225)))], (24306 ^ _777081) ^ [_1220362, _1220364] : [-(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), _1220362)))), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1220364))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1220362))) = 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), _1220364)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1220362)))], (24312 ^ _777081) ^ [_1220439, _1220441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1220439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220441)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1220441), _1220439)), _1220441) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1220441), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1220439), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (24322 ^ _777081) ^ [_1220624, _1220626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1220624), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(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)))), _1220626))), 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)))), _1220624)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1220626), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1220624))], (24328 ^ _777081) ^ [_1220774, _1220776] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220774)), -(c_SMT_Oz3div(_1220776, _1220774) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1220776), _1220774))], (24334 ^ _777081) ^ [_1220867, _1220869] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220867))), -(c_SMT_Oz3div(_1220869, _1220867) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1220869), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1220867))))], (24340 ^ _777081) ^ [_1220931, _1220933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220931)), -(c_SMT_Oz3mod(_1220933, _1220931) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1220933, _1220931))], (24346 ^ _777081) ^ [_1221020, _1221022] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1221020))), -(c_SMT_Oz3mod(_1221022, _1221020) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1221022, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1221020)))], (24352 ^ _777081) ^ [_1221070] : [class_Power_Opower(_1221070), -(c_Power_Opower__class_Opower(_1221070) = c_Power_Opower_Opower(_1221070, c_Groups_Oone__class_Oone(_1221070), c_Groups_Otimes__class_Otimes(_1221070)))], (24358 ^ _777081) ^ [_1221163, _1221165] : [class_Int_Onumber__ring(_1221163), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1221163), hAPP(c_Int_Onumber__class_Onumber__of(_1221163), 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)))), _1221165))) = hAPP(c_Int_Onumber__class_Onumber__of(_1221163), c_Int_OMin))], (24364 ^ _777081) ^ [_1221286, _1221288] : [class_Int_Onumber__ring(_1221286), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1221286), hAPP(c_Int_Onumber__class_Onumber__of(_1221286), 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)))), _1221288)) = c_Groups_Oone__class_Oone(_1221286))], (24370 ^ _777081) ^ [_1221397, _1221399, _1221401] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1221397, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221399), _1221401)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221399), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1221397), _1221399), _1221401))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1221397, _1221399)))], (24372 ^ _777081) ^ [_1221460, _1221462, _1221464] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221460), _1221462)), _1221464) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221460), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1221462), _1221464))), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221460), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1221462, _1221464))), _1221464)))], (24374 ^ _777081) ^ [_1221533, _1221535] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1221533), _1221535)), _1221535) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1221533), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1221533, _1221535)))], (24376 ^ _777081) ^ [_1221580, _1221582] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221580), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1221582), _1221580)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1221582), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1221582, _1221580)))], (24378 ^ _777081) ^ [_1221627, _1221629] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1221627, _1221629) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1221627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1221627), _1221629)), _1221629)))], (24380 ^ _777081) ^ [_1221674, _1221676, _1221678] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1221674), _1221676)), _1221678) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1221674), _1221678)), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1221676), _1221678))), 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, _1221674, _1221678)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1221676, _1221678))), _1221678)))], (24382 ^ _777081) ^ [_1221757, _1221759, _1221761] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221757), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1221759, _1221761)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221757), _1221759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221757), _1221761)))], (24384 ^ _777081) ^ [_1221810, _1221812, _1221814] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1221810, _1221812)), _1221814) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221810), _1221814), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221812), _1221814)))], (24386 ^ _777081) ^ [_1221863, _1221865] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1221863, _1221865)), _1221863)))], (24388 ^ _777081) ^ [_1221897, _1221899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1221897), _1221899)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1221897, _1221899) = _1221897)], (24394 ^ _777081) ^ [_1221992, _1221994, _1221996] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1221992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1221994), _1221996)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1221992), _1221994)), _1221996))], (24396 ^ _777081) ^ [_1222043, _1222045] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1222043), _1222045) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1222043, _1222045)), _1222045))], (24398 ^ _777081) ^ [_1222086, _1222088] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1222086), _1222088)), _1222086)))], (24400 ^ _777081) ^ [_1222122, _1222124, _1222126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1222122), _1222124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1222122), _1222126)), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1222124), _1222126))))], (24406 ^ _777081) ^ [_1222254] : [c_Int_OMin = c_Int_OBit0(_1222254)], (24408 ^ _777081) ^ [_1222288] : [c_Int_OBit0(_1222288) = c_Int_OMin], (24410 ^ _777081) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (24412 ^ _777081) ^ [_1222343] : [c_Int_OMin = c_Int_OBit1(_1222343), -(c_Int_OMin = _1222343)], (24418 ^ _777081) ^ [_1222418] : [c_Int_OMin = _1222418, -(c_Int_OMin = c_Int_OBit1(_1222418))], (24424 ^ _777081) ^ [_1222511] : [c_Int_OBit1(_1222511) = c_Int_OMin, -(_1222511 = c_Int_OMin)], (24430 ^ _777081) ^ [_1222586] : [_1222586 = c_Int_OMin, -(c_Int_OBit1(_1222586) = c_Int_OMin)], (24436 ^ _777081) ^ [] : [c_Int_OMin = c_Int_OPls], (24438 ^ _777081) ^ [] : [c_Int_OPls = c_Int_OMin], (24440 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (24442 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (24444 ^ _777081) ^ [_1222757] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1222757), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1222757)], (24446 ^ _777081) ^ [_1222786, _1222788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1222786), _1222788)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1222786), _1222788) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24452 ^ _777081) ^ [_1222897, _1222899, _1222901] : [_1222897 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1222897), _1222899)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1222897), _1222901)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24458 ^ _777081) ^ [_1223006, _1223008, _1223010] : [-(_1223006 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223006), _1223008)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223006), _1223010)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1223008), _1223010))], (24464 ^ _777081) ^ [_1223079, _1223081] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223079, _1223081)) = _1223081, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1223079), _1223081) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24470 ^ _777081) ^ [_1223178, _1223180] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223178, _1223180)) = _1223180), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1223178), _1223180) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223178, _1223180)))], (24476 ^ _777081) ^ [_1223237] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223237, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24478 ^ _777081) ^ [_1223264, _1223266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1223264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223266, _1223264)), _1223264)))], (24484 ^ _777081) ^ [_1223378, _1223380] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223378, _1223380) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1223378 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223380), 24487 ^ [_1223378, _1223380]))], (24491 ^ _777081) ^ [_1223483, _1223485] : [24492 ^ _777081 : [(24493 ^ _777081) ^ [_1223532] : [_1223483 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1223485), _1223532)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223483, _1223485) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24497 ^ _777081) ^ [_1223604, _1223606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1223604), _1223606)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223604, _1223606) = _1223604)], (24503 ^ _777081) ^ [_1223693, _1223695] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1223693), _1223695))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223693, _1223695) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223693), _1223695), _1223695))], (24509 ^ _777081) ^ [_1223746, _1223748] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1223746), _1223748))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223746, _1223748) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223746), _1223748), _1223748))], (24515 ^ _777081) ^ [_1223801, _1223803, _1223805] : [-(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), _1223801), _1223803)), _1223805), _1223803) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223805, _1223803))], (24517 ^ _777081) ^ [_1223848, _1223850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223848), _1223850)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1223850, _1223848) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1223850), _1223848), _1223848))], (24523 ^ _777081) ^ [_1223963, _1223965] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223963)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1223965)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1223963), _1223965)))], (24525 ^ _777081) ^ [_1224009, _1224011] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1224009), _1224011)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224009)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1224011)))], (24527 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24529 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (24531 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (24533 ^ _777081) ^ [_1224127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1224127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1224127)))], (24539 ^ _777081) ^ [_1224210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1224210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1224210))))], (24545 ^ _777081) ^ [_1224311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1224311)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224311), c_Int_OMin)))], (24551 ^ _777081) ^ [_1224406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224406), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1224406)), c_Int_OMin)))], (24557 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (24559 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (24561 ^ _777081) ^ [_1224561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1224561)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224561), c_Int_OMin)))], (24567 ^ _777081) ^ [_1224656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224656), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1224656)), c_Int_OMin)))], (24573 ^ _777081) ^ [_1224769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1224769))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1224769)))], (24579 ^ _777081) ^ [_1224852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1224852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1224852))))], (24585 ^ _777081) ^ [_1224953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1224953)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224953), c_Int_OMin)))], (24591 ^ _777081) ^ [_1225048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225048), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1225048)), c_Int_OMin)))], (24597 ^ _777081) ^ [_1225161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1225161))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1225161)))], (24603 ^ _777081) ^ [_1225244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1225244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1225244))))], (24609 ^ _777081) ^ [_1225333, _1225335] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225333), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225335)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1225333, _1225335)))], (24611 ^ _777081) ^ [_1225375, _1225377] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1225375, _1225377)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225375), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225377)))], (24613 ^ _777081) ^ [] : [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)], (24615 ^ _777081) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (24617 ^ _777081) ^ [_1225459] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1225459) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1225459))], (24619 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (24621 ^ _777081) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (24623 ^ _777081) ^ [_1225524] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225524), c_Int_OMin) = c_Int_Opred(_1225524))], (24625 ^ _777081) ^ [_1225555] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1225555) = c_Int_Opred(_1225555))], (24627 ^ _777081) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (24629 ^ _777081) ^ [_1225601] : [class_Int_Onumber__ring(_1225601), c_Int_Oiszero(_1225601, hAPP(c_Int_Onumber__class_Onumber__of(_1225601), c_Int_OMin))], (24635 ^ _777081) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (24637 ^ _777081) ^ [_1225703] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1225703), c_Int_OMin) = c_Int_Osucc(_1225703))], (24639 ^ _777081) ^ [_1225734, _1225736, _1225738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225734)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1225734), _1225736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1225738), _1225736)), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1225738), _1225734))))], (24649 ^ _777081) ^ [_1225915, _1225917, _1225919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225915)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1225915), _1225917)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1225915), _1225919)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1225917), _1225919))], (24655 ^ _777081) ^ [_1226046, _1226048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1226046)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1226046), _1226048)), _1226046) = _1226048)], (24661 ^ _777081) ^ [_1226151, _1226153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1226151)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1226153), _1226151)), _1226151) = _1226153)], (24667 ^ _777081) ^ [_1226256, _1226258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1226256)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1226258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1226258), _1226256)), _1226258)))], (24677 ^ _777081) ^ [_1226415, _1226417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1226415)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1226417, _1226415)), _1226415)))], (24683 ^ _777081) ^ [_1226514, _1226516, _1226518] : [-(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), _1226514), _1226516)), _1226518)), _1226516) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1226518), _1226516))], (24685 ^ _777081) ^ [_1226567, _1226569] : [class_Int_Onumber__ring(_1226567), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226567), hAPP(c_Int_Onumber__class_Onumber__of(_1226567), c_Int_OMin)), _1226569) = hAPP(c_Groups_Ouminus__class_Ouminus(_1226567), _1226569))], (24691 ^ _777081) ^ [_1226678, _1226680] : [class_Int_Onumber__ring(_1226678), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1226678), _1226680), hAPP(c_Int_Onumber__class_Onumber__of(_1226678), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1226678), _1226680))], (24697 ^ _777081) ^ [_1226789] : [class_Int_Onumber__ring(_1226789), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1226789), c_Groups_Oone__class_Oone(_1226789)) = hAPP(c_Int_Onumber__class_Onumber__of(_1226789), c_Int_OMin))], (24703 ^ _777081) ^ [_1226886] : [class_Int_Onumber__ring(_1226886), -(hAPP(c_Int_Onumber__class_Onumber__of(_1226886), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1226886), c_Groups_Oone__class_Oone(_1226886)))], (24709 ^ _777081) ^ [_1226983] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1226983), hAPP(c_Int_Onumber__class_Onumber__of(_1226983), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1226983)), class_Int_Onumber__ring(_1226983), class_Rings_Olinordered__idom(_1226983)], (24719 ^ _777081) ^ [_1227140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1227140)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227140), c_Int_OMin)))], (24725 ^ _777081) ^ [_1227235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227235), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1227235)), c_Int_OMin)))], (24731 ^ _777081) ^ [_1227348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1227348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1227348)))], (24737 ^ _777081) ^ [_1227431] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1227431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1227431))))], (24743 ^ _777081) ^ [_1227520] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1227520, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24745 ^ _777081) ^ [_1227547] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1227547)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1227547)))], (24747 ^ _777081) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (24749 ^ _777081) ^ [_1227613, _1227615] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1227613), _1227615) = c_Groups_Oone__class_Oone(tc_Int_Oint), 24754 ^ _777081 : [(24755 ^ _777081) ^ [] : [-(_1227613 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (24757 ^ _777081) ^ [] : [-(_1227615 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 24758 ^ _777081 : [(24759 ^ _777081) ^ [] : [-(_1227613 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (24761 ^ _777081) ^ [] : [-(_1227615 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (24763 ^ _777081) ^ [_1227797, _1227799] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1227797), _1227799) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 24764 ^ _777081 : [(24765 ^ _777081) ^ [] : [_1227797 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1227799 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (24771 ^ _777081) ^ [] : [_1227797 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1227799 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (24779 ^ _777081) ^ [_1228023, _1228025] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1228023), _1228025) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1228023 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1228023 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (24789 ^ _777081) ^ [_1228125] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1228125)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1228125)))], (24791 ^ _777081) ^ [_1228158] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1228158)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1228158)))], (24793 ^ _777081) ^ [_1228191, _1228193, _1228195, _1228197] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1228191, _1228193, _1228195), _1228197), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1228193)], (24795 ^ _777081) ^ [_1228230, _1228232, _1228234, _1228236, _1228238] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1228230, _1228232, _1228234), _1228236), hAPP(c_Nat_OSuc, _1228238)) = hAPP(hAPP(_1228234, _1228236), hAPP(hAPP(c_Power_Opower_Opower(_1228230, _1228232, _1228234), _1228236), _1228238)))], (24797 ^ _777081) ^ [_1228290] : [class_Int_Onumber__ring(_1228290), -(hAPP(c_Int_Oring__1__class_Oof__int(_1228290), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1228290), c_Int_OMin))], (24803 ^ _777081) ^ [_1228383] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1228383), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1228383))], (24805 ^ _777081) ^ [_1228415, _1228417] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1228415)), 24808 ^ _777081 : [(24809 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228417), _1228415)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1228417), _1228415) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24815 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228417), _1228415))), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1228417), _1228415) = hAPP(c_Nat_OSuc, hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1228417), _1228415)), _1228415)))]]], (24821 ^ _777081) ^ [_1228669, _1228671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1228669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228671), _1228669))), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1228671), _1228669) = hAPP(c_Nat_OSuc, hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1228671), _1228669)), _1228669)))], (24855 ^ _777081) ^ [_1229272, _1229274, _1229276] : [-(hBOOL(hAPP(_1229272, hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1229274), _1229276)))), 24858 ^ _777081 : [(24859 ^ _777081) ^ [] : [-(_1229276 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24861 ^ _777081) ^ [] : [hBOOL(hAPP(_1229272, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 24862 ^ _777081 : [(24863 ^ _777081) ^ [] : [_1229276 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24867 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24865 ^ [_1229272, _1229274, _1229276]), _1229276)))], (24869 ^ _777081) ^ [] : [-(_1229274 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1229276), 24864 ^ [_1229272, _1229274, _1229276])), 24865 ^ [_1229272, _1229274, _1229276]))], (24871 ^ _777081) ^ [] : [hBOOL(hAPP(_1229272, 24864 ^ [_1229272, _1229274, _1229276]))]]], (24831 ^ _777081) ^ [_1228835, _1228837, _1228839] : [hBOOL(hAPP(_1228835, hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1228837), _1228839))), 24834 ^ _777081 : [(24835 ^ _777081) ^ [] : [_1228839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1228835, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24841 ^ _777081) ^ [] : [-(_1228839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24844 ^ _777081 : [(24845 ^ _777081) ^ [_1229087, _1229089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1229087), _1228839)), _1228837 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1228839), _1229089)), _1229087), -(hBOOL(hAPP(_1228835, _1229089)))]]]]], (24875 ^ _777081) ^ [_1229694, _1229696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229694)), -(hAPP(c_Int_Onat, hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1229694), _1229696)) = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(c_Int_Onat, _1229694)), hAPP(c_Int_Onat, _1229696)))], (24881 ^ _777081) ^ [_1229817, _1229819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229819)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(c_Int_Onat, _1229817)), hAPP(c_Int_Onat, _1229819)) = hAPP(c_Int_Onat, hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1229817), _1229819)))], (24891 ^ _777081) ^ [_1229996, _1229998, _1230000, _1230002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1229996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1229998), _1230000)), -(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), _1230000), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1230002, _1229996))), _1229998)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1230000), _1229996))))], (24925 ^ _777081) ^ [_1230652, _1230654, _1230656] : [-(hBOOL(hAPP(_1230652, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1230654, _1230656)))), 24928 ^ _777081 : [(24929 ^ _777081) ^ [] : [-(_1230656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24931 ^ _777081) ^ [] : [hBOOL(hAPP(_1230652, _1230654))]], 24932 ^ _777081 : [(24933 ^ _777081) ^ [] : [_1230656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24937 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24935 ^ [_1230652, _1230654, _1230656]), _1230656)))], (24939 ^ _777081) ^ [] : [-(_1230654 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1230656), 24934 ^ [_1230652, _1230654, _1230656])), 24935 ^ [_1230652, _1230654, _1230656]))], (24941 ^ _777081) ^ [] : [hBOOL(hAPP(_1230652, 24935 ^ [_1230652, _1230654, _1230656]))]]], (24901 ^ _777081) ^ [_1230219, _1230221, _1230223] : [hBOOL(hAPP(_1230219, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1230221, _1230223))), 24904 ^ _777081 : [(24905 ^ _777081) ^ [] : [_1230223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1230219, _1230221)))], (24911 ^ _777081) ^ [] : [-(_1230223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24914 ^ _777081 : [(24915 ^ _777081) ^ [_1230467, _1230469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1230467), _1230223)), _1230221 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1230223), _1230469)), _1230467), -(hBOOL(hAPP(_1230219, _1230467)))]]]]], (24945 ^ _777081) ^ [_1231061, _1231063] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1231061)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1231061), _1231063)), _1231061) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (24951 ^ _777081) ^ [_1231168, _1231170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231170)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1231168, _1231170)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1231168), hAPP(c_Int_Onat, _1231170)))], (24961 ^ _777081) ^ [_1231339, _1231341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231341)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1231339), hAPP(c_Int_Onat, _1231341)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1231339, _1231341)))], (24971 ^ _777081) ^ [_1231510, _1231512] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1231510), hAPP(hAPP(c_Power_Opower__class_Opower(_1231510), hAPP(c_Int_Onumber__class_Onumber__of(_1231510), c_Int_OMin)), _1231512)) = c_Groups_Oone__class_Oone(_1231510)), class_Int_Onumber__ring(_1231510), class_Rings_Olinordered__idom(_1231510)], (24981 ^ _777081) ^ [_1231675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231675)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1231675) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (24987 ^ _777081) ^ [_1231760, _1231762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1231760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1231760), _1231762)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1231762), _1231760) = hAPP(c_Nat_OSuc, hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1231762), _1231760)), _1231760)))], (24997 ^ _777081) ^ [_1231963, _1231965, _1231967] : [hBOOL(hAPP(_1231963, hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1231965), _1231967))), 25002 ^ _777081 : [(25003 ^ _777081) ^ [] : [-(_1231967 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25005 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1231963, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 25007 ^ _777081 : [(25008 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1231967), 25006 ^ [_1231963, _1231965, _1231967])), _1231965)))], (25010 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1231965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1231967), hAPP(c_Nat_OSuc, 25006 ^ [_1231963, _1231965, _1231967])))))], (25012 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1231963, 25006 ^ [_1231963, _1231965, _1231967])))]]], (25014 ^ _777081) ^ [_1232267, _1232269, _1232271] : [-(hBOOL(hAPP(_1232267, hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1232269), _1232271)))), 25015 ^ _777081 : [(25016 ^ _777081) ^ [] : [_1232271 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1232267, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25022 ^ _777081) ^ [_1232435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232271), _1232435)), _1232269)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232271), hAPP(c_Nat_OSuc, _1232435)))), hBOOL(hAPP(_1232267, _1232435))]]], (25034 ^ _777081) ^ [_1232665, _1232667, _1232669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1232665)), 25037 ^ _777081 : [(25048 ^ _777081) ^ [] : [_1232667 = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1232669), _1232665), 25051 ^ _777081 : [(25052 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232665), _1232667)), _1232669)))], (25054 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232665), hAPP(c_Nat_OSuc, _1232667)))))]]], (25038 ^ _777081) ^ [] : [-(_1232667 = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1232669), _1232665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232665), _1232667)), _1232669)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1232665), hAPP(c_Nat_OSuc, _1232667))))]]], (25056 ^ _777081) ^ [_1233049, _1233051] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1233049), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1233051)))) = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1233049), 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)))), _1233051)))], (25058 ^ _777081) ^ [_1233098, _1233100] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1233098)))), _1233100) = 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)))), _1233098)), _1233100))], (25060 ^ _777081) ^ [_1233147, _1233149] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1233147)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233149)) = 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)))), _1233147)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233149)))], (25062 ^ _777081) ^ [_1233202] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1233202))), 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_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1233202), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (25064 ^ _777081) ^ [_1233246] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1233246), _1233246)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1233246)], (25066 ^ _777081) ^ [_1233281, _1233283] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1233281, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1233283)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1233281, 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)))), _1233283)))], (25068 ^ _777081) ^ [_1233326, _1233328] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1233326))), _1233328) = 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)))), _1233326), _1233328))], (25070 ^ _777081) ^ [_1233371, _1233373] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1233371))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233373)) = 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)))), _1233371), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233373)))], (25072 ^ _777081) ^ [_1233422] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1233422)), 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, _1233422, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (25074 ^ _777081) ^ [_1233468, _1233470] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233468))), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233468)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233470)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25080 ^ _777081) ^ [_1233573, _1233575] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233573)))), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233573)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233575)) = hAPP(c_Int_Onat, hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233573)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233575))))], (25086 ^ _777081) ^ [_1233652, _1233654] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233652))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233652), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233654)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25092 ^ _777081) ^ [_1233754, _1233756] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233754)))), 25095 ^ _777081 : [(25096 ^ _777081) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233756))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233754), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233756)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233754))], (25102 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233756)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233754), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1233756)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233754), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1233756))))]]], (25108 ^ _777081) ^ [_1234027, _1234029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234027)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1234027), _1234029)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1234027), _1234029) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (25118 ^ _777081) ^ [_1234194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234194)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1234194) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1234194), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (25124 ^ _777081) ^ [_1234293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1234293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1234293), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (25130 ^ _777081) ^ [_1234388] : [-(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), _1234388)) = hAPP(c_Int_Onat, 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), _1234388))))], (25132 ^ _777081) ^ [_1234438] : [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, _1234438, 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, _1234438, 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))], (25138 ^ _777081) ^ [_1234529] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1234529, 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, _1234529, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (25144 ^ _777081) ^ [_1234626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1234626)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1234626), 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)))))))], (25150 ^ _777081) ^ [_1234739] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1234739))), -(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), _1234739)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25156 ^ _777081) ^ [_1234832] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1234832)))), -(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), _1234832)) = 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), _1234832))))], (25162 ^ _777081) ^ [_1234896] : [_1234896 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1234896) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25168 ^ _777081) ^ [_1234972] : [-(_1234972 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 25171 ^ _777081 : [(25172 ^ _777081) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1234972, 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, _1234972) = 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(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral, _1234972), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (25178 ^ _777081) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1234972, 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, _1234972) = 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(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral, _1234972), 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)))]]], (25184 ^ _777081) ^ [_1235232, _1235234] : [-(c_Nitpick_Onat__lcm(_1235232, _1235234) = hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1235232), _1235234)), c_Nitpick_Onat__gcd(_1235232, _1235234)))], (25186 ^ _777081) ^ [] : [-(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)))], (25188 ^ _777081) ^ [_1235293, _1235295] : [-(c_Divides_Odivmod__int__rel(_1235293, _1235295) = 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, _1235293))), 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), _1235295)))))), 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)), _1235295))), 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)), _1235295))))), 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)), _1235295)))), 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), _1235295))), 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))))))))], (25190 ^ _777081) ^ [] : [-(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))], (25192 ^ _777081) ^ [_1235435, _1235437] : [_1235435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1235437, _1235435) = _1235437)], (25198 ^ _777081) ^ [_1235512, _1235514] : [-(_1235512 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1235514, _1235512) = c_Nitpick_Onat__gcd(_1235512, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1235514, _1235512)))], (25204 ^ _777081) ^ [_1235556, _1235558] : [-(_1235556 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1235558, _1235556), c_Divides_Odivmod__int(_1235558, _1235556))))], (25210 ^ _777081) ^ [] : [-(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))], (25212 ^ _777081) ^ [_1235618, _1235620] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1235618), _1235620) = 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), _1235618)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1235620)))))], (25214 ^ _777081) ^ [_1235667, _1235669] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1235667), _1235669) = c_Smallcheck_Osmall_H(_1235667, hAPP(c_Code__Numeral_Oint__of, _1235669), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1235669))))], (25216 ^ _777081) ^ [] : [-(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)))))], (25218 ^ _777081) ^ [_1235738, _1235740] : [_1235738 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1235738, _1235740) = _1235740)], (25224 ^ _777081) ^ [_1235815, _1235817] : [-(_1235815 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1235815, _1235817) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1235815), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1235817)))], (25230 ^ _777081) ^ [_1235868, _1235870] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1235868, _1235870) = c_Smallcheck_Ofull__small_H(_1235868, hAPP(c_Code__Numeral_Oint__of, _1235870), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1235870))))], (25232 ^ _777081) ^ [_1235910, _1235912, _1235914, _1235916, _1235918] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1235910, _1235912), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1235914), _1235916))), -(_1235912 = 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)), _1235918)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1235910, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235912), _1235918)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1235914), _1235918)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235912), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1235914, _1235918))), _1235916)))))], (25246 ^ _777081) ^ [] : [-(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))], (25248 ^ _777081) ^ [_1236234, _1236236, _1236238] : [-(hAPP(c_Divides_Oadjust(_1236234), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1236236), _1236238)) = 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), _1236238), _1236234)), 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)))), _1236236)), 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)))), _1236236)), _1236238))))], (25250 ^ _777081) ^ [_1236341, _1236343, _1236345, _1236347, _1236349, _1236351] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1236341, tc_fun(_1236343, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1236341, tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_fun(_1236343, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1236343, tc_fun(tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_fun(_1236343, tc_HOL_Obool)), _1236341), c_COMBC(_1236343, tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1236343, tc_prod(_1236341, _1236343)), tc_fun(_1236343, tc_fun(tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_HOL_Obool)), _1236341), hAPP(c_COMBB(tc_prod(_1236341, _1236343), tc_fun(tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_HOL_Obool), _1236343), c_member(tc_prod(_1236341, _1236343)))), c_Product__Type_OPair(_1236341, _1236343)))), _1236345)), hAPP(hAPP(c_COMBC(_1236341, tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_fun(_1236343, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1236343, tc_fun(tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_fun(_1236343, tc_HOL_Obool)), _1236341), c_COMBC(_1236343, tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1236343, tc_prod(_1236341, _1236343)), tc_fun(_1236343, tc_fun(tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_HOL_Obool)), _1236341), hAPP(c_COMBB(tc_prod(_1236341, _1236343), tc_fun(tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool), tc_HOL_Obool), _1236343), c_member(tc_prod(_1236341, _1236343)))), c_Product__Type_OPair(_1236341, _1236343)))), _1236347)), _1236349), _1236351)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1236341, _1236343)), hAPP(hAPP(c_Product__Type_OPair(_1236341, _1236343), _1236349), _1236351)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1236341, _1236343), tc_HOL_Obool)), _1236345), _1236347))))], (25256 ^ _777081) ^ [_1236998, _1237000, _1237002, _1237004, _1237006, _1237008] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1236998, _1237000)), hAPP(hAPP(c_Product__Type_OPair(_1236998, _1237000), _1237006), _1237008)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool)), _1237002), _1237004))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1236998, tc_fun(_1237000, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1236998, tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_fun(_1237000, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1237000, tc_fun(tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_fun(_1237000, tc_HOL_Obool)), _1236998), c_COMBC(_1237000, tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1237000, tc_prod(_1236998, _1237000)), tc_fun(_1237000, tc_fun(tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_HOL_Obool)), _1236998), hAPP(c_COMBB(tc_prod(_1236998, _1237000), tc_fun(tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_HOL_Obool), _1237000), c_member(tc_prod(_1236998, _1237000)))), c_Product__Type_OPair(_1236998, _1237000)))), _1237002)), hAPP(hAPP(c_COMBC(_1236998, tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_fun(_1237000, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1237000, tc_fun(tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_fun(_1237000, tc_HOL_Obool)), _1236998), c_COMBC(_1237000, tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1237000, tc_prod(_1236998, _1237000)), tc_fun(_1237000, tc_fun(tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_HOL_Obool)), _1236998), hAPP(c_COMBB(tc_prod(_1236998, _1237000), tc_fun(tc_fun(tc_prod(_1236998, _1237000), tc_HOL_Obool), tc_HOL_Obool), _1237000), c_member(tc_prod(_1236998, _1237000)))), c_Product__Type_OPair(_1236998, _1237000)))), _1237004)), _1237006), _1237008)))], (25262 ^ _777081) ^ [_1237682, _1237684, _1237686, _1237688] : [hAPP(hAPP(c_COMBC(_1237682, tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_fun(_1237684, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1237684, tc_fun(tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_fun(_1237684, tc_HOL_Obool)), _1237682), c_COMBC(_1237684, tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1237684, tc_prod(_1237682, _1237684)), tc_fun(_1237684, tc_fun(tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_HOL_Obool)), _1237682), hAPP(c_COMBB(tc_prod(_1237682, _1237684), tc_fun(tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_HOL_Obool), _1237684), c_member(tc_prod(_1237682, _1237684)))), c_Product__Type_OPair(_1237682, _1237684)))), _1237686) = hAPP(hAPP(c_COMBC(_1237682, tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_fun(_1237684, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1237684, tc_fun(tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_fun(_1237684, tc_HOL_Obool)), _1237682), c_COMBC(_1237684, tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1237684, tc_prod(_1237682, _1237684)), tc_fun(_1237684, tc_fun(tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_HOL_Obool)), _1237682), hAPP(c_COMBB(tc_prod(_1237682, _1237684), tc_fun(tc_fun(tc_prod(_1237682, _1237684), tc_HOL_Obool), tc_HOL_Obool), _1237684), c_member(tc_prod(_1237682, _1237684)))), c_Product__Type_OPair(_1237682, _1237684)))), _1237688), -(_1237686 = _1237688)], (25268 ^ _777081) ^ [_1238231, _1238233, _1238235, _1238237] : [_1238235 = _1238237, -(hAPP(hAPP(c_COMBC(_1238231, tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_fun(_1238233, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1238233, tc_fun(tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_fun(_1238233, tc_HOL_Obool)), _1238231), c_COMBC(_1238233, tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1238233, tc_prod(_1238231, _1238233)), tc_fun(_1238233, tc_fun(tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_HOL_Obool)), _1238231), hAPP(c_COMBB(tc_prod(_1238231, _1238233), tc_fun(tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_HOL_Obool), _1238233), c_member(tc_prod(_1238231, _1238233)))), c_Product__Type_OPair(_1238231, _1238233)))), _1238235) = hAPP(hAPP(c_COMBC(_1238231, tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_fun(_1238233, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1238233, tc_fun(tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_fun(_1238233, tc_HOL_Obool)), _1238231), c_COMBC(_1238233, tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1238233, tc_prod(_1238231, _1238233)), tc_fun(_1238233, tc_fun(tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_HOL_Obool)), _1238231), hAPP(c_COMBB(tc_prod(_1238231, _1238233), tc_fun(tc_fun(tc_prod(_1238231, _1238233), tc_HOL_Obool), tc_HOL_Obool), _1238233), c_member(tc_prod(_1238231, _1238233)))), c_Product__Type_OPair(_1238231, _1238233)))), _1238237))], (25274 ^ _777081) ^ [_1238807, _1238809, _1238811, _1238813] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1238807, tc_fun(_1238809, tc_HOL_Obool))), _1238811), _1238813)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1238807, _1238809)), hAPP(hAPP(c_Product__Type_OPair(_1238807, _1238809), _1238811), _1238813)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1238807, _1238809), tc_HOL_Obool)))))], (25280 ^ _777081) ^ [_1238964, _1238966, _1238968, _1238970] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1238964, _1238966)), hAPP(hAPP(c_Product__Type_OPair(_1238964, _1238966), _1238968), _1238970)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1238964, _1238966), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1238964, tc_fun(_1238966, tc_HOL_Obool))), _1238968), _1238970)))], (25286 ^ _777081) ^ [_1239148, _1239150, _1239152, _1239154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239148, tc_fun(_1239150, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1239148, tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_fun(_1239150, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1239150, tc_fun(tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_fun(_1239150, tc_HOL_Obool)), _1239148), c_COMBC(_1239150, tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1239150, tc_prod(_1239148, _1239150)), tc_fun(_1239150, tc_fun(tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_HOL_Obool)), _1239148), hAPP(c_COMBB(tc_prod(_1239148, _1239150), tc_fun(tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_HOL_Obool), _1239150), c_member(tc_prod(_1239148, _1239150)))), c_Product__Type_OPair(_1239148, _1239150)))), _1239152)), hAPP(hAPP(c_COMBC(_1239148, tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_fun(_1239150, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1239150, tc_fun(tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_fun(_1239150, tc_HOL_Obool)), _1239148), c_COMBC(_1239150, tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1239150, tc_prod(_1239148, _1239150)), tc_fun(_1239150, tc_fun(tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_HOL_Obool)), _1239148), hAPP(c_COMBB(tc_prod(_1239148, _1239150), tc_fun(tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool), tc_HOL_Obool), _1239150), c_member(tc_prod(_1239148, _1239150)))), c_Product__Type_OPair(_1239148, _1239150)))), _1239154))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1239148, _1239150), tc_HOL_Obool)), _1239152), _1239154)))], (25292 ^ _777081) ^ [_1239749, _1239751, _1239753, _1239755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool)), _1239753), _1239755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239749, tc_fun(_1239751, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1239749, tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_fun(_1239751, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1239751, tc_fun(tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_fun(_1239751, tc_HOL_Obool)), _1239749), c_COMBC(_1239751, tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1239751, tc_prod(_1239749, _1239751)), tc_fun(_1239751, tc_fun(tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_HOL_Obool)), _1239749), hAPP(c_COMBB(tc_prod(_1239749, _1239751), tc_fun(tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_HOL_Obool), _1239751), c_member(tc_prod(_1239749, _1239751)))), c_Product__Type_OPair(_1239749, _1239751)))), _1239753)), hAPP(hAPP(c_COMBC(_1239749, tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_fun(_1239751, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1239751, tc_fun(tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_fun(_1239751, tc_HOL_Obool)), _1239749), c_COMBC(_1239751, tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1239751, tc_prod(_1239749, _1239751)), tc_fun(_1239751, tc_fun(tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_HOL_Obool)), _1239749), hAPP(c_COMBB(tc_prod(_1239749, _1239751), tc_fun(tc_fun(tc_prod(_1239749, _1239751), tc_HOL_Obool), tc_HOL_Obool), _1239751), c_member(tc_prod(_1239749, _1239751)))), c_Product__Type_OPair(_1239749, _1239751)))), _1239755))))], (25298 ^ _777081) ^ [_1240383, _1240385, _1240387, _1240389, _1240391, _1240393] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1240383, tc_fun(_1240385, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1240383, tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_fun(_1240385, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1240385, tc_fun(tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_fun(_1240385, tc_HOL_Obool)), _1240383), c_COMBC(_1240385, tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1240385, tc_prod(_1240383, _1240385)), tc_fun(_1240385, tc_fun(tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_HOL_Obool)), _1240383), hAPP(c_COMBB(tc_prod(_1240383, _1240385), tc_fun(tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_HOL_Obool), _1240385), c_member(tc_prod(_1240383, _1240385)))), c_Product__Type_OPair(_1240383, _1240385)))), _1240387)), hAPP(hAPP(c_COMBC(_1240383, tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_fun(_1240385, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1240385, tc_fun(tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_fun(_1240385, tc_HOL_Obool)), _1240383), c_COMBC(_1240385, tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1240385, tc_prod(_1240383, _1240385)), tc_fun(_1240385, tc_fun(tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_HOL_Obool)), _1240383), hAPP(c_COMBB(tc_prod(_1240383, _1240385), tc_fun(tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool), tc_HOL_Obool), _1240385), c_member(tc_prod(_1240383, _1240385)))), c_Product__Type_OPair(_1240383, _1240385)))), _1240389)), _1240391), _1240393)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1240383, _1240385)), hAPP(hAPP(c_Product__Type_OPair(_1240383, _1240385), _1240391), _1240393)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1240383, _1240385), tc_HOL_Obool)), _1240387), _1240389))))], (25304 ^ _777081) ^ [_1241040, _1241042, _1241044, _1241046, _1241048, _1241050] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1241040, _1241042)), hAPP(hAPP(c_Product__Type_OPair(_1241040, _1241042), _1241048), _1241050)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool)), _1241044), _1241046))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1241040, tc_fun(_1241042, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1241040, tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_fun(_1241042, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1241042, tc_fun(tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_fun(_1241042, tc_HOL_Obool)), _1241040), c_COMBC(_1241042, tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1241042, tc_prod(_1241040, _1241042)), tc_fun(_1241042, tc_fun(tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_HOL_Obool)), _1241040), hAPP(c_COMBB(tc_prod(_1241040, _1241042), tc_fun(tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_HOL_Obool), _1241042), c_member(tc_prod(_1241040, _1241042)))), c_Product__Type_OPair(_1241040, _1241042)))), _1241044)), hAPP(hAPP(c_COMBC(_1241040, tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_fun(_1241042, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1241042, tc_fun(tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_fun(_1241042, tc_HOL_Obool)), _1241040), c_COMBC(_1241042, tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1241042, tc_prod(_1241040, _1241042)), tc_fun(_1241042, tc_fun(tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_HOL_Obool)), _1241040), hAPP(c_COMBB(tc_prod(_1241040, _1241042), tc_fun(tc_fun(tc_prod(_1241040, _1241042), tc_HOL_Obool), tc_HOL_Obool), _1241042), c_member(tc_prod(_1241040, _1241042)))), c_Product__Type_OPair(_1241040, _1241042)))), _1241046)), _1241048), _1241050)))], (25310 ^ _777081) ^ [_1241703, _1241705, _1241707, _1241709] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1241705, _1241703)), _1241707), _1241709) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1241705), hAPP(hAPP(c_COMBC(_1241705, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1241703, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1241705), c_Smallcheck_Osmall__class_Osmall(_1241703)), hAPP(hAPP(c_COMBB(tc_fun(_1241703, tc_prod(_1241705, _1241703)), tc_fun(_1241703, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1241705), hAPP(c_COMBB(tc_prod(_1241705, _1241703), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1241703), _1241707)), c_Product__Type_OPair(_1241705, _1241703)))), _1241709)), _1241709)), class_Smallcheck_Osmall(_1241703), class_Smallcheck_Osmall(_1241705)], (25320 ^ _777081) ^ [_1241988, _1241990, _1241992, _1241994, _1241996, _1241998] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1241988, _1241990), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1241992), _1241994))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1241988, _1241990), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1241996), _1241998))), -(_1241990 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1241994 = _1241998)], (25334 ^ _777081) ^ [_1242192, _1242194, _1242196, _1242198, _1242200, _1242202] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1242192, _1242194), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1242196), _1242198))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1242192, _1242194), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1242200), _1242202))), -(_1242194 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1242196 = _1242200)], (25348 ^ _777081) ^ [_1242396, _1242398, _1242400] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1242396, _1242396), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1242398), _1242400))), -(_1242396 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1242400 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25358 ^ _777081) ^ [_1242508] : [-(_1242508 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1242508), 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)))))], (25364 ^ _777081) ^ [_1242547, _1242549, _1242551] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1242547, _1242547), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1242549), _1242551))), -(_1242547 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1242549 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25374 ^ _777081) ^ [_1242663, _1242665, _1242667, _1242669] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1242663, _1242665), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1242667), _1242669))), -(_1242665 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242663, _1242665) = _1242669)], (25384 ^ _777081) ^ [_1242789, _1242791, _1242793, _1242795] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1242789, _1242791), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1242793), _1242795))), -(_1242791 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1242789), _1242791) = _1242793)], (25394 ^ _777081) ^ [_1242919, _1242921] : [-(c_Divides_Odivmod__int(_1242919, _1242921) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1242919), _1242921)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242919, _1242921)))], (25396 ^ _777081) ^ [_1242959, _1242961] : [-(_1242959 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1242961, _1242959), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1242961), _1242959)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1242961, _1242959)))))], (25402 ^ _777081) ^ [_1243016, _1243018, _1243020, _1243022, _1243024, _1243026, _1243028] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1243016, _1243018), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1243020), _1243022))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1243024, _1243018), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1243026), _1243028))), -(_1243018 = 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), _1243016), _1243024), _1243018), 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), _1243020), _1243026)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1243022), _1243028)), _1243018))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1243022), _1243028), _1243018)))))], (25416 ^ _777081) ^ [_1243326, _1243328, _1243330, _1243332] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1243326, _1243328), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1243330), _1243332))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243326), _1243328), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1243332), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243330)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243330)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1243332), 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), _1243328), _1243332))))))], (25422 ^ _777081) ^ [_1243553, _1243555, _1243557, _1243559] : [_1243553 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1243555), _1243557)), _1243559), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1243553, _1243555), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1243557), _1243559)))), 25429 ^ _777081 : [(25430 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243555)))], (25432 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243559), _1243555))]], 25437 ^ _777081 : [(25438 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243555))], (25440 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243555), _1243559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1243559), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (25448 ^ _777081) ^ [_1244015, _1244017, _1244019, _1244021, _1244023] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1244015, _1244017), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1244019), _1244021))), -(_1244017 = 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), _1244023), _1244015), _1244017), 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), _1244023), _1244019)), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244023), _1244021)), _1244017))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244023), _1244021), _1244017)))))], (25458 ^ _777081) ^ [_1244237] : [-(c_Divides_Oadjust(_1244237) = 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)), _1244237))))), 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)), _1244237))))), 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))))))))], (25460 ^ _777081) ^ [_1244298, _1244300, _1244302, _1244304, _1244306, _1244308, _1244310] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1244298, _1244300)), hAPP(hAPP(c_Product__Type_OPair(_1244298, _1244300), _1244302), _1244304)), _1244306)), -(hBOOL(hAPP(hAPP(c_member(_1244308), hAPP(hAPP(_1244310, _1244302), _1244304)), hAPP(c_Set_Oimage(tc_prod(_1244298, _1244300), _1244308, hAPP(c_Product__Type_Oprod_Oprod__case(_1244298, _1244300, _1244308), _1244310)), _1244306))))], (25466 ^ _777081) ^ [_1244492, _1244494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244492), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1244494, _1244492) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1244494), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1244492)))], (25472 ^ _777081) ^ [_1244598, _1244600] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1244598), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 25475 ^ _777081 : [(25476 ^ _777081) ^ [] : [25477 ^ _777081 : [(25478 ^ _777081) ^ [] : [_1244600 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (25480 ^ _777081) ^ [] : [_1244598 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1244600, _1244598) = 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)))], (25484 ^ _777081) ^ [] : [-(c_Nitpick_Onorm__frac(_1244600, _1244598) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1244600), _1244598)), 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)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1244600))), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1244598)))), -(_1244600 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1244598 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (25494 ^ _777081) ^ [_1244896] : [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), _1244896))), 25497 ^ _777081 : [(25498 ^ _777081) ^ [] : [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), _1244896)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244896)) = 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), _1244896))))], (25504 ^ _777081) ^ [] : [-(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), _1244896))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244896)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1244896)), 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), _1244896)))))]]], (25510 ^ _777081) ^ [_1245186, _1245188, _1245190, _1245192, _1245194] : [hBOOL(hAPP(hAPP(_1245186, _1245188), _1245190)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1245192, _1245194, tc_HOL_Obool), _1245186), hAPP(hAPP(c_Product__Type_OPair(_1245192, _1245194), _1245188), _1245190))))], (25516 ^ _777081) ^ [_1245315, _1245317, _1245319, _1245321, _1245323, _1245325] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1245315, tc_fun(_1245317, tc_HOL_Obool))), _1245319), _1245321), _1245323), _1245325)), -(hBOOL(hAPP(hAPP(_1245319, _1245323), _1245325))), -(hBOOL(hAPP(hAPP(_1245321, _1245323), _1245325)))], (25526 ^ _777081) ^ [_1245473, _1245475, _1245477, _1245479, _1245481, _1245483] : [25527 ^ _777081 : [(25528 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1245473, _1245475), _1245477))], (25530 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1245479, _1245475), _1245477))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1245481, tc_fun(_1245483, tc_HOL_Obool))), _1245479), _1245473), _1245475), _1245477)))], (25534 ^ _777081) ^ [_1245656, _1245658, _1245660, _1245662, _1245664, _1245666] : [hBOOL(hAPP(hAPP(_1245656, _1245658), _1245660)), hBOOL(hAPP(hAPP(_1245662, _1245658), _1245660)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1245664, tc_fun(_1245666, tc_HOL_Obool))), _1245656), _1245662), _1245658), _1245660)))], (25544 ^ _777081) ^ [_1245859, _1245861, _1245863, _1245865, _1245867, _1245869] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1245859, tc_fun(_1245861, tc_HOL_Obool))), _1245863), _1245865), _1245867), _1245869)), 25547 ^ _777081 : [(25548 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1245863, _1245867), _1245869)))], (25550 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1245865, _1245867), _1245869)))]]], (25552 ^ _777081) ^ [_1246032, _1246034, _1246036, _1246038, _1246040, _1246042, _1246044] : [hBOOL(hAPP(hAPP(c_member(_1246032), _1246034), hAPP(hAPP(_1246036, _1246038), _1246040))), -(hBOOL(hAPP(hAPP(c_member(_1246032), _1246034), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1246042, _1246044, tc_fun(_1246032, tc_HOL_Obool)), _1246036), hAPP(hAPP(c_Product__Type_OPair(_1246042, _1246044), _1246038), _1246040)))))], (25558 ^ _777081) ^ [_1246203, _1246205, _1246207, _1246209, _1246211] : [hBOOL(hAPP(hAPP(_1246203, _1246205), _1246207)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1246209, _1246211, tc_HOL_Obool), _1246203), hAPP(hAPP(c_Product__Type_OPair(_1246209, _1246211), _1246205), _1246207))))], (25564 ^ _777081) ^ [_1246350, _1246352, _1246354, _1246356] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1246350, tc_fun(_1246352, tc_HOL_Obool))), _1246354), _1246356))], (25566 ^ _777081) ^ [_1246392, _1246394, _1246396] : [-(c_Fun_Oinj__on(tc_prod(_1246392, _1246394), tc_prod(_1246394, _1246392), hAPP(c_Product__Type_Oprod_Oprod__case(_1246392, _1246394, tc_prod(_1246394, _1246392)), hAPP(c_COMBC(_1246394, _1246392, tc_prod(_1246394, _1246392)), c_Product__Type_OPair(_1246394, _1246392))), _1246396))], (25568 ^ _777081) ^ [_1246450, _1246452, _1246454, _1246456, _1246458, _1246460, _1246462] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1246450, _1246452, tc_fun(_1246454, tc_HOL_Obool)), _1246456), hAPP(hAPP(c_Product__Type_OPair(_1246450, _1246452), _1246458), _1246460)), _1246462)), -(hBOOL(hAPP(hAPP(hAPP(_1246456, _1246458), _1246460), _1246462)))], (25574 ^ _777081) ^ [_1246601, _1246603, _1246605, _1246607, _1246609, _1246611] : [hBOOL(hAPP(hAPP(_1246601, _1246603), _1246605)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1246607, tc_fun(_1246609, tc_HOL_Obool))), _1246601), _1246611), _1246603), _1246605)))], (25580 ^ _777081) ^ [_1246734, _1246736, _1246738, _1246740, _1246742, _1246744] : [hBOOL(hAPP(hAPP(_1246734, _1246736), _1246738)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1246740, tc_fun(_1246742, tc_HOL_Obool))), _1246744), _1246734), _1246736), _1246738)))], (25586 ^ _777081) ^ [_1246867, _1246869, _1246871] : [_1246867 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1246869, _1246869), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1246869, _1246869), tc_HOL_Obool)), _1246867), _1246871)))], (25592 ^ _777081) ^ [_1246988, _1246990, _1246992, _1246994, _1246996, _1246998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1246988, tc_fun(_1246990, tc_HOL_Obool))), _1246992), _1246994)), hBOOL(hAPP(hAPP(_1246992, _1246996), _1246998)), -(hBOOL(hAPP(hAPP(_1246994, _1246996), _1246998)))], (25602 ^ _777081) ^ [_1247179, _1247181, _1247183, _1247185, _1247187, _1247189] : [hBOOL(hAPP(hAPP(_1247179, _1247181), _1247183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1247185, tc_fun(_1247187, tc_HOL_Obool))), _1247179), _1247189)), -(hBOOL(hAPP(hAPP(_1247189, _1247181), _1247183)))], (25612 ^ _777081) ^ [_1247370, _1247372, _1247374, _1247376, _1247378, _1247380] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1247370, tc_fun(_1247372, tc_HOL_Obool))), _1247374), _1247376), _1247378), _1247380)), -(hBOOL(hAPP(hAPP(_1247374, _1247378), _1247380)))], (25618 ^ _777081) ^ [_1247503, _1247505, _1247507, _1247509, _1247511, _1247513] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1247503, tc_fun(_1247505, tc_HOL_Obool))), _1247507), _1247509), _1247511), _1247513)), -(hBOOL(hAPP(hAPP(_1247509, _1247511), _1247513)))], (25624 ^ _777081) ^ [_1247654, _1247656, _1247658] : [hBOOL(hAPP(_1247654, 25625 ^ [_1247654, _1247656, _1247658])), 25628 ^ _777081 : [(25629 ^ _777081) ^ [_1247765, _1247767] : [-(hBOOL(hAPP(_1247654, hAPP(hAPP(c_Product__Type_OPair(_1247656, _1247658), _1247767), _1247765))))]]], (25631 ^ _777081) ^ [_1247801, _1247803, _1247805] : [hBOOL(hAPP(_1247801, hAPP(hAPP(c_Product__Type_OPair(_1247803, _1247805), 25632 ^ [_1247801, _1247803, _1247805]), 25633 ^ [_1247801, _1247803, _1247805]))), 25636 ^ _777081 : [(25637 ^ _777081) ^ [_1247948] : [-(hBOOL(hAPP(_1247801, _1247948)))]]], (25639 ^ _777081) ^ [_1248006, _1248008, _1248010, _1248012, _1248014, _1248016] : [hAPP(hAPP(c_Product__Type_OPair(_1248006, _1248008), _1248010), _1248012) = hAPP(hAPP(c_Product__Type_OPair(_1248006, _1248008), _1248014), _1248016), 25642 ^ _777081 : [(25643 ^ _777081) ^ [] : [-(_1248010 = _1248014)], (25645 ^ _777081) ^ [] : [-(_1248012 = _1248016)]]], (25647 ^ _777081) ^ [_1248149, _1248151, _1248153, _1248155, _1248157, _1248159] : [-(hAPP(hAPP(c_Product__Type_OPair(_1248149, _1248151), _1248153), _1248155) = hAPP(hAPP(c_Product__Type_OPair(_1248149, _1248151), _1248157), _1248159)), _1248153 = _1248157, _1248155 = _1248159], (25657 ^ _777081) ^ [_1248332, _1248334, _1248336, _1248338, _1248340, _1248342] : [hAPP(hAPP(c_Product__Type_OPair(_1248332, _1248334), _1248336), _1248338) = hAPP(hAPP(c_Product__Type_OPair(_1248332, _1248334), _1248340), _1248342), 25660 ^ _777081 : [(25661 ^ _777081) ^ [] : [-(_1248336 = _1248340)], (25663 ^ _777081) ^ [] : [-(_1248338 = _1248342)]]], (25665 ^ _777081) ^ [_1248483, _1248485, _1248487, _1248489, _1248491, _1248493] : [_1248483 = _1248485, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1248487, _1248489, _1248491), _1248493), _1248483) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1248487, _1248489, _1248491), _1248493), _1248485))], (25671 ^ _777081) ^ [_1248608, _1248610] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1248608), 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)), _1248610)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1248608, _1248610), c_Divides_OnegDivAlg(_1248608, _1248610))))], (25681 ^ _777081) ^ [_1248767, _1248769, _1248771, _1248773, _1248775, _1248777, _1248779, _1248781] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1248767, _1248769, _1248771), _1248773), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1248775, _1248777, tc_prod(_1248767, _1248769)), _1248779), _1248781)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1248775, _1248777, _1248771), hAPP(hAPP(c_COMBB(tc_fun(_1248777, tc_prod(_1248767, _1248769)), tc_fun(_1248777, _1248771), _1248775), hAPP(c_COMBB(tc_prod(_1248767, _1248769), _1248771, _1248777), hAPP(c_Product__Type_Oprod_Oprod__case(_1248767, _1248769, _1248771), _1248773))), _1248779)), _1248781))], (25683 ^ _777081) ^ [_1248873, _1248875, _1248877, _1248879, _1248881, _1248883] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1248873, _1248875, _1248877), _1248879), hAPP(hAPP(c_Product__Type_OPair(_1248873, _1248875), _1248881), _1248883)) = hAPP(hAPP(_1248879, _1248881), _1248883))], (25685 ^ _777081) ^ [_1248931, _1248933, _1248935, _1248937, _1248939, _1248941] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1248931, _1248933, _1248935), _1248937), hAPP(hAPP(c_Product__Type_OPair(_1248931, _1248933), _1248939), _1248941)) = hAPP(hAPP(_1248937, _1248939), _1248941))], (25687 ^ _777081) ^ [_1248989, _1248991, _1248993, _1248995, _1248997] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1248989, _1248991, tc_HOL_Obool), _1248993), hAPP(hAPP(c_Product__Type_OPair(_1248989, _1248991), _1248995), _1248997))), -(hBOOL(hAPP(hAPP(_1248993, _1248995), _1248997)))], (25693 ^ _777081) ^ [_1249118, _1249120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1249118), 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)), _1249120)), -(c_Divides_OnegDivAlg(_1249118, _1249120) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1249118), _1249120)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1249118, _1249120)))], (25703 ^ _777081) ^ [_1249299] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1249299) = 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), _1249299), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (25705 ^ _777081) ^ [_1249334, _1249336, _1249338, _1249340] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1249334, _1249336, _1249338), hAPP(hAPP(c_COMBB(tc_fun(_1249336, tc_prod(_1249334, _1249336)), tc_fun(_1249336, _1249338), _1249334), hAPP(c_COMBB(tc_prod(_1249334, _1249336), _1249338, _1249336), _1249340)), c_Product__Type_OPair(_1249334, _1249336))) = _1249340)], (25707 ^ _777081) ^ [_1249402, _1249404, _1249406, _1249408] : [-(c_HOL_OThe(tc_prod(_1249402, _1249404), hAPP(c_Product__Type_Oprod_Oprod__case(_1249402, _1249404, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1249402, tc_fun(_1249404, tc_HOL_Obool), tc_fun(_1249404, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1249404, tc_HOL_Obool), tc_fun(_1249404, tc_HOL_Obool)), _1249402), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1249404)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1249402), c_fconj), hAPP(c_fequal, _1249406)))), hAPP(c_fequal, _1249408)))) = hAPP(hAPP(c_Product__Type_OPair(_1249402, _1249404), _1249406), _1249408))], (25709 ^ _777081) ^ [_1249508, _1249510, _1249512] : [-(c_HOL_OThe(tc_prod(_1249508, _1249510), _1249512) = c_HOL_OThe(tc_prod(_1249508, _1249510), hAPP(c_Product__Type_Oprod_Oprod__case(_1249508, _1249510, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1249510, tc_prod(_1249508, _1249510)), tc_fun(_1249510, tc_HOL_Obool), _1249508), hAPP(c_COMBB(tc_prod(_1249508, _1249510), tc_HOL_Obool, _1249510), _1249512)), c_Product__Type_OPair(_1249508, _1249510)))))], (25711 ^ _777081) ^ [_1249595, _1249597] : [25712 ^ _777081 : [(25713 ^ _777081) ^ [] : [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), _1249595), _1249597)))], (25715 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249597), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1249595, _1249597) = 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), _1249595), _1249597)))], (25719 ^ _777081) ^ [_1249754, _1249756] : [-(c_Divides_OnegDivAlg(_1249754, _1249756) = hAPP(c_Divides_Oadjust(_1249756), c_Divides_OnegDivAlg(_1249754, 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)))), _1249756)))), -(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), _1249754), _1249756)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249756), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25729 ^ _777081) ^ [_1249826, _1249828] : [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), _1249826))), 25732 ^ _777081 : [(25733 ^ _777081) ^ [] : [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), _1249828)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1249826)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1249828), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1249826)) = 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), _1249828)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1249826))))], (25739 ^ _777081) ^ [] : [-(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), _1249828)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1249826))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1249828), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1249826)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1249826)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1249828), 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), _1249826)))))]]], (25745 ^ _777081) ^ [_1250174, _1250176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250174)), 25748 ^ _777081 : [(25749 ^ _777081) ^ [] : [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), _1250176), _1250174))), -(c_Divides_OnegDivAlg(_1250176, _1250174) = 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), _1250176), _1250174)))], (25755 ^ _777081) ^ [] : [-(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), _1250176), _1250174)))), -(c_Divides_OnegDivAlg(_1250176, _1250174) = hAPP(c_Divides_Oadjust(_1250174), c_Divides_OnegDivAlg(_1250176, 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)))), _1250174))))]]], (25761 ^ _777081) ^ [_1250462, _1250464, _1250466, _1250468, _1250470] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1250462, _1250464, _1250466), _1250468), _1250470)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1250462, _1250464)), hAPP(hAPP(c_Product__Type_OPair(_1250462, _1250464), _1250468), _1250470)), _1250466)))], (25767 ^ _777081) ^ [_1250597, _1250599, _1250601, _1250603, _1250605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1250597, _1250599)), hAPP(hAPP(c_Product__Type_OPair(_1250597, _1250599), _1250603), _1250605)), _1250601)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1250597, _1250599, _1250601), _1250603), _1250605)))], (25773 ^ _777081) ^ [_1250738, _1250740] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1250738, _1250740) = hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral, _1250738), _1250740)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1250738, _1250740)))], (25775 ^ _777081) ^ [_1250797, _1250799] : [c_Nitpick_Orefl_H(_1250797, _1250799), 25778 ^ _777081 : [(25779 ^ _777081) ^ [_1250875] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1250797, _1250797)), hAPP(hAPP(c_Product__Type_OPair(_1250797, _1250797), _1250875), _1250875)), _1250799)))]]], (25781 ^ _777081) ^ [_1250917, _1250919] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1250917, _1250917)), hAPP(hAPP(c_Product__Type_OPair(_1250917, _1250917), 25782 ^ [_1250917, _1250919]), 25782 ^ [_1250917, _1250919])), _1250919)), -(c_Nitpick_Orefl_H(_1250917, _1250919))], (25788 ^ _777081) ^ [_1251084] : [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), _1251084))), 25791 ^ _777081 : [(25792 ^ _777081) ^ [] : [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), _1251084))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251084)) = 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)))], (25798 ^ _777081) ^ [] : [-(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), _1251084)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251084)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251084)), 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), _1251084)))))]]], (25804 ^ _777081) ^ [_1251344] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1251344) = 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)))], (25806 ^ _777081) ^ [_1251370, _1251372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251372)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1251370, _1251372), c_Divides_OposDivAlg(_1251370, _1251372))))], (25816 ^ _777081) ^ [_1251523, _1251525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251525)), -(c_Divides_OposDivAlg(_1251523, _1251525) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1251523), _1251525)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1251523, _1251525)))], (25826 ^ _777081) ^ [_1251698, _1251700] : [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), _1251698))), 25829 ^ _777081 : [(25830 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251700)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251698))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251700), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251698)) = 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), _1251700)))], (25836 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251700)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251698)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251700), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251698)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251698)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1251700), 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), _1251698)))))]]], (25842 ^ _777081) ^ [_1252016, _1252018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252016)), 25845 ^ _777081 : [(25846 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1252018), _1252016)), -(c_Divides_OposDivAlg(_1252018, _1252016) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252018))], (25852 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1252018), _1252016))), -(c_Divides_OposDivAlg(_1252018, _1252016) = hAPP(c_Divides_Oadjust(_1252016), c_Divides_OposDivAlg(_1252018, 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)))), _1252016))))]]], (25858 ^ _777081) ^ [_1252265, _1252267] : [25859 ^ _777081 : [(25860 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1252265), _1252267))], (25862 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252267), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1252265, _1252267) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252265))], (25866 ^ _777081) ^ [_1252406, _1252408] : [-(c_Divides_OposDivAlg(_1252406, _1252408) = hAPP(c_Divides_Oadjust(_1252408), c_Divides_OposDivAlg(_1252406, 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)))), _1252408)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1252406), _1252408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252408), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25902 ^ _777081) ^ [_1252854, _1252856] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252854))), 25905 ^ _777081 : [(25906 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252856)), -(c_Divides_Odivmod__int(_1252854, _1252856) = c_Divides_OnegDivAlg(_1252854, _1252856))], (25912 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252856))), -(c_Divides_Odivmod__int(_1252854, _1252856) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1252854), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1252856))))]]], (25876 ^ _777081) ^ [_1252484, _1252486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252484)), 25879 ^ _777081 : [(25880 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252486)), -(c_Divides_Odivmod__int(_1252484, _1252486) = c_Divides_OposDivAlg(_1252484, _1252486))], (25886 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252486))), 25889 ^ _777081 : [(25890 ^ _777081) ^ [] : [_1252484 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1252484, _1252486) = 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)))], (25896 ^ _777081) ^ [] : [-(_1252484 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1252484, _1252486) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1252484), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1252486))))]]]]], (25918 ^ _777081) ^ [_1253082, _1253084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1253082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253082), _1253084)), -(c_Divides_Odivmod__nat(_1253084, _1253082) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1253084), _1253082)), _1253082))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1253084), _1253082), _1253082)))], (25928 ^ _777081) ^ [_1253302, _1253304] : [_1253302 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1253302, _1253304) = 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)))], (25934 ^ _777081) ^ [_1253380, _1253382] : [-(_1253380 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25937 ^ _777081 : [(25938 ^ _777081) ^ [] : [_1253382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1253380, _1253382) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253380))], (25944 ^ _777081) ^ [] : [-(_1253382 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1253380, _1253382) = 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, _1253382))), 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)), _1253382)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253380))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1253382), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1253380), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1253380, _1253382)), 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), _1253382))))), c_Divides_Opdivmod(_1253380, _1253382)))))]]], (25950 ^ _777081) ^ [_1253749, _1253751] : [_1253749 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1253749, _1253751) = 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)))], (25956 ^ _777081) ^ [_1253827, _1253829] : [-(_1253827 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25959 ^ _777081 : [(25960 ^ _777081) ^ [] : [_1253829 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1253827, _1253829) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253827))], (25966 ^ _777081) ^ [] : [-(_1253829 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1253827, _1253829) = 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, _1253829))), 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, _1253827)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1253829))), c_Divides_Opdivmod(_1253827, _1253829)), 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), _1253829))))), c_Divides_Opdivmod(_1253827, _1253829)))))]]], (25972 ^ _777081) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (25974 ^ _777081) ^ [_1254157, _1254159, _1254161, _1254163, _1254165, _1254167] : [-(hAPP(c_Product__Type_Oapsnd(_1254157, _1254159, _1254161, _1254163), hAPP(hAPP(c_Product__Type_OPair(_1254161, _1254157), _1254165), _1254167)) = hAPP(hAPP(c_Product__Type_OPair(_1254161, _1254159), _1254165), hAPP(_1254163, _1254167)))], (25976 ^ _777081) ^ [_1254219] : [-(c_Divides_Odivmod__nat(_1254219, 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)), _1254219))], (25978 ^ _777081) ^ [_1254248, _1254250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1254248), _1254250)), -(c_Divides_Odivmod__nat(_1254248, _1254250) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254248))], (25984 ^ _777081) ^ [_1254347, _1254349] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1254347), _1254349)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1254347), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1254349)))], (25986 ^ _777081) ^ [_1254390, _1254392] : [-(c_Divides_Odivmod__nat(_1254390, _1254392) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1254390), _1254392)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1254390, _1254392)))], (25988 ^ _777081) ^ [_1254434, _1254436, _1254438] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1254434), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1254436)), _1254438)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1254434, _1254436), hAPP(c_Divides_OnegateSnd, _1254438))))], (25994 ^ _777081) ^ [_1254560, _1254562] : [25995 ^ _777081 : [(25996 ^ _777081) ^ [] : [_1254560 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25998 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1254562), _1254560))]], -(c_Divides_Odivmod__nat(_1254562, _1254560) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254562))], (26002 ^ _777081) ^ [_1254691, _1254693] : [-(c_Divides_Odivmod__nat(_1254693, _1254691) = 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), _1254693), _1254691), _1254691))), -(_1254691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1254693), _1254691)))], (26012 ^ _777081) ^ [_1254756, _1254758] : [-(c_Divides_Opdivmod(_1254756, _1254758) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254756)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254758))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254756), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254758))))], (26014 ^ _777081) ^ [_1254821, _1254823] : [_1254821 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1254823, _1254821) = 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), _1254823)))], (26020 ^ _777081) ^ [_1254910, _1254912] : [-(_1254910 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1254912, _1254910) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254912), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1254910)))], (26026 ^ _777081) ^ [_1254960, _1254962, _1254964, _1254966, _1254968] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1254960, _1254962), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1254964), _1254966))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254968)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1254960, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1254962), _1254968)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1254964), _1254968)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1254962), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1254964, _1254968))), _1254966)))))], (26040 ^ _777081) ^ [_1255267, _1255269, _1255271, _1255273, _1255275] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1255267, _1255269), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1255271), _1255273))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1255269)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1255275), _1255267), _1255269), 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), _1255275), _1255271)), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1255275), _1255273)), _1255269))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1255275), _1255273), _1255269)))))], (26050 ^ _777081) ^ [_1255536, _1255538] : [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), _1255536), _1255538))), 26053 ^ _777081 : [(26054 ^ _777081) ^ [] : [26055 ^ _777081 : [(26056 ^ _777081) ^ [] : [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), _1255536), _1255538)))], (26058 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1255538), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1255536, _1255538) = 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), _1255536), _1255538)))], (26062 ^ _777081) ^ [] : [-(c_Divides_OnegDivAlg(_1255536, _1255538) = hAPP(c_Divides_Oadjust(_1255538), c_Divides_OnegDivAlg(_1255536, 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)))), _1255538)))), -(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), _1255536), _1255538)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1255538), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (26072 ^ _777081) ^ [_1255883, _1255885, _1255887] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1255883), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1255885), _1255887)))), 26075 ^ _777081 : [(26076 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255885), _1255887)), -(c_Smallcheck_Osmall_H(_1255883, _1255885, _1255887) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (26082 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255885), _1255887))), -(c_Smallcheck_Osmall_H(_1255883, _1255885, _1255887) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1255883, _1255885, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1255887), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1255883, _1255887)))]]], (26098 ^ _777081) ^ [_1256373, _1256375, _1256377] : [26100 ^ _777081 : [(26101 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1256375, 26099 ^ [_1256373, _1256375, _1256377]), _1256377)))], (26103 ^ _777081) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1256373, _1256375), 26099 ^ [_1256373, _1256375, _1256377]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1256373, _1256375), _1256377)))], (26088 ^ _777081) ^ [_1256187, _1256189, _1256191] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1256187, _1256189), _1256191)), 26091 ^ _777081 : [(26092 ^ _777081) ^ [_1256272] : [hBOOL(hAPP(hAPP(_1256189, _1256272), _1256191)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1256187, _1256189), _1256272)))]]], (26117 ^ _777081) ^ [_1256763, _1256765, _1256767] : [26119 ^ _777081 : [(26120 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1256765, 26118 ^ [_1256763, _1256765, _1256767]), _1256767)))], (26122 ^ _777081) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1256763, _1256765), 26118 ^ [_1256763, _1256765, _1256767]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1256763, _1256765), _1256767)))], (26107 ^ _777081) ^ [_1256577, _1256579, _1256581] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1256577, _1256579), _1256581)), 26110 ^ _777081 : [(26111 ^ _777081) ^ [_1256662] : [hBOOL(hAPP(hAPP(_1256579, _1256662), _1256581)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1256577, _1256579), _1256662)))]]], (26126 ^ _777081) ^ [_1256949, _1256951, _1256953, _1256955] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1256949, _1256951), _1256953)), hBOOL(hAPP(hAPP(_1256951, _1256955), _1256953)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1256949, _1256951), _1256955)))], (26136 ^ _777081) ^ [_1257116, _1257118, _1257120, _1257122] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1257116, _1257118), _1257120)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1257116, _1257118), _1257122)), -(_1257120 = _1257122)], (26146 ^ _777081) ^ [_1257273, _1257275] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1257273, _1257275), c_Divides_Odivmod__nat(_1257273, _1257275))))], (26148 ^ _777081) ^ [_1257306, _1257308, _1257310] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1257306, _1257308), _1257310)), -(c_Divides_Odivmod__nat(_1257306, _1257308) = _1257310)], (26154 ^ _777081) ^ [_1257401, _1257403] : [-(c_Divides_Odivmod__nat(_1257401, _1257403) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1257401, _1257403)))], (26156 ^ _777081) ^ [_1257435, _1257437, _1257439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257435, tc_fun(_1257435, tc_HOL_Obool))), _1257437), _1257439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257435, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1257435, _1257439)), c_Wellfounded_Oaccp(_1257435, _1257437))))], (26162 ^ _777081) ^ [_1257572, _1257574, _1257576, _1257578] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1257572, _1257574), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1257576), _1257578))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1257572, _1257574) = _1257578)], (26168 ^ _777081) ^ [_1257683, _1257685, _1257687, _1257689] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1257683, _1257685), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1257687), _1257689))), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1257683), _1257685) = _1257687)], (26174 ^ _777081) ^ [_1257798, _1257800] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1257798, _1257800), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1257798), _1257800)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1257798, _1257800)))))], (26176 ^ _777081) ^ [_1257844, _1257846, _1257848, _1257850, _1257852, _1257854, _1257856] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1257844, _1257846), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1257848), _1257850))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1257852, _1257846), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1257854), _1257856))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1257846)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1257844), _1257852), _1257846), 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), _1257848), _1257854)), hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1257850), _1257856)), _1257846))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1257850), _1257856), _1257846)))))], (26190 ^ _777081) ^ [_1258205, _1258207] : [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), _1258205), _1258207))), 26193 ^ _777081 : [(26194 ^ _777081) ^ [] : [26195 ^ _777081 : [(26196 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258205), _1258207))], (26198 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1258207), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1258205, _1258207) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258205))], (26202 ^ _777081) ^ [] : [-(c_Divides_OposDivAlg(_1258205, _1258207) = hAPP(c_Divides_Oadjust(_1258207), c_Divides_OposDivAlg(_1258205, 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)))), _1258207)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258205), _1258207))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1258207), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (26212 ^ _777081) ^ [_1258528, _1258530] : [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), _1258528), _1258530))), 26215 ^ _777081 : [(26216 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258530), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1258528, _1258530) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1258528), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1258530)))], (26222 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1258530), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 26225 ^ _777081 : [(26226 ^ _777081) ^ [] : [26227 ^ _777081 : [(26228 ^ _777081) ^ [] : [_1258528 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (26230 ^ _777081) ^ [] : [_1258530 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1258528, _1258530) = 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)))], (26234 ^ _777081) ^ [] : [-(c_Nitpick_Onorm__frac(_1258528, _1258530) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1258528), _1258530)), 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)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1258528))), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1258530)))), -(_1258528 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1258530 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (26244 ^ _777081) ^ [_1259020, _1259022, _1259024] : [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), _1259020), _1259022))), -(hBOOL(hAPP(hAPP(_1259024, _1259020), _1259022))), 26251 ^ _777081 : [(26252 ^ _777081) ^ [] : [-(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), 26249 ^ [_1259020, _1259022, _1259024]), 26250 ^ [_1259020, _1259022, _1259024]))))], (26264 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1259024, 26249 ^ [_1259020, _1259022, _1259024]), 26250 ^ [_1259020, _1259022, _1259024]))], (26254 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1259024, 26249 ^ [_1259020, _1259022, _1259024]), 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)))), 26250 ^ [_1259020, _1259022, _1259024])))), -(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), 26249 ^ [_1259020, _1259022, _1259024]), 26250 ^ [_1259020, _1259022, _1259024])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 26250 ^ [_1259020, _1259022, _1259024]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (26268 ^ _777081) ^ [_1259515, _1259517, _1259519, _1259521] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1259515), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1259517), _1259519)))), -(hBOOL(hAPP(hAPP(hAPP(_1259521, _1259515), _1259517), _1259519))), 26276 ^ _777081 : [(26277 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), 26273 ^ [_1259515, _1259517, _1259519, _1259521]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 26274 ^ [_1259515, _1259517, _1259519, _1259521]), 26275 ^ [_1259515, _1259517, _1259519, _1259521])))))], (26289 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1259521, 26273 ^ [_1259515, _1259517, _1259519, _1259521]), 26274 ^ [_1259515, _1259517, _1259519, _1259521]), 26275 ^ [_1259515, _1259517, _1259519, _1259521]))], (26279 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 26274 ^ [_1259515, _1259517, _1259519, _1259521]), 26275 ^ [_1259515, _1259517, _1259519, _1259521]))), hAPP(26273 ^ [_1259515, _1259517, _1259519, _1259521], 26275 ^ [_1259515, _1259517, _1259519, _1259521]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1259521, 26273 ^ [_1259515, _1259517, _1259519, _1259521]), 26274 ^ [_1259515, _1259517, _1259519, _1259521]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26275 ^ [_1259515, _1259517, _1259519, _1259521]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (26293 ^ _777081) ^ [_1260254, _1260256, _1260258] : [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), _1260254), _1260256))), -(hBOOL(hAPP(hAPP(_1260258, _1260254), _1260256))), 26300 ^ _777081 : [(26301 ^ _777081) ^ [] : [-(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), 26298 ^ [_1260254, _1260256, _1260258]), 26299 ^ [_1260254, _1260256, _1260258]))))], (26313 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1260258, 26298 ^ [_1260254, _1260256, _1260258]), 26299 ^ [_1260254, _1260256, _1260258]))], (26303 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1260258, 26298 ^ [_1260254, _1260256, _1260258]), 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)))), 26299 ^ [_1260254, _1260256, _1260258])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 26298 ^ [_1260254, _1260256, _1260258]), 26299 ^ [_1260254, _1260256, _1260258]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 26299 ^ [_1260254, _1260256, _1260258]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (26317 ^ _777081) ^ [_1260740, _1260742] : [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), _1260740), _1260742))), 26320 ^ _777081 : [(26321 ^ _777081) ^ [] : [_1260742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1260740, _1260742) = _1260740)], (26327 ^ _777081) ^ [] : [-(_1260742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1260740, _1260742) = c_Nitpick_Onat__gcd(_1260742, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1260740, _1260742)))]]], (26333 ^ _777081) ^ [_1260958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1260958)), 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), _1260958)) = 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), _1260958))))))], (26339 ^ _777081) ^ [_1261114, _1261116, _1261118, _1261120] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1261114, _1261114)), hAPP(hAPP(c_Product__Type_OPair(_1261114, _1261114), _1261116), _1261118)), hAPP(c_Wellfounded_Omeasure(_1261114), _1261120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1261120, _1261116)), hAPP(_1261120, _1261118))))], (26345 ^ _777081) ^ [_1261261, _1261263, _1261265, _1261267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1261267, _1261263)), hAPP(_1261267, _1261265))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1261261, _1261261)), hAPP(hAPP(c_Product__Type_OPair(_1261261, _1261261), _1261263), _1261265)), hAPP(c_Wellfounded_Omeasure(_1261261), _1261267))))], (26351 ^ _777081) ^ [_1261414, _1261416, _1261418, _1261420] : [-(hAPP(c_Product__Type_Osnd(_1261414, _1261416), hAPP(hAPP(c_Product__Type_OPair(_1261414, _1261416), _1261418), _1261420)) = _1261420)], (26353 ^ _777081) ^ [_1261458, _1261460, _1261462, _1261464, _1261466] : [hAPP(c_Product__Type_Osnd(_1261458, _1261460), hAPP(hAPP(c_Product__Type_OPair(_1261458, _1261460), _1261462), _1261464)) = _1261466, -(_1261464 = _1261466)], (26359 ^ _777081) ^ [_1261571, _1261573, _1261575, _1261577, _1261579] : [-(hAPP(c_Product__Type_Osnd(_1261571, _1261573), hAPP(c_Product__Type_Oapsnd(_1261575, _1261573, _1261571, _1261577), _1261579)) = hAPP(_1261577, hAPP(c_Product__Type_Osnd(_1261571, _1261575), _1261579)))], (26361 ^ _777081) ^ [_1261652, _1261654, _1261656, _1261658, _1261660, _1261662] : [hAPP(c_Product__Type_Oapsnd(_1261652, _1261654, _1261656, _1261658), _1261660) = hAPP(c_Product__Type_Oapsnd(_1261652, _1261654, _1261656, _1261662), _1261660), -(hAPP(_1261658, hAPP(c_Product__Type_Osnd(_1261656, _1261652), _1261660)) = hAPP(_1261662, hAPP(c_Product__Type_Osnd(_1261656, _1261652), _1261660)))], (26367 ^ _777081) ^ [_1261801, _1261803, _1261805, _1261807, _1261809, _1261811] : [hAPP(_1261807, hAPP(c_Product__Type_Osnd(_1261805, _1261801), _1261809)) = hAPP(_1261811, hAPP(c_Product__Type_Osnd(_1261805, _1261801), _1261809)), -(hAPP(c_Product__Type_Oapsnd(_1261801, _1261803, _1261805, _1261807), _1261809) = hAPP(c_Product__Type_Oapsnd(_1261801, _1261803, _1261805, _1261811), _1261809))], (26373 ^ _777081) ^ [_1261956, _1261958, _1261960] : [-(hAPP(c_Product__Type_Osnd(_1261956, _1261958), _1261960) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1261956, _1261958, _1261958), hAPP(c_COMBK(tc_fun(_1261958, _1261958), _1261956), c_COMBI(_1261958))), _1261960))], (26375 ^ _777081) ^ [_1262010, _1262012] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1262010, _1262012) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1262010, _1262012)))], (26377 ^ _777081) ^ [_1262045, _1262047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1262045), 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)), _1262047)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1262045, _1262047) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1262045, _1262047)))], (26387 ^ _777081) ^ [_1262208, _1262210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262210)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1262208, _1262210) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1262208, _1262210)))], (26397 ^ _777081) ^ [_1262365] : [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), _1262365))), -(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), _1262365)) = 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), _1262365))))], (26403 ^ _777081) ^ [_1262482, _1262484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1262482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1262484), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1262482, _1262484) = 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), _1262482), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1262484)))))], (26413 ^ _777081) ^ [_1262663, _1262665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1262663), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1262665), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1262663, _1262665) = 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), _1262663), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1262665)))))], (26423 ^ _777081) ^ [_1262850, _1262852, _1262854] : [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), _1262850), _1262852))), -(hBOOL(hAPP(hAPP(_1262854, _1262850), _1262852))), 26430 ^ _777081 : [(26431 ^ _777081) ^ [] : [-(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), 26428 ^ [_1262850, _1262852, _1262854]), 26429 ^ [_1262850, _1262852, _1262854]))))], (26439 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1262854, 26428 ^ [_1262850, _1262852, _1262854]), 26429 ^ [_1262850, _1262852, _1262854]))], (26433 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 26429 ^ [_1262850, _1262852, _1262854]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1262854, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 26428 ^ [_1262850, _1262852, _1262854])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 26429 ^ [_1262850, _1262852, _1262854]))))]]], (26443 ^ _777081) ^ [_1263323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1263323)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(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), _1263323)) = 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), _1263323))))))], (26449 ^ _777081) ^ [_1263456, _1263458, _1263460] : [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), _1263456), _1263458))), -(hBOOL(hAPP(hAPP(_1263460, _1263456), _1263458))), 26456 ^ _777081 : [(26457 ^ _777081) ^ [] : [-(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), 26454 ^ [_1263456, _1263458, _1263460]), 26455 ^ [_1263456, _1263458, _1263460]))))], (26465 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1263460, 26454 ^ [_1263456, _1263458, _1263460]), 26455 ^ [_1263456, _1263458, _1263460]))], (26459 ^ _777081) ^ [] : [-(26455 ^ [_1263456, _1263458, _1263460] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1263460, 26455 ^ [_1263456, _1263458, _1263460]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 26454 ^ [_1263456, _1263458, _1263460], 26455 ^ [_1263456, _1263458, _1263460]))))]]], (26469 ^ _777081) ^ [_1263878, _1263880, _1263882, _1263884, _1263886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1263878, _1263880)), hAPP(_1263878, _1263882))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1263884, _1263884)), hAPP(hAPP(c_Product__Type_OPair(_1263884, _1263884), _1263880), _1263882)), _1263886)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1263884, _1263884)), hAPP(hAPP(c_Product__Type_OPair(_1263884, _1263884), _1263880), _1263882)), c_Wellfounded_Omlex__prod(_1263884, _1263878, _1263886))))], (26479 ^ _777081) ^ [_1264146, _1264148, _1264150, _1264152] : [_1264146 = _1264148, 26482 ^ _777081 : [(26483 ^ _777081) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1264150, _1264152), _1264146) = hAPP(c_Product__Type_Ofst(_1264150, _1264152), _1264148))], (26485 ^ _777081) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1264150, _1264152), _1264146) = hAPP(c_Product__Type_Osnd(_1264150, _1264152), _1264148))]]], (26487 ^ _777081) ^ [_1264297, _1264299, _1264301, _1264303] : [-(_1264297 = _1264299), hAPP(c_Product__Type_Ofst(_1264301, _1264303), _1264297) = hAPP(c_Product__Type_Ofst(_1264301, _1264303), _1264299), hAPP(c_Product__Type_Osnd(_1264301, _1264303), _1264297) = hAPP(c_Product__Type_Osnd(_1264301, _1264303), _1264299)], (26497 ^ _777081) ^ [_1264484, _1264486, _1264488, _1264490] : [hAPP(c_Product__Type_Ofst(_1264484, _1264486), _1264488) = hAPP(c_Product__Type_Ofst(_1264484, _1264486), _1264490), hAPP(c_Product__Type_Osnd(_1264484, _1264486), _1264488) = hAPP(c_Product__Type_Osnd(_1264484, _1264486), _1264490), -(_1264488 = _1264490)], (26507 ^ _777081) ^ [_1264669, _1264671, _1264673, _1264675, _1264677] : [hAPP(c_Product__Type_Ofst(_1264669, _1264671), hAPP(hAPP(c_Product__Type_OPair(_1264669, _1264671), _1264673), _1264675)) = _1264677, -(_1264673 = _1264677)], (26513 ^ _777081) ^ [_1264782, _1264784, _1264786, _1264788] : [-(hAPP(c_Product__Type_Ofst(_1264782, _1264784), hAPP(hAPP(c_Product__Type_OPair(_1264782, _1264784), _1264786), _1264788)) = _1264786)], (26515 ^ _777081) ^ [_1264826, _1264828, _1264830, _1264832, _1264834] : [-(hAPP(c_Product__Type_Ofst(_1264826, _1264828), hAPP(c_Product__Type_Oapsnd(_1264830, _1264828, _1264826, _1264832), _1264834)) = hAPP(c_Product__Type_Ofst(_1264826, _1264830), _1264834))], (26517 ^ _777081) ^ [_1264877, _1264879, _1264881] : [-(hAPP(c_Product__Type_Ofst(_1264877, _1264879), _1264881) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1264877, _1264879, _1264877), c_COMBK(_1264877, _1264879)), _1264881))], (26519 ^ _777081) ^ [_1264923, _1264925, _1264927] : [-(hAPP(hAPP(c_Product__Type_OPair(_1264923, _1264925), hAPP(c_Product__Type_Ofst(_1264923, _1264925), _1264927)), hAPP(c_Product__Type_Osnd(_1264923, _1264925), _1264927)) = _1264927)], (26521 ^ _777081) ^ [_1264971, _1264973, _1264975] : [-(_1264971 = hAPP(hAPP(c_Product__Type_OPair(_1264973, _1264975), hAPP(c_Product__Type_Ofst(_1264973, _1264975), _1264971)), hAPP(c_Product__Type_Osnd(_1264973, _1264975), _1264971)))], (26523 ^ _777081) ^ [_1265019, _1265021, _1265023, _1265025, _1265027] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1265019, _1265021, _1265023), _1265025), _1265027) = hAPP(hAPP(_1265025, hAPP(c_Product__Type_Ofst(_1265019, _1265021), _1265027)), hAPP(c_Product__Type_Osnd(_1265019, _1265021), _1265027)))], (26525 ^ _777081) ^ [_1265078, _1265080] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1265078), _1265080) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1265078, _1265080)))], (26527 ^ _777081) ^ [_1265115, _1265117] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1265115, _1265117) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1265115, _1265117)))], (26529 ^ _777081) ^ [_1265150, _1265152, _1265154, _1265156, _1265158] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1265150, _1265152, _1265154), _1265156), _1265158) = hAPP(hAPP(_1265156, hAPP(c_Product__Type_Ofst(_1265150, _1265152), _1265158)), hAPP(c_Product__Type_Osnd(_1265150, _1265152), _1265158)))], (26531 ^ _777081) ^ [_1265209, _1265211, _1265213, _1265215, _1265217, _1265219] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1265209, _1265211), _1265211, _1265213), hAPP(hAPP(c_COMBB(_1265215, tc_fun(_1265211, _1265213), tc_prod(_1265209, _1265211)), _1265217), hAPP(hAPP(c_COMBB(_1265209, _1265215, tc_prod(_1265209, _1265211)), _1265219), c_Product__Type_Ofst(_1265209, _1265211)))), c_Product__Type_Osnd(_1265209, _1265211)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1265209, _1265211, _1265213), hAPP(hAPP(c_COMBB(_1265215, tc_fun(_1265211, _1265213), _1265209), _1265217), _1265219)))], (26533 ^ _777081) ^ [_1265310, _1265312, _1265314, _1265316, _1265318] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1265310, _1265312, _1265314), _1265316), _1265318) = hAPP(hAPP(_1265316, hAPP(c_Product__Type_Ofst(_1265310, _1265312), _1265318)), hAPP(c_Product__Type_Osnd(_1265310, _1265312), _1265318)))], (26535 ^ _777081) ^ [_1265369, _1265371, _1265373] : [-(c_HOL_OThe(tc_prod(_1265369, _1265371), hAPP(c_Product__Type_Oprod_Oprod__case(_1265369, _1265371, tc_HOL_Obool), _1265373)) = c_HOL_OThe(tc_prod(_1265369, _1265371), hAPP(hAPP(c_COMBS(tc_prod(_1265369, _1265371), _1265371, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1265369, tc_fun(_1265371, tc_HOL_Obool), tc_prod(_1265369, _1265371)), _1265373), c_Product__Type_Ofst(_1265369, _1265371))), c_Product__Type_Osnd(_1265369, _1265371))))], (26537 ^ _777081) ^ [_1265450, _1265452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265450), 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)), _1265452)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1265450), _1265452) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1265450, _1265452)))], (26547 ^ _777081) ^ [_1265617, _1265619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1265617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1265619)), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1265617), _1265619) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1265617, _1265619)))], (26557 ^ _777081) ^ [_1265778] : [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), _1265778))), -(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), _1265778)) = 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), _1265778))))], (26563 ^ _777081) ^ [_1265893, _1265895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1265893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1265895), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1265893), _1265895) = 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), _1265893), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1265895)))))], (26573 ^ _777081) ^ [_1266078, _1266080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1266078), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1266080), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _1266078), _1266080) = 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), _1266078), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1266080)))))], (26583 ^ _777081) ^ [_1266269, _1266271, _1266273, _1266275, _1266277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1266269, _1266271)), hAPP(_1266269, _1266273))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1266275, _1266275)), hAPP(hAPP(c_Product__Type_OPair(_1266275, _1266275), _1266271), _1266273)), c_Wellfounded_Omlex__prod(_1266275, _1266269, _1266277))))], (26589 ^ _777081) ^ [_1266420, _1266422, _1266424, _1266426, _1266428] : [-(c_Product__Type_Oprod_Oprod__size(_1266420, _1266422, _1266424, _1266426, _1266428) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1266424, hAPP(c_Product__Type_Ofst(_1266420, _1266422), _1266428))), hAPP(_1266426, hAPP(c_Product__Type_Osnd(_1266420, _1266422), _1266428)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26591 ^ _777081) ^ [_1266487, _1266489, _1266491, _1266493, _1266495] : [hBOOL(hAPP(hAPP(_1266487, _1266489), _1266491)), -(hBOOL(hAPP(hAPP(_1266487, hAPP(c_Product__Type_Osnd(_1266493, _1266495), hAPP(hAPP(c_Product__Type_OPair(_1266493, _1266495), _1266491), _1266489))), hAPP(c_Product__Type_Ofst(_1266493, _1266495), hAPP(hAPP(c_Product__Type_OPair(_1266493, _1266495), _1266491), _1266489)))))], (26597 ^ _777081) ^ [_1266650, _1266652, _1266654, _1266656, _1266658, _1266660] : [hBOOL(hAPP(_1266650, _1266652)), hBOOL(hAPP(_1266654, _1266656)), 26604 ^ _777081 : [(26605 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1266650, hAPP(c_Product__Type_Ofst(_1266658, _1266660), hAPP(hAPP(c_Product__Type_OPair(_1266658, _1266660), _1266652), _1266656)))))], (26607 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1266654, hAPP(c_Product__Type_Osnd(_1266658, _1266660), hAPP(hAPP(c_Product__Type_OPair(_1266658, _1266660), _1266652), _1266656)))))]]], (26609 ^ _777081) ^ [_1266897] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1266897)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1266897)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26611 ^ _777081) ^ [_1266947, _1266949] : [c_Code__Numeral_OSuc__code__numeral(_1266947) = c_Code__Numeral_OSuc__code__numeral(_1266949), -(_1266947 = _1266949)], (26617 ^ _777081) ^ [_1267028, _1267030] : [_1267028 = _1267030, -(c_Code__Numeral_OSuc__code__numeral(_1267028) = c_Code__Numeral_OSuc__code__numeral(_1267030))], (26623 ^ _777081) ^ [_1267124] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1267124)], (26625 ^ _777081) ^ [_1267158] : [c_Code__Numeral_OSuc__code__numeral(_1267158) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (26627 ^ _777081) ^ [_1267183, _1267185] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _1267183), _1267185) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1267183, _1267185)))], (26629 ^ _777081) ^ [_1267220] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1267220)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1267220)], (26663 ^ _777081) ^ [_1267805, _1267807, _1267809] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1267805, _1267807), _1267809))), _1267805 = 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), _1267809)), _1267807)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1267809)), 26670 ^ _777081 : [(26671 ^ _777081) ^ [] : [-(_1267807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26673 ^ _777081) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1267809) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 26674 ^ _777081 : [(26675 ^ _777081) ^ [] : [_1267807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (26677 ^ _777081) ^ [] : [26678 ^ _777081 : [(26679 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1267807)))], (26681 ^ _777081) ^ [] : [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), _1267809))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1267809)), _1267807))]], 26686 ^ _777081 : [(26687 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1267807))], (26689 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1267807), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1267809))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1267809)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (26631 ^ _777081) ^ [_1267269, _1267271, _1267273] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1267269, _1267271), _1267273)), 26634 ^ _777081 : [(26635 ^ _777081) ^ [] : [-(_1267269 = 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), _1267273)), _1267271)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1267273)))], (26637 ^ _777081) ^ [] : [_1267271 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1267273) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26643 ^ _777081) ^ [] : [-(_1267271 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 26646 ^ _777081 : [(26647 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1267271)), 26650 ^ _777081 : [(26651 ^ _777081) ^ [] : [-(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), _1267273))))], (26653 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1267273)), _1267271)))]]], (26655 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1267271))), 26658 ^ _777081 : [(26659 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1267271), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1267273))))], (26661 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1267273)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (26697 ^ _777081) ^ [_1268414] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1268414)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1268414)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (26699 ^ _777081) ^ [_1268451, _1268453, _1268455, _1268457, _1268459, _1268461] : [-(c_Product__Type_Oprod_Oprod__rec(_1268451, _1268453, _1268455, _1268457, hAPP(hAPP(c_Product__Type_OPair(_1268451, _1268453), _1268459), _1268461)) = hAPP(hAPP(_1268457, _1268459), _1268461))], (26701 ^ _777081) ^ [_1268538, _1268540, _1268542, _1268544, _1268546, _1268548, _1268550, _1268552] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1268538, _1268540), tc_prod(_1268538, _1268540))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1268538, _1268540), tc_prod(_1268538, _1268540)), hAPP(hAPP(c_Product__Type_OPair(_1268538, _1268540), _1268542), _1268544)), hAPP(hAPP(c_Product__Type_OPair(_1268538, _1268540), _1268546), _1268548))), c_Wellfounded_Olex__prod(_1268538, _1268540, _1268550, _1268552))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1268538, _1268538)), hAPP(hAPP(c_Product__Type_OPair(_1268538, _1268538), _1268542), _1268546)), _1268550))), 26708 ^ _777081 : [(26709 ^ _777081) ^ [] : [-(_1268542 = _1268546)], (26711 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1268540, _1268540)), hAPP(hAPP(c_Product__Type_OPair(_1268540, _1268540), _1268544), _1268548)), _1268552)))]]], (26713 ^ _777081) ^ [_1268863, _1268865, _1268867, _1268869, _1268871, _1268873, _1268875, _1268877] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1268863, _1268865), tc_prod(_1268863, _1268865))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1268863, _1268865), tc_prod(_1268863, _1268865)), hAPP(hAPP(c_Product__Type_OPair(_1268863, _1268865), _1268867), _1268869)), hAPP(hAPP(c_Product__Type_OPair(_1268863, _1268865), _1268871), _1268873))), c_Wellfounded_Olex__prod(_1268863, _1268865, _1268875, _1268877)))), 26714 ^ _777081 : [(26715 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1268863, _1268863)), hAPP(hAPP(c_Product__Type_OPair(_1268863, _1268863), _1268867), _1268871)), _1268875))], (26717 ^ _777081) ^ [] : [_1268867 = _1268871, hBOOL(hAPP(hAPP(c_member(tc_prod(_1268865, _1268865)), hAPP(hAPP(c_Product__Type_OPair(_1268865, _1268865), _1268869), _1268873)), _1268877))]]], (26725 ^ _777081) ^ [_1269238, _1269240, _1269242, _1269244, _1269246, _1269248, _1269250] : [-(hAPP(c_Product__Type_Oapfst(_1269238, _1269240, _1269242, _1269244), hAPP(c_Product__Type_Oapsnd(_1269246, _1269242, _1269238, _1269248), _1269250)) = hAPP(hAPP(c_Product__Type_OPair(_1269240, _1269242), hAPP(_1269244, hAPP(c_Product__Type_Ofst(_1269238, _1269246), _1269250))), hAPP(_1269248, hAPP(c_Product__Type_Osnd(_1269238, _1269246), _1269250))))], (26727 ^ _777081) ^ [_1269316, _1269318, _1269320, _1269322, _1269324, _1269326] : [-(hAPP(c_Product__Type_Oapfst(_1269316, _1269318, _1269320, _1269322), hAPP(hAPP(c_Product__Type_OPair(_1269316, _1269320), _1269324), _1269326)) = hAPP(hAPP(c_Product__Type_OPair(_1269318, _1269320), hAPP(_1269322, _1269324)), _1269326))], (26729 ^ _777081) ^ [_1269405, _1269407, _1269409, _1269411, _1269413, _1269415] : [hAPP(c_Product__Type_Oapfst(_1269405, _1269407, _1269409, _1269411), _1269413) = hAPP(c_Product__Type_Oapfst(_1269405, _1269407, _1269409, _1269415), _1269413), -(hAPP(_1269411, hAPP(c_Product__Type_Ofst(_1269405, _1269409), _1269413)) = hAPP(_1269415, hAPP(c_Product__Type_Ofst(_1269405, _1269409), _1269413)))], (26735 ^ _777081) ^ [_1269554, _1269556, _1269558, _1269560, _1269562, _1269564] : [hAPP(_1269560, hAPP(c_Product__Type_Ofst(_1269554, _1269558), _1269562)) = hAPP(_1269564, hAPP(c_Product__Type_Ofst(_1269554, _1269558), _1269562)), -(hAPP(c_Product__Type_Oapfst(_1269554, _1269556, _1269558, _1269560), _1269562) = hAPP(c_Product__Type_Oapfst(_1269554, _1269556, _1269558, _1269564), _1269562))], (26741 ^ _777081) ^ [_1269709, _1269711, _1269713, _1269715, _1269717] : [-(hAPP(c_Product__Type_Ofst(_1269709, _1269711), hAPP(c_Product__Type_Oapfst(_1269713, _1269709, _1269711, _1269715), _1269717)) = hAPP(_1269715, hAPP(c_Product__Type_Ofst(_1269713, _1269711), _1269717)))], (26743 ^ _777081) ^ [_1269763, _1269765, _1269767, _1269769, _1269771] : [-(hAPP(c_Product__Type_Osnd(_1269763, _1269765), hAPP(c_Product__Type_Oapfst(_1269767, _1269763, _1269765, _1269769), _1269771)) = hAPP(c_Product__Type_Osnd(_1269767, _1269765), _1269771))], (26745 ^ _777081) ^ [_1269814, _1269816, _1269818, _1269820, _1269822, _1269824, _1269826] : [-(hAPP(c_Product__Type_Oapsnd(_1269814, _1269816, _1269818, _1269820), hAPP(c_Product__Type_Oapfst(_1269822, _1269818, _1269814, _1269824), _1269826)) = hAPP(c_Product__Type_Oapfst(_1269822, _1269818, _1269816, _1269824), hAPP(c_Product__Type_Oapsnd(_1269814, _1269816, _1269822, _1269820), _1269826)))], (26747 ^ _777081) ^ [] : [-(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))], (26749 ^ _777081) ^ [_1269899, _1269901, _1269903, _1269905, _1269907, _1269909, _1269911] : [-(hAPP(c_Product__Type_Oapsnd(_1269899, _1269901, _1269903, _1269905), hAPP(c_Product__Type_Oapfst(_1269907, _1269903, _1269899, _1269909), _1269911)) = hAPP(hAPP(c_Product__Type_OPair(_1269903, _1269901), hAPP(_1269909, hAPP(c_Product__Type_Ofst(_1269907, _1269899), _1269911))), hAPP(_1269905, hAPP(c_Product__Type_Osnd(_1269907, _1269899), _1269911))))], (26751 ^ _777081) ^ [_1269977, _1269979, _1269981, _1269983, _1269985, _1269987, _1269989] : [hBOOL(hAPP(_1269977, _1269979)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1269981, _1269981)), hAPP(hAPP(c_Product__Type_OPair(_1269981, _1269981), _1269983), _1269985)), hAPP(_1269987, _1269979))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1269989, _1269981), tc_prod(_1269989, _1269981))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1269989, _1269981), tc_prod(_1269989, _1269981)), hAPP(hAPP(c_Product__Type_OPair(_1269989, _1269981), _1269979), _1269983)), hAPP(hAPP(c_Product__Type_OPair(_1269989, _1269981), _1269979), _1269985))), c_Recdef_Osame__fst(_1269989, _1269981, _1269977, _1269987))))], (26761 ^ _777081) ^ [_1270282, _1270284, _1270286, _1270288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1270282), _1270284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1270286), _1270288)), -(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), _1270282), _1270286)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1270284), _1270288))), c_FunDef_Opair__less)))], (26771 ^ _777081) ^ [_1270485, _1270487, _1270489, _1270491] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1270485, _1270487, _1270489, c_Code__Numeral_OSuc__code__numeral(_1270491)) = hAPP(_1270489, _1270491))], (26773 ^ _777081) ^ [_1270542, _1270544, _1270546] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1270542, hAPP(hAPP(c_COMBC(_1270542, tc_fun(tc_prod(_1270542, _1270542), tc_HOL_Obool), tc_fun(_1270542, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1270542, tc_fun(tc_fun(tc_prod(_1270542, _1270542), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1270542, _1270542), tc_HOL_Obool), tc_fun(_1270542, tc_HOL_Obool)), _1270542), c_COMBC(_1270542, tc_fun(tc_prod(_1270542, _1270542), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1270542, tc_prod(_1270542, _1270542)), tc_fun(_1270542, tc_fun(tc_fun(tc_prod(_1270542, _1270542), tc_HOL_Obool), tc_HOL_Obool)), _1270542), hAPP(c_COMBB(tc_prod(_1270542, _1270542), tc_fun(tc_fun(tc_prod(_1270542, _1270542), tc_HOL_Obool), tc_HOL_Obool), _1270542), c_member(tc_prod(_1270542, _1270542)))), c_Product__Type_OPair(_1270542, _1270542)))), _1270544)), _1270546)), -(hBOOL(hAPP(hAPP(c_member(_1270542), _1270546), c_Wellfounded_Oacc(_1270542, _1270544))))], (26779 ^ _777081) ^ [_1270883, _1270885, _1270887] : [hBOOL(hAPP(hAPP(c_member(_1270883), _1270887), c_Wellfounded_Oacc(_1270883, _1270885))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1270883, hAPP(hAPP(c_COMBC(_1270883, tc_fun(tc_prod(_1270883, _1270883), tc_HOL_Obool), tc_fun(_1270883, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1270883, tc_fun(tc_fun(tc_prod(_1270883, _1270883), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1270883, _1270883), tc_HOL_Obool), tc_fun(_1270883, tc_HOL_Obool)), _1270883), c_COMBC(_1270883, tc_fun(tc_prod(_1270883, _1270883), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1270883, tc_prod(_1270883, _1270883)), tc_fun(_1270883, tc_fun(tc_fun(tc_prod(_1270883, _1270883), tc_HOL_Obool), tc_HOL_Obool)), _1270883), hAPP(c_COMBB(tc_prod(_1270883, _1270883), tc_fun(tc_fun(tc_prod(_1270883, _1270883), tc_HOL_Obool), tc_HOL_Obool), _1270883), c_member(tc_prod(_1270883, _1270883)))), c_Product__Type_OPair(_1270883, _1270883)))), _1270885)), _1270887)))], (26785 ^ _777081) ^ [_1271230, _1271232, _1271234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1271230, _1271230), tc_HOL_Obool)), _1271232), _1271234)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1271230, tc_HOL_Obool)), c_Wellfounded_Oacc(_1271230, _1271234)), c_Wellfounded_Oacc(_1271230, _1271232))))], (26791 ^ _777081) ^ [_1271367, _1271369, _1271371, _1271373] : [hBOOL(hAPP(hAPP(c_member(_1271367), _1271369), c_Wellfounded_Oacc(_1271367, _1271371))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1271367, _1271367)), hAPP(hAPP(c_Product__Type_OPair(_1271367, _1271367), _1271373), _1271369)), _1271371)), -(hBOOL(hAPP(hAPP(c_member(_1271367), _1271373), c_Wellfounded_Oacc(_1271367, _1271371))))], (26811 ^ _777081) ^ [_1271853, _1271855, _1271857] : [26813 ^ _777081 : [(26814 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1271853, _1271853)), hAPP(hAPP(c_Product__Type_OPair(_1271853, _1271853), 26812 ^ [_1271853, _1271855, _1271857]), _1271855)), _1271857)))], (26816 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1271853), 26812 ^ [_1271853, _1271855, _1271857]), c_Wellfounded_Oacc(_1271853, _1271857)))]], -(hBOOL(hAPP(hAPP(c_member(_1271853), _1271855), c_Wellfounded_Oacc(_1271853, _1271857))))], (26801 ^ _777081) ^ [_1271600, _1271602, _1271604] : [hBOOL(hAPP(hAPP(c_member(_1271600), _1271602), c_Wellfounded_Oacc(_1271600, _1271604))), 26804 ^ _777081 : [(26805 ^ _777081) ^ [_1271714] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1271600, _1271600)), hAPP(hAPP(c_Product__Type_OPair(_1271600, _1271600), _1271714), _1271602)), _1271604)), -(hBOOL(hAPP(hAPP(c_member(_1271600), _1271714), c_Wellfounded_Oacc(_1271600, _1271604))))]]], (26820 ^ _777081) ^ [_1272093, _1272095, _1272097, _1272099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1272093), _1272095)), -(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), _1272093), _1272097)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1272095), _1272099))), c_FunDef_Opair__less)))], (26826 ^ _777081) ^ [_1272230, _1272232, _1272234] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1272230, _1272232, _1272234, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1272232)], (26828 ^ _777081) ^ [_1272262, _1272264, _1272266, _1272268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1272262), _1272264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1272266), _1272268)), -(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), _1272262), _1272266)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1272264), _1272268))), c_FunDef_Opair__leq)))], (26838 ^ _777081) ^ [_1272465, _1272467, _1272469, _1272471] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1272465), _1272467)), 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)), _1272465), _1272469)), 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)), _1272467), _1272471)), 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)), _1272467), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1272469), _1272471))), c_FunDef_Omin__strict)))], (26852 ^ _777081) ^ [_1272746, _1272748, _1272750, _1272752] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1272746), _1272748)), 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)), _1272750), _1272746)), 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)), _1272752), _1272748)), 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)), _1272750), _1272752)), _1272748)), c_FunDef_Omax__strict)))], (26866 ^ _777081) ^ [_1273027, _1273029, _1273031, _1273033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1273027), _1273029)), -(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), _1273027), _1273031)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1273029), _1273033))), c_FunDef_Opair__leq)))], (26872 ^ _777081) ^ [_1273160] : [-(_1273160 = 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)), _1273160), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (26878 ^ _777081) ^ [_1273205, _1273207, _1273209, _1273211] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1273205), _1273207)), 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)), _1273209), _1273205)), 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)), _1273211), _1273207)), 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)), _1273209), _1273211)), _1273207)), c_FunDef_Omax__weak)))], (26892 ^ _777081) ^ [_1273486, _1273488, _1273490, _1273492] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1273486), _1273488)), 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)), _1273486), _1273490)), 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)), _1273488), _1273492)), 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)), _1273488), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1273490), _1273492))), c_FunDef_Omin__weak)))], (26906 ^ _777081) ^ [_1273767] : [-(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)), _1273767), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (26908 ^ _777081) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (26910 ^ _777081) ^ [] : [-(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)))))], (26912 ^ _777081) ^ [] : [-(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)))))], (26914 ^ _777081) ^ [] : [-(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)))], (26916 ^ _777081) ^ [] : [-(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)))], (26918 ^ _777081) ^ [_1273906, _1273908] : [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), _1273906), _1273908)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1273906), _1273908)))], (26924 ^ _777081) ^ [_1274011, _1274013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1274011), _1274013)), -(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), _1274011), _1274013)), c_Wellfounded_Oless__than)))], (26930 ^ _777081) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (26932 ^ _777081) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (26934 ^ _777081) ^ [_1274158, _1274160, _1274162, _1274164, _1274166, _1274168] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1274158, tc_HOL_Obool), tc_fun(_1274158, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1274158, tc_HOL_Obool), tc_fun(_1274158, tc_HOL_Obool)), _1274160), _1274162)), c_Wellfounded_Omax__ext(_1274158, _1274164))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1274158, tc_HOL_Obool), tc_fun(_1274158, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1274158, tc_HOL_Obool), tc_fun(_1274158, tc_HOL_Obool)), _1274166), _1274168)), c_Wellfounded_Omax__ext(_1274158, _1274164))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1274158, tc_HOL_Obool), tc_fun(_1274158, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1274158, tc_HOL_Obool), tc_fun(_1274158, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274158, tc_HOL_Obool)), _1274160), _1274166)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1274158, tc_HOL_Obool)), _1274162), _1274168))), c_Wellfounded_Omax__ext(_1274158, _1274164))))], (26944 ^ _777081) ^ [_1274572, _1274574, _1274576, _1274578] : [c_Wellfounded_Omax__extp(_1274572, hAPP(hAPP(c_COMBC(_1274572, tc_fun(tc_prod(_1274572, _1274572), tc_HOL_Obool), tc_fun(_1274572, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1274572, tc_fun(tc_fun(tc_prod(_1274572, _1274572), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1274572, _1274572), tc_HOL_Obool), tc_fun(_1274572, tc_HOL_Obool)), _1274572), c_COMBC(_1274572, tc_fun(tc_prod(_1274572, _1274572), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1274572, tc_prod(_1274572, _1274572)), tc_fun(_1274572, tc_fun(tc_fun(tc_prod(_1274572, _1274572), tc_HOL_Obool), tc_HOL_Obool)), _1274572), hAPP(c_COMBB(tc_prod(_1274572, _1274572), tc_fun(tc_fun(tc_prod(_1274572, _1274572), tc_HOL_Obool), tc_HOL_Obool), _1274572), c_member(tc_prod(_1274572, _1274572)))), c_Product__Type_OPair(_1274572, _1274572)))), _1274574), _1274576, _1274578), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1274572, tc_HOL_Obool), tc_fun(_1274572, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1274572, tc_HOL_Obool), tc_fun(_1274572, tc_HOL_Obool)), _1274576), _1274578)), c_Wellfounded_Omax__ext(_1274572, _1274574))))], (26950 ^ _777081) ^ [_1274957, _1274959, _1274961, _1274963] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1274957, tc_HOL_Obool), tc_fun(_1274957, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1274957, tc_HOL_Obool), tc_fun(_1274957, tc_HOL_Obool)), _1274961), _1274963)), c_Wellfounded_Omax__ext(_1274957, _1274959))), -(c_Wellfounded_Omax__extp(_1274957, hAPP(hAPP(c_COMBC(_1274957, tc_fun(tc_prod(_1274957, _1274957), tc_HOL_Obool), tc_fun(_1274957, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1274957, tc_fun(tc_fun(tc_prod(_1274957, _1274957), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1274957, _1274957), tc_HOL_Obool), tc_fun(_1274957, tc_HOL_Obool)), _1274957), c_COMBC(_1274957, tc_fun(tc_prod(_1274957, _1274957), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1274957, tc_prod(_1274957, _1274957)), tc_fun(_1274957, tc_fun(tc_fun(tc_prod(_1274957, _1274957), tc_HOL_Obool), tc_HOL_Obool)), _1274957), hAPP(c_COMBB(tc_prod(_1274957, _1274957), tc_fun(tc_fun(tc_prod(_1274957, _1274957), tc_HOL_Obool), tc_HOL_Obool), _1274957), c_member(tc_prod(_1274957, _1274957)))), c_Product__Type_OPair(_1274957, _1274957)))), _1274959), _1274961, _1274963))], (26956 ^ _777081) ^ [_1275348, _1275350, _1275352] : [-(c_Wellfounded_Omlex__prod(_1275348, _1275350, _1275352) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1275348), _1275348), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1275348, c_Wellfounded_Oless__than, _1275352)), hAPP(hAPP(c_COMBS(_1275348, _1275348, tc_prod(tc_Nat_Onat, _1275348)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1275348, tc_prod(tc_Nat_Onat, _1275348)), _1275348), c_Product__Type_OPair(tc_Nat_Onat, _1275348)), _1275350)), c_COMBI(_1275348))))], (26958 ^ _777081) ^ [_1275451, _1275453, _1275455, _1275457] : [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), _1275451), _1275453)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1275455), _1275457))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1275451), _1275457) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1275455), _1275453))], (26964 ^ _777081) ^ [_1275598, _1275600, _1275602, _1275604] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1275598), _1275604) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1275602), _1275600), -(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), _1275598), _1275600)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1275602), _1275604))), c_Int_Ointrel)))], (26970 ^ _777081) ^ [_1275751, _1275753, _1275755, _1275757] : [c_FunDef_Oreduction__pair(_1275751, _1275753), -(c_FunDef_Oreduction__pair(_1275755, hAPP(hAPP(c_FunDef_Orp__inv__image(_1275751, _1275755), _1275753), _1275757)))], (26976 ^ _777081) ^ [_1275850, _1275852] : [-(c_FunDef_Orp__inv__image(_1275850, _1275852) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1275850, _1275850), tc_HOL_Obool), tc_fun(tc_prod(_1275850, _1275850), tc_HOL_Obool), tc_fun(tc_fun(_1275852, _1275850), tc_prod(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1275850, _1275850), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1275850, _1275850), tc_HOL_Obool), tc_fun(tc_fun(_1275852, _1275850), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1275850, _1275850), tc_HOL_Obool), tc_fun(tc_fun(_1275852, _1275850), tc_prod(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1275852, _1275850), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool)), tc_fun(tc_fun(_1275852, _1275850), tc_prod(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1275850, _1275850), tc_HOL_Obool), tc_fun(tc_fun(_1275852, _1275850), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1275850, _1275850), tc_HOL_Obool), tc_fun(tc_fun(_1275852, _1275850), tc_prod(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool))))), tc_fun(tc_prod(_1275850, _1275850), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1275852, _1275850), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool)), tc_fun(tc_fun(_1275852, _1275850), tc_prod(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool))), tc_fun(tc_prod(_1275850, _1275850), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1275852, _1275850), tc_fun(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1275852, _1275850), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool)), tc_fun(tc_fun(_1275852, _1275850), tc_prod(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool)))), tc_fun(tc_prod(_1275850, _1275850), tc_HOL_Obool)), c_COMBS(tc_fun(_1275852, _1275850), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1275852, _1275850), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool)), tc_fun(tc_fun(_1275852, _1275850), tc_fun(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool)))), tc_fun(tc_prod(_1275850, _1275850), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool))), tc_fun(_1275852, _1275850)), c_Product__Type_OPair(tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool), tc_fun(tc_prod(_1275852, _1275852), tc_HOL_Obool)))), c_Relation_Oinv__image(_1275850, _1275852))))), c_Relation_Oinv__image(_1275850, _1275852))))], (26978 ^ _777081) ^ [_1276390, _1276392, _1276394, _1276396, _1276398, _1276400] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1276390, _1276390)), hAPP(hAPP(c_Product__Type_OPair(_1276390, _1276390), _1276392), _1276394)), hAPP(hAPP(c_Relation_Oinv__image(_1276396, _1276390), _1276398), _1276400))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1276396, _1276396)), hAPP(hAPP(c_Product__Type_OPair(_1276396, _1276396), hAPP(_1276400, _1276392)), hAPP(_1276400, _1276394))), _1276398)))], (26984 ^ _777081) ^ [_1276577, _1276579, _1276581, _1276583, _1276585, _1276587] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1276583, _1276583)), hAPP(hAPP(c_Product__Type_OPair(_1276583, _1276583), hAPP(_1276587, _1276579)), hAPP(_1276587, _1276581))), _1276585)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1276577, _1276577)), hAPP(hAPP(c_Product__Type_OPair(_1276577, _1276577), _1276579), _1276581)), hAPP(hAPP(c_Relation_Oinv__image(_1276583, _1276577), _1276585), _1276587))))], (26990 ^ _777081) ^ [_1276785, _1276787] : [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)), _1276785), 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)), _1276787), 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)), _1276785), _1276787)), c_Int_Ointrel)))], (26996 ^ _777081) ^ [_1276916, _1276918] : [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)), _1276916), _1276918)), 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)), _1276916), 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)), _1276918), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (27002 ^ _777081) ^ [_1277053] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1277053)), -(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))), _1277053)), c_FunDef_Omax__weak)))], (27008 ^ _777081) ^ [_1277148] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1277148)), -(_1277148 = 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))), _1277148)), c_FunDef_Omax__strict)))], (27018 ^ _777081) ^ [_1277258, _1277260, _1277262, _1277264, _1277266, _1277268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1277258, _1277260), tc_HOL_Obool)), _1277262), _1277264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277258, tc_HOL_Obool)), _1277266), _1277268)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277260, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1277258, _1277260, _1277262), _1277266)), hAPP(c_Relation_OImage(_1277258, _1277260, _1277264), _1277268))))], (27028 ^ _777081) ^ [_1277497, _1277499, _1277501, _1277503, _1277505] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277497, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1277499, _1277497, _1277501), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1277499, tc_HOL_Obool)), _1277503), _1277505))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1277497, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1277499, _1277497, _1277501), _1277503)), hAPP(c_Relation_OImage(_1277499, _1277497, _1277501), _1277505)))))], (27030 ^ _777081) ^ [_1277581, _1277583, _1277585, _1277587, _1277589] : [-(hAPP(c_Relation_OImage(_1277581, _1277583, _1277585), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277581, tc_HOL_Obool)), _1277587), _1277589)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277583, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1277581, _1277583, _1277585), _1277587)), hAPP(c_Relation_OImage(_1277581, _1277583, _1277585), _1277589)))], (27032 ^ _777081) ^ [_1277655, _1277657, _1277659] : [-(hAPP(c_Relation_OImage(_1277655, _1277657, _1277659), c_Orderings_Obot__class_Obot(tc_fun(_1277655, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1277657, tc_HOL_Obool)))], (27034 ^ _777081) ^ [_1277699, _1277701, _1277703, _1277705, _1277707] : [-(hAPP(c_Relation_OImage(_1277699, _1277701, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1277699, _1277701), tc_HOL_Obool)), _1277703), _1277705)), _1277707) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277701, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1277699, _1277701, _1277703), _1277707)), hAPP(c_Relation_OImage(_1277699, _1277701, _1277705), _1277707)))], (27036 ^ _777081) ^ [_1277776, _1277778, _1277780, _1277782, _1277784, _1277786] : [hBOOL(hAPP(hAPP(c_member(_1277776), _1277778), _1277780)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1277776, _1277782)), hAPP(hAPP(c_Product__Type_OPair(_1277776, _1277782), _1277778), _1277784)), _1277786)), -(hBOOL(hAPP(hAPP(c_member(_1277782), _1277784), hAPP(c_Relation_OImage(_1277776, _1277782, _1277786), _1277780))))], (27046 ^ _777081) ^ [_1278025, _1278027, _1278029, _1278031, _1278033] : [hBOOL(hAPP(hAPP(c_member(_1278025), _1278027), hAPP(c_Relation_OImage(_1278029, _1278025, _1278031), _1278033))), 27050 ^ _777081 : [(27051 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1278029), 27049 ^ [_1278025, _1278027, _1278029, _1278031, _1278033]), _1278033)))], (27053 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1278029, _1278025)), hAPP(hAPP(c_Product__Type_OPair(_1278029, _1278025), 27049 ^ [_1278025, _1278027, _1278029, _1278031, _1278033]), _1278027)), _1278031)))]]], (27055 ^ _777081) ^ [_1278241, _1278243, _1278245, _1278247, _1278249] : [-(hBOOL(hAPP(hAPP(c_member(_1278241), _1278243), hAPP(c_Relation_OImage(_1278245, _1278241, _1278247), _1278249)))), 27056 ^ _777081 : [(27057 ^ _777081) ^ [_1278327] : [hBOOL(hAPP(hAPP(c_member(_1278245), _1278327), _1278249)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1278245, _1278241)), hAPP(hAPP(c_Product__Type_OPair(_1278245, _1278241), _1278327), _1278243)), _1278247))]]], (27065 ^ _777081) ^ [_1278531, _1278533, _1278535, _1278537, _1278539] : [hBOOL(hAPP(hAPP(c_member(_1278531), _1278533), hAPP(c_Relation_OImage(_1278535, _1278531, _1278537), hAPP(hAPP(c_Set_Oinsert(_1278535), _1278539), c_Orderings_Obot__class_Obot(tc_fun(_1278535, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1278535, _1278531)), hAPP(hAPP(c_Product__Type_OPair(_1278535, _1278531), _1278539), _1278533)), _1278537)))], (27071 ^ _777081) ^ [_1278702, _1278704, _1278706, _1278708, _1278710] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1278706, _1278702)), hAPP(hAPP(c_Product__Type_OPair(_1278706, _1278702), _1278710), _1278704)), _1278708)), -(hBOOL(hAPP(hAPP(c_member(_1278702), _1278704), hAPP(c_Relation_OImage(_1278706, _1278702, _1278708), hAPP(hAPP(c_Set_Oinsert(_1278706), _1278710), c_Orderings_Obot__class_Obot(tc_fun(_1278706, tc_HOL_Obool)))))))], (27077 ^ _777081) ^ [_1278879] : [-(c_Wellfounded_Omeasure(_1278879) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1278879), c_Wellfounded_Oless__than))], (27079 ^ _777081) ^ [_1278910, _1278912, _1278914] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1278910), _1278912)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1278910), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278910, tc_HOL_Obool)), _1278912), _1278914))))], (27085 ^ _777081) ^ [_1279027, _1279029, _1279031] : [27086 ^ _777081 : [(27087 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279027), _1279029))], (27089 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279027), _1279031))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279027), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1279027, tc_HOL_Obool)), _1279029), _1279031))))], (27093 ^ _777081) ^ [_1279190, _1279192, _1279194, _1279196] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279190), _1279192)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279194), hAPP(c_Set_Oimage(_1279190, _1279194, _1279196), _1279192))))], (27099 ^ _777081) ^ [_1279301, _1279303, _1279305] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1279301), _1279303)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279301), hAPP(hAPP(c_Set_Oinsert(_1279301), _1279305), _1279303))))], (27105 ^ _777081) ^ [_1279412] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279412), c_Orderings_Obot__class_Obot(tc_fun(_1279412, tc_HOL_Obool)))))], (27107 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (27109 ^ _777081) ^ [_1279480] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1279480)), -(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)), _1279480))))], (27115 ^ _777081) ^ [_1279565] : [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)), _1279565))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1279565)))], (27121 ^ _777081) ^ [_1279656] : [c_Nat__Transfer_Onat__set(_1279656), 27124 ^ _777081 : [(27125 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1279656)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1279656))))], (27131 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1279656))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1279656)))]]], (27137 ^ _777081) ^ [_1279876, _1279878] : [class_Finite__Set_Ofinite(_1279876), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279876), _1279878)))], (27143 ^ _777081) ^ [_1279959, _1279961] : [class_Finite__Set_Ofinite(_1279959), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1279959), _1279961)))], (27149 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (27151 ^ _777081) ^ [_1280060, _1280062, _1280064, _1280066, _1280068] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1280060)), hAPP(c_Set_Oimage(_1280062, tc_Option_Ooption(_1280060), _1280064), c_Orderings_Otop__class_Otop(tc_fun(_1280062, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1280060)), hAPP(c_Set_Oimage(_1280062, tc_Option_Ooption(_1280060), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1280062, tc_Option_Ooption(_1280060)), _1280064), _1280066), hAPP(c_Option_Ooption_OSome(_1280060), _1280068))), c_Orderings_Otop__class_Otop(tc_fun(_1280062, tc_HOL_Obool))))))], (27157 ^ _777081) ^ [_1280261] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1280261), c_Orderings_Obot__class_Obot(tc_fun(_1280261, tc_HOL_Obool)))))], (27159 ^ _777081) ^ [_1280311, _1280313, _1280315] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1280311), hAPP(hAPP(c_Set_Oinsert(_1280311), _1280313), _1280315))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1280311), _1280315)))], (27165 ^ _777081) ^ [_1280418, _1280420, _1280422] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1280418), _1280422)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1280418), hAPP(hAPP(c_Set_Oinsert(_1280418), _1280420), _1280422))))], (27171 ^ _777081) ^ [_1280531, _1280533, _1280535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280531, tc_HOL_Obool)), _1280533), _1280535)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1280531), _1280535)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1280531), _1280533)))], (27181 ^ _777081) ^ [_1280700, _1280702, _1280704] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1280700), _1280702)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1280700, tc_HOL_Obool)), _1280704), _1280702)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1280700), _1280704)))], (27191 ^ _777081) ^ [_1280869, _1280871] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1280869, _1280871)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1280869, _1280871), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1280871), c_Orderings_Otop__class_Otop(tc_fun(_1280871, tc_HOL_Obool)))))], (27197 ^ _777081) ^ [_1280994] : [class_Finite__Set_Ofinite(_1280994), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1280994), c_Orderings_Otop__class_Otop(tc_fun(_1280994, tc_HOL_Obool)))))], (27203 ^ _777081) ^ [_1281085, _1281087, _1281089] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1281085), _1281087)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281085), _1281089)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281085), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281085, tc_HOL_Obool)), _1281087), _1281089))))], (27213 ^ _777081) ^ [_1281282, _1281284, _1281286] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1281282), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281282, tc_HOL_Obool)), _1281284), _1281286))), 27216 ^ _777081 : [(27217 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281282), _1281284)))], (27219 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281282), _1281286)))]]], (27221 ^ _777081) ^ [_1281429, _1281431, _1281433] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281429), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281429, tc_HOL_Obool)), _1281431), _1281433)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281429), _1281431)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281429), _1281433))], (27231 ^ _777081) ^ [_1281610, _1281612, _1281614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1281610), _1281612)), 27234 ^ _777081 : [(27235 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1281610), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1281610, tc_HOL_Obool)), _1281614), _1281612))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281610), _1281614)))], (27241 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1281610), _1281614)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281610), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1281610, tc_HOL_Obool)), _1281614), _1281612))))]]], (27247 ^ _777081) ^ [_1281909, _1281911, _1281913, _1281915] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1281909, _1281911)), c_Sum__Type_OPlus(_1281909, _1281911, _1281913, _1281915))), 27250 ^ _777081 : [(27251 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281909), _1281913)))], (27253 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1281911), _1281915)))]]], (27255 ^ _777081) ^ [_1282052, _1282054, _1282056, _1282058] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1282052, _1282054)), c_Sum__Type_OPlus(_1282052, _1282054, _1282056, _1282058)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282052), _1282056)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282054), _1282058))], (27265 ^ _777081) ^ [_1282231, _1282233, _1282235, _1282237] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282231), _1282233)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282235), _1282237)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1282231, _1282235)), c_Sum__Type_OPlus(_1282231, _1282235, _1282233, _1282237))))], (27275 ^ _777081) ^ [_1282408, _1282410, _1282412, _1282414] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1282408, _1282410)), c_Sum__Type_OPlus(_1282408, _1282410, _1282412, _1282414))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282408), _1282412)))], (27281 ^ _777081) ^ [_1282521, _1282523, _1282525, _1282527] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1282521, _1282523)), c_Sum__Type_OPlus(_1282521, _1282523, _1282525, _1282527))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282523), _1282527)))], (27287 ^ _777081) ^ [_1282634, _1282636, _1282638, _1282640, _1282642] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282634), _1282636)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1282638, tc_HOL_Obool)), _1282640), hAPP(c_Set_Oimage(_1282634, _1282638, _1282642), _1282636))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282638), _1282640)))], (27297 ^ _777081) ^ [_1282846, _1282848, _1282850, _1282852] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282846), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1282846, tc_HOL_Obool)), _1282848), hAPP(hAPP(c_Set_Oinsert(_1282846), _1282850), _1282852)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282846), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1282846, tc_HOL_Obool)), _1282848), _1282852))))], (27303 ^ _777081) ^ [_1282999, _1283001, _1283003, _1283005] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1282999), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1282999, tc_HOL_Obool)), _1283001), _1283005))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1282999), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1282999, tc_HOL_Obool)), _1283001), hAPP(hAPP(c_Set_Oinsert(_1282999), _1283003), _1283005)))))], (27309 ^ _777081) ^ [_1283158, _1283160, _1283162, _1283164] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283158), hAPP(c_Set_Oimage(_1283160, _1283158, _1283162), _1283164))), c_Fun_Oinj__on(_1283160, _1283158, _1283162, _1283164), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283160), _1283164)))], (27319 ^ _777081) ^ [_1283329, _1283331] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283329), _1283331)), 27322 ^ _777081 : [(27323 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283329), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283329, tc_HOL_Obool)), _1283331))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283329), c_Orderings_Otop__class_Otop(tc_fun(_1283329, tc_HOL_Obool)))))], (27329 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283329), c_Orderings_Otop__class_Otop(tc_fun(_1283329, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283329), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1283329, tc_HOL_Obool)), _1283331))))]]], (27335 ^ _777081) ^ [_1283607, _1283609] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283607), c_Orderings_Otop__class_Otop(tc_fun(_1283607, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1283609), c_Orderings_Otop__class_Otop(tc_fun(_1283609, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1283607, _1283609)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1283607, _1283609), tc_HOL_Obool)))))], (27345 ^ _777081) ^ [_1283802, _1283804, _1283806, _1283808, _1283810] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283802), hAPP(c_Set_Oimage(_1283804, _1283802, _1283806), c_Orderings_Otop__class_Otop(tc_fun(_1283804, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283808), hAPP(c_Set_Oimage(_1283804, _1283808, hAPP(hAPP(c_COMBB(_1283802, _1283808, _1283804), _1283810), _1283806)), c_Orderings_Otop__class_Otop(tc_fun(_1283804, tc_HOL_Obool))))))], (27351 ^ _777081) ^ [_1283984, _1283986] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1283984, _1283986)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1283984, _1283986), tc_HOL_Obool)))), 27354 ^ _777081 : [(27355 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283984), c_Orderings_Otop__class_Otop(tc_fun(_1283984, tc_HOL_Obool)))))], (27357 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1283986), c_Orderings_Otop__class_Otop(tc_fun(_1283986, tc_HOL_Obool)))))]]], (27359 ^ _777081) ^ [_1284149, _1284151] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1284149, _1284151)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1284149, _1284151), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284149), c_Orderings_Otop__class_Otop(tc_fun(_1284149, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1284151), c_Orderings_Otop__class_Otop(tc_fun(_1284151, tc_HOL_Obool))))], (27369 ^ _777081) ^ [_1284346, _1284348, _1284350] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1284346), _1284348)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284346, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1284346, _1284346, _1284350), _1284348)), _1284348)), c_Fun_Oinj__on(_1284346, _1284346, _1284350, _1284348), -(hAPP(c_Set_Oimage(_1284346, _1284346, _1284350), _1284348) = _1284348)], (27383 ^ _777081) ^ [_1284593, _1284595, _1284597] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1284593), _1284595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1284593, tc_HOL_Obool)), _1284595), hAPP(c_Set_Oimage(_1284593, _1284593, _1284597), _1284595))), -(c_Fun_Oinj__on(_1284593, _1284593, _1284597, _1284595))], (27393 ^ _777081) ^ [_1284772, _1284774] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1284772), c_Orderings_Otop__class_Otop(tc_fun(_1284772, tc_HOL_Obool)))), c_Fun_Oinj__on(_1284772, _1284772, _1284774, c_Orderings_Otop__class_Otop(tc_fun(_1284772, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1284772, _1284772, _1284774), c_Orderings_Otop__class_Otop(tc_fun(_1284772, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1284772, tc_HOL_Obool)))], (27403 ^ _777081) ^ [_1284967, _1284969] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1284967), c_Orderings_Otop__class_Otop(tc_fun(_1284967, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1284967, _1284967, _1284969), c_Orderings_Otop__class_Otop(tc_fun(_1284967, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1284967, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1284967, _1284967, _1284969, c_Orderings_Otop__class_Otop(tc_fun(_1284967, tc_HOL_Obool))))], (27413 ^ _777081) ^ [_1285174] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1285174)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1285174), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1285174), c_Orderings_Otop__class_Otop(tc_fun(_1285174, tc_HOL_Obool)))))], (27419 ^ _777081) ^ [_1285289] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1285289), c_Orderings_Otop__class_Otop(tc_fun(_1285289, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1285289)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1285289), tc_HOL_Obool)))))], (27425 ^ _777081) ^ [_1285410, _1285412, _1285414, _1285416] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1285410), hAPP(c_Set_Ovimage(_1285410, _1285412, _1285414), _1285416))), hAPP(c_Set_Oimage(_1285410, _1285412, _1285414), c_Orderings_Otop__class_Otop(tc_fun(_1285410, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1285412, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1285412), _1285416)))], (27435 ^ _777081) ^ [_1285611, _1285613, _1285615, _1285617] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1285611), _1285613)), c_Fun_Oinj__on(_1285615, _1285611, _1285617, c_Orderings_Otop__class_Otop(tc_fun(_1285615, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1285615), hAPP(c_Set_Ovimage(_1285615, _1285611, _1285617), _1285613))))], (27445 ^ _777081) ^ [_1285810, _1285812, _1285814] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1285810, tc_HOL_Obool), tc_fun(_1285810, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1285810, tc_HOL_Obool), tc_fun(_1285810, tc_HOL_Obool)), _1285812), _1285814)), c_Wellfounded_Ofinite__psubset(_1285810))), 27448 ^ _777081 : [(27449 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1285810, tc_HOL_Obool)), _1285812), _1285814)))], (27451 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1285810), _1285814)))]]], (27453 ^ _777081) ^ [_1286005, _1286007, _1286009] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1286005, tc_HOL_Obool), tc_fun(_1286005, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1286005, tc_HOL_Obool), tc_fun(_1286005, tc_HOL_Obool)), _1286007), _1286009)), c_Wellfounded_Ofinite__psubset(_1286005)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1286005, tc_HOL_Obool)), _1286007), _1286009)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286005), _1286009))], (27463 ^ _777081) ^ [_1286234, _1286236, _1286238] : [class_Rings_Oring__1(_1286234), -(hAPP(c_Int_Oring__1__class_Oof__int(_1286234), 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), _1286236), _1286238)), 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(_1286234), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1286234), _1286236)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1286234), _1286238)))], (27469 ^ _777081) ^ [] : [-(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))))))], (27471 ^ _777081) ^ [_1286411, _1286413, _1286415, _1286417] : [-(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), _1286411), _1286413)), 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), _1286415), _1286417)), 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), _1286411), _1286415)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1286413), _1286417))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1286411), _1286417)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1286413), _1286415)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (27473 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (27475 ^ _777081) ^ [_1286560, _1286562] : [-(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), _1286560), _1286562)), 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), _1286562), _1286560)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (27477 ^ _777081) ^ [] : [-(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))))))], (27479 ^ _777081) ^ [_1286642] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1286642) = 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), _1286642), 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))))))], (27481 ^ _777081) ^ [_1286686, _1286688, _1286690, _1286692] : [-(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), _1286686), _1286688)), 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), _1286690), _1286692)), 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), _1286686), _1286690)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1286688), _1286692))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (27483 ^ _777081) ^ [_1286787, _1286789] : [-(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), _1286787), _1286789)), 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), _1286787), _1286789))], (27485 ^ _777081) ^ [_1286860, _1286862, _1286864, _1286866] : [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), _1286860), _1286862)), 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), _1286864), _1286866)), 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), _1286860), _1286866)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1286864), _1286862))))], (27491 ^ _777081) ^ [_1287053, _1287055, _1287057, _1287059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1287053), _1287059)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1287057), _1287055))), -(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), _1287053), _1287055)), 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), _1287057), _1287059)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (27497 ^ _777081) ^ [_1287273, _1287275, _1287277, _1287279] : [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), _1287273), _1287275)), 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), _1287277), _1287279)), 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), _1287273), _1287279)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1287277), _1287275))))], (27503 ^ _777081) ^ [_1287466, _1287468, _1287470, _1287472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1287466), _1287472)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1287470), _1287468))), -(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), _1287466), _1287468)), 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), _1287470), _1287472)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (27509 ^ _777081) ^ [_1287680, _1287682] : [c_Relation_Oirrefl(_1287680, _1287682), 27512 ^ _777081 : [(27513 ^ _777081) ^ [_1287762] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1287680, _1287680)), hAPP(hAPP(c_Product__Type_OPair(_1287680, _1287680), _1287762), _1287762)), _1287682))]]], (27515 ^ _777081) ^ [_1287802, _1287804] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1287802, _1287802)), hAPP(hAPP(c_Product__Type_OPair(_1287802, _1287802), 27516 ^ [_1287802, _1287804]), 27516 ^ [_1287802, _1287804])), _1287804))), -(c_Relation_Oirrefl(_1287802, _1287804))], (27522 ^ _777081) ^ [_1287873, _1287875, _1287877, _1287879, _1287881, _1287883, _1287885, _1287887, _1287889] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1287873), _1287875)), 27528 ^ _777081 : [(27529 ^ _777081) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_1287877, _1287879, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1287877)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1287877), hAPP(_1287881, 27527 ^ [_1287873, _1287875, _1287877, _1287879, _1287881, _1287883, _1287885, _1287887, _1287889])), hAPP(_1287883, 27527 ^ [_1287873, _1287875, _1287877, _1287879, _1287881, _1287883, _1287885, _1287887, _1287889])), hAPP(_1287885, 27527 ^ [_1287873, _1287875, _1287877, _1287879, _1287881, _1287883, _1287885, _1287887, _1287889]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1287877), tc_HOL_Obool)))))], (27531 ^ _777081) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_1287877, _1287879, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1287877)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1287877), hAPP(_1287887, 27527 ^ [_1287873, _1287875, _1287877, _1287879, _1287881, _1287883, _1287885, _1287887, _1287889])), hAPP(_1287883, 27527 ^ [_1287873, _1287875, _1287877, _1287879, _1287881, _1287883, _1287885, _1287887, _1287889])), hAPP(_1287889, 27527 ^ [_1287873, _1287875, _1287877, _1287879, _1287881, _1287883, _1287885, _1287887, _1287889]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1287877), tc_HOL_Obool))))]], c_Hoare__Mirabelle_Ohoare__derivs(_1287877, _1287879, hAPP(c_Set_Oimage(_1287873, tc_Hoare__Mirabelle_Otriple(_1287877), hAPP(hAPP(c_COMBS(_1287873, tc_fun(_1287877, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1287877)), hAPP(hAPP(c_COMBS(_1287873, tc_Com_Ocom, tc_fun(tc_fun(_1287877, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1287877))), hAPP(hAPP(c_COMBB(tc_fun(_1287877, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1287877, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1287877))), _1287873), c_Hoare__Mirabelle_Otriple_Otriple(_1287877)), _1287881)), _1287883)), _1287885)), _1287875)), -(c_Hoare__Mirabelle_Ohoare__derivs(_1287877, _1287879, hAPP(c_Set_Oimage(_1287873, tc_Hoare__Mirabelle_Otriple(_1287877), hAPP(hAPP(c_COMBS(_1287873, tc_fun(_1287877, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1287877)), hAPP(hAPP(c_COMBS(_1287873, tc_Com_Ocom, tc_fun(tc_fun(_1287877, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1287877))), hAPP(hAPP(c_COMBB(tc_fun(_1287877, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_1287877, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_1287877))), _1287873), c_Hoare__Mirabelle_Otriple_Otriple(_1287877)), _1287887)), _1287883)), _1287889)), _1287875)))], (27539 ^ _777081) ^ [_1288762, _1288764, _1288766, _1288768, _1288770, _1288772, _1288774, _1288776] : [c_Finite__Set_Ofolding__image__simple(_1288762, _1288764, _1288766, _1288768, _1288770, _1288772), hBOOL(hAPP(c_Finite__Set_Ofinite(_1288764), _1288774)), hBOOL(hAPP(hAPP(c_member(_1288764), _1288776), _1288774)), -(hAPP(_1288772, _1288774) = hAPP(hAPP(_1288766, hAPP(_1288770, _1288776)), hAPP(_1288772, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1288764, tc_HOL_Obool)), _1288774), hAPP(hAPP(c_Set_Oinsert(_1288764), _1288776), c_Orderings_Obot__class_Obot(tc_fun(_1288764, tc_HOL_Obool)))))))], (27553 ^ _777081) ^ [_1289087, _1289089, _1289091, _1289093, _1289095] : [c_Finite__Set_Ofolding__one(_1289087, _1289089, _1289091), hBOOL(hAPP(c_Finite__Set_Ofinite(_1289087), _1289093)), hBOOL(hAPP(hAPP(c_member(_1289087), _1289095), _1289093)), 27564 ^ _777081 : [(27565 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289087, tc_HOL_Obool)), _1289093), hAPP(hAPP(c_Set_Oinsert(_1289087), _1289095), c_Orderings_Obot__class_Obot(tc_fun(_1289087, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1289087, tc_HOL_Obool)), -(hAPP(_1289091, _1289093) = _1289095)], (27571 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289087, tc_HOL_Obool)), _1289093), hAPP(hAPP(c_Set_Oinsert(_1289087), _1289095), c_Orderings_Obot__class_Obot(tc_fun(_1289087, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1289087, tc_HOL_Obool))), -(hAPP(_1289091, _1289093) = hAPP(hAPP(_1289089, _1289095), hAPP(_1289091, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289087, tc_HOL_Obool)), _1289093), hAPP(hAPP(c_Set_Oinsert(_1289087), _1289095), c_Orderings_Obot__class_Obot(tc_fun(_1289087, tc_HOL_Obool)))))))]]], (27577 ^ _777081) ^ [_1289609, _1289611, _1289613, _1289615, _1289617, _1289619] : [c_Finite__Set_Ofolding__image__simple(_1289609, _1289611, _1289613, _1289615, _1289617, _1289619), -(hAPP(_1289619, c_Orderings_Obot__class_Obot(tc_fun(_1289611, tc_HOL_Obool))) = _1289615)], (27583 ^ _777081) ^ [_1289718, _1289720, _1289722, _1289724] : [c_Finite__Set_Ofolding__one(_1289718, _1289720, _1289722), -(hAPP(_1289722, hAPP(hAPP(c_Set_Oinsert(_1289718), _1289724), c_Orderings_Obot__class_Obot(tc_fun(_1289718, tc_HOL_Obool)))) = _1289724)], (27589 ^ _777081) ^ [_1289833, _1289835, _1289837, _1289839, _1289841, _1289843, _1289845, _1289847] : [c_Finite__Set_Ofolding__image__simple(_1289833, _1289835, _1289837, _1289839, _1289841, _1289843), hBOOL(hAPP(c_Finite__Set_Ofinite(_1289835), _1289845)), -(hBOOL(hAPP(hAPP(c_member(_1289835), _1289847), _1289845))), -(hAPP(_1289843, hAPP(hAPP(c_Set_Oinsert(_1289835), _1289847), _1289845)) = hAPP(hAPP(_1289837, hAPP(_1289841, _1289847)), hAPP(_1289843, _1289845)))], (27603 ^ _777081) ^ [_1290077, _1290079, _1290081, _1290083, _1290085, _1290087, _1290089, _1290091] : [c_Finite__Set_Ofolding__image__simple(_1290077, _1290079, _1290081, _1290083, _1290085, _1290087), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290079), _1290089)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290079), _1290091)), -(hAPP(hAPP(_1290081, hAPP(_1290087, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290079, tc_HOL_Obool)), _1290089), _1290091))), hAPP(_1290087, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290079, tc_HOL_Obool)), _1290089), _1290091))) = hAPP(hAPP(_1290081, hAPP(_1290087, _1290089)), hAPP(_1290087, _1290091)))], (27617 ^ _777081) ^ [_1290410, _1290412, _1290414, _1290416, _1290418] : [c_Finite__Set_Ofolding__one(_1290410, _1290412, _1290414), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290410), _1290416)), -(hBOOL(hAPP(hAPP(c_member(_1290410), _1290418), _1290416))), -(_1290416 = c_Orderings_Obot__class_Obot(tc_fun(_1290410, tc_HOL_Obool))), -(hAPP(_1290414, hAPP(hAPP(c_Set_Oinsert(_1290410), _1290418), _1290416)) = hAPP(hAPP(_1290412, _1290418), hAPP(_1290414, _1290416)))], (27635 ^ _777081) ^ [_1290655, _1290657, _1290659, _1290661, _1290663, _1290665, _1290667, _1290669] : [c_Finite__Set_Ofolding__image__simple(_1290655, _1290657, _1290659, _1290661, _1290663, _1290665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290657), _1290667)), -(hAPP(_1290665, hAPP(hAPP(c_Set_Oinsert(_1290657), _1290669), _1290667)) = hAPP(hAPP(_1290659, hAPP(_1290663, _1290669)), hAPP(_1290665, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290657, tc_HOL_Obool)), _1290667), hAPP(hAPP(c_Set_Oinsert(_1290657), _1290669), c_Orderings_Obot__class_Obot(tc_fun(_1290657, tc_HOL_Obool)))))))], (27645 ^ _777081) ^ [_1290918, _1290920, _1290922, _1290924, _1290926] : [c_Finite__Set_Ofolding__one(_1290918, _1290920, _1290922), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290918), _1290924)), 27652 ^ _777081 : [(27653 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290918, tc_HOL_Obool)), _1290924), hAPP(hAPP(c_Set_Oinsert(_1290918), _1290926), c_Orderings_Obot__class_Obot(tc_fun(_1290918, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1290918, tc_HOL_Obool)), -(hAPP(_1290922, hAPP(hAPP(c_Set_Oinsert(_1290918), _1290926), _1290924)) = _1290926)], (27659 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290918, tc_HOL_Obool)), _1290924), hAPP(hAPP(c_Set_Oinsert(_1290918), _1290926), c_Orderings_Obot__class_Obot(tc_fun(_1290918, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1290918, tc_HOL_Obool))), -(hAPP(_1290922, hAPP(hAPP(c_Set_Oinsert(_1290918), _1290926), _1290924)) = hAPP(hAPP(_1290920, _1290926), hAPP(_1290922, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1290918, tc_HOL_Obool)), _1290924), hAPP(hAPP(c_Set_Oinsert(_1290918), _1290926), c_Orderings_Obot__class_Obot(tc_fun(_1290918, tc_HOL_Obool)))))))]]], (27665 ^ _777081) ^ [_1291400, _1291402, _1291404, _1291406, _1291408] : [c_Finite__Set_Ofolding__one(_1291400, _1291402, _1291404), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291400), _1291406)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291400), _1291408)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1291400, tc_HOL_Obool)), _1291406), _1291408) = c_Orderings_Obot__class_Obot(tc_fun(_1291400, tc_HOL_Obool))), -(hAPP(hAPP(_1291402, hAPP(_1291404, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1291400, tc_HOL_Obool)), _1291406), _1291408))), hAPP(_1291404, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1291400, tc_HOL_Obool)), _1291406), _1291408))) = hAPP(hAPP(_1291402, hAPP(_1291404, _1291406)), hAPP(_1291404, _1291408)))], (27683 ^ _777081) ^ [_1291756, _1291758, _1291760, _1291762, _1291764] : [c_Finite__Set_Ofolding__one(_1291756, _1291758, _1291760), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291756), _1291762)), -(_1291762 = c_Orderings_Obot__class_Obot(tc_fun(_1291756, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291756), _1291764)), -(_1291764 = c_Orderings_Obot__class_Obot(tc_fun(_1291756, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1291756, tc_HOL_Obool)), _1291762), _1291764) = c_Orderings_Obot__class_Obot(tc_fun(_1291756, tc_HOL_Obool)), -(hAPP(_1291760, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1291756, tc_HOL_Obool)), _1291762), _1291764)) = hAPP(hAPP(_1291758, hAPP(_1291760, _1291762)), hAPP(_1291760, _1291764)))], (27709 ^ _777081) ^ [_1292257, _1292259, _1292261, _1292263, _1292265, _1292267, _1292269, _1292271] : [c_Finite__Set_Ofolding__image__simple(_1292257, _1292259, _1292261, _1292263, _1292265, _1292267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292259), _1292269)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292259), _1292271)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1292259, tc_HOL_Obool)), _1292269), _1292271) = c_Orderings_Obot__class_Obot(tc_fun(_1292259, tc_HOL_Obool)), -(hAPP(_1292267, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292259, tc_HOL_Obool)), _1292269), _1292271)) = hAPP(hAPP(_1292261, hAPP(_1292267, _1292269)), hAPP(_1292267, _1292271)))], (27729 ^ _777081) ^ [_1292646] : [-(_1292646 = 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), 27726 ^ [_1292646]), 27727 ^ [_1292646])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (27742 ^ _777081) ^ [_1292896] : [27744 ^ _777081 : [(27745 ^ _777081) ^ [_1292972] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27743 ^ [_1292896, _1292972]), _1292896)))], (27747 ^ _777081) ^ [_1293006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27743 ^ [_1292896, _1293006]), _1293006))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1292896)))], (27731 ^ _777081) ^ [_1292709] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1292709)), 27735 ^ _777081 : [(27736 ^ _777081) ^ [_1292789] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1292789), _1292709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1292789), 27734 ^ [_1292709])))]]], (27762 ^ _777081) ^ [_1293274] : [27764 ^ _777081 : [(27765 ^ _777081) ^ [_1293350] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27763 ^ [_1293274, _1293350]), _1293274)))], (27767 ^ _777081) ^ [_1293384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 27763 ^ [_1293274, _1293384]), _1293384))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1293274)))], (27751 ^ _777081) ^ [_1293087] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1293087)), 27755 ^ _777081 : [(27756 ^ _777081) ^ [_1293167] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1293167), _1293087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1293167), 27754 ^ [_1293087])))]]], (27771 ^ _777081) ^ [_1293453, _1293455, _1293457, _1293459] : [-(hAPP(c_Relation_OField(_1293453), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1293453, _1293453)), hAPP(hAPP(c_Product__Type_OPair(_1293453, _1293453), _1293455), _1293457)), _1293459)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293453, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1293453), _1293455), hAPP(hAPP(c_Set_Oinsert(_1293453), _1293457), c_Orderings_Obot__class_Obot(tc_fun(_1293453, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1293453), _1293459)))], (27773 ^ _777081) ^ [_1293544] : [-(hAPP(c_Relation_OField(_1293544), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1293544, _1293544), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1293544, tc_HOL_Obool)))], (27775 ^ _777081) ^ [_1293585, _1293587, _1293589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1293585, _1293585), tc_HOL_Obool)), _1293587), _1293589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1293585, tc_HOL_Obool)), hAPP(c_Relation_OField(_1293585), _1293587)), hAPP(c_Relation_OField(_1293585), _1293589))))], (27781 ^ _777081) ^ [_1293730, _1293732, _1293734] : [-(hAPP(c_Relation_OField(_1293730), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1293730, _1293730), tc_HOL_Obool)), _1293732), _1293734)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293730, tc_HOL_Obool)), hAPP(c_Relation_OField(_1293730), _1293732)), hAPP(c_Relation_OField(_1293730), _1293734)))], (27783 ^ _777081) ^ [_1293797, _1293799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1293797, _1293797)), _1293799)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1293797), hAPP(c_Relation_OField(_1293797), _1293799))))], (27789 ^ _777081) ^ [_1293927, _1293929, _1293931, _1293933] : [hBOOL(hAPP(hAPP(c_member(_1293927), _1293929), c_SetInterval_Oord_OatMost(_1293927, _1293931, _1293933))), -(hBOOL(hAPP(hAPP(_1293931, _1293929), _1293933)))], (27795 ^ _777081) ^ [_1294036, _1294038, _1294040, _1294042] : [hBOOL(hAPP(hAPP(_1294040, _1294038), _1294042)), -(hBOOL(hAPP(hAPP(c_member(_1294036), _1294038), c_SetInterval_Oord_OatMost(_1294036, _1294040, _1294042))))], (27801 ^ _777081) ^ [_1294172, _1294174, _1294176, _1294178] : [hBOOL(hAPP(hAPP(c_member(_1294172), _1294174), c_SetInterval_Oord_OatLeast(_1294172, _1294176, _1294178))), -(hBOOL(hAPP(hAPP(_1294176, _1294178), _1294174)))], (27807 ^ _777081) ^ [_1294281, _1294283, _1294285, _1294287] : [hBOOL(hAPP(hAPP(_1294285, _1294287), _1294283)), -(hBOOL(hAPP(hAPP(c_member(_1294281), _1294283), c_SetInterval_Oord_OatLeast(_1294281, _1294285, _1294287))))], (27813 ^ _777081) ^ [_1294417, _1294419, _1294421, _1294423] : [hBOOL(hAPP(hAPP(c_member(_1294417), _1294419), c_SetInterval_Oord_OlessThan(_1294417, _1294421, _1294423))), -(hBOOL(hAPP(hAPP(_1294421, _1294419), _1294423)))], (27819 ^ _777081) ^ [_1294526, _1294528, _1294530, _1294532] : [hBOOL(hAPP(hAPP(_1294530, _1294528), _1294532)), -(hBOOL(hAPP(hAPP(c_member(_1294526), _1294528), c_SetInterval_Oord_OlessThan(_1294526, _1294530, _1294532))))], (27825 ^ _777081) ^ [_1294662, _1294664, _1294666, _1294668] : [hBOOL(hAPP(hAPP(c_member(_1294662), _1294664), c_SetInterval_Oord_OgreaterThan(_1294662, _1294666, _1294668))), -(hBOOL(hAPP(hAPP(_1294666, _1294668), _1294664)))], (27831 ^ _777081) ^ [_1294771, _1294773, _1294775, _1294777] : [hBOOL(hAPP(hAPP(_1294775, _1294777), _1294773)), -(hBOOL(hAPP(hAPP(c_member(_1294771), _1294773), c_SetInterval_Oord_OgreaterThan(_1294771, _1294775, _1294777))))], (27837 ^ _777081) ^ [_1294913, _1294915, _1294917, _1294919, _1294921, _1294923] : [hBOOL(hAPP(hAPP(c_member(_1294913), _1294915), c_SetInterval_Oord_OgreaterThanAtMost(_1294913, _1294917, _1294919, _1294921, _1294923))), 27840 ^ _777081 : [(27841 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1294919, _1294921), _1294915)))], (27843 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1294917, _1294915), _1294923)))]]], (27845 ^ _777081) ^ [_1295066, _1295068, _1295070, _1295072, _1295074, _1295076] : [-(hBOOL(hAPP(hAPP(c_member(_1295066), _1295068), c_SetInterval_Oord_OgreaterThanAtMost(_1295066, _1295070, _1295072, _1295074, _1295076)))), hBOOL(hAPP(hAPP(_1295072, _1295074), _1295068)), hBOOL(hAPP(hAPP(_1295070, _1295068), _1295076))], (27855 ^ _777081) ^ [_1295286, _1295288, _1295290, _1295292, _1295294, _1295296] : [hBOOL(hAPP(hAPP(c_member(_1295286), _1295288), c_SetInterval_Oord_OatLeastLessThan(_1295286, _1295290, _1295292, _1295294, _1295296))), 27858 ^ _777081 : [(27859 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1295290, _1295294), _1295288)))], (27861 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1295292, _1295288), _1295296)))]]], (27863 ^ _777081) ^ [_1295439, _1295441, _1295443, _1295445, _1295447, _1295449] : [-(hBOOL(hAPP(hAPP(c_member(_1295439), _1295441), c_SetInterval_Oord_OatLeastLessThan(_1295439, _1295443, _1295445, _1295447, _1295449)))), hBOOL(hAPP(hAPP(_1295443, _1295447), _1295441)), hBOOL(hAPP(hAPP(_1295445, _1295441), _1295449))], (27873 ^ _777081) ^ [_1295656, _1295658, _1295660, _1295662, _1295664] : [hBOOL(hAPP(hAPP(c_member(_1295656), _1295658), c_SetInterval_Oord_OgreaterThanLessThan(_1295656, _1295660, _1295662, _1295664))), 27876 ^ _777081 : [(27877 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1295660, _1295662), _1295658)))], (27879 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1295660, _1295658), _1295664)))]]], (27881 ^ _777081) ^ [_1295805, _1295807, _1295809, _1295811, _1295813] : [-(hBOOL(hAPP(hAPP(c_member(_1295805), _1295807), c_SetInterval_Oord_OgreaterThanLessThan(_1295805, _1295809, _1295811, _1295813)))), hBOOL(hAPP(hAPP(_1295809, _1295811), _1295807)), hBOOL(hAPP(hAPP(_1295809, _1295807), _1295813))], (27891 ^ _777081) ^ [_1296016, _1296018, _1296020, _1296022, _1296024] : [hBOOL(hAPP(hAPP(c_member(_1296016), _1296018), c_SetInterval_Oord_OatLeastAtMost(_1296016, _1296020, _1296022, _1296024))), 27894 ^ _777081 : [(27895 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1296020, _1296022), _1296018)))], (27897 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1296020, _1296018), _1296024)))]]], (27899 ^ _777081) ^ [_1296165, _1296167, _1296169, _1296171, _1296173] : [-(hBOOL(hAPP(hAPP(c_member(_1296165), _1296167), c_SetInterval_Oord_OatLeastAtMost(_1296165, _1296169, _1296171, _1296173)))), hBOOL(hAPP(hAPP(_1296169, _1296171), _1296167)), hBOOL(hAPP(hAPP(_1296169, _1296167), _1296173))], (27909 ^ _777081) ^ [_1296352, _1296354, _1296356] : [class_Lattices_Olattice(_1296352), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296352), _1296354)), hBOOL(hAPP(hAPP(c_member(_1296352), _1296356), _1296354)), 27920 ^ _777081 : [(27921 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1296352, tc_HOL_Obool)), _1296354), hAPP(hAPP(c_Set_Oinsert(_1296352), _1296356), c_Orderings_Obot__class_Obot(tc_fun(_1296352, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1296352, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1296352, _1296354) = _1296356)], (27927 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1296352, tc_HOL_Obool)), _1296354), hAPP(hAPP(c_Set_Oinsert(_1296352), _1296356), c_Orderings_Obot__class_Obot(tc_fun(_1296352, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1296352, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1296352, _1296354) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1296352), _1296356), c_Big__Operators_Olattice__class_OInf__fin(_1296352, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1296352, tc_HOL_Obool)), _1296354), hAPP(hAPP(c_Set_Oinsert(_1296352), _1296356), c_Orderings_Obot__class_Obot(tc_fun(_1296352, tc_HOL_Obool)))))))]]], (27933 ^ _777081) ^ [_1296858, _1296860, _1296862] : [class_Lattices_Olattice(_1296858), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296858), _1296860)), hBOOL(hAPP(hAPP(c_member(_1296858), _1296862), _1296860)), 27944 ^ _777081 : [(27945 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1296858, tc_HOL_Obool)), _1296860), hAPP(hAPP(c_Set_Oinsert(_1296858), _1296862), c_Orderings_Obot__class_Obot(tc_fun(_1296858, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1296858, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1296858, _1296860) = _1296862)], (27951 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1296858, tc_HOL_Obool)), _1296860), hAPP(hAPP(c_Set_Oinsert(_1296858), _1296862), c_Orderings_Obot__class_Obot(tc_fun(_1296858, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1296858, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1296858, _1296860) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1296858), _1296862), c_Big__Operators_Olattice__class_OSup__fin(_1296858, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1296858, tc_HOL_Obool)), _1296860), hAPP(hAPP(c_Set_Oinsert(_1296858), _1296862), c_Orderings_Obot__class_Obot(tc_fun(_1296858, tc_HOL_Obool)))))))]]], (27957 ^ _777081) ^ [_1297364, _1297366, _1297368] : [class_Orderings_Olinorder(_1297364), hBOOL(hAPP(c_Finite__Set_Ofinite(_1297364), _1297366)), hBOOL(hAPP(hAPP(c_member(_1297364), _1297368), _1297366)), 27968 ^ _777081 : [(27969 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1297364, tc_HOL_Obool)), _1297366), hAPP(hAPP(c_Set_Oinsert(_1297364), _1297368), c_Orderings_Obot__class_Obot(tc_fun(_1297364, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1297364, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1297364, _1297366) = _1297368)], (27975 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1297364, tc_HOL_Obool)), _1297366), hAPP(hAPP(c_Set_Oinsert(_1297364), _1297368), c_Orderings_Obot__class_Obot(tc_fun(_1297364, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1297364, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1297364, _1297366) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1297364), _1297368), c_Big__Operators_Olinorder__class_OMax(_1297364, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1297364, tc_HOL_Obool)), _1297366), hAPP(hAPP(c_Set_Oinsert(_1297364), _1297368), c_Orderings_Obot__class_Obot(tc_fun(_1297364, tc_HOL_Obool)))))))]]], (27981 ^ _777081) ^ [_1297870, _1297872, _1297874] : [class_Orderings_Olinorder(_1297870), hBOOL(hAPP(c_Finite__Set_Ofinite(_1297870), _1297872)), hBOOL(hAPP(hAPP(c_member(_1297870), _1297874), _1297872)), 27992 ^ _777081 : [(27993 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1297870, tc_HOL_Obool)), _1297872), hAPP(hAPP(c_Set_Oinsert(_1297870), _1297874), c_Orderings_Obot__class_Obot(tc_fun(_1297870, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1297870, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1297870, _1297872) = _1297874)], (27999 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1297870, tc_HOL_Obool)), _1297872), hAPP(hAPP(c_Set_Oinsert(_1297870), _1297874), c_Orderings_Obot__class_Obot(tc_fun(_1297870, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1297870, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1297870, _1297872) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1297870), _1297874), c_Big__Operators_Olinorder__class_OMin(_1297870, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1297870, tc_HOL_Obool)), _1297872), hAPP(hAPP(c_Set_Oinsert(_1297870), _1297874), c_Orderings_Obot__class_Obot(tc_fun(_1297870, tc_HOL_Obool)))))))]]], (28005 ^ _777081) ^ [_1298376, _1298378] : [class_Lattices_Olattice(_1298376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298376), _1298378)), -(_1298378 = c_Orderings_Obot__class_Obot(tc_fun(_1298376, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298376), c_Big__Operators_Olattice__class_OInf__fin(_1298376, _1298378)), c_Big__Operators_Olattice__class_OSup__fin(_1298376, _1298378))))], (28019 ^ _777081) ^ [_1298562, _1298564] : [class_Groups_Olinordered__ab__group__add(_1298562), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298562), _1298564)), -(_1298564 = c_Orderings_Obot__class_Obot(tc_fun(_1298562, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1298562), c_Big__Operators_Olinorder__class_OMax(_1298562, _1298564)) = c_Big__Operators_Olinorder__class_OMin(_1298562, hAPP(c_Set_Oimage(_1298562, _1298562, c_Groups_Ouminus__class_Ouminus(_1298562)), _1298564)))], (28033 ^ _777081) ^ [_1298762, _1298764] : [class_Groups_Olinordered__ab__group__add(_1298762), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298762), _1298764)), -(_1298764 = c_Orderings_Obot__class_Obot(tc_fun(_1298762, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1298762), c_Big__Operators_Olinorder__class_OMin(_1298762, _1298764)) = c_Big__Operators_Olinorder__class_OMax(_1298762, hAPP(c_Set_Oimage(_1298762, _1298762, c_Groups_Ouminus__class_Ouminus(_1298762)), _1298764)))], (28047 ^ _777081) ^ [_1298962, _1298964] : [class_Orderings_Olinorder(_1298962), -(c_Big__Operators_Olinorder__class_OMax(_1298962, hAPP(hAPP(c_Set_Oinsert(_1298962), _1298964), c_Orderings_Obot__class_Obot(tc_fun(_1298962, tc_HOL_Obool)))) = _1298964)], (28053 ^ _777081) ^ [_1299069, _1299071] : [class_Orderings_Olinorder(_1299069), -(c_Big__Operators_Olinorder__class_OMin(_1299069, hAPP(hAPP(c_Set_Oinsert(_1299069), _1299071), c_Orderings_Obot__class_Obot(tc_fun(_1299069, tc_HOL_Obool)))) = _1299071)], (28059 ^ _777081) ^ [_1299176, _1299178] : [class_Lattices_Olattice(_1299176), -(c_Big__Operators_Olattice__class_OInf__fin(_1299176, hAPP(hAPP(c_Set_Oinsert(_1299176), _1299178), c_Orderings_Obot__class_Obot(tc_fun(_1299176, tc_HOL_Obool)))) = _1299178)], (28065 ^ _777081) ^ [_1299283, _1299285] : [class_Lattices_Olattice(_1299283), -(c_Big__Operators_Olattice__class_OSup__fin(_1299283, hAPP(hAPP(c_Set_Oinsert(_1299283), _1299285), c_Orderings_Obot__class_Obot(tc_fun(_1299283, tc_HOL_Obool)))) = _1299285)], (28071 ^ _777081) ^ [_1299390, _1299392, _1299394] : [class_Orderings_Olinorder(_1299390), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299390), _1299392)), hBOOL(hAPP(hAPP(c_member(_1299390), _1299394), _1299392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299390), _1299394), c_Big__Operators_Olinorder__class_OMax(_1299390, _1299392))))], (28085 ^ _777081) ^ [_1299617, _1299619, _1299621] : [class_Orderings_Olinorder(_1299617), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299617), _1299619)), hBOOL(hAPP(hAPP(c_member(_1299617), _1299621), _1299619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299617), c_Big__Operators_Olinorder__class_OMin(_1299617, _1299619)), _1299621)))], (28099 ^ _777081) ^ [_1299844, _1299846] : [class_Orderings_Olinorder(_1299844), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299844), _1299846)), -(_1299846 = c_Orderings_Obot__class_Obot(tc_fun(_1299844, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1299844), c_Big__Operators_Olinorder__class_OMin(_1299844, _1299846)), _1299846)))], (28113 ^ _777081) ^ [_1300024, _1300026] : [class_Orderings_Olinorder(_1300024), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300024), _1300026)), -(_1300026 = c_Orderings_Obot__class_Obot(tc_fun(_1300024, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1300024), c_Big__Operators_Olinorder__class_OMax(_1300024, _1300026)), _1300026)))], (28127 ^ _777081) ^ [_1300204, _1300206, _1300208] : [class_Lattices_Olattice(_1300204), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300204), _1300206)), hBOOL(hAPP(hAPP(c_member(_1300204), _1300208), _1300206)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1300204), _1300208), c_Big__Operators_Olattice__class_OSup__fin(_1300204, _1300206)) = c_Big__Operators_Olattice__class_OSup__fin(_1300204, _1300206))], (28141 ^ _777081) ^ [_1300439, _1300441, _1300443] : [class_Lattices_Olattice(_1300439), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300439), _1300441)), hBOOL(hAPP(hAPP(c_member(_1300439), _1300443), _1300441)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1300439), _1300443), c_Big__Operators_Olattice__class_OInf__fin(_1300439, _1300441)) = _1300443)], (28155 ^ _777081) ^ [_1300668, _1300670, _1300672] : [class_Lattices_Olattice(_1300668), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300668), _1300670)), hBOOL(hAPP(hAPP(c_member(_1300668), _1300672), _1300670)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1300668), _1300672), c_Big__Operators_Olattice__class_OSup__fin(_1300668, _1300670)) = _1300672)], (28169 ^ _777081) ^ [_1300897, _1300899, _1300901] : [class_Lattices_Olattice(_1300897), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300897), _1300899)), hBOOL(hAPP(hAPP(c_member(_1300897), _1300901), _1300899)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1300897), _1300901), c_Big__Operators_Olattice__class_OInf__fin(_1300897, _1300899)) = c_Big__Operators_Olattice__class_OInf__fin(_1300897, _1300899))], (28183 ^ _777081) ^ [_1301132, _1301134, _1301136] : [class_Orderings_Olinorder(_1301132), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301132), _1301134)), hBOOL(hAPP(hAPP(c_member(_1301132), _1301136), _1301134)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1301132), _1301136), c_Big__Operators_Olinorder__class_OMin(_1301132, _1301134)) = c_Big__Operators_Olinorder__class_OMin(_1301132, _1301134))], (28197 ^ _777081) ^ [_1301367, _1301369, _1301371] : [class_Orderings_Olinorder(_1301367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301367), _1301369)), hBOOL(hAPP(hAPP(c_member(_1301367), _1301371), _1301369)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1301367), _1301371), c_Big__Operators_Olinorder__class_OMax(_1301367, _1301369)) = c_Big__Operators_Olinorder__class_OMax(_1301367, _1301369))], (28211 ^ _777081) ^ [_1301602, _1301604, _1301606] : [class_Orderings_Olinorder(_1301602), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301602, tc_HOL_Obool)), _1301604), _1301606)), -(_1301604 = c_Orderings_Obot__class_Obot(tc_fun(_1301602, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301602), _1301606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301602), c_Big__Operators_Olinorder__class_OMax(_1301602, _1301604)), c_Big__Operators_Olinorder__class_OMax(_1301602, _1301606))))], (28229 ^ _777081) ^ [_1301908, _1301910, _1301912] : [class_Orderings_Olinorder(_1301908), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301908, tc_HOL_Obool)), _1301910), _1301912)), -(_1301910 = c_Orderings_Obot__class_Obot(tc_fun(_1301908, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301908), _1301912)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301908), c_Big__Operators_Olinorder__class_OMin(_1301908, _1301912)), c_Big__Operators_Olinorder__class_OMin(_1301908, _1301910))))], (28247 ^ _777081) ^ [_1302214, _1302216, _1302218] : [class_Lattices_Olattice(_1302214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302214), _1302216)), -(_1302216 = c_Orderings_Obot__class_Obot(tc_fun(_1302214, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1302214, hAPP(hAPP(c_Set_Oinsert(_1302214), _1302218), _1302216)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1302214), _1302218), c_Big__Operators_Olattice__class_OSup__fin(_1302214, _1302216)))], (28261 ^ _777081) ^ [_1302422, _1302424, _1302426] : [class_Lattices_Olattice(_1302422), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302422), _1302424)), -(_1302424 = c_Orderings_Obot__class_Obot(tc_fun(_1302422, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1302422, hAPP(hAPP(c_Set_Oinsert(_1302422), _1302426), _1302424)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1302422), _1302426), c_Big__Operators_Olattice__class_OInf__fin(_1302422, _1302424)))], (28275 ^ _777081) ^ [_1302630, _1302632, _1302634] : [class_Orderings_Olinorder(_1302630), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302630), _1302632)), -(_1302632 = c_Orderings_Obot__class_Obot(tc_fun(_1302630, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1302630, hAPP(hAPP(c_Set_Oinsert(_1302630), _1302634), _1302632)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1302630), _1302634), c_Big__Operators_Olinorder__class_OMin(_1302630, _1302632)))], (28289 ^ _777081) ^ [_1302838, _1302840, _1302842] : [class_Orderings_Olinorder(_1302838), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302838), _1302840)), -(_1302840 = c_Orderings_Obot__class_Obot(tc_fun(_1302838, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1302838, hAPP(hAPP(c_Set_Oinsert(_1302838), _1302842), _1302840)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1302838), _1302842), c_Big__Operators_Olinorder__class_OMax(_1302838, _1302840)))], (28303 ^ _777081) ^ [_1303046, _1303048, _1303050] : [class_Lattices_Olattice(_1303046), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303046), _1303048)), -(_1303050 = c_Orderings_Obot__class_Obot(tc_fun(_1303046, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1303046, tc_HOL_Obool)), _1303050), _1303048)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1303046), c_Big__Operators_Olattice__class_OSup__fin(_1303046, _1303050)), c_Big__Operators_Olattice__class_OSup__fin(_1303046, _1303048)) = c_Big__Operators_Olattice__class_OSup__fin(_1303046, _1303048))], (28321 ^ _777081) ^ [_1303360, _1303362, _1303364] : [class_Lattices_Olattice(_1303360), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303360), _1303362)), -(_1303364 = c_Orderings_Obot__class_Obot(tc_fun(_1303360, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1303360, tc_HOL_Obool)), _1303364), _1303362)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1303360), c_Big__Operators_Olattice__class_OInf__fin(_1303360, _1303364)), c_Big__Operators_Olattice__class_OInf__fin(_1303360, _1303362)) = c_Big__Operators_Olattice__class_OInf__fin(_1303360, _1303362))], (28339 ^ _777081) ^ [_1303674, _1303676, _1303678] : [class_Orderings_Olinorder(_1303674), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303674), _1303676)), -(_1303678 = c_Orderings_Obot__class_Obot(tc_fun(_1303674, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1303674, tc_HOL_Obool)), _1303678), _1303676)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1303674), c_Big__Operators_Olinorder__class_OMin(_1303674, _1303678)), c_Big__Operators_Olinorder__class_OMin(_1303674, _1303676)) = c_Big__Operators_Olinorder__class_OMin(_1303674, _1303676))], (28357 ^ _777081) ^ [_1303988, _1303990, _1303992] : [class_Lattices_Olattice(_1303988), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303988), _1303990)), -(_1303990 = c_Orderings_Obot__class_Obot(tc_fun(_1303988, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303988), _1303992)), -(_1303992 = c_Orderings_Obot__class_Obot(tc_fun(_1303988, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1303988, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1303988, tc_HOL_Obool)), _1303990), _1303992)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1303988), c_Big__Operators_Olattice__class_OSup__fin(_1303988, _1303990)), c_Big__Operators_Olattice__class_OSup__fin(_1303988, _1303992)))], (28379 ^ _777081) ^ [_1304337, _1304339, _1304341] : [class_Orderings_Olinorder(_1304337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304337), _1304339)), -(_1304341 = c_Orderings_Obot__class_Obot(tc_fun(_1304337, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1304337, tc_HOL_Obool)), _1304341), _1304339)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1304337), c_Big__Operators_Olinorder__class_OMax(_1304337, _1304341)), c_Big__Operators_Olinorder__class_OMax(_1304337, _1304339)) = c_Big__Operators_Olinorder__class_OMax(_1304337, _1304339))], (28397 ^ _777081) ^ [_1304651, _1304653, _1304655] : [class_Lattices_Olattice(_1304651), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304651), _1304653)), -(_1304653 = c_Orderings_Obot__class_Obot(tc_fun(_1304651, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304651), _1304655)), -(_1304655 = c_Orderings_Obot__class_Obot(tc_fun(_1304651, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1304651, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1304651, tc_HOL_Obool)), _1304653), _1304655)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1304651), c_Big__Operators_Olattice__class_OInf__fin(_1304651, _1304653)), c_Big__Operators_Olattice__class_OInf__fin(_1304651, _1304655)))], (28419 ^ _777081) ^ [_1305000, _1305002, _1305004] : [class_Orderings_Olinorder(_1305000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305000), _1305002)), -(_1305002 = c_Orderings_Obot__class_Obot(tc_fun(_1305000, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305000), _1305004)), -(_1305004 = c_Orderings_Obot__class_Obot(tc_fun(_1305000, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1305000, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305000, tc_HOL_Obool)), _1305002), _1305004)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1305000), c_Big__Operators_Olinorder__class_OMin(_1305000, _1305002)), c_Big__Operators_Olinorder__class_OMin(_1305000, _1305004)))], (28441 ^ _777081) ^ [_1305349, _1305351, _1305353] : [class_Orderings_Olinorder(_1305349), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305349), _1305351)), -(_1305351 = c_Orderings_Obot__class_Obot(tc_fun(_1305349, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305349), _1305353)), -(_1305353 = c_Orderings_Obot__class_Obot(tc_fun(_1305349, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1305349, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1305349, tc_HOL_Obool)), _1305351), _1305353)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1305349), c_Big__Operators_Olinorder__class_OMax(_1305349, _1305351)), c_Big__Operators_Olinorder__class_OMax(_1305349, _1305353)))], (28463 ^ _777081) ^ [_1305698, _1305700, _1305702] : [class_Lattices_Olattice(_1305698), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305698), _1305700)), -(hBOOL(hAPP(hAPP(c_member(_1305698), _1305702), _1305700))), -(_1305700 = c_Orderings_Obot__class_Obot(tc_fun(_1305698, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1305698, hAPP(hAPP(c_Set_Oinsert(_1305698), _1305702), _1305700)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1305698), _1305702), c_Big__Operators_Olattice__class_OSup__fin(_1305698, _1305700)))], (28481 ^ _777081) ^ [_1305935, _1305937, _1305939] : [class_Lattices_Olattice(_1305935), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305935), _1305937)), -(hBOOL(hAPP(hAPP(c_member(_1305935), _1305939), _1305937))), -(_1305937 = c_Orderings_Obot__class_Obot(tc_fun(_1305935, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1305935, hAPP(hAPP(c_Set_Oinsert(_1305935), _1305939), _1305937)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1305935), _1305939), c_Big__Operators_Olattice__class_OInf__fin(_1305935, _1305937)))], (28499 ^ _777081) ^ [_1306172, _1306174, _1306176] : [class_Orderings_Olinorder(_1306172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306172), _1306174)), -(hBOOL(hAPP(hAPP(c_member(_1306172), _1306176), _1306174))), -(_1306174 = c_Orderings_Obot__class_Obot(tc_fun(_1306172, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1306172, hAPP(hAPP(c_Set_Oinsert(_1306172), _1306176), _1306174)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1306172), _1306176), c_Big__Operators_Olinorder__class_OMin(_1306172, _1306174)))], (28517 ^ _777081) ^ [_1306409, _1306411, _1306413] : [class_Orderings_Olinorder(_1306409), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306409), _1306411)), -(hBOOL(hAPP(hAPP(c_member(_1306409), _1306413), _1306411))), -(_1306411 = c_Orderings_Obot__class_Obot(tc_fun(_1306409, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1306409, hAPP(hAPP(c_Set_Oinsert(_1306409), _1306413), _1306411)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306409), _1306413), c_Big__Operators_Olinorder__class_OMax(_1306409, _1306411)))], (28535 ^ _777081) ^ [_1306646, _1306648, _1306650] : [class_Lattices_Olattice(_1306646), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306646), _1306648)), 28542 ^ _777081 : [(28543 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1306646, tc_HOL_Obool)), _1306648), hAPP(hAPP(c_Set_Oinsert(_1306646), _1306650), c_Orderings_Obot__class_Obot(tc_fun(_1306646, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1306646, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1306646, hAPP(hAPP(c_Set_Oinsert(_1306646), _1306650), _1306648)) = _1306650)], (28549 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1306646, tc_HOL_Obool)), _1306648), hAPP(hAPP(c_Set_Oinsert(_1306646), _1306650), c_Orderings_Obot__class_Obot(tc_fun(_1306646, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1306646, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1306646, hAPP(hAPP(c_Set_Oinsert(_1306646), _1306650), _1306648)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1306646), _1306650), c_Big__Operators_Olattice__class_OSup__fin(_1306646, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1306646, tc_HOL_Obool)), _1306648), hAPP(hAPP(c_Set_Oinsert(_1306646), _1306650), c_Orderings_Obot__class_Obot(tc_fun(_1306646, tc_HOL_Obool)))))))]]], (28555 ^ _777081) ^ [_1307116, _1307118, _1307120] : [class_Lattices_Olattice(_1307116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307116), _1307118)), 28562 ^ _777081 : [(28563 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307116, tc_HOL_Obool)), _1307118), hAPP(hAPP(c_Set_Oinsert(_1307116), _1307120), c_Orderings_Obot__class_Obot(tc_fun(_1307116, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1307116, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1307116, hAPP(hAPP(c_Set_Oinsert(_1307116), _1307120), _1307118)) = _1307120)], (28569 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307116, tc_HOL_Obool)), _1307118), hAPP(hAPP(c_Set_Oinsert(_1307116), _1307120), c_Orderings_Obot__class_Obot(tc_fun(_1307116, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1307116, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1307116, hAPP(hAPP(c_Set_Oinsert(_1307116), _1307120), _1307118)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1307116), _1307120), c_Big__Operators_Olattice__class_OInf__fin(_1307116, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307116, tc_HOL_Obool)), _1307118), hAPP(hAPP(c_Set_Oinsert(_1307116), _1307120), c_Orderings_Obot__class_Obot(tc_fun(_1307116, tc_HOL_Obool)))))))]]], (28575 ^ _777081) ^ [_1307586, _1307588, _1307590] : [class_Orderings_Olinorder(_1307586), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307586), _1307588)), 28582 ^ _777081 : [(28583 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307586, tc_HOL_Obool)), _1307588), hAPP(hAPP(c_Set_Oinsert(_1307586), _1307590), c_Orderings_Obot__class_Obot(tc_fun(_1307586, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1307586, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1307586, hAPP(hAPP(c_Set_Oinsert(_1307586), _1307590), _1307588)) = _1307590)], (28589 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307586, tc_HOL_Obool)), _1307588), hAPP(hAPP(c_Set_Oinsert(_1307586), _1307590), c_Orderings_Obot__class_Obot(tc_fun(_1307586, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1307586, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1307586, hAPP(hAPP(c_Set_Oinsert(_1307586), _1307590), _1307588)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1307586), _1307590), c_Big__Operators_Olinorder__class_OMin(_1307586, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307586, tc_HOL_Obool)), _1307588), hAPP(hAPP(c_Set_Oinsert(_1307586), _1307590), c_Orderings_Obot__class_Obot(tc_fun(_1307586, tc_HOL_Obool)))))))]]], (28595 ^ _777081) ^ [_1308056, _1308058, _1308060] : [class_Orderings_Olinorder(_1308056), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308056), _1308058)), 28602 ^ _777081 : [(28603 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308056, tc_HOL_Obool)), _1308058), hAPP(hAPP(c_Set_Oinsert(_1308056), _1308060), c_Orderings_Obot__class_Obot(tc_fun(_1308056, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1308056, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1308056, hAPP(hAPP(c_Set_Oinsert(_1308056), _1308060), _1308058)) = _1308060)], (28609 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308056, tc_HOL_Obool)), _1308058), hAPP(hAPP(c_Set_Oinsert(_1308056), _1308060), c_Orderings_Obot__class_Obot(tc_fun(_1308056, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1308056, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1308056, hAPP(hAPP(c_Set_Oinsert(_1308056), _1308060), _1308058)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1308056), _1308060), c_Big__Operators_Olinorder__class_OMax(_1308056, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308056, tc_HOL_Obool)), _1308058), hAPP(hAPP(c_Set_Oinsert(_1308056), _1308060), c_Orderings_Obot__class_Obot(tc_fun(_1308056, tc_HOL_Obool)))))))]]], (28615 ^ _777081) ^ [_1308526, _1308528, _1308530] : [class_Lattices_Olattice(_1308526), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308526), _1308528)), -(_1308528 = c_Orderings_Obot__class_Obot(tc_fun(_1308526, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308526), _1308530)), -(_1308530 = c_Orderings_Obot__class_Obot(tc_fun(_1308526, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308526, tc_HOL_Obool)), _1308528), _1308530) = c_Orderings_Obot__class_Obot(tc_fun(_1308526, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1308526, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308526, tc_HOL_Obool)), _1308528), _1308530)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1308526), c_Big__Operators_Olattice__class_OSup__fin(_1308526, _1308528)), c_Big__Operators_Olattice__class_OSup__fin(_1308526, _1308530)))], (28641 ^ _777081) ^ [_1309003, _1309005, _1309007] : [class_Lattices_Olattice(_1309003), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309003), _1309005)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309003), _1309007)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309003, tc_HOL_Obool)), _1309005), _1309007) = c_Orderings_Obot__class_Obot(tc_fun(_1309003, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1309003), c_Big__Operators_Olattice__class_OSup__fin(_1309003, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309003, tc_HOL_Obool)), _1309005), _1309007))), c_Big__Operators_Olattice__class_OSup__fin(_1309003, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309003, tc_HOL_Obool)), _1309005), _1309007))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1309003), c_Big__Operators_Olattice__class_OSup__fin(_1309003, _1309005)), c_Big__Operators_Olattice__class_OSup__fin(_1309003, _1309007)))], (28659 ^ _777081) ^ [_1309351, _1309353, _1309355] : [class_Lattices_Olattice(_1309351), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309351), _1309353)), -(_1309353 = c_Orderings_Obot__class_Obot(tc_fun(_1309351, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309351), _1309355)), -(_1309355 = c_Orderings_Obot__class_Obot(tc_fun(_1309351, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309351, tc_HOL_Obool)), _1309353), _1309355) = c_Orderings_Obot__class_Obot(tc_fun(_1309351, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1309351, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309351, tc_HOL_Obool)), _1309353), _1309355)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1309351), c_Big__Operators_Olattice__class_OInf__fin(_1309351, _1309353)), c_Big__Operators_Olattice__class_OInf__fin(_1309351, _1309355)))], (28685 ^ _777081) ^ [_1309828, _1309830, _1309832] : [class_Lattices_Olattice(_1309828), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309828), _1309830)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309828), _1309832)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309828, tc_HOL_Obool)), _1309830), _1309832) = c_Orderings_Obot__class_Obot(tc_fun(_1309828, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1309828), c_Big__Operators_Olattice__class_OInf__fin(_1309828, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309828, tc_HOL_Obool)), _1309830), _1309832))), c_Big__Operators_Olattice__class_OInf__fin(_1309828, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309828, tc_HOL_Obool)), _1309830), _1309832))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1309828), c_Big__Operators_Olattice__class_OInf__fin(_1309828, _1309830)), c_Big__Operators_Olattice__class_OInf__fin(_1309828, _1309832)))], (28703 ^ _777081) ^ [_1310176, _1310178, _1310180] : [class_Orderings_Olinorder(_1310176), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310176), _1310178)), -(_1310178 = c_Orderings_Obot__class_Obot(tc_fun(_1310176, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310176), _1310180)), -(_1310180 = c_Orderings_Obot__class_Obot(tc_fun(_1310176, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310176, tc_HOL_Obool)), _1310178), _1310180) = c_Orderings_Obot__class_Obot(tc_fun(_1310176, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1310176, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310176, tc_HOL_Obool)), _1310178), _1310180)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1310176), c_Big__Operators_Olinorder__class_OMin(_1310176, _1310178)), c_Big__Operators_Olinorder__class_OMin(_1310176, _1310180)))], (28729 ^ _777081) ^ [_1310653, _1310655, _1310657] : [class_Orderings_Olinorder(_1310653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310653), _1310655)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310653), _1310657)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310653, tc_HOL_Obool)), _1310655), _1310657) = c_Orderings_Obot__class_Obot(tc_fun(_1310653, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1310653), c_Big__Operators_Olinorder__class_OMin(_1310653, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310653, tc_HOL_Obool)), _1310655), _1310657))), c_Big__Operators_Olinorder__class_OMin(_1310653, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310653, tc_HOL_Obool)), _1310655), _1310657))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1310653), c_Big__Operators_Olinorder__class_OMin(_1310653, _1310655)), c_Big__Operators_Olinorder__class_OMin(_1310653, _1310657)))], (28747 ^ _777081) ^ [_1311001, _1311003, _1311005] : [class_Orderings_Olinorder(_1311001), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311001), _1311003)), -(_1311003 = c_Orderings_Obot__class_Obot(tc_fun(_1311001, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311001), _1311005)), -(_1311005 = c_Orderings_Obot__class_Obot(tc_fun(_1311001, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311001, tc_HOL_Obool)), _1311003), _1311005) = c_Orderings_Obot__class_Obot(tc_fun(_1311001, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1311001, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311001, tc_HOL_Obool)), _1311003), _1311005)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1311001), c_Big__Operators_Olinorder__class_OMax(_1311001, _1311003)), c_Big__Operators_Olinorder__class_OMax(_1311001, _1311005)))], (28773 ^ _777081) ^ [_1311478, _1311480, _1311482] : [class_Orderings_Olinorder(_1311478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311478), _1311480)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311478), _1311482)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311478, tc_HOL_Obool)), _1311480), _1311482) = c_Orderings_Obot__class_Obot(tc_fun(_1311478, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1311478), c_Big__Operators_Olinorder__class_OMax(_1311478, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311478, tc_HOL_Obool)), _1311480), _1311482))), c_Big__Operators_Olinorder__class_OMax(_1311478, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311478, tc_HOL_Obool)), _1311480), _1311482))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1311478), c_Big__Operators_Olinorder__class_OMax(_1311478, _1311480)), c_Big__Operators_Olinorder__class_OMax(_1311478, _1311482)))], (28791 ^ _777081) ^ [_1311826, _1311828] : [class_Orderings_Olinorder(_1311826), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311826), _1311828)), -(_1311828 = c_Orderings_Obot__class_Obot(tc_fun(_1311826, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1311826), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1311826), 28804 ^ [_1311826, _1311828]), 28805 ^ [_1311826, _1311828])), hAPP(hAPP(c_Set_Oinsert(_1311826), 28804 ^ [_1311826, _1311828]), hAPP(hAPP(c_Set_Oinsert(_1311826), 28805 ^ [_1311826, _1311828]), c_Orderings_Obot__class_Obot(tc_fun(_1311826, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1311826), c_Big__Operators_Olinorder__class_OMax(_1311826, _1311828)), _1311828)))], (28811 ^ _777081) ^ [_1312270, _1312272] : [class_Orderings_Olinorder(_1312270), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312270), _1312272)), -(_1312272 = c_Orderings_Obot__class_Obot(tc_fun(_1312270, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1312270), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1312270), 28824 ^ [_1312270, _1312272]), 28825 ^ [_1312270, _1312272])), hAPP(hAPP(c_Set_Oinsert(_1312270), 28824 ^ [_1312270, _1312272]), hAPP(hAPP(c_Set_Oinsert(_1312270), 28825 ^ [_1312270, _1312272]), c_Orderings_Obot__class_Obot(tc_fun(_1312270, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1312270), c_Big__Operators_Olinorder__class_OMin(_1312270, _1312272)), _1312272)))], (28831 ^ _777081) ^ [_1312714, _1312716] : [class_Lattices_Olattice(_1312714), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312714), _1312716)), -(_1312716 = c_Orderings_Obot__class_Obot(tc_fun(_1312714, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1312714), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1312714), 28844 ^ [_1312714, _1312716]), 28845 ^ [_1312714, _1312716])), hAPP(hAPP(c_Set_Oinsert(_1312714), 28844 ^ [_1312714, _1312716]), hAPP(hAPP(c_Set_Oinsert(_1312714), 28845 ^ [_1312714, _1312716]), c_Orderings_Obot__class_Obot(tc_fun(_1312714, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1312714), c_Big__Operators_Olattice__class_OInf__fin(_1312714, _1312716)), _1312716)))], (28851 ^ _777081) ^ [_1313158, _1313160] : [class_Lattices_Olattice(_1313158), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313158), _1313160)), -(_1313160 = c_Orderings_Obot__class_Obot(tc_fun(_1313158, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1313158), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1313158), 28864 ^ [_1313158, _1313160]), 28865 ^ [_1313158, _1313160])), hAPP(hAPP(c_Set_Oinsert(_1313158), 28864 ^ [_1313158, _1313160]), hAPP(hAPP(c_Set_Oinsert(_1313158), 28865 ^ [_1313158, _1313160]), c_Orderings_Obot__class_Obot(tc_fun(_1313158, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1313158), c_Big__Operators_Olattice__class_OSup__fin(_1313158, _1313160)), _1313160)))], (28871 ^ _777081) ^ [_1313602, _1313604, _1313606] : [class_Orderings_Olinorder(_1313602), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313602), _1313604)), hBOOL(hAPP(hAPP(c_member(_1313602), _1313606), _1313604)), 28882 ^ _777081 : [(28883 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1313602, tc_HOL_Obool)), _1313604), hAPP(hAPP(c_Set_Oinsert(_1313602), _1313606), c_Orderings_Obot__class_Obot(tc_fun(_1313602, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1313602, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1313602, c_Orderings_Oord__class_Omax(_1313602), _1313604) = _1313606)], (28889 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1313602, tc_HOL_Obool)), _1313604), hAPP(hAPP(c_Set_Oinsert(_1313602), _1313606), c_Orderings_Obot__class_Obot(tc_fun(_1313602, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1313602, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1313602, c_Orderings_Oord__class_Omax(_1313602), _1313604) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1313602), _1313606), c_Big__Operators_Olattice_OSup__fin(_1313602, c_Orderings_Oord__class_Omax(_1313602), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1313602, tc_HOL_Obool)), _1313604), hAPP(hAPP(c_Set_Oinsert(_1313602), _1313606), c_Orderings_Obot__class_Obot(tc_fun(_1313602, tc_HOL_Obool)))))))]]], (28895 ^ _777081) ^ [_1314126, _1314128, _1314130] : [class_Orderings_Olinorder(_1314126), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314126), _1314128)), hBOOL(hAPP(hAPP(c_member(_1314126), _1314130), _1314128)), 28906 ^ _777081 : [(28907 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314126, tc_HOL_Obool)), _1314128), hAPP(hAPP(c_Set_Oinsert(_1314126), _1314130), c_Orderings_Obot__class_Obot(tc_fun(_1314126, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1314126, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1314126, c_Orderings_Oord__class_Omin(_1314126), _1314128) = _1314130)], (28913 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314126, tc_HOL_Obool)), _1314128), hAPP(hAPP(c_Set_Oinsert(_1314126), _1314130), c_Orderings_Obot__class_Obot(tc_fun(_1314126, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1314126, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1314126, c_Orderings_Oord__class_Omin(_1314126), _1314128) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314126), _1314130), c_Big__Operators_Olattice_OInf__fin(_1314126, c_Orderings_Oord__class_Omin(_1314126), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314126, tc_HOL_Obool)), _1314128), hAPP(hAPP(c_Set_Oinsert(_1314126), _1314130), c_Orderings_Obot__class_Obot(tc_fun(_1314126, tc_HOL_Obool)))))))]]], (28919 ^ _777081) ^ [_1314650, _1314652, _1314654, _1314656] : [c_Finite__Set_Ofolding__one(_1314650, _1314652, _1314654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314650), _1314656)), -(_1314656 = c_Orderings_Obot__class_Obot(tc_fun(_1314650, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1314650), hAPP(hAPP(_1314652, 28932 ^ [_1314650, _1314652, _1314654, _1314656]), 28933 ^ [_1314650, _1314652, _1314654, _1314656])), hAPP(hAPP(c_Set_Oinsert(_1314650), 28932 ^ [_1314650, _1314652, _1314654, _1314656]), hAPP(hAPP(c_Set_Oinsert(_1314650), 28933 ^ [_1314650, _1314652, _1314654, _1314656]), c_Orderings_Obot__class_Obot(tc_fun(_1314650, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1314650), hAPP(_1314654, _1314656)), _1314656)))], (28939 ^ _777081) ^ [_1315136, _1315138, _1315140] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1315136), _1315138)), hBOOL(hAPP(hAPP(c_member(_1315136), _1315140), _1315138)), -(hAPP(c_Finite__Set_Ocard(_1315136), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1315136, tc_HOL_Obool)), _1315138), hAPP(hAPP(c_Set_Oinsert(_1315136), _1315140), c_Orderings_Obot__class_Obot(tc_fun(_1315136, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1315136), _1315138)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (28949 ^ _777081) ^ [_1315371] : [c_Nat__Transfer_Onat__set(_1315371), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1315371) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1315371)))], (28955 ^ _777081) ^ [_1315462, _1315464, _1315466, _1315468] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1315462), _1315464)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315466), _1315468)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1315462, _1315466)), c_Sum__Type_OPlus(_1315462, _1315466, _1315464, _1315468)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1315462), _1315464)), hAPP(c_Finite__Set_Ocard(_1315466), _1315468)))], (28965 ^ _777081) ^ [_1315673] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1315673) = 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)), _1315673)))], (28967 ^ _777081) ^ [] : [-(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))], (28979 ^ _777081) ^ [_1315943, _1315945, _1315947, _1315949] : [28980 ^ _777081 : [(28981 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1315943), _1315945)))], (28983 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1315947), _1315949)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1315943, _1315947)), c_Sum__Type_OPlus(_1315943, _1315947, _1315945, _1315949)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28969 ^ _777081) ^ [_1315738, _1315740, _1315742, _1315744] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1315738, _1315742)), c_Sum__Type_OPlus(_1315738, _1315742, _1315740, _1315744)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1315738), _1315740)), hAPP(c_Finite__Set_Ocard(_1315742), _1315744))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315738), _1315740)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315742), _1315744))], (28987 ^ _777081) ^ [_1316043] : [-(hAPP(c_Finite__Set_Ocard(_1316043), c_Orderings_Obot__class_Obot(tc_fun(_1316043, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28989 ^ _777081) ^ [_1316072, _1316074] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1316072), _1316074))), -(hAPP(c_Finite__Set_Ocard(_1316072), _1316074) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28995 ^ _777081) ^ [_1316117, _1316119] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1316117), c_Orderings_Otop__class_Otop(tc_fun(_1316117, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1316117), _1316119) = hAPP(c_Finite__Set_Ocard(_1316117), c_Orderings_Otop__class_Otop(tc_fun(_1316117, tc_HOL_Obool))), -(_1316119 = c_Orderings_Otop__class_Otop(tc_fun(_1316117, tc_HOL_Obool)))], (29005 ^ _777081) ^ [_1316304, _1316306, _1316308, _1316310] : [c_Fun_Oinj__on(_1316304, _1316306, _1316308, _1316310), -(hAPP(c_Finite__Set_Ocard(_1316306), hAPP(c_Set_Oimage(_1316304, _1316306, _1316308), _1316310)) = hAPP(c_Finite__Set_Ocard(_1316304), _1316310))], (29011 ^ _777081) ^ [_1316423, _1316425] : [class_Orderings_Olinorder(_1316423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316423), _1316425)), -(_1316425 = c_Orderings_Obot__class_Obot(tc_fun(_1316423, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1316423), c_Big__Operators_Olattice_OInf__fin(_1316423, c_Orderings_Oord__class_Omin(_1316423), _1316425)), c_Big__Operators_Olattice_OSup__fin(_1316423, c_Orderings_Oord__class_Omax(_1316423), _1316425))))], (29035 ^ _777081) ^ [_1316791, _1316793] : [29036 ^ _777081 : [(29037 ^ _777081) ^ [] : [_1316793 = c_Orderings_Obot__class_Obot(tc_fun(_1316791, tc_HOL_Obool))], (29039 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1316791), _1316793)))]], -(hAPP(c_Finite__Set_Ocard(_1316791), _1316793) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29025 ^ _777081) ^ [_1316636, _1316638] : [hAPP(c_Finite__Set_Ocard(_1316636), _1316638) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1316638 = c_Orderings_Obot__class_Obot(tc_fun(_1316636, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316636), _1316638))], (29043 ^ _777081) ^ [_1316935, _1316937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1316935), _1316937))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1316935), _1316937)))], (29049 ^ _777081) ^ [_1317034, _1317036, _1317038] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317034), _1317036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1317034), _1317036)), hAPP(c_Finite__Set_Ocard(_1317034), hAPP(hAPP(c_Set_Oinsert(_1317034), _1317038), _1317036)))))], (29055 ^ _777081) ^ [_1317167, _1317169, _1317171] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317167), _1317169)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317167, tc_HOL_Obool)), _1317171), _1317169)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1317167), _1317169)), hAPP(c_Finite__Set_Ocard(_1317167), _1317171))), -(_1317171 = _1317169)], (29069 ^ _777081) ^ [_1317412, _1317414, _1317416] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317412), _1317414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317412, tc_HOL_Obool)), _1317416), _1317414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1317412), _1317416)), hAPP(c_Finite__Set_Ocard(_1317412), _1317414))))], (29079 ^ _777081) ^ [_1317603, _1317605, _1317607, _1317609] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317603), _1317605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1317607), hAPP(c_Set_Oimage(_1317603, _1317607, _1317609), _1317605))), hAPP(c_Finite__Set_Ocard(_1317603), _1317605))))], (29085 ^ _777081) ^ [_1317736, _1317738, _1317740, _1317742] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317736), _1317738)), 29088 ^ _777081 : [(29089 ^ _777081) ^ [] : [c_Fun_Oinj__on(_1317736, _1317740, _1317742, _1317738), -(hAPP(c_Finite__Set_Ocard(_1317740), hAPP(c_Set_Oimage(_1317736, _1317740, _1317742), _1317738)) = hAPP(c_Finite__Set_Ocard(_1317736), _1317738))], (29095 ^ _777081) ^ [] : [hAPP(c_Finite__Set_Ocard(_1317740), hAPP(c_Set_Oimage(_1317736, _1317740, _1317742), _1317738)) = hAPP(c_Finite__Set_Ocard(_1317736), _1317738), -(c_Fun_Oinj__on(_1317736, _1317740, _1317742, _1317738))]]], (29101 ^ _777081) ^ [_1318020, _1318022, _1318024, _1318026] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1318020), _1318022)), hAPP(c_Finite__Set_Ocard(_1318024), hAPP(c_Set_Oimage(_1318020, _1318024, _1318026), _1318022)) = hAPP(c_Finite__Set_Ocard(_1318020), _1318022), -(c_Fun_Oinj__on(_1318020, _1318024, _1318026, _1318022))], (29111 ^ _777081) ^ [_1318203, _1318205, _1318207, _1318209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1318203), hAPP(c_Set_Oimage(_1318205, _1318203, _1318207), _1318209))), hAPP(c_Finite__Set_Ocard(_1318205), _1318209))), c_Fun_Oinj__on(_1318205, _1318203, _1318207, _1318209)], (29117 ^ _777081) ^ [_1318333, _1318335, _1318337] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1318333), _1318335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1318333, tc_HOL_Obool)), _1318337), _1318335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1318333), _1318337)), hAPP(c_Finite__Set_Ocard(_1318333), _1318335))))], (29127 ^ _777081) ^ [_1318524, _1318526, _1318528] : [class_Orderings_Olinorder(_1318524), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318524), _1318526)), hBOOL(hAPP(hAPP(c_member(_1318524), _1318528), _1318526)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318524), _1318528), c_Big__Operators_Olattice_OInf__fin(_1318524, c_Orderings_Oord__class_Omin(_1318524), _1318526)) = c_Big__Operators_Olattice_OInf__fin(_1318524, c_Orderings_Oord__class_Omin(_1318524), _1318526))], (29141 ^ _777081) ^ [_1318771, _1318773, _1318775] : [class_Orderings_Olinorder(_1318771), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318771), _1318773)), hBOOL(hAPP(hAPP(c_member(_1318771), _1318775), _1318773)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1318771), _1318775), c_Big__Operators_Olattice_OSup__fin(_1318771, c_Orderings_Oord__class_Omax(_1318771), _1318773)) = c_Big__Operators_Olattice_OSup__fin(_1318771, c_Orderings_Oord__class_Omax(_1318771), _1318773))], (29155 ^ _777081) ^ [_1319018, _1319020] : [class_Orderings_Olinorder(_1319018), -(c_Big__Operators_Olattice_OInf__fin(_1319018, c_Orderings_Oord__class_Omin(_1319018), hAPP(hAPP(c_Set_Oinsert(_1319018), _1319020), c_Orderings_Obot__class_Obot(tc_fun(_1319018, tc_HOL_Obool)))) = _1319020)], (29161 ^ _777081) ^ [_1319131, _1319133] : [class_Orderings_Olinorder(_1319131), -(c_Big__Operators_Olattice_OSup__fin(_1319131, c_Orderings_Oord__class_Omax(_1319131), hAPP(hAPP(c_Set_Oinsert(_1319131), _1319133), c_Orderings_Obot__class_Obot(tc_fun(_1319131, tc_HOL_Obool)))) = _1319133)], (29167 ^ _777081) ^ [_1319244, _1319246, _1319248] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1319244), _1319246)), 29170 ^ _777081 : [(29171 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1319244), _1319248), _1319246)), -(hAPP(c_Finite__Set_Ocard(_1319244), hAPP(hAPP(c_Set_Oinsert(_1319244), _1319248), _1319246)) = hAPP(c_Finite__Set_Ocard(_1319244), _1319246))], (29177 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1319244), _1319248), _1319246))), -(hAPP(c_Finite__Set_Ocard(_1319244), hAPP(hAPP(c_Set_Oinsert(_1319244), _1319248), _1319246)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1319244), _1319246)))]]], (29183 ^ _777081) ^ [_1319538, _1319540, _1319542] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1319538), _1319540)), -(hBOOL(hAPP(hAPP(c_member(_1319538), _1319542), _1319540))), -(hAPP(c_Finite__Set_Ocard(_1319538), hAPP(hAPP(c_Set_Oinsert(_1319538), _1319542), _1319540)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1319538), _1319540)))], (29193 ^ _777081) ^ [_1319711, _1319713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1319711), _1319713))), 29196 ^ _777081 : [(29197 ^ _777081) ^ [] : [_1319713 = c_Orderings_Obot__class_Obot(tc_fun(_1319711, tc_HOL_Obool))], (29199 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1319711), _1319713)))]]], (29201 ^ _777081) ^ [_1319852, _1319854] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1319852), _1319854)))), -(_1319854 = c_Orderings_Obot__class_Obot(tc_fun(_1319852, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319852), _1319854))], (29211 ^ _777081) ^ [_1320018] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1320018), c_Orderings_Otop__class_Otop(tc_fun(_1320018, 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(_1320018), c_Orderings_Otop__class_Otop(tc_fun(_1320018, tc_HOL_Obool))))))], (29217 ^ _777081) ^ [_1320135, _1320137, _1320139] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1320135), _1320137)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320135), _1320139)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1320135), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320135, tc_HOL_Obool)), _1320137), _1320139))), hAPP(c_Finite__Set_Ocard(_1320135), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320135, tc_HOL_Obool)), _1320137), _1320139))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1320135), _1320137)), hAPP(c_Finite__Set_Ocard(_1320135), _1320139)))], (29227 ^ _777081) ^ [_1320392, _1320394, _1320396] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1320392), _1320394)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320392), _1320396)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1320392), _1320394)), hAPP(c_Finite__Set_Ocard(_1320392), _1320396)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1320392), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320392, tc_HOL_Obool)), _1320394), _1320396))), hAPP(c_Finite__Set_Ocard(_1320392), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320392, tc_HOL_Obool)), _1320394), _1320396))))], (29237 ^ _777081) ^ [_1320649, _1320651, _1320653, _1320655, _1320657, _1320659] : [c_Fun_Oinj__on(_1320649, _1320651, _1320653, _1320655), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1320651, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1320649, _1320651, _1320653), _1320655)), _1320657)), c_Fun_Oinj__on(_1320651, _1320649, _1320659, _1320657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1320649, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1320651, _1320649, _1320659), _1320657)), _1320655)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320649), _1320655)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320651), _1320657)), -(hAPP(c_Finite__Set_Ocard(_1320649), _1320655) = hAPP(c_Finite__Set_Ocard(_1320651), _1320657))], (29263 ^ _777081) ^ [_1321146, _1321148, _1321150] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1321146), _1321148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1321146, tc_HOL_Obool)), _1321148), _1321150)), -(hAPP(c_Finite__Set_Ocard(_1321146), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321146, tc_HOL_Obool)), _1321150), _1321148)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1321146), _1321150)), hAPP(c_Finite__Set_Ocard(_1321146), _1321148)))], (29273 ^ _777081) ^ [_1321371, _1321373, _1321375] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1321371), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321371, tc_HOL_Obool)), _1321373), _1321375))), -(hAPP(c_Finite__Set_Ocard(_1321371), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321371, tc_HOL_Obool)), _1321373), _1321375)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1321371), _1321373)), hAPP(c_Finite__Set_Ocard(_1321371), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321371, tc_HOL_Obool)), _1321373), _1321375))))], (29279 ^ _777081) ^ [_1321566, _1321568, _1321570] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1321566), _1321568)), -(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(_1321566), _1321570)), hAPP(c_Finite__Set_Ocard(_1321566), _1321568))), hAPP(c_Finite__Set_Ocard(_1321566), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1321566, tc_HOL_Obool)), _1321570), _1321568)))))], (29285 ^ _777081) ^ [] : [-(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))))], (29287 ^ _777081) ^ [_1321745, _1321747, _1321749] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1321745), _1321747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1321745, tc_HOL_Obool)), _1321749), _1321747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1321745), _1321749)), hAPP(c_Finite__Set_Ocard(_1321745), _1321747))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1321745, tc_HOL_Obool)), _1321749), _1321747)))], (29301 ^ _777081) ^ [_1322010, _1322012, _1322014] : [class_Orderings_Olinorder(_1322010), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322010), _1322012)), -(_1322012 = c_Orderings_Obot__class_Obot(tc_fun(_1322010, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1322010, c_Orderings_Oord__class_Omin(_1322010), hAPP(hAPP(c_Set_Oinsert(_1322010), _1322014), _1322012)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1322010), _1322014), c_Big__Operators_Olattice_OInf__fin(_1322010, c_Orderings_Oord__class_Omin(_1322010), _1322012)))], (29315 ^ _777081) ^ [_1322230, _1322232, _1322234] : [class_Orderings_Olinorder(_1322230), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322230), _1322232)), -(_1322232 = c_Orderings_Obot__class_Obot(tc_fun(_1322230, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1322230, c_Orderings_Oord__class_Omax(_1322230), hAPP(hAPP(c_Set_Oinsert(_1322230), _1322234), _1322232)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322230), _1322234), c_Big__Operators_Olattice_OSup__fin(_1322230, c_Orderings_Oord__class_Omax(_1322230), _1322232)))], (29329 ^ _777081) ^ [_1322450, _1322452, _1322454] : [class_Orderings_Olinorder(_1322450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322450), _1322452)), -(_1322454 = c_Orderings_Obot__class_Obot(tc_fun(_1322450, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322450, tc_HOL_Obool)), _1322454), _1322452)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1322450), c_Big__Operators_Olattice_OInf__fin(_1322450, c_Orderings_Oord__class_Omin(_1322450), _1322454)), c_Big__Operators_Olattice_OInf__fin(_1322450, c_Orderings_Oord__class_Omin(_1322450), _1322452)) = c_Big__Operators_Olattice_OInf__fin(_1322450, c_Orderings_Oord__class_Omin(_1322450), _1322452))], (29347 ^ _777081) ^ [_1322782, _1322784, _1322786] : [class_Orderings_Olinorder(_1322782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322782), _1322784)), -(_1322786 = c_Orderings_Obot__class_Obot(tc_fun(_1322782, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1322782, tc_HOL_Obool)), _1322786), _1322784)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322782), c_Big__Operators_Olattice_OSup__fin(_1322782, c_Orderings_Oord__class_Omax(_1322782), _1322786)), c_Big__Operators_Olattice_OSup__fin(_1322782, c_Orderings_Oord__class_Omax(_1322782), _1322784)) = c_Big__Operators_Olattice_OSup__fin(_1322782, c_Orderings_Oord__class_Omax(_1322782), _1322784))], (29365 ^ _777081) ^ [_1323114, _1323116, _1323118] : [class_Orderings_Olinorder(_1323114), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323114), _1323116)), hBOOL(hAPP(hAPP(c_member(_1323114), _1323118), _1323116)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1323114), _1323118), c_Big__Operators_Olattice_OInf__fin(_1323114, c_Orderings_Oord__class_Omin(_1323114), _1323116)) = _1323118)], (29379 ^ _777081) ^ [_1323349, _1323351, _1323353] : [class_Orderings_Olinorder(_1323349), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323349), _1323351)), hBOOL(hAPP(hAPP(c_member(_1323349), _1323353), _1323351)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1323349), _1323353), c_Big__Operators_Olattice_OSup__fin(_1323349, c_Orderings_Oord__class_Omax(_1323349), _1323351)) = _1323353)], (29393 ^ _777081) ^ [_1323584, _1323586, _1323588] : [class_Orderings_Olinorder(_1323584), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323584), _1323586)), -(_1323586 = c_Orderings_Obot__class_Obot(tc_fun(_1323584, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323584), _1323588)), -(_1323588 = c_Orderings_Obot__class_Obot(tc_fun(_1323584, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1323584, c_Orderings_Oord__class_Omin(_1323584), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1323584, tc_HOL_Obool)), _1323586), _1323588)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1323584), c_Big__Operators_Olattice_OInf__fin(_1323584, c_Orderings_Oord__class_Omin(_1323584), _1323586)), c_Big__Operators_Olattice_OInf__fin(_1323584, c_Orderings_Oord__class_Omin(_1323584), _1323588)))], (29415 ^ _777081) ^ [_1323951, _1323953, _1323955] : [class_Orderings_Olinorder(_1323951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323951), _1323953)), -(_1323953 = c_Orderings_Obot__class_Obot(tc_fun(_1323951, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323951), _1323955)), -(_1323955 = c_Orderings_Obot__class_Obot(tc_fun(_1323951, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1323951, c_Orderings_Oord__class_Omax(_1323951), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1323951, tc_HOL_Obool)), _1323953), _1323955)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1323951), c_Big__Operators_Olattice_OSup__fin(_1323951, c_Orderings_Oord__class_Omax(_1323951), _1323953)), c_Big__Operators_Olattice_OSup__fin(_1323951, c_Orderings_Oord__class_Omax(_1323951), _1323955)))], (29437 ^ _777081) ^ [_1324318, _1324320, _1324322] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1324318), _1324320)), -(hAPP(c_Finite__Set_Ocard(_1324318), hAPP(hAPP(c_Set_Oinsert(_1324318), _1324322), _1324320)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1324318), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324318, tc_HOL_Obool)), _1324320), hAPP(hAPP(c_Set_Oinsert(_1324318), _1324322), c_Orderings_Obot__class_Obot(tc_fun(_1324318, tc_HOL_Obool)))))))], (29443 ^ _777081) ^ [_1324495, _1324497, _1324499] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1324495), _1324497)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324495), _1324499)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324495, tc_HOL_Obool)), _1324497), _1324499) = c_Orderings_Obot__class_Obot(tc_fun(_1324495, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1324495), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1324495, tc_HOL_Obool)), _1324497), _1324499)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1324495), _1324497)), hAPP(c_Finite__Set_Ocard(_1324495), _1324499)))], (29457 ^ _777081) ^ [_1324794, _1324796, _1324798] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1324794), _1324796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1324794), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1324794, tc_HOL_Obool)), _1324796), hAPP(hAPP(c_Set_Oinsert(_1324794), _1324798), c_Orderings_Obot__class_Obot(tc_fun(_1324794, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1324794), _1324796))))], (29463 ^ _777081) ^ [_1324959, _1324961, _1324963] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1324959), _1324961)), -(hBOOL(hAPP(hAPP(c_member(_1324959), _1324963), _1324961))), -(hAPP(c_Finite__Set_Ocard(_1324959), hAPP(hAPP(c_Set_Oinsert(_1324959), _1324963), _1324961)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1324959), _1324961)))], (29473 ^ _777081) ^ [_1325117, _1325119, _1325121, _1325123, _1325125] : [c_Fun_Oinj__on(_1325117, _1325119, _1325121, _1325123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1325119, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1325117, _1325119, _1325121), _1325123)), _1325125)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325119), _1325125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1325117), _1325123)), hAPP(c_Finite__Set_Ocard(_1325119), _1325125))))], (29487 ^ _777081) ^ [_1325392, _1325394, _1325396, _1325398] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1325392), _1325394)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325396), _1325398)), 29494 ^ _777081 : [(29505 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1325392), _1325394)), hAPP(c_Finite__Set_Ocard(_1325396), _1325398))), 29509 ^ _777081 : [(29510 ^ _777081) ^ [] : [-(c_Fun_Oinj__on(_1325392, _1325396, 29508 ^ [_1325392, _1325394, _1325396, _1325398], _1325394))], (29512 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1325396, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1325392, _1325396, 29508 ^ [_1325392, _1325394, _1325396, _1325398]), _1325394)), _1325398)))]]], (29495 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1325392), _1325394)), hAPP(c_Finite__Set_Ocard(_1325396), _1325398)))), 29496 ^ _777081 : [(29497 ^ _777081) ^ [_1325603] : [c_Fun_Oinj__on(_1325392, _1325396, _1325603, _1325394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1325396, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1325392, _1325396, _1325603), _1325394)), _1325398))]]]]], (29514 ^ _777081) ^ [_1325919, _1325921, _1325923] : [class_Orderings_Olinorder(_1325919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325919), _1325921)), -(hBOOL(hAPP(hAPP(c_member(_1325919), _1325923), _1325921))), -(_1325921 = c_Orderings_Obot__class_Obot(tc_fun(_1325919, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1325919, c_Orderings_Oord__class_Omin(_1325919), hAPP(hAPP(c_Set_Oinsert(_1325919), _1325923), _1325921)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1325919), _1325923), c_Big__Operators_Olattice_OInf__fin(_1325919, c_Orderings_Oord__class_Omin(_1325919), _1325921)))], (29532 ^ _777081) ^ [_1326168, _1326170, _1326172] : [class_Orderings_Olinorder(_1326168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326168), _1326170)), -(hBOOL(hAPP(hAPP(c_member(_1326168), _1326172), _1326170))), -(_1326170 = c_Orderings_Obot__class_Obot(tc_fun(_1326168, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1326168, c_Orderings_Oord__class_Omax(_1326168), hAPP(hAPP(c_Set_Oinsert(_1326168), _1326172), _1326170)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1326168), _1326172), c_Big__Operators_Olattice_OSup__fin(_1326168, c_Orderings_Oord__class_Omax(_1326168), _1326170)))], (29550 ^ _777081) ^ [_1326417, _1326419, _1326421] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1326417), _1326419)), hBOOL(hAPP(hAPP(c_member(_1326417), _1326421), _1326419)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1326417), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326417, tc_HOL_Obool)), _1326419), hAPP(hAPP(c_Set_Oinsert(_1326417), _1326421), c_Orderings_Obot__class_Obot(tc_fun(_1326417, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1326417), _1326419))], (29560 ^ _777081) ^ [_1326646, _1326648, _1326650, _1326652] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1326646), _1326648)), hBOOL(hAPP(hAPP(c_member(_1326646), _1326650), _1326648)), hBOOL(hAPP(hAPP(c_member(_1326646), _1326652), _1326648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1326646), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326646, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1326646, tc_HOL_Obool)), _1326648), hAPP(hAPP(c_Set_Oinsert(_1326646), _1326650), c_Orderings_Obot__class_Obot(tc_fun(_1326646, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1326646), _1326652), c_Orderings_Obot__class_Obot(tc_fun(_1326646, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1326646), _1326648))))], (29574 ^ _777081) ^ [_1327001, _1327003, _1327005] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327001), _1327003)), hBOOL(hAPP(hAPP(c_member(_1327001), _1327005), _1327003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1327001), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327001, tc_HOL_Obool)), _1327003), hAPP(hAPP(c_Set_Oinsert(_1327001), _1327005), c_Orderings_Obot__class_Obot(tc_fun(_1327001, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1327001), _1327003))))], (29584 ^ _777081) ^ [_1327234, _1327236, _1327238] : [class_Orderings_Olinorder(_1327234), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327234), _1327236)), 29591 ^ _777081 : [(29592 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327234, tc_HOL_Obool)), _1327236), hAPP(hAPP(c_Set_Oinsert(_1327234), _1327238), c_Orderings_Obot__class_Obot(tc_fun(_1327234, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1327234, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1327234, c_Orderings_Oord__class_Omin(_1327234), hAPP(hAPP(c_Set_Oinsert(_1327234), _1327238), _1327236)) = _1327238)], (29598 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327234, tc_HOL_Obool)), _1327236), hAPP(hAPP(c_Set_Oinsert(_1327234), _1327238), c_Orderings_Obot__class_Obot(tc_fun(_1327234, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1327234, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1327234, c_Orderings_Oord__class_Omin(_1327234), hAPP(hAPP(c_Set_Oinsert(_1327234), _1327238), _1327236)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1327234), _1327238), c_Big__Operators_Olattice_OInf__fin(_1327234, c_Orderings_Oord__class_Omin(_1327234), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327234, tc_HOL_Obool)), _1327236), hAPP(hAPP(c_Set_Oinsert(_1327234), _1327238), c_Orderings_Obot__class_Obot(tc_fun(_1327234, tc_HOL_Obool)))))))]]], (29604 ^ _777081) ^ [_1327722, _1327724, _1327726] : [class_Orderings_Olinorder(_1327722), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327722), _1327724)), 29611 ^ _777081 : [(29612 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327722, tc_HOL_Obool)), _1327724), hAPP(hAPP(c_Set_Oinsert(_1327722), _1327726), c_Orderings_Obot__class_Obot(tc_fun(_1327722, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1327722, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1327722, c_Orderings_Oord__class_Omax(_1327722), hAPP(hAPP(c_Set_Oinsert(_1327722), _1327726), _1327724)) = _1327726)], (29618 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327722, tc_HOL_Obool)), _1327724), hAPP(hAPP(c_Set_Oinsert(_1327722), _1327726), c_Orderings_Obot__class_Obot(tc_fun(_1327722, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1327722, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1327722, c_Orderings_Oord__class_Omax(_1327722), hAPP(hAPP(c_Set_Oinsert(_1327722), _1327726), _1327724)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1327722), _1327726), c_Big__Operators_Olattice_OSup__fin(_1327722, c_Orderings_Oord__class_Omax(_1327722), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327722, tc_HOL_Obool)), _1327724), hAPP(hAPP(c_Set_Oinsert(_1327722), _1327726), c_Orderings_Obot__class_Obot(tc_fun(_1327722, tc_HOL_Obool)))))))]]], (29624 ^ _777081) ^ [_1328210, _1328212, _1328214] : [class_Orderings_Olinorder(_1328210), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328210), _1328212)), -(_1328212 = c_Orderings_Obot__class_Obot(tc_fun(_1328210, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328210), _1328214)), -(_1328214 = c_Orderings_Obot__class_Obot(tc_fun(_1328210, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328210, tc_HOL_Obool)), _1328212), _1328214) = c_Orderings_Obot__class_Obot(tc_fun(_1328210, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1328210, c_Orderings_Oord__class_Omin(_1328210), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328210, tc_HOL_Obool)), _1328212), _1328214)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1328210), c_Big__Operators_Olattice_OInf__fin(_1328210, c_Orderings_Oord__class_Omin(_1328210), _1328212)), c_Big__Operators_Olattice_OInf__fin(_1328210, c_Orderings_Oord__class_Omin(_1328210), _1328214)))], (29650 ^ _777081) ^ [_1328705, _1328707, _1328709] : [class_Orderings_Olinorder(_1328705), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328705), _1328707)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328705), _1328709)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328705, tc_HOL_Obool)), _1328707), _1328709) = c_Orderings_Obot__class_Obot(tc_fun(_1328705, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1328705), c_Big__Operators_Olattice_OInf__fin(_1328705, c_Orderings_Oord__class_Omin(_1328705), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328705, tc_HOL_Obool)), _1328707), _1328709))), c_Big__Operators_Olattice_OInf__fin(_1328705, c_Orderings_Oord__class_Omin(_1328705), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328705, tc_HOL_Obool)), _1328707), _1328709))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1328705), c_Big__Operators_Olattice_OInf__fin(_1328705, c_Orderings_Oord__class_Omin(_1328705), _1328707)), c_Big__Operators_Olattice_OInf__fin(_1328705, c_Orderings_Oord__class_Omin(_1328705), _1328709)))], (29668 ^ _777081) ^ [_1329077, _1329079, _1329081] : [class_Orderings_Olinorder(_1329077), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329077), _1329079)), -(_1329079 = c_Orderings_Obot__class_Obot(tc_fun(_1329077, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329077), _1329081)), -(_1329081 = c_Orderings_Obot__class_Obot(tc_fun(_1329077, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329077, tc_HOL_Obool)), _1329079), _1329081) = c_Orderings_Obot__class_Obot(tc_fun(_1329077, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1329077, c_Orderings_Oord__class_Omax(_1329077), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329077, tc_HOL_Obool)), _1329079), _1329081)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1329077), c_Big__Operators_Olattice_OSup__fin(_1329077, c_Orderings_Oord__class_Omax(_1329077), _1329079)), c_Big__Operators_Olattice_OSup__fin(_1329077, c_Orderings_Oord__class_Omax(_1329077), _1329081)))], (29694 ^ _777081) ^ [_1329572, _1329574, _1329576] : [class_Orderings_Olinorder(_1329572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329572), _1329574)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329572), _1329576)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329572, tc_HOL_Obool)), _1329574), _1329576) = c_Orderings_Obot__class_Obot(tc_fun(_1329572, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1329572), c_Big__Operators_Olattice_OSup__fin(_1329572, c_Orderings_Oord__class_Omax(_1329572), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329572, tc_HOL_Obool)), _1329574), _1329576))), c_Big__Operators_Olattice_OSup__fin(_1329572, c_Orderings_Oord__class_Omax(_1329572), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329572, tc_HOL_Obool)), _1329574), _1329576))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1329572), c_Big__Operators_Olattice_OSup__fin(_1329572, c_Orderings_Oord__class_Omax(_1329572), _1329574)), c_Big__Operators_Olattice_OSup__fin(_1329572, c_Orderings_Oord__class_Omax(_1329572), _1329576)))], (29712 ^ _777081) ^ [_1329944, _1329946, _1329948, _1329950] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1329944), _1329946)), hBOOL(hAPP(hAPP(c_member(_1329944), _1329948), _1329946)), -(hBOOL(hAPP(hAPP(c_member(_1329944), _1329948), _1329950))), -(hAPP(c_Finite__Set_Ocard(_1329944), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329944, tc_HOL_Obool)), _1329946), hAPP(hAPP(c_Set_Oinsert(_1329944), _1329948), _1329950))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1329944), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1329944, tc_HOL_Obool)), _1329946), _1329950))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (29726 ^ _777081) ^ [_1330224, _1330226, _1330228] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330224), _1330226)), -(hAPP(c_Finite__Set_Ocard(_1330224), hAPP(hAPP(c_Set_Oinsert(_1330224), _1330228), _1330226)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1330224), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1330224, tc_HOL_Obool)), _1330226), hAPP(hAPP(c_Set_Oinsert(_1330224), _1330228), c_Orderings_Obot__class_Obot(tc_fun(_1330224, tc_HOL_Obool)))))))], (29732 ^ _777081) ^ [_1330401, _1330403] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1330401, _1330403)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1330401, _1330403), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1330403), c_Orderings_Otop__class_Otop(tc_fun(_1330403, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1330401), c_Orderings_Otop__class_Otop(tc_fun(_1330401, tc_HOL_Obool)))))], (29742 ^ _777081) ^ [_1330561, _1330563, _1330565] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330561), _1330563)), hBOOL(hAPP(hAPP(c_member(_1330561), _1330565), _1330563)), -(hAPP(c_Finite__Set_Ocard(_1330561), _1330563) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1330561), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1330561, tc_HOL_Obool)), _1330563), hAPP(hAPP(c_Set_Oinsert(_1330561), _1330565), c_Orderings_Obot__class_Obot(tc_fun(_1330561, tc_HOL_Obool)))))))], (29752 ^ _777081) ^ [_1330790, _1330792, _1330794] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330790), _1330792)), 29755 ^ _777081 : [(29756 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1330790), _1330794), _1330792)), -(hAPP(c_Finite__Set_Ocard(_1330790), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1330790, tc_HOL_Obool)), _1330792), hAPP(hAPP(c_Set_Oinsert(_1330790), _1330794), c_Orderings_Obot__class_Obot(tc_fun(_1330790, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1330790), _1330792)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (29762 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1330790), _1330794), _1330792))), -(hAPP(c_Finite__Set_Ocard(_1330790), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1330790, tc_HOL_Obool)), _1330792), hAPP(hAPP(c_Set_Oinsert(_1330790), _1330794), c_Orderings_Obot__class_Obot(tc_fun(_1330790, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1330790), _1330792))]]], (29768 ^ _777081) ^ [_1331154, _1331156, _1331158] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1331154), _1331156)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331154), _1331158)), 29778 ^ _777081 : [(29779 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1331154), 29777 ^ [_1331154, _1331156, _1331158]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1331154, tc_HOL_Obool)), _1331156), _1331158))))], (29781 ^ _777081) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1331154), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1331154, tc_HOL_Obool)), _1331156), _1331158)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1331154), _1331156)), hAPP(c_Finite__Set_Ocard(_1331154), _1331158)))], (29785 ^ _777081) ^ [_1331498, _1331500] : [class_Orderings_Olinorder(_1331498), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331498), _1331500)), -(_1331500 = c_Orderings_Obot__class_Obot(tc_fun(_1331498, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1331498), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1331498), 29798 ^ [_1331498, _1331500]), 29799 ^ [_1331498, _1331500])), hAPP(hAPP(c_Set_Oinsert(_1331498), 29798 ^ [_1331498, _1331500]), hAPP(hAPP(c_Set_Oinsert(_1331498), 29799 ^ [_1331498, _1331500]), c_Orderings_Obot__class_Obot(tc_fun(_1331498, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1331498), c_Big__Operators_Olattice_OSup__fin(_1331498, c_Orderings_Oord__class_Omax(_1331498), _1331500)), _1331500)))], (29805 ^ _777081) ^ [_1331948, _1331950] : [class_Orderings_Olinorder(_1331948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331948), _1331950)), -(_1331950 = c_Orderings_Obot__class_Obot(tc_fun(_1331948, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1331948), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1331948), 29818 ^ [_1331948, _1331950]), 29819 ^ [_1331948, _1331950])), hAPP(hAPP(c_Set_Oinsert(_1331948), 29818 ^ [_1331948, _1331950]), hAPP(hAPP(c_Set_Oinsert(_1331948), 29819 ^ [_1331948, _1331950]), c_Orderings_Obot__class_Obot(tc_fun(_1331948, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1331948), c_Big__Operators_Olattice_OInf__fin(_1331948, c_Orderings_Oord__class_Omin(_1331948), _1331950)), _1331950)))], (29825 ^ _777081) ^ [_1332416, _1332418, _1332420] : [hAPP(c_Finite__Set_Ocard(_1332416), _1332418) = hAPP(c_Nat_OSuc, _1332420), 29830 ^ _777081 : [(29831 ^ _777081) ^ [] : [-(_1332418 = hAPP(hAPP(c_Set_Oinsert(_1332416), 29828 ^ [_1332416, _1332418, _1332420]), 29829 ^ [_1332416, _1332418, _1332420]))], (29833 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1332416), 29828 ^ [_1332416, _1332418, _1332420]), 29829 ^ [_1332416, _1332418, _1332420]))], (29835 ^ _777081) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1332416), 29829 ^ [_1332416, _1332418, _1332420]) = _1332420)], (29837 ^ _777081) ^ [] : [_1332420 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(29829 ^ [_1332416, _1332418, _1332420] = c_Orderings_Obot__class_Obot(tc_fun(_1332416, tc_HOL_Obool)))]]], (29843 ^ _777081) ^ [_1332834, _1332836, _1332838] : [-(hAPP(c_Finite__Set_Ocard(_1332834), _1332836) = hAPP(c_Nat_OSuc, _1332838)), 29844 ^ _777081 : [(29845 ^ _777081) ^ [_1332934, _1332936] : [_1332836 = hAPP(hAPP(c_Set_Oinsert(_1332834), _1332936), _1332934), -(hBOOL(hAPP(hAPP(c_member(_1332834), _1332936), _1332934))), hAPP(c_Finite__Set_Ocard(_1332834), _1332934) = _1332838, 29856 ^ _777081 : [(29857 ^ _777081) ^ [] : [-(_1332838 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29859 ^ _777081) ^ [] : [_1332934 = c_Orderings_Obot__class_Obot(tc_fun(_1332834, tc_HOL_Obool))]]]]], (29863 ^ _777081) ^ [_1333256, _1333258] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1333256, _1333258)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1333258), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1333256), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (29865 ^ _777081) ^ [_1333303, _1333305, _1333307, _1333309, _1333311, _1333313] : [class_Groups_Ocomm__monoid__mult(_1333303), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333305), _1333307)), 29872 ^ _777081 : [(29873 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1333305), _1333309), _1333307)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333305, _1333303), hAPP(hAPP(c_COMBC(_1333305, _1333303, _1333303), hAPP(hAPP(c_COMBS(_1333305, _1333303, tc_fun(_1333303, _1333303)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1333303, tc_fun(_1333303, _1333303)), _1333305), c_If(_1333303)), hAPP(hAPP(c_COMBC(_1333305, _1333305, tc_HOL_Obool), c_fequal), _1333309))), _1333311)), _1333313)), _1333307) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333303), hAPP(_1333311, _1333309)), hAPP(hAPP(c_Power_Opower__class_Opower(_1333303), _1333313), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1333305), _1333307)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (29879 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1333305), _1333309), _1333307))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333305, _1333303), hAPP(hAPP(c_COMBC(_1333305, _1333303, _1333303), hAPP(hAPP(c_COMBS(_1333305, _1333303, tc_fun(_1333303, _1333303)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1333303, tc_fun(_1333303, _1333303)), _1333305), c_If(_1333303)), hAPP(hAPP(c_COMBC(_1333305, _1333305, tc_HOL_Obool), c_fequal), _1333309))), _1333311)), _1333313)), _1333307) = hAPP(hAPP(c_Power_Opower__class_Opower(_1333303), _1333313), hAPP(c_Finite__Set_Ocard(_1333305), _1333307)))]]], (29885 ^ _777081) ^ [_1333915, _1333917, _1333919, _1333921, _1333923] : [class_Groups_Ocomm__monoid__mult(_1333915), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333917), _1333919)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333917), _1333921)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1333917, tc_HOL_Obool)), _1333919), _1333921) = c_Orderings_Obot__class_Obot(tc_fun(_1333917, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1333915, _1333917, c_Groups_Otimes__class_Otimes(_1333915)), _1333923), c_Groups_Oone__class_Oone(_1333915)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1333917, tc_HOL_Obool)), _1333919), _1333921)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1333915), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1333915, _1333917, c_Groups_Otimes__class_Otimes(_1333915)), _1333923), c_Groups_Oone__class_Oone(_1333915)), _1333919)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1333915, _1333917, c_Groups_Otimes__class_Otimes(_1333915)), _1333923), c_Groups_Oone__class_Oone(_1333915)), _1333921)))], (29903 ^ _777081) ^ [_1334358, _1334360, _1334362] : [class_Orderings_Olinorder(_1334358), hAPP(_1334360, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1334358), 29908 ^ [_1334358, _1334360, _1334362]), 29909 ^ [_1334358, _1334360, _1334362])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1334358), hAPP(_1334360, 29908 ^ [_1334358, _1334360, _1334362])), hAPP(_1334360, 29909 ^ [_1334358, _1334360, _1334362])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334358), _1334362)), -(_1334362 = c_Orderings_Obot__class_Obot(tc_fun(_1334358, tc_HOL_Obool))), -(hAPP(_1334360, c_Big__Operators_Olattice_OSup__fin(_1334358, c_Orderings_Oord__class_Omax(_1334358), _1334362)) = c_Big__Operators_Olattice_OSup__fin(_1334358, c_Orderings_Oord__class_Omax(_1334358), hAPP(c_Set_Oimage(_1334358, _1334358, _1334360), _1334362)))], (29923 ^ _777081) ^ [_1334773, _1334775] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1334773, _1334775))))], (29925 ^ _777081) ^ [_1334804, _1334806, _1334808] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1334804), _1334806), _1334808) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1334804), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1334804, tc_Int_Oint), _1334806), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1334808))), class_Groups_Ocomm__monoid__add(_1334804), class_Groups_Ocomm__monoid__mult(_1334804)], (29935 ^ _777081) ^ [_1334995, _1334997, _1334999, _1335001] : [class_Groups_Ocomm__monoid__mult(_1334995), 29938 ^ _777081 : [(29939 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1334997), _1334999)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1334997, _1334995), _1335001), _1334999) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1334995, _1334997, c_Groups_Otimes__class_Otimes(_1334995)), _1335001), c_Groups_Oone__class_Oone(_1334995)), _1334999))], (29945 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1334997), _1334999))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1334997, _1334995), _1335001), _1334999) = c_Groups_Oone__class_Oone(_1334995))]]], (29951 ^ _777081) ^ [_1335267, _1335269, _1335271, _1335273] : [class_Groups_Ocomm__monoid__mult(_1335267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335269), _1335271)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335269, _1335267), _1335273), _1335271) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1335267, _1335269, c_Groups_Otimes__class_Otimes(_1335267)), _1335273), c_Groups_Oone__class_Oone(_1335267)), _1335271))], (29961 ^ _777081) ^ [_1335462, _1335464, _1335466, _1335468] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1335462), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335464, tc_Nat_Onat), _1335466), _1335468)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335464, _1335462), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1335462, _1335464), c_Nat_Osemiring__1__class_Oof__nat(_1335462)), _1335466)), _1335468)), class_Groups_Ocomm__monoid__mult(_1335462), class_Rings_Osemiring__1(_1335462)], (29971 ^ _777081) ^ [_1335665, _1335667, _1335669] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335665, tc_Nat_Onat), _1335667), _1335669)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335665, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1335665), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1335667)), _1335669))], (29973 ^ _777081) ^ [_1335723, _1335725, _1335727, _1335729] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1335723), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335725, tc_Int_Oint), _1335727), _1335729)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335725, _1335723), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1335723, _1335725), c_Int_Oring__1__class_Oof__int(_1335723)), _1335727)), _1335729)), class_Groups_Ocomm__monoid__mult(_1335723), class_Rings_Oring__1(_1335723)], (29983 ^ _777081) ^ [_1335926, _1335928, _1335930] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335926, tc_Nat_Onat), _1335928), _1335930) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335926, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1335926), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1335928)), _1335930)))], (29985 ^ _777081) ^ [_1335984, _1335986, _1335988] : [class_Groups_Ocomm__monoid__mult(_1335984), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1335986, _1335984), hAPP(c_COMBK(_1335984, _1335986), c_Groups_Oone__class_Oone(_1335984))), _1335988) = c_Groups_Oone__class_Oone(_1335984))], (29991 ^ _777081) ^ [_1336099, _1336101, _1336103, _1336105, _1336107] : [class_Groups_Ocomm__monoid__mult(_1336099), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336101, _1336099), hAPP(hAPP(c_COMBS(_1336101, _1336099, _1336099), hAPP(hAPP(c_COMBB(_1336099, tc_fun(_1336099, _1336099), _1336101), c_Groups_Otimes__class_Otimes(_1336099)), _1336103)), _1336105)), _1336107) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336099), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336101, _1336099), _1336103), _1336107)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336101, _1336099), _1336105), _1336107)))], (29997 ^ _777081) ^ [_1336300, _1336302, _1336304, _1336306] : [class_Fields_Olinordered__field(_1336300), -(hAPP(c_Groups_Oabs__class_Oabs(_1336300), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336302, _1336300), _1336304), _1336306)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336302, _1336300), hAPP(hAPP(c_COMBB(_1336300, _1336300, _1336302), c_Groups_Oabs__class_Oabs(_1336300)), _1336304)), _1336306))], (30003 ^ _777081) ^ [_1336449, _1336451, _1336453, _1336455, _1336457] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1336449, _1336451, _1336453), _1336455), _1336457), c_Orderings_Obot__class_Obot(tc_fun(_1336451, tc_HOL_Obool))) = _1336457)], (30005 ^ _777081) ^ [_1336498, _1336500, _1336502, _1336504] : [class_Rings_Ocomm__semiring__1(_1336498), class_Rings_Ono__zero__divisors(_1336498), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336500), _1336502)), 30016 ^ _777081 : [(30017 ^ _777081) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336500, _1336498), _1336504), _1336502) = c_Groups_Ozero__class_Ozero(_1336498), 30021 ^ _777081 : [(30022 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1336500), 30020 ^ [_1336498, _1336500, _1336502, _1336504]), _1336502)))], (30024 ^ _777081) ^ [] : [-(hAPP(_1336504, 30020 ^ [_1336498, _1336500, _1336502, _1336504]) = c_Groups_Ozero__class_Ozero(_1336498))]]], (30026 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336500, _1336498), _1336504), _1336502) = c_Groups_Ozero__class_Ozero(_1336498)), 30027 ^ _777081 : [(30028 ^ _777081) ^ [_1336876] : [hBOOL(hAPP(hAPP(c_member(_1336500), _1336876), _1336502)), hAPP(_1336504, _1336876) = c_Groups_Ozero__class_Ozero(_1336498)]]]]], (30036 ^ _777081) ^ [_1337031, _1337033, _1337035, _1337037] : [class_Rings_Ocomm__semiring__1(_1337031), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337033), _1337035)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337033, _1337031), _1337037), _1337035) = c_Groups_Ozero__class_Ozero(_1337031)), 30045 ^ _777081 : [(30046 ^ _777081) ^ [_1337212] : [hBOOL(hAPP(hAPP(c_member(_1337033), _1337212), _1337035)), hAPP(_1337037, _1337212) = c_Groups_Ozero__class_Ozero(_1337031)]]], (30054 ^ _777081) ^ [_1337361, _1337363, _1337365] : [class_Groups_Ocomm__monoid__mult(_1337361), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337363, _1337361), _1337365), c_Orderings_Obot__class_Obot(tc_fun(_1337363, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1337361))], (30060 ^ _777081) ^ [_1337470, _1337472, _1337474] : [class_Groups_Ocomm__monoid__mult(_1337470), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337472, _1337470), _1337474), c_Orderings_Obot__class_Obot(tc_fun(_1337472, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1337470))], (30066 ^ _777081) ^ [_1337579, _1337581, _1337583, _1337585] : [class_Groups_Ocomm__monoid__mult(_1337579), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337581), _1337583))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337581, _1337579), _1337585), _1337583) = c_Groups_Oone__class_Oone(_1337579))], (30076 ^ _777081) ^ [_1337703, _1337705, _1337707, _1337709] : [class_Groups_Ocomm__monoid__mult(_1337703), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337705), _1337707))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337705, _1337703), _1337709), _1337707) = c_Groups_Oone__class_Oone(_1337703))], (30086 ^ _777081) ^ [_1337827, _1337829, _1337831] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1337827), _1337829)), 30089 ^ _777081 : [(30100 ^ _777081) ^ [] : [30102 ^ _777081 : [(30103 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1337827), 30101 ^ [_1337827, _1337829, _1337831]), _1337829)))], (30105 ^ _777081) ^ [] : [hAPP(_1337831, 30101 ^ [_1337827, _1337829, _1337831]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337827, tc_Nat_Onat), _1337831), _1337829) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (30090 ^ _777081) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1337827, tc_Nat_Onat), _1337831), _1337829) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 30093 ^ _777081 : [(30094 ^ _777081) ^ [_1337989] : [hBOOL(hAPP(hAPP(c_member(_1337827), _1337989), _1337829)), -(hAPP(_1337831, _1337989) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (30109 ^ _777081) ^ [_1338247, _1338249, _1338251] : [class_Groups_Ocomm__monoid__add(_1338247), class_Groups_Ocomm__monoid__mult(_1338247), c_Nat__Transfer_Onat__set(_1338249), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1338247), _1338251), _1338249) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1338247), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1338247, tc_Nat_Onat), _1338251), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1338249)))], (30123 ^ _777081) ^ [_1338492, _1338494, _1338496, _1338498, _1338500] : [class_Groups_Ocomm__monoid__mult(_1338492), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338494), _1338496)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338494, _1338492), hAPP(hAPP(c_COMBS(_1338494, _1338492, _1338492), hAPP(hAPP(c_COMBB(_1338492, tc_fun(_1338492, _1338492), _1338494), c_Groups_Otimes__class_Otimes(_1338492)), _1338498)), _1338500)), _1338496) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1338492), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338494, _1338492), _1338498), _1338496)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338494, _1338492), _1338500), _1338496)))], (30133 ^ _777081) ^ [_1338759, _1338761, _1338763] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338759), _1338761)), 30136 ^ _777081 : [(30147 ^ _777081) ^ [] : [30149 ^ _777081 : [(30150 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1338759), 30148 ^ [_1338759, _1338761, _1338763]), _1338761)))], (30152 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1338763, 30148 ^ [_1338759, _1338761, _1338763])))]], -(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(_1338759, tc_Nat_Onat), _1338763), _1338761))))], (30137 ^ _777081) ^ [] : [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(_1338759, tc_Nat_Onat), _1338763), _1338761))), 30140 ^ _777081 : [(30141 ^ _777081) ^ [_1338927] : [hBOOL(hAPP(hAPP(c_member(_1338759), _1338927), _1338761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1338763, _1338927))))]]]]], (30156 ^ _777081) ^ [_1339195, _1339197, _1339199, _1339201, _1339203, _1339205, _1339207] : [c_Finite__Set_Ofolding__image__simple(_1339195, _1339197, _1339199, _1339201, _1339203, _1339205), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339197), _1339207)), -(hAPP(_1339205, _1339207) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1339195, _1339197, _1339199), _1339203), _1339201), _1339207))], (30166 ^ _777081) ^ [_1339392, _1339394, _1339396] : [class_Orderings_Oorder(_1339392), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1339392), _1339394), _1339396)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1339392, _1339396, _1339394) = c_Orderings_Obot__class_Obot(tc_fun(_1339392, tc_HOL_Obool)))], (30176 ^ _777081) ^ [_1339555, _1339557, _1339559] : [class_Groups_Oordered__ab__group__add(_1339555), -(hAPP(c_Set_Oimage(_1339555, _1339555, c_Groups_Ouminus__class_Ouminus(_1339555)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1339555, _1339557, _1339559)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1339555, hAPP(c_Groups_Ouminus__class_Ouminus(_1339555), _1339559), hAPP(c_Groups_Ouminus__class_Ouminus(_1339555), _1339557)))], (30182 ^ _777081) ^ [_1339686, _1339688, _1339690, _1339692, _1339694] : [class_Groups_Ocomm__monoid__mult(_1339686), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339688), _1339690)), 30189 ^ _777081 : [(30190 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1339688), _1339692), _1339690)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1339688, _1339686), hAPP(hAPP(c_COMBC(_1339688, _1339686, _1339686), hAPP(hAPP(c_COMBS(_1339688, _1339686, tc_fun(_1339686, _1339686)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1339686, tc_fun(_1339686, _1339686)), _1339688), c_If(_1339686)), hAPP(c_fequal, _1339692))), _1339694)), c_Groups_Oone__class_Oone(_1339686))), _1339690) = hAPP(_1339694, _1339692))], (30196 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339688), _1339692), _1339690))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1339688, _1339686), hAPP(hAPP(c_COMBC(_1339688, _1339686, _1339686), hAPP(hAPP(c_COMBS(_1339688, _1339686, tc_fun(_1339686, _1339686)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1339686, tc_fun(_1339686, _1339686)), _1339688), c_If(_1339686)), hAPP(c_fequal, _1339692))), _1339694)), c_Groups_Oone__class_Oone(_1339686))), _1339690) = c_Groups_Oone__class_Oone(_1339686))]]], (30202 ^ _777081) ^ [_1340196, _1340198, _1340200, _1340202, _1340204] : [class_Groups_Ocomm__monoid__mult(_1340196), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340198), _1340200)), 30209 ^ _777081 : [(30210 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1340198), _1340202), _1340200)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340198, _1340196), hAPP(hAPP(c_COMBC(_1340198, _1340196, _1340196), hAPP(hAPP(c_COMBS(_1340198, _1340196, tc_fun(_1340196, _1340196)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1340196, tc_fun(_1340196, _1340196)), _1340198), c_If(_1340196)), hAPP(hAPP(c_COMBC(_1340198, _1340198, tc_HOL_Obool), c_fequal), _1340202))), _1340204)), c_Groups_Oone__class_Oone(_1340196))), _1340200) = hAPP(_1340204, _1340202))], (30216 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1340198), _1340202), _1340200))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340198, _1340196), hAPP(hAPP(c_COMBC(_1340198, _1340196, _1340196), hAPP(hAPP(c_COMBS(_1340198, _1340196, tc_fun(_1340196, _1340196)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1340196, tc_fun(_1340196, _1340196)), _1340198), c_If(_1340196)), hAPP(hAPP(c_COMBC(_1340198, _1340198, tc_HOL_Obool), c_fequal), _1340202))), _1340204)), c_Groups_Oone__class_Oone(_1340196))), _1340200) = c_Groups_Oone__class_Oone(_1340196))]]], (30222 ^ _777081) ^ [_1340734, _1340736, _1340738, _1340740] : [class_Groups_Ocomm__monoid__mult(_1340734), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340736), _1340738)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340736, _1340734), hAPP(c_COMBK(_1340734, _1340736), _1340740)), _1340738) = hAPP(hAPP(c_Power_Opower__class_Opower(_1340734), _1340740), hAPP(c_Finite__Set_Ocard(_1340736), _1340738)))], (30232 ^ _777081) ^ [_1340933, _1340935, _1340937, _1340939, _1340941] : [class_Groups_Ocomm__monoid__mult(_1340933), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340935), _1340937)), -(hBOOL(hAPP(hAPP(c_member(_1340935), _1340939), _1340937))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340935, _1340933), _1340941), hAPP(hAPP(c_Set_Oinsert(_1340935), _1340939), _1340937)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1340933), hAPP(_1340941, _1340939)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1340935, _1340933), _1340941), _1340937)))], (30246 ^ _777081) ^ [_1341183, _1341185, _1341187, _1341189, _1341191] : [class_Groups_Ocomm__monoid__mult(_1341183), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341185), _1341187)), -(hBOOL(hAPP(hAPP(c_member(_1341185), _1341189), _1341187))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341185, _1341183), _1341191), hAPP(hAPP(c_Set_Oinsert(_1341185), _1341189), _1341187)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341183), hAPP(_1341191, _1341189)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341185, _1341183), _1341191), _1341187)))], (30260 ^ _777081) ^ [_1341433, _1341435, _1341437, _1341439, _1341441] : [class_Groups_Ocomm__monoid__mult(_1341433), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341435), _1341437)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341435), _1341439)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341433), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341435, _1341433), _1341441), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341435, tc_HOL_Obool)), _1341437), _1341439))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341435, _1341433), _1341441), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341435, tc_HOL_Obool)), _1341437), _1341439))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341433), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341435, _1341433), _1341441), _1341437)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341435, _1341433), _1341441), _1341439)))], (30274 ^ _777081) ^ [_1341794, _1341796, _1341798, _1341800, _1341802] : [class_Groups_Ocomm__monoid__mult(_1341794), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341796), _1341798)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341796), _1341800)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341794), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341796, _1341794), _1341802), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1341796, tc_HOL_Obool)), _1341798), _1341800))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341796, _1341794), _1341802), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1341796, tc_HOL_Obool)), _1341798), _1341800))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341794), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341796, _1341794), _1341802), _1341798)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1341796, _1341794), _1341802), _1341800)))], (30288 ^ _777081) ^ [_1342155, _1342157, _1342159, _1342161, _1342163] : [class_Groups_Ocomm__monoid__mult(_1342155), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342157), _1342159)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1342155, _1342157, c_Groups_Otimes__class_Otimes(_1342155)), hAPP(hAPP(c_COMBS(_1342157, _1342155, _1342155), hAPP(hAPP(c_COMBB(_1342155, tc_fun(_1342155, _1342155), _1342157), c_Groups_Otimes__class_Otimes(_1342155)), _1342161)), _1342163)), c_Groups_Oone__class_Oone(_1342155)), _1342159) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342155), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1342155, _1342157, c_Groups_Otimes__class_Otimes(_1342155)), _1342161), c_Groups_Oone__class_Oone(_1342155)), _1342159)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1342155, _1342157, c_Groups_Otimes__class_Otimes(_1342155)), _1342163), c_Groups_Oone__class_Oone(_1342155)), _1342159)))], (30298 ^ _777081) ^ [_1342470, _1342472, _1342474, _1342476, _1342478, _1342480] : [class_Groups_Oab__semigroup__mult(_1342470), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342472), _1342474)), -(hBOOL(hAPP(hAPP(c_member(_1342472), _1342476), _1342474))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1342470, _1342472, c_Groups_Otimes__class_Otimes(_1342470)), _1342478), _1342480), hAPP(hAPP(c_Set_Oinsert(_1342472), _1342476), _1342474)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342470), hAPP(_1342478, _1342476)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1342470, _1342472, c_Groups_Otimes__class_Otimes(_1342470)), _1342478), _1342480), _1342474)))], (30312 ^ _777081) ^ [_1342748, _1342750, _1342752, _1342754, _1342756] : [class_Orderings_Olinorder(_1342748), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1342748, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1342748, _1342750, _1342752)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1342748, _1342754, _1342756)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1342748, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1342748), _1342750), _1342754), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1342748), _1342752), _1342756)))], (30318 ^ _777081) ^ [_1342907, _1342909, _1342911, _1342913, _1342915] : [class_Groups_Ocomm__monoid__mult(_1342907), hBOOL(hAPP(c_Finite__Set_Ofinite(_1342909), _1342911)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342909, _1342907), _1342913), hAPP(hAPP(c_Set_Oinsert(_1342909), _1342915), _1342911)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342907), hAPP(_1342913, _1342915)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1342909, _1342907), _1342913), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1342909, tc_HOL_Obool)), _1342911), hAPP(hAPP(c_Set_Oinsert(_1342909), _1342915), c_Orderings_Obot__class_Obot(tc_fun(_1342909, tc_HOL_Obool)))))))], (30328 ^ _777081) ^ [_1343176, _1343178, _1343180, _1343182, _1343184] : [class_Groups_Ocomm__monoid__mult(_1343176), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343178), _1343180)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343178), _1343182)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343178, tc_HOL_Obool)), _1343180), _1343182) = c_Orderings_Obot__class_Obot(tc_fun(_1343178, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343178, _1343176), _1343184), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1343178, tc_HOL_Obool)), _1343180), _1343182)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343176), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343178, _1343176), _1343184), _1343180)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343178, _1343176), _1343184), _1343182)))], (30346 ^ _777081) ^ [_1343571, _1343573, _1343575, _1343577, _1343579] : [class_Groups_Ocomm__monoid__mult(_1343571), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343573), _1343575)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343573), _1343577)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343573, tc_HOL_Obool)), _1343575), _1343577) = c_Orderings_Obot__class_Obot(tc_fun(_1343573, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343573, _1343571), _1343579), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1343573, tc_HOL_Obool)), _1343575), _1343577)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343571), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343573, _1343571), _1343579), _1343575)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343573, _1343571), _1343579), _1343577)))], (30364 ^ _777081) ^ [_1343966, _1343968, _1343970, _1343972, _1343974] : [class_Groups_Ocomm__monoid__mult(_1343966), hBOOL(hAPP(c_Finite__Set_Ofinite(_1343968), _1343970)), hBOOL(hAPP(hAPP(c_member(_1343968), _1343972), _1343970)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343968, _1343966), _1343974), _1343970) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343966), hAPP(_1343974, _1343972)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343968, _1343966), _1343974), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1343968, tc_HOL_Obool)), _1343970), hAPP(hAPP(c_Set_Oinsert(_1343968), _1343972), c_Orderings_Obot__class_Obot(tc_fun(_1343968, tc_HOL_Obool)))))))], (30378 ^ _777081) ^ [_1344291, _1344293, _1344295, _1344297, _1344299] : [class_Groups_Ocomm__monoid__mult(_1344291), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344293), _1344295)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344293), _1344297)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1344291), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1344291, _1344293, c_Groups_Otimes__class_Otimes(_1344291)), _1344299), c_Groups_Oone__class_Oone(_1344291)), _1344295)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1344291, _1344293, c_Groups_Otimes__class_Otimes(_1344291)), _1344299), c_Groups_Oone__class_Oone(_1344291)), _1344297)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1344291), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1344291, _1344293, c_Groups_Otimes__class_Otimes(_1344291)), _1344299), c_Groups_Oone__class_Oone(_1344291)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1344293, tc_HOL_Obool)), _1344295), _1344297))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1344291, _1344293, c_Groups_Otimes__class_Otimes(_1344291)), _1344299), c_Groups_Oone__class_Oone(_1344291)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1344293, tc_HOL_Obool)), _1344295), _1344297))))], (30392 ^ _777081) ^ [_1344716, _1344718, _1344720, _1344722] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1344716), _1344718)), -(hAPP(c_Set_Oimage(_1344716, _1344720, _1344722), _1344718) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1344720, tc_HOL_Obool), _1344716, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1344720, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1344716, tc_fun(_1344720, tc_HOL_Obool), tc_fun(_1344720, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1344720, tc_fun(tc_fun(_1344720, tc_HOL_Obool), tc_fun(_1344720, tc_HOL_Obool)), _1344716), c_Set_Oinsert(_1344720)), _1344722)), c_Orderings_Obot__class_Obot(tc_fun(_1344720, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1344720, tc_HOL_Obool))), _1344718))], (30398 ^ _777081) ^ [_1344964, _1344966] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1344964), _1344966)), -(hAPP(c_Finite__Set_Ocard(_1344964), _1344966) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1344964, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1344964), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1344966))], (30404 ^ _777081) ^ [_1345091, _1345093] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1345091), _1345093))), -(hAPP(c_Finite__Set_Ocard(_1345091), _1345093) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30410 ^ _777081) ^ [_1345138, _1345140] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1345138), _1345140)), -(hAPP(c_Finite__Set_Ocard(_1345138), _1345140) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1345138, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1345138), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1345140))], (30416 ^ _777081) ^ [_1345271, _1345273, _1345275, _1345277, _1345279, _1345281, _1345283] : [c_Big__Operators_Ocomm__monoid__big(_1345271, _1345273, _1345275, _1345277, _1345279), 30419 ^ _777081 : [(30420 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1345273), _1345281)), -(hAPP(hAPP(_1345279, _1345283), _1345281) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1345271, _1345273, _1345275), _1345283), _1345277), _1345281))], (30426 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1345273), _1345281))), -(hAPP(hAPP(_1345279, _1345283), _1345281) = _1345277)]]], (30432 ^ _777081) ^ [_1345539, _1345541, _1345543, _1345545, _1345547] : [class_Groups_Ocomm__monoid__mult(_1345539), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345541), _1345543)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345541), _1345545)), 30446 ^ _777081 : [(30447 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1345541), 30445 ^ [_1345539, _1345541, _1345543, _1345545, _1345547]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1345541, tc_HOL_Obool)), _1345543), _1345545))))], (30449 ^ _777081) ^ [] : [hAPP(_1345547, 30445 ^ [_1345539, _1345541, _1345543, _1345545, _1345547]) = c_Groups_Oone__class_Oone(_1345539)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1345539, _1345541, c_Groups_Otimes__class_Otimes(_1345539)), _1345547), c_Groups_Oone__class_Oone(_1345539)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1345541, tc_HOL_Obool)), _1345543), _1345545)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345539), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1345539, _1345541, c_Groups_Otimes__class_Otimes(_1345539)), _1345547), c_Groups_Oone__class_Oone(_1345539)), _1345543)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1345539, _1345541, c_Groups_Otimes__class_Otimes(_1345539)), _1345547), c_Groups_Oone__class_Oone(_1345539)), _1345545)))], (30453 ^ _777081) ^ [_1346082, _1346084, _1346086, _1346088, _1346090] : [class_Groups_Ocomm__monoid__mult(_1346082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346084), _1346086)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346084), _1346088)), 30467 ^ _777081 : [(30468 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1346084), 30466 ^ [_1346082, _1346084, _1346086, _1346088, _1346090]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346084, tc_HOL_Obool)), _1346086), _1346088))))], (30470 ^ _777081) ^ [] : [hAPP(_1346090, 30466 ^ [_1346082, _1346084, _1346086, _1346088, _1346090]) = c_Groups_Oone__class_Oone(_1346082)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346084, _1346082), _1346090), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1346084, tc_HOL_Obool)), _1346086), _1346088)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346082), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346084, _1346082), _1346090), _1346086)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346084, _1346082), _1346090), _1346088)))], (30474 ^ _777081) ^ [_1346577, _1346579, _1346581, _1346583, _1346585] : [class_Groups_Ocomm__monoid__mult(_1346577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346579), _1346581)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1346579), _1346583)), 30488 ^ _777081 : [(30489 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1346579), 30487 ^ [_1346577, _1346579, _1346581, _1346583, _1346585]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1346579, tc_HOL_Obool)), _1346581), _1346583))))], (30491 ^ _777081) ^ [] : [hAPP(_1346585, 30487 ^ [_1346577, _1346579, _1346581, _1346583, _1346585]) = c_Groups_Oone__class_Oone(_1346577)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346579, _1346577), _1346585), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1346579, tc_HOL_Obool)), _1346581), _1346583)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346577), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346579, _1346577), _1346585), _1346581)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1346579, _1346577), _1346585), _1346583)))], (30495 ^ _777081) ^ [_1347072, _1347074] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1347072, _1347074))))], (30497 ^ _777081) ^ [_1347103, _1347105] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1347103, _1347105)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1347105), hAPP(c_Nat_OSuc, _1347103)))], (30499 ^ _777081) ^ [_1347144, _1347146, _1347148, _1347150, _1347152, _1347154, _1347156] : [c_Big__Operators_Ocomm__monoid__big(_1347144, _1347146, _1347148, _1347150, _1347152), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1347146), _1347154))), -(hAPP(hAPP(_1347152, _1347156), _1347154) = _1347150)], (30509 ^ _777081) ^ [_1347272, _1347274, _1347276] : [30511 ^ _777081 : [(30512 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347272), 30510 ^ [_1347272, _1347274, _1347276]), _1347274)))], (30514 ^ _777081) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1347276, 30510 ^ [_1347272, _1347274, _1347276]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1347272, tc_Int_Oint), _1347276), _1347274) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1347272, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1347272), c_Int_Onat), _1347276)), _1347274)))], (30518 ^ _777081) ^ [_1347502, _1347504, _1347506] : [class_Orderings_Olinorder(_1347502), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347502), _1347504), _1347506)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1347502, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1347502, _1347504, _1347506)), hAPP(hAPP(c_Set_Oinsert(_1347502), _1347506), c_Orderings_Obot__class_Obot(tc_fun(_1347502, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1347502, _1347504, _1347506))], (30528 ^ _777081) ^ [_1347711, _1347713, _1347715, _1347717, _1347719] : [class_Fields_Ofield(_1347711), hBOOL(hAPP(c_Finite__Set_Ofinite(_1347713), _1347715)), -(hAPP(_1347717, _1347719) = c_Groups_Ozero__class_Ozero(_1347711)), 30539 ^ _777081 : [(30540 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1347713), _1347719), _1347715)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1347713, _1347711), _1347717), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1347713, tc_HOL_Obool)), _1347715), hAPP(hAPP(c_Set_Oinsert(_1347713), _1347719), c_Orderings_Obot__class_Obot(tc_fun(_1347713, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347711), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1347713, _1347711), _1347717), _1347715)), hAPP(_1347717, _1347719)))], (30546 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347713), _1347719), _1347715))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1347713, _1347711), _1347717), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1347713, tc_HOL_Obool)), _1347715), hAPP(hAPP(c_Set_Oinsert(_1347713), _1347719), c_Orderings_Obot__class_Obot(tc_fun(_1347713, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1347713, _1347711), _1347717), _1347715))]]], (30552 ^ _777081) ^ [_1348252, _1348254] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1348252, _1348254))))], (30554 ^ _777081) ^ [_1348283, _1348285] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1348283, _1348285))))], (30556 ^ _777081) ^ [_1348314, _1348316, _1348318, _1348320] : [class_Rings_Odivision__ring(_1348314), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348314), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1348314), _1348316), _1348318)), _1348320) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1348314), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348314), _1348316), _1348320)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348314), _1348318), _1348320)))], (30562 ^ _777081) ^ [_1348473, _1348475, _1348477, _1348479] : [class_Fields_Ofield__inverse__zero(_1348473), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1348473), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348473), _1348475), _1348477)), _1348479) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348473), hAPP(hAPP(c_Power_Opower__class_Opower(_1348473), _1348475), _1348479)), hAPP(hAPP(c_Power_Opower__class_Opower(_1348473), _1348477), _1348479)))], (30568 ^ _777081) ^ [_1348632, _1348634, _1348636, _1348638] : [class_Rings_Odivision__ring(_1348632), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348632), _1348634), _1348636)), _1348638) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1348632), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348632), _1348634), _1348638)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348632), _1348636), _1348638)))], (30574 ^ _777081) ^ [_1348791, _1348793, _1348795, _1348797] : [class_Rings_Odivision__ring(_1348791), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348791), _1348793), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348791), _1348795), _1348797)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348791), _1348793), _1348795)), _1348797))], (30580 ^ _777081) ^ [_1348934, _1348936, _1348938] : [class_Rings_Odivision__ring(_1348934), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1348934), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348934), _1348936), _1348938)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348934), hAPP(c_Groups_Ouminus__class_Ouminus(_1348934), _1348936)), _1348938))], (30586 ^ _777081) ^ [_1349063, _1349065] : [class_Rings_Odivision__ring(_1349063), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349063), _1349065), c_Groups_Oone__class_Oone(_1349063)) = _1349065)], (30592 ^ _777081) ^ [_1349158, _1349160] : [class_Rings_Odivision__ring(_1349158), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349158), c_Groups_Ozero__class_Ozero(_1349158)), _1349160) = c_Groups_Ozero__class_Ozero(_1349158))], (30598 ^ _777081) ^ [_1349257, _1349259] : [class_Rings_Odivision__ring__inverse__zero(_1349257), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349257), _1349259), c_Groups_Ozero__class_Ozero(_1349257)) = c_Groups_Ozero__class_Ozero(_1349257))], (30604 ^ _777081) ^ [_1349356, _1349358, _1349360, _1349362] : [class_Rings_Odivision__ring(_1349356), -(_1349358 = c_Groups_Ozero__class_Ozero(_1349356)), 30611 ^ _777081 : [(30612 ^ _777081) ^ [] : [_1349360 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349356), _1349362), _1349358), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349356), _1349360), _1349358) = _1349362)], (30618 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349356), _1349360), _1349358) = _1349362, -(_1349360 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349356), _1349362), _1349358))]]], (30624 ^ _777081) ^ [_1349684, _1349686, _1349688, _1349690] : [class_Rings_Odivision__ring(_1349684), -(_1349686 = c_Groups_Ozero__class_Ozero(_1349684)), 30631 ^ _777081 : [(30632 ^ _777081) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349684), _1349688), _1349686) = _1349690, -(_1349688 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349684), _1349690), _1349686))], (30638 ^ _777081) ^ [] : [_1349688 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349684), _1349690), _1349686), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349684), _1349688), _1349686) = _1349690)]]], (30644 ^ _777081) ^ [_1350012, _1350014, _1350016, _1350018] : [class_Rings_Odivision__ring(_1350012), -(_1350014 = c_Groups_Ozero__class_Ozero(_1350012)), _1350016 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350012), _1350018), _1350014), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350012), _1350016), _1350014) = _1350018)], (30658 ^ _777081) ^ [_1350242, _1350244, _1350246, _1350248] : [class_Rings_Odivision__ring(_1350242), -(_1350244 = c_Groups_Ozero__class_Ozero(_1350242)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350242), _1350246), _1350244) = _1350248, -(_1350246 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350242), _1350248), _1350244))], (30672 ^ _777081) ^ [_1350472, _1350474, _1350476] : [class_Rings_Odivision__ring(_1350472), -(_1350474 = c_Groups_Ozero__class_Ozero(_1350472)), 30679 ^ _777081 : [(30680 ^ _777081) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350472), _1350476), _1350474) = c_Groups_Oone__class_Oone(_1350472), -(_1350476 = _1350474)], (30686 ^ _777081) ^ [] : [_1350476 = _1350474, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350472), _1350476), _1350474) = c_Groups_Oone__class_Oone(_1350472))]]], (30692 ^ _777081) ^ [_1350774, _1350776] : [class_Rings_Odivision__ring(_1350774), -(_1350776 = c_Groups_Ozero__class_Ozero(_1350774)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350774), _1350776), _1350776) = c_Groups_Oone__class_Oone(_1350774))], (30702 ^ _777081) ^ [_1350888, _1350890] : [class_Rings_Odivision__ring__inverse__zero(_1350888), 30705 ^ _777081 : [(30706 ^ _777081) ^ [] : [_1350890 = c_Groups_Ozero__class_Ozero(_1350888), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350888), _1350890), _1350890) = c_Groups_Ozero__class_Ozero(_1350888))], (30712 ^ _777081) ^ [] : [-(_1350890 = c_Groups_Ozero__class_Ozero(_1350888)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350888), _1350890), _1350890) = c_Groups_Oone__class_Oone(_1350888))]]], (30718 ^ _777081) ^ [_1351110, _1351112, _1351114] : [class_Rings_Odivision__ring(_1351110), -(_1351112 = c_Groups_Ozero__class_Ozero(_1351110)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351110), hAPP(c_Groups_Ouminus__class_Ouminus(_1351110), _1351114)), hAPP(c_Groups_Ouminus__class_Ouminus(_1351110), _1351112)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351110), _1351114), _1351112))], (30728 ^ _777081) ^ [_1351258, _1351260, _1351262] : [class_Rings_Odivision__ring(_1351258), -(_1351260 = c_Groups_Ozero__class_Ozero(_1351258)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1351258), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351258), _1351262), _1351260)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351258), _1351262), hAPP(c_Groups_Ouminus__class_Ouminus(_1351258), _1351260)))], (30738 ^ _777081) ^ [_1351406, _1351408, _1351410, _1351412] : [class_Fields_Ofield(_1351406), -(_1351408 = c_Groups_Ozero__class_Ozero(_1351406)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1351406), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351406), _1351410), _1351408)), _1351412) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351406), hAPP(hAPP(c_Power_Opower__class_Opower(_1351406), _1351410), _1351412)), hAPP(hAPP(c_Power_Opower__class_Opower(_1351406), _1351408), _1351412)))], (30748 ^ _777081) ^ [_1351584, _1351586, _1351588] : [class_Fields_Ofield__inverse__zero(_1351584), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351584), c_Groups_Oone__class_Oone(_1351584)), hAPP(hAPP(c_Power_Opower__class_Opower(_1351584), _1351586), _1351588)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1351584), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351584), c_Groups_Oone__class_Oone(_1351584)), _1351586)), _1351588))], (30754 ^ _777081) ^ [_1351733, _1351735, _1351737, _1351739, _1351741] : [class_Fields_Ofield__inverse__zero(_1351733), hBOOL(hAPP(c_Finite__Set_Ofinite(_1351735), _1351737)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351735, _1351733), hAPP(hAPP(c_COMBS(_1351735, _1351733, _1351733), hAPP(hAPP(c_COMBB(_1351733, tc_fun(_1351733, _1351733), _1351735), c_Rings_Oinverse__class_Odivide(_1351733)), _1351739)), _1351741)), _1351737) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351733), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351735, _1351733), _1351739), _1351737)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351735, _1351733), _1351741), _1351737)))], (30764 ^ _777081) ^ [_1352000, _1352002, _1352004] : [class_Orderings_Oorder(_1352000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1352000), _1352002), _1352004)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1352000, _1352004, _1352002) = c_Orderings_Obot__class_Obot(tc_fun(_1352000, tc_HOL_Obool)))], (30774 ^ _777081) ^ [_1352163, _1352165, _1352167] : [class_Orderings_Oorder(_1352163), 30777 ^ _777081 : [(30778 ^ _777081) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1352163, _1352165, _1352167) = c_Orderings_Obot__class_Obot(tc_fun(_1352163, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352163), _1352165), _1352167))], (30784 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352163), _1352165), _1352167))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1352163, _1352165, _1352167) = c_Orderings_Obot__class_Obot(tc_fun(_1352163, tc_HOL_Obool)))]]], (30790 ^ _777081) ^ [_1352382, _1352384, _1352386] : [class_Orderings_Oorder(_1352382), 30793 ^ _777081 : [(30794 ^ _777081) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1352382, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1352382, _1352384, _1352386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352382), _1352384), _1352386))], (30800 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352382), _1352384), _1352386))), -(c_Orderings_Obot__class_Obot(tc_fun(_1352382, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1352382, _1352384, _1352386))]]], (30806 ^ _777081) ^ [_1352601, _1352603, _1352605, _1352607] : [class_Orderings_Olinorder(_1352601), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1352601), _1352603), _1352605)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1352601), _1352605), _1352607)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1352601, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1352601, _1352603, _1352605)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1352601, _1352605, _1352607)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1352601, _1352603, _1352607))], (30820 ^ _777081) ^ [_1352866, _1352868, _1352870, _1352872] : [class_Fields_Ofield__inverse__zero(_1352866), class_Int_Onumber(_1352866), 30827 ^ _777081 : [(30844 ^ _777081) ^ [] : [-(_1352868 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352866), _1352870), hAPP(c_Int_Onumber__class_Onumber__of(_1352866), _1352872))), 30847 ^ _777081 : [(30848 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1352866), _1352872) = c_Groups_Ozero__class_Ozero(_1352866)], (30850 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1352866), _1352868), hAPP(c_Int_Onumber__class_Onumber__of(_1352866), _1352872)) = _1352870]], 30851 ^ _777081 : [(30852 ^ _777081) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1352866), _1352872) = c_Groups_Ozero__class_Ozero(_1352866))], (30854 ^ _777081) ^ [] : [_1352868 = c_Groups_Ozero__class_Ozero(_1352866)]]], (30828 ^ _777081) ^ [] : [_1352868 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352866), _1352870), hAPP(c_Int_Onumber__class_Onumber__of(_1352866), _1352872)), 30831 ^ _777081 : [(30832 ^ _777081) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1352866), _1352872) = c_Groups_Ozero__class_Ozero(_1352866)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1352866), _1352868), hAPP(c_Int_Onumber__class_Onumber__of(_1352866), _1352872)) = _1352870)], (30838 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1352866), _1352872) = c_Groups_Ozero__class_Ozero(_1352866), -(_1352868 = c_Groups_Ozero__class_Ozero(_1352866))]]]]], (30858 ^ _777081) ^ [_1353476, _1353478, _1353480, _1353482] : [class_Fields_Ofield__inverse__zero(_1353476), class_Int_Onumber(_1353476), 30865 ^ _777081 : [(30882 ^ _777081) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1353476), _1353478) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353476), _1353480), _1353482)), 30885 ^ _777081 : [(30886 ^ _777081) ^ [] : [_1353482 = c_Groups_Ozero__class_Ozero(_1353476)], (30888 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353476), hAPP(c_Int_Onumber__class_Onumber__of(_1353476), _1353478)), _1353482) = _1353480]], 30889 ^ _777081 : [(30890 ^ _777081) ^ [] : [-(_1353482 = c_Groups_Ozero__class_Ozero(_1353476))], (30892 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1353476), _1353478) = c_Groups_Ozero__class_Ozero(_1353476)]]], (30866 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1353476), _1353478) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353476), _1353480), _1353482), 30869 ^ _777081 : [(30870 ^ _777081) ^ [] : [-(_1353482 = c_Groups_Ozero__class_Ozero(_1353476)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353476), hAPP(c_Int_Onumber__class_Onumber__of(_1353476), _1353478)), _1353482) = _1353480)], (30876 ^ _777081) ^ [] : [_1353482 = c_Groups_Ozero__class_Ozero(_1353476), -(hAPP(c_Int_Onumber__class_Onumber__of(_1353476), _1353478) = c_Groups_Ozero__class_Ozero(_1353476))]]]]], (30896 ^ _777081) ^ [_1354071, _1354073, _1354075, _1354077] : [class_Fields_Ofield__inverse__zero(_1354071), class_Int_Onumber(_1354071), 30903 ^ _777081 : [(30920 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354071), _1354073), _1354075) = hAPP(c_Int_Onumber__class_Onumber__of(_1354071), _1354077)), 30923 ^ _777081 : [(30924 ^ _777081) ^ [] : [_1354075 = c_Groups_Ozero__class_Ozero(_1354071)], (30926 ^ _777081) ^ [] : [_1354073 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354071), hAPP(c_Int_Onumber__class_Onumber__of(_1354071), _1354077)), _1354075)]], 30927 ^ _777081 : [(30928 ^ _777081) ^ [] : [-(_1354075 = c_Groups_Ozero__class_Ozero(_1354071))], (30930 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1354071), _1354077) = c_Groups_Ozero__class_Ozero(_1354071)]]], (30904 ^ _777081) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354071), _1354073), _1354075) = hAPP(c_Int_Onumber__class_Onumber__of(_1354071), _1354077), 30907 ^ _777081 : [(30908 ^ _777081) ^ [] : [-(_1354075 = c_Groups_Ozero__class_Ozero(_1354071)), -(_1354073 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354071), hAPP(c_Int_Onumber__class_Onumber__of(_1354071), _1354077)), _1354075))], (30914 ^ _777081) ^ [] : [_1354075 = c_Groups_Ozero__class_Ozero(_1354071), -(hAPP(c_Int_Onumber__class_Onumber__of(_1354071), _1354077) = c_Groups_Ozero__class_Ozero(_1354071))]]]]], (30934 ^ _777081) ^ [_1354666, _1354668, _1354670, _1354672] : [class_Fields_Ofield__inverse__zero(_1354666), class_Int_Onumber(_1354666), 30941 ^ _777081 : [(30958 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354666), _1354668), hAPP(c_Int_Onumber__class_Onumber__of(_1354666), _1354670)) = _1354672), 30961 ^ _777081 : [(30962 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1354666), _1354670) = c_Groups_Ozero__class_Ozero(_1354666)], (30964 ^ _777081) ^ [] : [_1354668 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354666), _1354672), hAPP(c_Int_Onumber__class_Onumber__of(_1354666), _1354670))]], 30965 ^ _777081 : [(30966 ^ _777081) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1354666), _1354670) = c_Groups_Ozero__class_Ozero(_1354666))], (30968 ^ _777081) ^ [] : [_1354672 = c_Groups_Ozero__class_Ozero(_1354666)]]], (30942 ^ _777081) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354666), _1354668), hAPP(c_Int_Onumber__class_Onumber__of(_1354666), _1354670)) = _1354672, 30945 ^ _777081 : [(30946 ^ _777081) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1354666), _1354670) = c_Groups_Ozero__class_Ozero(_1354666)), -(_1354668 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354666), _1354672), hAPP(c_Int_Onumber__class_Onumber__of(_1354666), _1354670)))], (30952 ^ _777081) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1354666), _1354670) = c_Groups_Ozero__class_Ozero(_1354666), -(_1354672 = c_Groups_Ozero__class_Ozero(_1354666))]]]]], (30972 ^ _777081) ^ [_1355276, _1355278, _1355280, _1355282] : [class_Orderings_Oorder(_1355276), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1355276, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1355276, _1355278, _1355280)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1355276, _1355280, _1355282)) = c_Orderings_Obot__class_Obot(tc_fun(_1355276, tc_HOL_Obool)))], (30978 ^ _777081) ^ [_1355403, _1355405] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355403), _1355405), hAPP(c_Int_Onumber__class_Onumber__of(_1355403), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1355403)), class_Fields_Ofield__inverse__zero(_1355403), class_Int_Onumber__ring(_1355403)], (30988 ^ _777081) ^ [_1355558, _1355560] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355558), _1355560), hAPP(c_Int_Onumber__class_Onumber__of(_1355558), c_Int_OBit1(c_Int_OPls))) = _1355560), class_Fields_Ofield(_1355558), class_Int_Onumber__ring(_1355558)], (30998 ^ _777081) ^ [_1355709, _1355711] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355709), _1355711), hAPP(c_Int_Onumber__class_Onumber__of(_1355709), c_Int_OBit1(c_Int_OPls))) = _1355711), class_Fields_Ofield(_1355709), class_Int_Onumber__ring(_1355709)], (31008 ^ _777081) ^ [_1355860, _1355862] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355860), _1355862), hAPP(c_Int_Onumber__class_Onumber__of(_1355860), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1355860), _1355862)), class_Fields_Ofield__inverse__zero(_1355860), class_Int_Onumber__ring(_1355860)], (31018 ^ _777081) ^ [_1356021, _1356023] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1356021, _1356023)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1356023), _1356021))], (31020 ^ _777081) ^ [_1356059, _1356061, _1356063, _1356065] : [class_Fields_Olinordered__field__inverse__zero(_1356059), class_Int_Onumber(_1356059), 31027 ^ _777081 : [(31054 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356059), _1356061), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063))), _1356065))), 31057 ^ _777081 : [(31058 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), c_Groups_Ozero__class_Ozero(_1356059)), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063))))], (31060 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), _1356061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356059), _1356065), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063))))]], 31061 ^ _777081 : [(31062 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), c_Groups_Ozero__class_Ozero(_1356059)), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063)))], (31064 ^ _777081) ^ [] : [31065 ^ _777081 : [(31066 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063)), c_Groups_Ozero__class_Ozero(_1356059))))], (31068 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356059), _1356065), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063))), _1356061))]], 31069 ^ _777081 : [(31070 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063)), c_Groups_Ozero__class_Ozero(_1356059)))], (31072 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), c_Groups_Ozero__class_Ozero(_1356059)), _1356065))]]]]], (31028 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356059), _1356061), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063))), _1356065)), 31031 ^ _777081 : [(31032 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), c_Groups_Ozero__class_Ozero(_1356059)), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), _1356061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356059), _1356065), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063)))))], (31038 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), c_Groups_Ozero__class_Ozero(_1356059)), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063)))), 31041 ^ _777081 : [(31042 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063)), c_Groups_Ozero__class_Ozero(_1356059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1356059), _1356065), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063))), _1356061)))], (31048 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), hAPP(c_Int_Onumber__class_Onumber__of(_1356059), _1356063)), c_Groups_Ozero__class_Ozero(_1356059)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356059), c_Groups_Ozero__class_Ozero(_1356059)), _1356065)))]]]]]]], (31076 ^ _777081) ^ [_1357173, _1357175, _1357177, _1357179] : [class_Fields_Olinordered__field__inverse__zero(_1357173), class_Int_Onumber(_1357173), 31083 ^ _777081 : [(31110 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357173), _1357175), _1357177)), hAPP(c_Int_Onumber__class_Onumber__of(_1357173), _1357179)))), 31113 ^ _777081 : [(31114 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), c_Groups_Ozero__class_Ozero(_1357173)), _1357177)))], (31116 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), _1357175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357173), hAPP(c_Int_Onumber__class_Onumber__of(_1357173), _1357179)), _1357177)))]], 31117 ^ _777081 : [(31118 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), c_Groups_Ozero__class_Ozero(_1357173)), _1357177))], (31120 ^ _777081) ^ [] : [31121 ^ _777081 : [(31122 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), _1357177), c_Groups_Ozero__class_Ozero(_1357173))))], (31124 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357173), hAPP(c_Int_Onumber__class_Onumber__of(_1357173), _1357179)), _1357177)), _1357175))]], 31125 ^ _777081 : [(31126 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), _1357177), c_Groups_Ozero__class_Ozero(_1357173)))], (31128 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), c_Groups_Ozero__class_Ozero(_1357173)), hAPP(c_Int_Onumber__class_Onumber__of(_1357173), _1357179)))]]]]], (31084 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357173), _1357175), _1357177)), hAPP(c_Int_Onumber__class_Onumber__of(_1357173), _1357179))), 31087 ^ _777081 : [(31088 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), c_Groups_Ozero__class_Ozero(_1357173)), _1357177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), _1357175), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357173), hAPP(c_Int_Onumber__class_Onumber__of(_1357173), _1357179)), _1357177))))], (31094 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), c_Groups_Ozero__class_Ozero(_1357173)), _1357177))), 31097 ^ _777081 : [(31098 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), _1357177), c_Groups_Ozero__class_Ozero(_1357173))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357173), hAPP(c_Int_Onumber__class_Onumber__of(_1357173), _1357179)), _1357177)), _1357175)))], (31104 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), _1357177), c_Groups_Ozero__class_Ozero(_1357173)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357173), c_Groups_Ozero__class_Ozero(_1357173)), hAPP(c_Int_Onumber__class_Onumber__of(_1357173), _1357179))))]]]]]]], (31132 ^ _777081) ^ [_1358242, _1358244, _1358246, _1358248] : [class_Fields_Olinordered__field__inverse__zero(_1358242), class_Int_Onumber(_1358242), 31139 ^ _777081 : [(31166 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), hAPP(c_Int_Onumber__class_Onumber__of(_1358242), _1358244)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358242), _1358246), _1358248)))), 31169 ^ _777081 : [(31170 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), c_Groups_Ozero__class_Ozero(_1358242)), _1358248)))], (31172 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358242), hAPP(c_Int_Onumber__class_Onumber__of(_1358242), _1358244)), _1358248)), _1358246))]], 31173 ^ _777081 : [(31174 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), c_Groups_Ozero__class_Ozero(_1358242)), _1358248))], (31176 ^ _777081) ^ [] : [31177 ^ _777081 : [(31178 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), _1358248), c_Groups_Ozero__class_Ozero(_1358242))))], (31180 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), _1358246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358242), hAPP(c_Int_Onumber__class_Onumber__of(_1358242), _1358244)), _1358248)))]], 31181 ^ _777081 : [(31182 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), _1358248), c_Groups_Ozero__class_Ozero(_1358242)))], (31184 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), hAPP(c_Int_Onumber__class_Onumber__of(_1358242), _1358244)), c_Groups_Ozero__class_Ozero(_1358242)))]]]]], (31140 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), hAPP(c_Int_Onumber__class_Onumber__of(_1358242), _1358244)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358242), _1358246), _1358248))), 31143 ^ _777081 : [(31144 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), c_Groups_Ozero__class_Ozero(_1358242)), _1358248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358242), hAPP(c_Int_Onumber__class_Onumber__of(_1358242), _1358244)), _1358248)), _1358246)))], (31150 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), c_Groups_Ozero__class_Ozero(_1358242)), _1358248))), 31153 ^ _777081 : [(31154 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), _1358248), c_Groups_Ozero__class_Ozero(_1358242))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), _1358246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358242), hAPP(c_Int_Onumber__class_Onumber__of(_1358242), _1358244)), _1358248))))], (31160 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), _1358248), c_Groups_Ozero__class_Ozero(_1358242)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358242), hAPP(c_Int_Onumber__class_Onumber__of(_1358242), _1358244)), c_Groups_Ozero__class_Ozero(_1358242))))]]]]]]], (31188 ^ _777081) ^ [_1359311, _1359313, _1359315, _1359317] : [class_Fields_Olinordered__field__inverse__zero(_1359311), class_Int_Onumber(_1359311), 31195 ^ _777081 : [(31222 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), _1359313), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359311), _1359315), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317))))), 31225 ^ _777081 : [(31226 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), c_Groups_Ozero__class_Ozero(_1359311)), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317))))], (31228 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359311), _1359313), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317))), _1359315))]], 31229 ^ _777081 : [(31230 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), c_Groups_Ozero__class_Ozero(_1359311)), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317)))], (31232 ^ _777081) ^ [] : [31233 ^ _777081 : [(31234 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317)), c_Groups_Ozero__class_Ozero(_1359311))))], (31236 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), _1359315), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359311), _1359313), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317))))]], 31237 ^ _777081 : [(31238 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317)), c_Groups_Ozero__class_Ozero(_1359311)))], (31240 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), _1359313), c_Groups_Ozero__class_Ozero(_1359311)))]]]]], (31196 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), _1359313), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359311), _1359315), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317)))), 31199 ^ _777081 : [(31200 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), c_Groups_Ozero__class_Ozero(_1359311)), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359311), _1359313), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317))), _1359315)))], (31206 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), c_Groups_Ozero__class_Ozero(_1359311)), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317)))), 31209 ^ _777081 : [(31210 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317)), c_Groups_Ozero__class_Ozero(_1359311))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), _1359315), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359311), _1359313), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317)))))], (31216 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), hAPP(c_Int_Onumber__class_Onumber__of(_1359311), _1359317)), c_Groups_Ozero__class_Ozero(_1359311)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359311), _1359313), c_Groups_Ozero__class_Ozero(_1359311))))]]]]]]], (31244 ^ _777081) ^ [_1360425, _1360427, _1360429, _1360431] : [class_Fields_Ofield(_1360425), -(_1360427 = c_Groups_Ozero__class_Ozero(_1360425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1360429), _1360431)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1360425), _1360427), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1360431), _1360429)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360425), hAPP(hAPP(c_Power_Opower__class_Opower(_1360425), _1360427), _1360431)), hAPP(hAPP(c_Power_Opower__class_Opower(_1360425), _1360427), _1360429)))], (31258 ^ _777081) ^ [_1360709, _1360711] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360709), hAPP(c_Int_Onumber__class_Onumber__of(_1360709), c_Int_OMin)), _1360711) = hAPP(c_Groups_Ouminus__class_Ouminus(_1360709), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360709), c_Groups_Oone__class_Oone(_1360709)), _1360711))), class_Fields_Ofield__inverse__zero(_1360709), class_Int_Onumber__ring(_1360709)], (31268 ^ _777081) ^ [_1360890, _1360892, _1360894, _1360896, _1360898] : [class_Orderings_Olinorder(_1360890), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360890, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1360890, _1360892, _1360894)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1360890, _1360896, _1360898)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1360890, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1360890), _1360892), _1360896), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1360890), _1360894), _1360898)))], (31274 ^ _777081) ^ [_1361049, _1361051, _1361053, _1361055] : [class_Orderings_Oorder(_1361049), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1361049, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1361049, _1361051, _1361053)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1361049, _1361053, _1361055)) = c_Orderings_Obot__class_Obot(tc_fun(_1361049, tc_HOL_Obool)))], (31280 ^ _777081) ^ [_1361176, _1361178, _1361180, _1361182] : [class_Fields_Olinordered__field__inverse__zero(_1361176), class_Int_Onumber(_1361176), 31287 ^ _777081 : [(31314 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361176), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1361176), _1361178), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180))), _1361182))), 31317 ^ _777081 : [(31318 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361176), c_Groups_Ozero__class_Ozero(_1361176)), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180))))], (31320 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361176), _1361178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361176), _1361182), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180))))]], 31321 ^ _777081 : [(31322 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361176), c_Groups_Ozero__class_Ozero(_1361176)), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180)))], (31324 ^ _777081) ^ [] : [31325 ^ _777081 : [(31326 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361176), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180)), c_Groups_Ozero__class_Ozero(_1361176))))], (31328 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361176), _1361182), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180))), _1361178))]], 31329 ^ _777081 : [(31330 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361176), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180)), c_Groups_Ozero__class_Ozero(_1361176)))], (31332 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361176), c_Groups_Ozero__class_Ozero(_1361176)), _1361182))]]]]], (31288 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361176), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1361176), _1361178), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180))), _1361182)), 31291 ^ _777081 : [(31292 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361176), c_Groups_Ozero__class_Ozero(_1361176)), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361176), _1361178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361176), _1361182), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180)))))], (31298 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361176), c_Groups_Ozero__class_Ozero(_1361176)), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180)))), 31301 ^ _777081 : [(31302 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361176), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180)), c_Groups_Ozero__class_Ozero(_1361176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361176), _1361182), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180))), _1361178)))], (31308 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361176), hAPP(c_Int_Onumber__class_Onumber__of(_1361176), _1361180)), c_Groups_Ozero__class_Ozero(_1361176)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1361176), c_Groups_Ozero__class_Ozero(_1361176)), _1361182)))]]]]]]], (31336 ^ _777081) ^ [_1362290, _1362292, _1362294, _1362296] : [class_Fields_Olinordered__field__inverse__zero(_1362290), class_Int_Onumber(_1362290), 31343 ^ _777081 : [(31370 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362290), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362290), _1362292), _1362294)), hAPP(c_Int_Onumber__class_Onumber__of(_1362290), _1362296)))), 31373 ^ _777081 : [(31374 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362290), c_Groups_Ozero__class_Ozero(_1362290)), _1362294)))], (31376 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362290), _1362292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362290), hAPP(c_Int_Onumber__class_Onumber__of(_1362290), _1362296)), _1362294)))]], 31377 ^ _777081 : [(31378 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362290), c_Groups_Ozero__class_Ozero(_1362290)), _1362294))], (31380 ^ _777081) ^ [] : [31381 ^ _777081 : [(31382 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362290), _1362294), c_Groups_Ozero__class_Ozero(_1362290))))], (31384 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362290), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362290), hAPP(c_Int_Onumber__class_Onumber__of(_1362290), _1362296)), _1362294)), _1362292))]], 31385 ^ _777081 : [(31386 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362290), _1362294), c_Groups_Ozero__class_Ozero(_1362290)))], (31388 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362290), c_Groups_Ozero__class_Ozero(_1362290)), hAPP(c_Int_Onumber__class_Onumber__of(_1362290), _1362296)))]]]]], (31344 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362290), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362290), _1362292), _1362294)), hAPP(c_Int_Onumber__class_Onumber__of(_1362290), _1362296))), 31347 ^ _777081 : [(31348 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362290), c_Groups_Ozero__class_Ozero(_1362290)), _1362294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362290), _1362292), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362290), hAPP(c_Int_Onumber__class_Onumber__of(_1362290), _1362296)), _1362294))))], (31354 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362290), c_Groups_Ozero__class_Ozero(_1362290)), _1362294))), 31357 ^ _777081 : [(31358 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362290), _1362294), c_Groups_Ozero__class_Ozero(_1362290))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362290), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362290), hAPP(c_Int_Onumber__class_Onumber__of(_1362290), _1362296)), _1362294)), _1362292)))], (31364 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1362290), _1362294), c_Groups_Ozero__class_Ozero(_1362290)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362290), c_Groups_Ozero__class_Ozero(_1362290)), hAPP(c_Int_Onumber__class_Onumber__of(_1362290), _1362296))))]]]]]]], (31392 ^ _777081) ^ [_1363359, _1363361, _1363363, _1363365] : [class_Fields_Olinordered__field__inverse__zero(_1363359), class_Int_Onumber(_1363359), 31399 ^ _777081 : [(31426 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363359), hAPP(c_Int_Onumber__class_Onumber__of(_1363359), _1363361)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363359), _1363363), _1363365)))), 31429 ^ _777081 : [(31430 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363359), c_Groups_Ozero__class_Ozero(_1363359)), _1363365)))], (31432 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363359), hAPP(c_Int_Onumber__class_Onumber__of(_1363359), _1363361)), _1363365)), _1363363))]], 31433 ^ _777081 : [(31434 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363359), c_Groups_Ozero__class_Ozero(_1363359)), _1363365))], (31436 ^ _777081) ^ [] : [31437 ^ _777081 : [(31438 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363359), _1363365), c_Groups_Ozero__class_Ozero(_1363359))))], (31440 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363359), _1363363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363359), hAPP(c_Int_Onumber__class_Onumber__of(_1363359), _1363361)), _1363365)))]], 31441 ^ _777081 : [(31442 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363359), _1363365), c_Groups_Ozero__class_Ozero(_1363359)))], (31444 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363359), hAPP(c_Int_Onumber__class_Onumber__of(_1363359), _1363361)), c_Groups_Ozero__class_Ozero(_1363359)))]]]]], (31400 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363359), hAPP(c_Int_Onumber__class_Onumber__of(_1363359), _1363361)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363359), _1363363), _1363365))), 31403 ^ _777081 : [(31404 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363359), c_Groups_Ozero__class_Ozero(_1363359)), _1363365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363359), hAPP(c_Int_Onumber__class_Onumber__of(_1363359), _1363361)), _1363365)), _1363363)))], (31410 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363359), c_Groups_Ozero__class_Ozero(_1363359)), _1363365))), 31413 ^ _777081 : [(31414 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363359), _1363365), c_Groups_Ozero__class_Ozero(_1363359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363359), _1363363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363359), hAPP(c_Int_Onumber__class_Onumber__of(_1363359), _1363361)), _1363365))))], (31420 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363359), _1363365), c_Groups_Ozero__class_Ozero(_1363359)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363359), hAPP(c_Int_Onumber__class_Onumber__of(_1363359), _1363361)), c_Groups_Ozero__class_Ozero(_1363359))))]]]]]]], (31448 ^ _777081) ^ [_1364428, _1364430, _1364432, _1364434] : [class_Fields_Olinordered__field__inverse__zero(_1364428), class_Int_Onumber(_1364428), 31455 ^ _777081 : [(31482 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364428), _1364430), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364428), _1364432), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434))))), 31485 ^ _777081 : [(31486 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364428), c_Groups_Ozero__class_Ozero(_1364428)), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434))))], (31488 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364428), _1364430), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434))), _1364432))]], 31489 ^ _777081 : [(31490 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364428), c_Groups_Ozero__class_Ozero(_1364428)), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434)))], (31492 ^ _777081) ^ [] : [31493 ^ _777081 : [(31494 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364428), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434)), c_Groups_Ozero__class_Ozero(_1364428))))], (31496 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364428), _1364432), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364428), _1364430), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434))))]], 31497 ^ _777081 : [(31498 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364428), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434)), c_Groups_Ozero__class_Ozero(_1364428)))], (31500 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364428), _1364430), c_Groups_Ozero__class_Ozero(_1364428)))]]]]], (31456 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364428), _1364430), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364428), _1364432), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434)))), 31459 ^ _777081 : [(31460 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364428), c_Groups_Ozero__class_Ozero(_1364428)), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364428), _1364430), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434))), _1364432)))], (31466 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364428), c_Groups_Ozero__class_Ozero(_1364428)), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434)))), 31469 ^ _777081 : [(31470 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364428), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434)), c_Groups_Ozero__class_Ozero(_1364428))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364428), _1364432), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364428), _1364430), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434)))))], (31476 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364428), hAPP(c_Int_Onumber__class_Onumber__of(_1364428), _1364434)), c_Groups_Ozero__class_Ozero(_1364428)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364428), _1364430), c_Groups_Ozero__class_Ozero(_1364428))))]]]]]]], (31504 ^ _777081) ^ [_1365542, _1365544] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1365542, _1365544)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1365544), _1365542)))], (31506 ^ _777081) ^ [_1365583, _1365585, _1365587, _1365589] : [class_Orderings_Olinorder(_1365583), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365583), _1365585), _1365587)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365583), _1365587), _1365589)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1365583, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1365583, _1365585, _1365587)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1365583, _1365587, _1365589)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1365583, _1365585, _1365589))], (31520 ^ _777081) ^ [_1365848, _1365850] : [class_Fields_Olinordered__field__inverse__zero(_1365848), class_Int_Onumber__ring(_1365848), 31527 ^ _777081 : [(31528 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365848), c_Groups_Ozero__class_Ozero(_1365848)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365848), _1365850), hAPP(c_Int_Onumber__class_Onumber__of(_1365848), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365848), c_Groups_Ozero__class_Ozero(_1365848)), _1365850)))], (31534 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365848), c_Groups_Ozero__class_Ozero(_1365848)), _1365850)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365848), c_Groups_Ozero__class_Ozero(_1365848)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365848), _1365850), hAPP(c_Int_Onumber__class_Onumber__of(_1365848), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (31540 ^ _777081) ^ [_1366198, _1366200] : [class_Fields_Olinordered__field__inverse__zero(_1366198), class_Int_Onumber__ring(_1366198), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366198), c_Groups_Ozero__class_Ozero(_1366198)), _1366200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366198), c_Groups_Ozero__class_Ozero(_1366198)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1366198), _1366200), hAPP(c_Int_Onumber__class_Onumber__of(_1366198), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (31554 ^ _777081) ^ [_1366439, _1366441, _1366443, _1366445] : [class_Fields_Olinordered__field__inverse__zero(_1366439), 31557 ^ _777081 : [(31584 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366439), _1366441), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1366439), _1366443), _1366445)))), 31587 ^ _777081 : [(31588 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366439), c_Groups_Ozero__class_Ozero(_1366439)), _1366445)))], (31590 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366439), _1366441), _1366445)), _1366443))]], 31591 ^ _777081 : [(31592 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366439), c_Groups_Ozero__class_Ozero(_1366439)), _1366445))], (31594 ^ _777081) ^ [] : [31595 ^ _777081 : [(31596 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366439), _1366445), c_Groups_Ozero__class_Ozero(_1366439))))], (31598 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366439), _1366443), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366439), _1366441), _1366445)))]], 31599 ^ _777081 : [(31600 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366439), _1366445), c_Groups_Ozero__class_Ozero(_1366439)))], (31602 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366439), _1366441), c_Groups_Ozero__class_Ozero(_1366439)))]]]]], (31558 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366439), _1366441), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1366439), _1366443), _1366445))), 31561 ^ _777081 : [(31562 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366439), c_Groups_Ozero__class_Ozero(_1366439)), _1366445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366439), _1366441), _1366445)), _1366443)))], (31568 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366439), c_Groups_Ozero__class_Ozero(_1366439)), _1366445))), 31571 ^ _777081 : [(31572 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366439), _1366445), c_Groups_Ozero__class_Ozero(_1366439))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366439), _1366443), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366439), _1366441), _1366445))))], (31578 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366439), _1366445), c_Groups_Ozero__class_Ozero(_1366439)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366439), _1366441), c_Groups_Ozero__class_Ozero(_1366439))))]]]]]]], (31606 ^ _777081) ^ [_1367392, _1367394, _1367396, _1367398] : [class_Fields_Olinordered__field__inverse__zero(_1367392), 31609 ^ _777081 : [(31636 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367392), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1367392), _1367394), _1367396)), _1367398))), 31639 ^ _777081 : [(31640 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367392), c_Groups_Ozero__class_Ozero(_1367392)), _1367396)))], (31642 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367392), _1367394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1367392), _1367398), _1367396)))]], 31643 ^ _777081 : [(31644 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367392), c_Groups_Ozero__class_Ozero(_1367392)), _1367396))], (31646 ^ _777081) ^ [] : [31647 ^ _777081 : [(31648 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367392), _1367396), c_Groups_Ozero__class_Ozero(_1367392))))], (31650 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367392), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1367392), _1367398), _1367396)), _1367394))]], 31651 ^ _777081 : [(31652 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367392), _1367396), c_Groups_Ozero__class_Ozero(_1367392)))], (31654 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367392), c_Groups_Ozero__class_Ozero(_1367392)), _1367398))]]]]], (31610 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367392), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1367392), _1367394), _1367396)), _1367398)), 31613 ^ _777081 : [(31614 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367392), c_Groups_Ozero__class_Ozero(_1367392)), _1367396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367392), _1367394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1367392), _1367398), _1367396))))], (31620 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367392), c_Groups_Ozero__class_Ozero(_1367392)), _1367396))), 31623 ^ _777081 : [(31624 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367392), _1367396), c_Groups_Ozero__class_Ozero(_1367392))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367392), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1367392), _1367398), _1367396)), _1367394)))], (31630 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1367392), _1367396), c_Groups_Ozero__class_Ozero(_1367392)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367392), c_Groups_Ozero__class_Ozero(_1367392)), _1367398)))]]]]]]], (31658 ^ _777081) ^ [_1368345, _1368347, _1368349, _1368351] : [class_Fields_Olinordered__field(_1368345), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368345), c_Groups_Ozero__class_Ozero(_1368345)), _1368347)), 31665 ^ _777081 : [(31666 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368345), _1368349), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1368345), _1368351), _1368347))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368345), _1368349), _1368347)), _1368351)))], (31672 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368345), _1368349), _1368347)), _1368351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368345), _1368349), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1368345), _1368351), _1368347))))]]], (31678 ^ _777081) ^ [_1368726, _1368728, _1368730, _1368732, _1368734] : [class_Fields_Ofield__inverse__zero(_1368726), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368726), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1368726), _1368728), _1368730)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1368726), _1368732), _1368734)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1368726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368726), _1368728), _1368732)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368726), _1368730), _1368734)))], (31684 ^ _777081) ^ [_1368903, _1368905, _1368907] : [class_Fields_Ofield__inverse__zero(_1368903), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1368903), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1368903), _1368905), _1368907)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1368903), _1368905), hAPP(c_Groups_Ouminus__class_Ouminus(_1368903), _1368907)))], (31690 ^ _777081) ^ [_1369032, _1369034, _1369036] : [class_Fields_Ofield__inverse__zero(_1369032), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1369032), hAPP(c_Groups_Ouminus__class_Ouminus(_1369032), _1369034)), hAPP(c_Groups_Ouminus__class_Ouminus(_1369032), _1369036)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1369032), _1369034), _1369036))], (31696 ^ _777081) ^ [_1369161, _1369163, _1369165] : [class_Fields_Olinordered__field__inverse__zero(_1369161), -(hAPP(c_Groups_Oabs__class_Oabs(_1369161), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1369161), _1369163), _1369165)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1369161), hAPP(c_Groups_Oabs__class_Oabs(_1369161), _1369163)), hAPP(c_Groups_Oabs__class_Oabs(_1369161), _1369165)))], (31702 ^ _777081) ^ [_1369300, _1369302, _1369304, _1369306] : [class_Fields_Olinordered__field__inverse__zero(_1369300), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369300), _1369302), _1369304)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369300), _1369306), c_Groups_Ozero__class_Ozero(_1369300))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369300), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1369300), _1369304), _1369306)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1369300), _1369302), _1369306))))], (31716 ^ _777081) ^ [_1369569, _1369571, _1369573, _1369575] : [class_Fields_Olinordered__field__inverse__zero(_1369569), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369569), _1369571), _1369573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369569), c_Groups_Ozero__class_Ozero(_1369569)), _1369575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369569), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1369569), _1369571), _1369575)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1369569), _1369573), _1369575))))], (31730 ^ _777081) ^ [_1369838, _1369840, _1369842] : [class_Fields_Olinordered__field__inverse__zero(_1369838), 31733 ^ _777081 : [(31734 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369838), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1369838), _1369840), _1369842)), c_Groups_Ozero__class_Ozero(_1369838))), 31739 ^ _777081 : [(31740 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369838), c_Groups_Ozero__class_Ozero(_1369838)), _1369840)))], (31742 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369838), _1369842), c_Groups_Ozero__class_Ozero(_1369838))))]], 31743 ^ _777081 : [(31744 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369838), _1369840), c_Groups_Ozero__class_Ozero(_1369838))))], (31746 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369838), c_Groups_Ozero__class_Ozero(_1369838)), _1369842)))]]], (31748 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369838), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1369838), _1369840), _1369842)), c_Groups_Ozero__class_Ozero(_1369838)))), 31749 ^ _777081 : [(31750 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369838), c_Groups_Ozero__class_Ozero(_1369838)), _1369840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369838), _1369842), c_Groups_Ozero__class_Ozero(_1369838)))], (31756 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369838), _1369840), c_Groups_Ozero__class_Ozero(_1369838))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369838), c_Groups_Ozero__class_Ozero(_1369838)), _1369842))]]]]], (31764 ^ _777081) ^ [_1370428, _1370430, _1370432] : [class_Fields_Olinordered__field__inverse__zero(_1370428), 31767 ^ _777081 : [(31768 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370428), c_Groups_Ozero__class_Ozero(_1370428)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1370428), _1370430), _1370432))), 31773 ^ _777081 : [(31774 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370428), c_Groups_Ozero__class_Ozero(_1370428)), _1370430)))], (31776 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370428), c_Groups_Ozero__class_Ozero(_1370428)), _1370432)))]], 31777 ^ _777081 : [(31778 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370428), _1370430), c_Groups_Ozero__class_Ozero(_1370428))))], (31780 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370428), _1370432), c_Groups_Ozero__class_Ozero(_1370428))))]]], (31782 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370428), c_Groups_Ozero__class_Ozero(_1370428)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1370428), _1370430), _1370432)))), 31783 ^ _777081 : [(31784 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370428), c_Groups_Ozero__class_Ozero(_1370428)), _1370430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370428), c_Groups_Ozero__class_Ozero(_1370428)), _1370432))], (31790 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370428), _1370430), c_Groups_Ozero__class_Ozero(_1370428))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370428), _1370432), c_Groups_Ozero__class_Ozero(_1370428)))]]]]], (31798 ^ _777081) ^ [_1371018, _1371020, _1371022] : [class_Fields_Olinordered__field__inverse__zero(_1371018), 31801 ^ _777081 : [(31802 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371018), c_Groups_Ozero__class_Ozero(_1371018)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1371018), _1371020), _1371022))), 31807 ^ _777081 : [(31808 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371018), c_Groups_Ozero__class_Ozero(_1371018)), _1371020)))], (31810 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371018), c_Groups_Ozero__class_Ozero(_1371018)), _1371022)))]], 31811 ^ _777081 : [(31812 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371018), _1371020), c_Groups_Ozero__class_Ozero(_1371018))))], (31814 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371018), _1371022), c_Groups_Ozero__class_Ozero(_1371018))))]]], (31816 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371018), c_Groups_Ozero__class_Ozero(_1371018)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1371018), _1371020), _1371022)))), 31817 ^ _777081 : [(31818 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371018), c_Groups_Ozero__class_Ozero(_1371018)), _1371020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371018), c_Groups_Ozero__class_Ozero(_1371018)), _1371022))], (31824 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371018), _1371020), c_Groups_Ozero__class_Ozero(_1371018))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371018), _1371022), c_Groups_Ozero__class_Ozero(_1371018)))]]]]], (31832 ^ _777081) ^ [_1371608, _1371610, _1371612] : [class_Fields_Olinordered__field__inverse__zero(_1371608), 31835 ^ _777081 : [(31836 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371608), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1371608), _1371610), _1371612)), c_Groups_Ozero__class_Ozero(_1371608))), 31841 ^ _777081 : [(31842 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371608), c_Groups_Ozero__class_Ozero(_1371608)), _1371610)))], (31844 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371608), _1371612), c_Groups_Ozero__class_Ozero(_1371608))))]], 31845 ^ _777081 : [(31846 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371608), _1371610), c_Groups_Ozero__class_Ozero(_1371608))))], (31848 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371608), c_Groups_Ozero__class_Ozero(_1371608)), _1371612)))]]], (31850 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371608), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1371608), _1371610), _1371612)), c_Groups_Ozero__class_Ozero(_1371608)))), 31851 ^ _777081 : [(31852 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371608), c_Groups_Ozero__class_Ozero(_1371608)), _1371610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371608), _1371612), c_Groups_Ozero__class_Ozero(_1371608)))], (31858 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371608), _1371610), c_Groups_Ozero__class_Ozero(_1371608))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371608), c_Groups_Ozero__class_Ozero(_1371608)), _1371612))]]]]], (31866 ^ _777081) ^ [_1372198, _1372200, _1372202] : [class_Fields_Olinordered__field(_1372198), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372198), c_Groups_Ozero__class_Ozero(_1372198)), _1372200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372198), c_Groups_Ozero__class_Ozero(_1372198)), _1372202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372198), c_Groups_Ozero__class_Ozero(_1372198)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1372198), _1372200), _1372202))))], (31880 ^ _777081) ^ [_1372453, _1372455, _1372457] : [class_Fields_Olinordered__field(_1372453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372453), c_Groups_Ozero__class_Ozero(_1372453)), _1372455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372453), _1372457), c_Groups_Ozero__class_Ozero(_1372453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372453), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1372453), _1372455), _1372457)), c_Groups_Ozero__class_Ozero(_1372453))))], (31894 ^ _777081) ^ [_1372708, _1372710, _1372712] : [class_Fields_Olinordered__field(_1372708), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372708), _1372710), c_Groups_Ozero__class_Ozero(_1372708))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372708), c_Groups_Ozero__class_Ozero(_1372708)), _1372712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372708), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1372708), _1372710), _1372712)), c_Groups_Ozero__class_Ozero(_1372708))))], (31908 ^ _777081) ^ [_1372963, _1372965, _1372967] : [class_Fields_Olinordered__field(_1372963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372963), _1372965), c_Groups_Ozero__class_Ozero(_1372963))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372963), _1372967), c_Groups_Ozero__class_Ozero(_1372963))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1372963), c_Groups_Ozero__class_Ozero(_1372963)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1372963), _1372965), _1372967))))], (31922 ^ _777081) ^ [_1373218, _1373220, _1373222, _1373224] : [class_Fields_Olinordered__field(_1373218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373218), _1373220), _1373222)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373218), c_Groups_Ozero__class_Ozero(_1373218)), _1373224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373218), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1373218), _1373220), _1373224)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1373218), _1373222), _1373224))))], (31936 ^ _777081) ^ [_1373487, _1373489, _1373491, _1373493] : [class_Fields_Olinordered__field(_1373487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373487), _1373489), _1373491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373487), _1373493), c_Groups_Ozero__class_Ozero(_1373487))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1373487), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1373487), _1373491), _1373493)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1373487), _1373489), _1373493))))], (31950 ^ _777081) ^ [_1373756, _1373758, _1373760, _1373762] : [class_Fields_Ofield__inverse__zero(_1373756), 31953 ^ _777081 : [(31970 ^ _777081) ^ [] : [-(_1373758 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1373756), _1373760), _1373762)), 31973 ^ _777081 : [(31974 ^ _777081) ^ [] : [_1373762 = c_Groups_Ozero__class_Ozero(_1373756)], (31976 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1373756), _1373758), _1373762) = _1373760]], 31977 ^ _777081 : [(31978 ^ _777081) ^ [] : [-(_1373762 = c_Groups_Ozero__class_Ozero(_1373756))], (31980 ^ _777081) ^ [] : [_1373758 = c_Groups_Ozero__class_Ozero(_1373756)]]], (31954 ^ _777081) ^ [] : [_1373758 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1373756), _1373760), _1373762), 31957 ^ _777081 : [(31958 ^ _777081) ^ [] : [-(_1373762 = c_Groups_Ozero__class_Ozero(_1373756)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1373756), _1373758), _1373762) = _1373760)], (31964 ^ _777081) ^ [] : [_1373762 = c_Groups_Ozero__class_Ozero(_1373756), -(_1373758 = c_Groups_Ozero__class_Ozero(_1373756))]]]]], (31984 ^ _777081) ^ [_1374250, _1374252, _1374254, _1374256] : [class_Fields_Ofield__inverse__zero(_1374250), 31987 ^ _777081 : [(32004 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1374250), _1374252), _1374254) = _1374256), 32007 ^ _777081 : [(32008 ^ _777081) ^ [] : [_1374254 = c_Groups_Ozero__class_Ozero(_1374250)], (32010 ^ _777081) ^ [] : [_1374252 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374250), _1374256), _1374254)]], 32011 ^ _777081 : [(32012 ^ _777081) ^ [] : [-(_1374254 = c_Groups_Ozero__class_Ozero(_1374250))], (32014 ^ _777081) ^ [] : [_1374256 = c_Groups_Ozero__class_Ozero(_1374250)]]], (31988 ^ _777081) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1374250), _1374252), _1374254) = _1374256, 31991 ^ _777081 : [(31992 ^ _777081) ^ [] : [-(_1374254 = c_Groups_Ozero__class_Ozero(_1374250)), -(_1374252 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374250), _1374256), _1374254))], (31998 ^ _777081) ^ [] : [_1374254 = c_Groups_Ozero__class_Ozero(_1374250), -(_1374256 = c_Groups_Ozero__class_Ozero(_1374250))]]]]], (32018 ^ _777081) ^ [_1374744, _1374746, _1374748, _1374750] : [class_Fields_Ofield__inverse__zero(_1374744), -(_1374746 = c_Groups_Ozero__class_Ozero(_1374744)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1374744), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374744), _1374748), _1374746)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374744), _1374750), _1374746)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1374744), _1374748), _1374750))], (32028 ^ _777081) ^ [_1374906, _1374908, _1374910, _1374912] : [class_Fields_Ofield__inverse__zero(_1374906), -(_1374908 = c_Groups_Ozero__class_Ozero(_1374906)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1374906), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374906), _1374908), _1374910)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1374906), _1374908), _1374912)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1374906), _1374910), _1374912))], (32038 ^ _777081) ^ [_1375068, _1375070, _1375072, _1375074, _1375076] : [class_Fields_Ofield(_1375068), -(_1375070 = c_Groups_Ozero__class_Ozero(_1375068)), -(_1375072 = c_Groups_Ozero__class_Ozero(_1375068)), 32049 ^ _777081 : [(32050 ^ _777081) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1375068), _1375074), _1375070) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1375068), _1375076), _1375072), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1375068), _1375074), _1375072) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1375068), _1375076), _1375070))], (32056 ^ _777081) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1375068), _1375074), _1375072) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1375068), _1375076), _1375070), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1375068), _1375074), _1375070) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1375068), _1375076), _1375072))]]], (32062 ^ _777081) ^ [_1375517, _1375519, _1375521] : [class_Fields_Olinordered__field(_1375517), -(_1375519 = c_Groups_Ozero__class_Ozero(_1375517)), -(hAPP(c_Groups_Oabs__class_Oabs(_1375517), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1375517), _1375521), _1375519)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1375517), hAPP(c_Groups_Oabs__class_Oabs(_1375517), _1375521)), hAPP(c_Groups_Oabs__class_Oabs(_1375517), _1375519)))], (32072 ^ _777081) ^ [_1375675, _1375677, _1375679] : [class_Fields_Olinordered__field(_1375675), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375675), c_Groups_Ozero__class_Ozero(_1375675)), _1375677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1375675), c_Groups_Ozero__class_Ozero(_1375675)), _1375679)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375675), c_Groups_Ozero__class_Ozero(_1375675)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1375675), _1375677), _1375679))))], (32086 ^ _777081) ^ [_1375930, _1375932, _1375934] : [class_Fields_Olinordered__field(_1375930), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375930), c_Groups_Ozero__class_Ozero(_1375930)), _1375932)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1375930), _1375934), c_Groups_Ozero__class_Ozero(_1375930))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1375930), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1375930), _1375932), _1375934)), c_Groups_Ozero__class_Ozero(_1375930))))], (32100 ^ _777081) ^ [_1376185, _1376187, _1376189, _1376191, _1376193] : [class_Fields_Olinordered__field(_1376185), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376185), c_Groups_Ozero__class_Ozero(_1376185)), _1376187)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376185), _1376187), _1376189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376185), c_Groups_Ozero__class_Ozero(_1376185)), _1376191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376185), _1376191), _1376193)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376185), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1376185), _1376187), _1376193)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1376185), _1376189), _1376191))))], (32122 ^ _777081) ^ [_1376608, _1376610, _1376612, _1376614, _1376616] : [class_Fields_Olinordered__field(_1376608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376608), c_Groups_Ozero__class_Ozero(_1376608)), _1376610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376608), _1376610), _1376612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376608), c_Groups_Ozero__class_Ozero(_1376608)), _1376614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376608), _1376614), _1376616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1376608), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1376608), _1376610), _1376616)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1376608), _1376612), _1376614))))], (32144 ^ _777081) ^ [_1377031, _1377033, _1377035, _1377037, _1377039] : [class_Fields_Olinordered__field(_1377031), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377031), c_Groups_Ozero__class_Ozero(_1377031)), _1377033)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377031), _1377033), _1377035)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377031), c_Groups_Ozero__class_Ozero(_1377031)), _1377037)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377031), _1377037), _1377039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377031), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1377031), _1377033), _1377039)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1377031), _1377035), _1377037))))], (32166 ^ _777081) ^ [_1377454, _1377456, _1377458] : [class_Fields_Olinordered__field(_1377454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377454), _1377456), c_Groups_Ozero__class_Ozero(_1377454))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377454), c_Groups_Ozero__class_Ozero(_1377454)), _1377458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377454), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1377454), _1377456), _1377458)), c_Groups_Ozero__class_Ozero(_1377454))))], (32180 ^ _777081) ^ [_1377709, _1377711, _1377713] : [class_Fields_Olinordered__field(_1377709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377709), _1377711), c_Groups_Ozero__class_Ozero(_1377709))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377709), _1377713), c_Groups_Ozero__class_Ozero(_1377709))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1377709), c_Groups_Ozero__class_Ozero(_1377709)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1377709), _1377711), _1377713))))], (32194 ^ _777081) ^ [_1377964, _1377966, _1377968, _1377970] : [class_Fields_Olinordered__field__inverse__zero(_1377964), 32197 ^ _777081 : [(32224 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), _1377966), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1377964), _1377968), _1377970)))), 32227 ^ _777081 : [(32228 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), c_Groups_Ozero__class_Ozero(_1377964)), _1377970)))], (32230 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377964), _1377966), _1377970)), _1377968))]], 32231 ^ _777081 : [(32232 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), c_Groups_Ozero__class_Ozero(_1377964)), _1377970))], (32234 ^ _777081) ^ [] : [32235 ^ _777081 : [(32236 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), _1377970), c_Groups_Ozero__class_Ozero(_1377964))))], (32238 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), _1377968), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377964), _1377966), _1377970)))]], 32239 ^ _777081 : [(32240 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), _1377970), c_Groups_Ozero__class_Ozero(_1377964)))], (32242 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), _1377966), c_Groups_Ozero__class_Ozero(_1377964)))]]]]], (32198 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), _1377966), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1377964), _1377968), _1377970))), 32201 ^ _777081 : [(32202 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), c_Groups_Ozero__class_Ozero(_1377964)), _1377970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377964), _1377966), _1377970)), _1377968)))], (32208 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), c_Groups_Ozero__class_Ozero(_1377964)), _1377970))), 32211 ^ _777081 : [(32212 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), _1377970), c_Groups_Ozero__class_Ozero(_1377964))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), _1377968), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1377964), _1377966), _1377970))))], (32218 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), _1377970), c_Groups_Ozero__class_Ozero(_1377964)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1377964), _1377966), c_Groups_Ozero__class_Ozero(_1377964))))]]]]]]], (32246 ^ _777081) ^ [_1378917, _1378919, _1378921, _1378923] : [class_Fields_Olinordered__field__inverse__zero(_1378917), 32249 ^ _777081 : [(32276 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1378917), _1378919), _1378921)), _1378923))), 32279 ^ _777081 : [(32280 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), c_Groups_Ozero__class_Ozero(_1378917)), _1378921)))], (32282 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), _1378919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1378917), _1378923), _1378921)))]], 32283 ^ _777081 : [(32284 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), c_Groups_Ozero__class_Ozero(_1378917)), _1378921))], (32286 ^ _777081) ^ [] : [32287 ^ _777081 : [(32288 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), _1378921), c_Groups_Ozero__class_Ozero(_1378917))))], (32290 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1378917), _1378923), _1378921)), _1378919))]], 32291 ^ _777081 : [(32292 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), _1378921), c_Groups_Ozero__class_Ozero(_1378917)))], (32294 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), c_Groups_Ozero__class_Ozero(_1378917)), _1378923))]]]]], (32250 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1378917), _1378919), _1378921)), _1378923)), 32253 ^ _777081 : [(32254 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), c_Groups_Ozero__class_Ozero(_1378917)), _1378921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), _1378919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1378917), _1378923), _1378921))))], (32260 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), c_Groups_Ozero__class_Ozero(_1378917)), _1378921))), 32263 ^ _777081 : [(32264 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), _1378921), c_Groups_Ozero__class_Ozero(_1378917))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1378917), _1378923), _1378921)), _1378919)))], (32270 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), _1378921), c_Groups_Ozero__class_Ozero(_1378917)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1378917), c_Groups_Ozero__class_Ozero(_1378917)), _1378923)))]]]]]]], (32298 ^ _777081) ^ [_1379870, _1379872, _1379874, _1379876] : [class_Fields_Olinordered__field(_1379870), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379870), c_Groups_Ozero__class_Ozero(_1379870)), _1379872)), 32305 ^ _777081 : [(32306 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379870), _1379874), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1379870), _1379876), _1379872))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1379870), _1379874), _1379872)), _1379876)))], (32312 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1379870), _1379874), _1379872)), _1379876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1379870), _1379874), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1379870), _1379876), _1379872))))]]], (32318 ^ _777081) ^ [_1380251, _1380253, _1380255, _1380257] : [class_Fields_Olinordered__field(_1380251), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380251), c_Groups_Ozero__class_Ozero(_1380251)), _1380253)), 32325 ^ _777081 : [(32326 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380251), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1380251), _1380255), _1380253)), _1380257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380251), _1380255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1380251), _1380257), _1380253))))], (32332 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380251), _1380255), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1380251), _1380257), _1380253))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380251), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1380251), _1380255), _1380253)), _1380257)))]]], (32338 ^ _777081) ^ [_1380632, _1380634, _1380636, _1380638] : [class_Fields_Olinordered__field(_1380632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380632), c_Groups_Ozero__class_Ozero(_1380632)), _1380634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380632), _1380636), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1380632), _1380638), _1380634))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380632), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1380632), _1380636), _1380634)), _1380638)))], (32352 ^ _777081) ^ [_1380901, _1380903, _1380905, _1380907] : [class_Fields_Olinordered__field(_1380901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380901), c_Groups_Ozero__class_Ozero(_1380901)), _1380903)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1380901), _1380905), _1380903)), _1380907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1380901), _1380905), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1380901), _1380907), _1380903))))], (32366 ^ _777081) ^ [_1381170, _1381172, _1381174, _1381176] : [class_Fields_Olinordered__field(_1381170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381170), _1381172), c_Groups_Ozero__class_Ozero(_1381170))), 32373 ^ _777081 : [(32374 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381170), _1381174), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381170), _1381176), _1381172))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381170), _1381176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381170), _1381174), _1381172))))], (32380 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381170), _1381176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381170), _1381174), _1381172))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381170), _1381174), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381170), _1381176), _1381172))))]]], (32386 ^ _777081) ^ [_1381551, _1381553, _1381555, _1381557] : [class_Fields_Olinordered__field(_1381551), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381551), _1381553), c_Groups_Ozero__class_Ozero(_1381551))), 32393 ^ _777081 : [(32394 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381551), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381551), _1381555), _1381553)), _1381557)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381551), _1381557), _1381553)), _1381555)))], (32400 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381551), _1381557), _1381553)), _1381555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381551), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381551), _1381555), _1381553)), _1381557)))]]], (32406 ^ _777081) ^ [_1381932, _1381934, _1381936, _1381938] : [class_Fields_Olinordered__field(_1381932), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381932), _1381934), _1381936)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381932), c_Groups_Ozero__class_Ozero(_1381932)), _1381938)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381932), c_Groups_Ozero__class_Ozero(_1381932)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1381932), _1381936), _1381934))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381932), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381932), _1381938), _1381936)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1381932), _1381938), _1381934))))], (32424 ^ _777081) ^ [_1382291, _1382293, _1382295, _1382297] : [class_Fields_Olinordered__field(_1382291), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382291), _1382293), _1382295)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382291), _1382297), c_Groups_Ozero__class_Ozero(_1382291))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382291), c_Groups_Ozero__class_Ozero(_1382291)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382291), _1382293), _1382295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1382291), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382291), _1382297), _1382293)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382291), _1382297), _1382295))))], (32442 ^ _777081) ^ [_1382650, _1382652, _1382654, _1382656, _1382658] : [class_Fields_Ofield(_1382650), -(_1382652 = c_Groups_Ozero__class_Ozero(_1382650)), -(_1382654 = c_Groups_Ozero__class_Ozero(_1382650)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382650), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382650), _1382656), _1382652)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382650), _1382658), _1382654)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382650), _1382656), _1382654)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382650), _1382658), _1382652))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382650), _1382652), _1382654)))], (32456 ^ _777081) ^ [_1382897, _1382899, _1382901, _1382903] : [class_Fields_Ofield(_1382897), -(_1382899 = c_Groups_Ozero__class_Ozero(_1382897)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382897), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382897), _1382901), _1382899)), _1382903) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1382897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382897), _1382901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382897), _1382899), _1382903))), _1382899))], (32466 ^ _777081) ^ [_1383075, _1383077, _1383079, _1383081] : [class_Fields_Ofield__inverse__zero(_1383075), -(_1383077 = c_Groups_Ozero__class_Ozero(_1383075)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1383075), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383075), _1383079), _1383077)), _1383081) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383075), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1383075), _1383079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383075), _1383081), _1383077))), _1383077))], (32476 ^ _777081) ^ [_1383253, _1383255, _1383257, _1383259] : [class_Fields_Ofield(_1383253), -(_1383255 = c_Groups_Ozero__class_Ozero(_1383253)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1383253), _1383257), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383253), _1383259), _1383255)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383253), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1383253), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383253), _1383255), _1383257)), _1383259)), _1383255))], (32486 ^ _777081) ^ [_1383431, _1383433, _1383435, _1383437] : [class_Fields_Ofield__inverse__zero(_1383431), -(_1383433 = c_Groups_Ozero__class_Ozero(_1383431)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1383431), _1383435), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383431), _1383437), _1383433)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383431), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1383431), _1383437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383431), _1383435), _1383433))), _1383433))], (32496 ^ _777081) ^ [_1383609, _1383611, _1383613, _1383615] : [class_Fields_Ofield(_1383609), -(_1383611 = c_Groups_Ozero__class_Ozero(_1383609)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1383609), _1383613), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383609), _1383615), _1383611)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383609), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1383609), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383609), _1383611), _1383613)), _1383615)), _1383611))], (32506 ^ _777081) ^ [_1383787, _1383789, _1383791, _1383793] : [class_Fields_Ofield(_1383787), -(_1383789 = c_Groups_Ozero__class_Ozero(_1383787)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1383787), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383787), _1383791), _1383789)), _1383793) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383787), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1383787), _1383791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383787), _1383789), _1383793))), _1383789))], (32516 ^ _777081) ^ [_1383965, _1383967, _1383969, _1383971, _1383973] : [class_Fields_Ofield(_1383965), -(_1383967 = c_Groups_Ozero__class_Ozero(_1383965)), -(_1383969 = c_Groups_Ozero__class_Ozero(_1383965)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1383965), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383965), _1383971), _1383967)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383965), _1383973), _1383969)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1383965), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1383965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383965), _1383971), _1383969)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383965), _1383973), _1383967))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383965), _1383967), _1383969)))], (32530 ^ _777081) ^ [_1384212, _1384214, _1384216] : [class_Fields_Olinordered__field(_1384212), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384212), _1384214), _1384216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384212), _1384214), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1384212), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384212), _1384214), _1384216)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384212), c_Groups_Oone__class_Oone(_1384212)), c_Groups_Oone__class_Oone(_1384212))))))], (32540 ^ _777081) ^ [_1384427, _1384429, _1384431] : [class_Fields_Olinordered__field(_1384427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384427), _1384429), _1384431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384427), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1384427), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384427), _1384429), _1384431)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384427), c_Groups_Oone__class_Oone(_1384427)), c_Groups_Oone__class_Oone(_1384427)))), _1384431)))], (32550 ^ _777081) ^ [_1384642, _1384644, _1384646] : [class_Fields_Olinordered__field__inverse__zero(_1384642), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384642), c_Groups_Ozero__class_Ozero(_1384642)), _1384644)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1384642), hAPP(c_Groups_Oabs__class_Oabs(_1384642), _1384646)), _1384644) = hAPP(c_Groups_Oabs__class_Oabs(_1384642), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1384642), _1384646), _1384644)))], (32560 ^ _777081) ^ [_1384843, _1384845, _1384847, _1384849] : [class_Fields_Olinordered__field__inverse__zero(_1384843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384843), _1384845), _1384847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384843), _1384849), c_Groups_Ozero__class_Ozero(_1384843))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1384843), c_Groups_Ozero__class_Ozero(_1384843)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384843), _1384845), _1384847))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384843), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1384843), _1384849), _1384845)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1384843), _1384849), _1384847))))], (32578 ^ _777081) ^ [_1385202, _1385204, _1385206, _1385208] : [class_Fields_Olinordered__field(_1385202), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385202), _1385204), _1385206)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385202), c_Groups_Ozero__class_Ozero(_1385202)), _1385208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385202), c_Groups_Ozero__class_Ozero(_1385202)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385202), _1385206), _1385204))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385202), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385202), _1385208), _1385206)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385202), _1385208), _1385204))))], (32596 ^ _777081) ^ [_1385561, _1385563, _1385565, _1385567] : [class_Fields_Olinordered__field(_1385561), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385561), _1385563), c_Groups_Ozero__class_Ozero(_1385561))), 32603 ^ _777081 : [(32604 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385561), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385561), _1385565), _1385563)), _1385567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385561), _1385567), _1385563)), _1385565)))], (32610 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385561), _1385567), _1385563)), _1385565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385561), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385561), _1385565), _1385563)), _1385567)))]]], (32616 ^ _777081) ^ [_1385942, _1385944, _1385946, _1385948] : [class_Fields_Olinordered__field(_1385942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1385942), _1385944), c_Groups_Ozero__class_Ozero(_1385942))), 32623 ^ _777081 : [(32624 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385942), _1385946), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385942), _1385948), _1385944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385942), _1385948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385942), _1385946), _1385944))))], (32630 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385942), _1385948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385942), _1385946), _1385944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1385942), _1385946), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385942), _1385948), _1385944))))]]], (32636 ^ _777081) ^ [_1386323, _1386325, _1386327, _1386329] : [class_Fields_Olinordered__field(_1386323), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386323), c_Groups_Ozero__class_Ozero(_1386323)), _1386325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386323), _1386327), _1386325)), _1386329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386323), _1386327), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386323), _1386329), _1386325))))], (32650 ^ _777081) ^ [_1386592, _1386594, _1386596, _1386598] : [class_Fields_Olinordered__field(_1386592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386592), c_Groups_Ozero__class_Ozero(_1386592)), _1386594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386592), _1386596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386592), _1386598), _1386594))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386592), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386592), _1386596), _1386594)), _1386598)))], (32664 ^ _777081) ^ [_1386861, _1386863, _1386865, _1386867] : [class_Fields_Olinordered__field(_1386861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1386861), c_Groups_Ozero__class_Ozero(_1386861)), _1386863)), 32671 ^ _777081 : [(32672 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386861), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386861), _1386865), _1386863)), _1386867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386861), _1386865), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386861), _1386867), _1386863))))], (32678 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386861), _1386865), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386861), _1386867), _1386863))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1386861), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386861), _1386865), _1386863)), _1386867)))]]], (32684 ^ _777081) ^ [_1387242, _1387244, _1387246, _1387248, _1387250] : [class_Fields_Ofield(_1387242), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387244), _1387246)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387244), _1387248)), 32698 ^ _777081 : [(32699 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1387244), 32697 ^ [_1387242, _1387244, _1387246, _1387248, _1387250]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1387244, tc_HOL_Obool)), _1387246), _1387248))))], (32701 ^ _777081) ^ [] : [-(hAPP(_1387250, 32697 ^ [_1387242, _1387244, _1387246, _1387248, _1387250]) = c_Groups_Ozero__class_Ozero(_1387242))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387244, _1387242), _1387250), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1387244, tc_HOL_Obool)), _1387246), _1387248)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387242), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387244, _1387242), _1387250), _1387246)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387244, _1387242), _1387250), _1387248))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1387244, _1387242), _1387250), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1387244, tc_HOL_Obool)), _1387246), _1387248))))], (32705 ^ _777081) ^ [_1387738, _1387740, _1387742] : [class_Orderings_Olinorder(_1387738), hAPP(_1387740, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1387738), 32710 ^ [_1387738, _1387740, _1387742]), 32711 ^ [_1387738, _1387740, _1387742])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1387738), hAPP(_1387740, 32710 ^ [_1387738, _1387740, _1387742])), hAPP(_1387740, 32711 ^ [_1387738, _1387740, _1387742])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1387738), _1387742)), -(_1387742 = c_Orderings_Obot__class_Obot(tc_fun(_1387738, tc_HOL_Obool))), -(hAPP(_1387740, c_Big__Operators_Olattice_OInf__fin(_1387738, c_Orderings_Oord__class_Omin(_1387738), _1387742)) = c_Big__Operators_Olattice_OInf__fin(_1387738, c_Orderings_Oord__class_Omin(_1387738), hAPP(c_Set_Oimage(_1387738, _1387738, _1387740), _1387742)))], (32725 ^ _777081) ^ [_1388153, _1388155, _1388157] : [class_Orderings_Olinorder(_1388153), hAPP(_1388155, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1388153), 32730 ^ [_1388153, _1388155, _1388157]), 32731 ^ [_1388153, _1388155, _1388157])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1388153), hAPP(_1388155, 32730 ^ [_1388153, _1388155, _1388157])), hAPP(_1388155, 32731 ^ [_1388153, _1388155, _1388157])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388153), _1388157)), -(_1388157 = c_Orderings_Obot__class_Obot(tc_fun(_1388153, tc_HOL_Obool))), -(hAPP(_1388155, c_Big__Operators_Olinorder__class_OMax(_1388153, _1388157)) = c_Big__Operators_Olinorder__class_OMax(_1388153, hAPP(c_Set_Oimage(_1388153, _1388153, _1388155), _1388157)))], (32745 ^ _777081) ^ [_1388556, _1388558, _1388560] : [class_Orderings_Olinorder(_1388556), hAPP(_1388558, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1388556), 32750 ^ [_1388556, _1388558, _1388560]), 32751 ^ [_1388556, _1388558, _1388560])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1388556), hAPP(_1388558, 32750 ^ [_1388556, _1388558, _1388560])), hAPP(_1388558, 32751 ^ [_1388556, _1388558, _1388560])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388556), _1388560)), -(_1388560 = c_Orderings_Obot__class_Obot(tc_fun(_1388556, tc_HOL_Obool))), -(hAPP(_1388558, c_Big__Operators_Olinorder__class_OMin(_1388556, _1388560)) = c_Big__Operators_Olinorder__class_OMin(_1388556, hAPP(c_Set_Oimage(_1388556, _1388556, _1388558), _1388560)))], (32765 ^ _777081) ^ [_1388959, _1388961, _1388963] : [class_Lattices_Olattice(_1388959), hAPP(_1388961, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1388959), 32770 ^ [_1388959, _1388961, _1388963]), 32771 ^ [_1388959, _1388961, _1388963])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1388959), hAPP(_1388961, 32770 ^ [_1388959, _1388961, _1388963])), hAPP(_1388961, 32771 ^ [_1388959, _1388961, _1388963])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1388959), _1388963)), -(_1388963 = c_Orderings_Obot__class_Obot(tc_fun(_1388959, tc_HOL_Obool))), -(hAPP(_1388961, c_Big__Operators_Olattice__class_OInf__fin(_1388959, _1388963)) = c_Big__Operators_Olattice__class_OInf__fin(_1388959, hAPP(c_Set_Oimage(_1388959, _1388959, _1388961), _1388963)))], (32785 ^ _777081) ^ [_1389362, _1389364, _1389366] : [class_Lattices_Olattice(_1389362), hAPP(_1389364, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1389362), 32790 ^ [_1389362, _1389364, _1389366]), 32791 ^ [_1389362, _1389364, _1389366])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1389362), hAPP(_1389364, 32790 ^ [_1389362, _1389364, _1389366])), hAPP(_1389364, 32791 ^ [_1389362, _1389364, _1389366])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389362), _1389366)), -(_1389366 = c_Orderings_Obot__class_Obot(tc_fun(_1389362, tc_HOL_Obool))), -(hAPP(_1389364, c_Big__Operators_Olattice__class_OSup__fin(_1389362, _1389366)) = c_Big__Operators_Olattice__class_OSup__fin(_1389362, hAPP(c_Set_Oimage(_1389362, _1389362, _1389364), _1389366)))], (32805 ^ _777081) ^ [_1389765, _1389767, _1389769, _1389771, _1389773] : [hBOOL(hAPP(hAPP(c_member(_1389765), _1389767), hAPP(c_Relation_OImage(_1389769, _1389765, _1389771), _1389773))), 32809 ^ _777081 : [(32810 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1389769, _1389765)), hAPP(hAPP(c_Product__Type_OPair(_1389769, _1389765), 32808 ^ [_1389765, _1389767, _1389769, _1389771, _1389773]), _1389767)), _1389771)))], (32812 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389769), 32808 ^ [_1389765, _1389767, _1389769, _1389771, _1389773]), _1389773)))]]], (32814 ^ _777081) ^ [_1389989, _1389991, _1389993, _1389995, _1389997] : [class_Groups_Ocomm__monoid__mult(_1389989), hBOOL(hAPP(c_Finite__Set_Ofinite(_1389991), _1389993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1389991, tc_HOL_Obool)), _1389995), _1389993)), 32828 ^ _777081 : [(32829 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1389991), 32827 ^ [_1389989, _1389991, _1389993, _1389995, _1389997]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1389991, tc_HOL_Obool)), _1389993), _1389995))))], (32831 ^ _777081) ^ [] : [hAPP(_1389997, 32827 ^ [_1389989, _1389991, _1389993, _1389995, _1389997]) = c_Groups_Oone__class_Oone(_1389989)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389991, _1389989), _1389997), _1389993) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1389991, _1389989), _1389997), _1389995))], (32835 ^ _777081) ^ [_1390440, _1390442, _1390444, _1390446, _1390448] : [class_Groups_Ocomm__monoid__mult(_1390440), hBOOL(hAPP(c_Finite__Set_Ofinite(_1390442), _1390444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1390442, tc_HOL_Obool)), _1390446), _1390444)), 32849 ^ _777081 : [(32850 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1390442), 32848 ^ [_1390440, _1390442, _1390444, _1390446, _1390448]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1390442, tc_HOL_Obool)), _1390444), _1390446))))], (32852 ^ _777081) ^ [] : [hAPP(_1390448, 32848 ^ [_1390440, _1390442, _1390444, _1390446, _1390448]) = c_Groups_Oone__class_Oone(_1390440)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1390442, _1390440), _1390448), _1390446) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1390442, _1390440), _1390448), _1390444))], (32856 ^ _777081) ^ [_1390891, _1390893] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1390891), _1390893)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1390891, tc_HOL_Obool)), hAPP(c_Set_OPow(_1390891), _1390893)) = 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(_1390891), _1390893)))], (32862 ^ _777081) ^ [_1391018, _1391020, _1391022] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1391018), _1391020)), hBOOL(hAPP(_1391022, _1391020)), 32873 ^ _777081 : [(32874 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1391018), 32872 ^ [_1391018, _1391020, _1391022])))], (32876 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1391018), 32871 ^ [_1391018, _1391020, _1391022]), 32872 ^ [_1391018, _1391020, _1391022])))], (32878 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1391022, 32872 ^ [_1391018, _1391020, _1391022])))], (32880 ^ _777081) ^ [] : [hBOOL(hAPP(_1391022, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1391018, tc_HOL_Obool)), 32872 ^ [_1391018, _1391020, _1391022]), hAPP(hAPP(c_Set_Oinsert(_1391018), 32871 ^ [_1391018, _1391020, _1391022]), c_Orderings_Obot__class_Obot(tc_fun(_1391018, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1391022, c_Orderings_Obot__class_Obot(tc_fun(_1391018, tc_HOL_Obool)))))], (32884 ^ _777081) ^ [_1391543, _1391545, _1391547, _1391549] : [class_Orderings_Olinorder(_1391543), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391543), _1391545), _1391547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1391543), _1391547), _1391549)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1391543, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1391543, _1391545, _1391547)), c_SetInterval_Oord__class_OatLeastAtMost(_1391543, _1391547, _1391549)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1391543, _1391545, _1391549))], (32898 ^ _777081) ^ [_1391808, _1391810] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1391808, _1391810))))], (32900 ^ _777081) ^ [_1391839, _1391841] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1391839, _1391841))))], (32902 ^ _777081) ^ [_1391870, _1391872, _1391874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1391870, tc_HOL_Obool)), _1391872), _1391874)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1391870, tc_HOL_Obool)), _1391872), hAPP(c_Set_OPow(_1391870), _1391874))))], (32908 ^ _777081) ^ [_1392015, _1392017, _1392019] : [hAPP(c_Set_Oimage(_1392017, tc_fun(_1392017, tc_HOL_Obool), _1392015), _1392019) = hAPP(c_Set_OPow(_1392017), _1392019)], (32910 ^ _777081) ^ [_1392057, _1392059, _1392061, _1392063, _1392065] : [hAPP(c_Set_Oimage(_1392057, _1392059, _1392061), _1392063) = _1392065, -(hAPP(c_Set_Oimage(tc_fun(_1392057, tc_HOL_Obool), tc_fun(_1392059, tc_HOL_Obool), c_Set_Oimage(_1392057, _1392059, _1392061)), hAPP(c_Set_OPow(_1392057), _1392063)) = hAPP(c_Set_OPow(_1392059), _1392065))], (32916 ^ _777081) ^ [_1392208, _1392210] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1392208, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1392208, tc_HOL_Obool))), hAPP(c_Set_OPow(_1392208), _1392210))))], (32918 ^ _777081) ^ [_1392271, _1392273, _1392275] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1392271, tc_HOL_Obool)), _1392273), hAPP(c_Set_OPow(_1392271), _1392275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1392271, tc_HOL_Obool)), _1392273), _1392275)))], (32924 ^ _777081) ^ [_1392396, _1392398, _1392400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1392396, tc_HOL_Obool)), _1392398), _1392400)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1392396, tc_HOL_Obool)), _1392398), hAPP(c_Set_OPow(_1392396), _1392400))))], (32930 ^ _777081) ^ [_1392527, _1392529, _1392531] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1392527, tc_HOL_Obool)), _1392529), hAPP(c_Set_OPow(_1392527), _1392531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1392527, tc_HOL_Obool)), _1392529), _1392531)))], (32936 ^ _777081) ^ [_1392656, _1392658] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1392656, tc_HOL_Obool)), _1392658), hAPP(c_Set_OPow(_1392656), _1392658))))], (32938 ^ _777081) ^ [_1392696, _1392698, _1392700] : [-(hAPP(c_Set_OPow(_1392696), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1392696, tc_HOL_Obool)), _1392698), _1392700)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1392696, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1392696), _1392698)), hAPP(c_Set_OPow(_1392696), _1392700)))], (32940 ^ _777081) ^ [_1392763, _1392765, _1392767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1392763, tc_HOL_Obool)), _1392765), _1392767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1392763, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1392763), _1392765)), hAPP(c_Set_OPow(_1392763), _1392767))))], (32946 ^ _777081) ^ [_1392908, _1392910, _1392912] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1392908, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1392908, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1392908), _1392910)), hAPP(c_Set_OPow(_1392908), _1392912))), hAPP(c_Set_OPow(_1392908), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1392908, tc_HOL_Obool)), _1392910), _1392912)))))], (32948 ^ _777081) ^ [_1393000, _1393002] : [hAPP(c_Set_OPow(_1393000), _1393002) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1393000, tc_HOL_Obool), tc_HOL_Obool))], (32950 ^ _777081) ^ [_1393053, _1393055] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1393053, tc_HOL_Obool)), hAPP(c_Set_OPow(_1393053), _1393055))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1393053), _1393055)))], (32956 ^ _777081) ^ [_1393158, _1393160] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1393158), _1393160)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1393158, tc_HOL_Obool)), hAPP(c_Set_OPow(_1393158), _1393160))))], (32962 ^ _777081) ^ [_1393269] : [-(hAPP(c_Set_OPow(_1393269), c_Orderings_Obot__class_Obot(tc_fun(_1393269, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1393269, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1393269, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1393269, tc_HOL_Obool), tc_HOL_Obool))))], (32964 ^ _777081) ^ [_1393326, _1393328, _1393330] : [-(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)), _1393326)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1393328, _1393330)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1393328), _1393326), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1393330), _1393326)))], (32966 ^ _777081) ^ [_1393383, _1393385] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1393383, _1393385)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1393383), hAPP(c_Nat_OSuc, _1393385)))], (32968 ^ _777081) ^ [_1393425, _1393427, _1393429] : [-(hAPP(c_Set_OPow(_1393425), hAPP(hAPP(c_Set_Oinsert(_1393425), _1393427), _1393429)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1393425, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1393425), _1393429)), hAPP(c_Set_Oimage(tc_fun(_1393425, tc_HOL_Obool), tc_fun(_1393425, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1393425), _1393427)), hAPP(c_Set_OPow(_1393425), _1393429))))], (32970 ^ _777081) ^ [_1393507, _1393509] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1393507, _1393509) = 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), _1393507), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1393509))))], (32972 ^ _777081) ^ [_1393549] : [-(hAPP(c_Set_OPow(_1393549), c_Orderings_Otop__class_Otop(tc_fun(_1393549, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1393549, tc_HOL_Obool), tc_HOL_Obool)))], (32974 ^ _777081) ^ [_1393590, _1393592] : [c_Nat__Transfer_Ois__nat(_1393590), c_Nat__Transfer_Ois__nat(_1393592), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1393590, _1393592) = 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, _1393590), hAPP(c_Int_Onat, _1393592))))], (32984 ^ _777081) ^ [_1393749, _1393751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1393749), hAPP(c_Nat_OSuc, _1393751))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1393749, hAPP(c_Nat_OSuc, _1393751)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1393751)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1393749, _1393751)))], (32990 ^ _777081) ^ [_1393882, _1393884] : [c_Nat__Transfer_Ois__nat(_1393882), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1393882, _1393884)))], (32996 ^ _777081) ^ [_1393963, _1393965, _1393967] : [class_Orderings_Oorder(_1393963), 32999 ^ _777081 : [(33000 ^ _777081) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1393963, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1393963, _1393965, _1393967), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393963), _1393965), _1393967))], (33006 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393963), _1393965), _1393967))), -(c_Orderings_Obot__class_Obot(tc_fun(_1393963, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1393963, _1393965, _1393967))]]], (33012 ^ _777081) ^ [_1394182, _1394184, _1394186] : [class_Orderings_Oorder(_1394182), 33015 ^ _777081 : [(33016 ^ _777081) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1394182, _1394184, _1394186) = c_Orderings_Obot__class_Obot(tc_fun(_1394182, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394182), _1394184), _1394186))], (33022 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394182), _1394184), _1394186))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1394182, _1394184, _1394186) = c_Orderings_Obot__class_Obot(tc_fun(_1394182, tc_HOL_Obool)))]]], (33028 ^ _777081) ^ [_1394401, _1394403, _1394405] : [class_Orderings_Oorder(_1394401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394401), _1394403), _1394405)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1394401, _1394405, _1394403) = c_Orderings_Obot__class_Obot(tc_fun(_1394401, tc_HOL_Obool)))], (33038 ^ _777081) ^ [_1394564, _1394566, _1394568, _1394570, _1394572] : [class_Orderings_Oorder(_1394564), 33041 ^ _777081 : [(33042 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1394564, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1394564, _1394566, _1394568)), c_SetInterval_Oord__class_OatLeastAtMost(_1394564, _1394570, _1394572))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394564), _1394566), _1394568)), 33049 ^ _777081 : [(33050 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394564), _1394570), _1394566)))], (33052 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394564), _1394568), _1394572)))]]], (33054 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1394564, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1394564, _1394566, _1394568)), c_SetInterval_Oord__class_OatLeastAtMost(_1394564, _1394570, _1394572)))), 33055 ^ _777081 : [(33056 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394564), _1394566), _1394568)))], (33058 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394564), _1394570), _1394566)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394564), _1394568), _1394572))]]]]], (33066 ^ _777081) ^ [_1395067, _1395069] : [class_Orderings_Oorder(_1395067), -(c_SetInterval_Oord__class_OatLeastAtMost(_1395067, _1395069, _1395069) = hAPP(hAPP(c_Set_Oinsert(_1395067), _1395069), c_Orderings_Obot__class_Obot(tc_fun(_1395067, tc_HOL_Obool))))], (33072 ^ _777081) ^ [_1395176, _1395178, _1395180, _1395182] : [class_Orderings_Oorder(_1395176), 33075 ^ _777081 : [(33076 ^ _777081) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1395176, _1395178, _1395180) = hAPP(hAPP(c_Set_Oinsert(_1395176), _1395182), c_Orderings_Obot__class_Obot(tc_fun(_1395176, tc_HOL_Obool))), 33079 ^ _777081 : [(33080 ^ _777081) ^ [] : [-(_1395178 = _1395180)], (33082 ^ _777081) ^ [] : [-(_1395180 = _1395182)]]], (33084 ^ _777081) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1395176, _1395178, _1395180) = hAPP(hAPP(c_Set_Oinsert(_1395176), _1395182), c_Orderings_Obot__class_Obot(tc_fun(_1395176, tc_HOL_Obool)))), _1395178 = _1395180, _1395180 = _1395182]]], (33094 ^ _777081) ^ [_1395520, _1395522, _1395524] : [class_Orderings_Oorder(_1395520), _1395522 = _1395524, -(c_SetInterval_Oord__class_OatLeastAtMost(_1395520, _1395522, _1395524) = hAPP(hAPP(c_Set_Oinsert(_1395520), _1395522), c_Orderings_Obot__class_Obot(tc_fun(_1395520, tc_HOL_Obool))))], (33104 ^ _777081) ^ [_1395685, _1395687, _1395689] : [class_Groups_Oordered__ab__group__add(_1395685), -(hAPP(c_Set_Oimage(_1395685, _1395685, c_Groups_Ouminus__class_Ouminus(_1395685)), c_SetInterval_Oord__class_OatLeastAtMost(_1395685, _1395687, _1395689)) = c_SetInterval_Oord__class_OatLeastAtMost(_1395685, hAPP(c_Groups_Ouminus__class_Ouminus(_1395685), _1395689), hAPP(c_Groups_Ouminus__class_Ouminus(_1395685), _1395687)))], (33110 ^ _777081) ^ [_1395816, _1395818, _1395820, _1395822, _1395824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1395816, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1395818, _1395816, _1395820), _1395822)), _1395824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1395816, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1395818, tc_HOL_Obool), tc_fun(_1395816, tc_HOL_Obool), c_Set_Oimage(_1395818, _1395816, _1395820)), hAPP(c_Set_OPow(_1395818), _1395822))), hAPP(c_Set_OPow(_1395816), _1395824))))], (33116 ^ _777081) ^ [_1396013, _1396015] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1396013), _1396015) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1396013, _1396015))], (33118 ^ _777081) ^ [_1396049, _1396051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396049)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1396049, _1396051)))], (33124 ^ _777081) ^ [_1396136, _1396138] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1396136, _1396138)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1396138)), _1396136))], (33126 ^ _777081) ^ [_1396177, _1396179] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1396177), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1396179) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1396177, _1396179))], (33128 ^ _777081) ^ [_1396216, _1396218, _1396220, _1396222, _1396224] : [class_Orderings_Olinorder(_1396216), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1396216, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1396216, _1396218, _1396220)), c_SetInterval_Oord__class_OatLeastAtMost(_1396216, _1396222, _1396224)) = c_SetInterval_Oord__class_OatLeastAtMost(_1396216, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1396216), _1396218), _1396222), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1396216), _1396220), _1396224)))], (33134 ^ _777081) ^ [_1396375, _1396377, _1396379, _1396381, _1396383] : [class_Orderings_Oorder(_1396375), 33137 ^ _777081 : [(33138 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1396375, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1396375, _1396377, _1396379)), c_SetInterval_Oord__class_OatLeastAtMost(_1396375, _1396381, _1396383))), 33141 ^ _777081 : [(33156 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396375), _1396381), _1396383)))], (33142 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396375), _1396377), _1396379)), 33145 ^ _777081 : [(33146 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396375), _1396381), _1396377)))], (33148 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396375), _1396379), _1396383)))], (33150 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396375), _1396381), _1396377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396375), _1396379), _1396383)))]]]]], (33158 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1396375, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1396375, _1396377, _1396379)), c_SetInterval_Oord__class_OatLeastAtMost(_1396375, _1396381, _1396383)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396375), _1396381), _1396383)), 33161 ^ _777081 : [(33162 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396375), _1396377), _1396379)))], (33164 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396375), _1396381), _1396377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396375), _1396379), _1396383)), 33171 ^ _777081 : [(33172 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396375), _1396381), _1396377))], (33174 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396375), _1396379), _1396383))]]]]]]], (33180 ^ _777081) ^ [_1397146, _1397148, _1397150, _1397152] : [class_Orderings_Olinorder(_1397146), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397146), _1397148), _1397150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1397146), _1397150), _1397152)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1397146, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1397146, _1397148, _1397150)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1397146, _1397150, _1397152)) = c_SetInterval_Oord__class_OatLeastAtMost(_1397146, _1397148, _1397152))], (33194 ^ _777081) ^ [_1397411, _1397413, _1397415, _1397417] : [class_Orderings_Oorder(_1397411), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397411, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1397411, _1397413, _1397415)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1397411, _1397415, _1397417)) = c_Orderings_Obot__class_Obot(tc_fun(_1397411, tc_HOL_Obool)))], (33200 ^ _777081) ^ [_1397538, _1397540, _1397542, _1397544] : [class_Orderings_Oorder(_1397538), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397538, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1397538, _1397540, _1397542)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1397538, _1397542, _1397544)) = c_Orderings_Obot__class_Obot(tc_fun(_1397538, tc_HOL_Obool)))], (33206 ^ _777081) ^ [_1397665, _1397667, _1397669, _1397671] : [class_Orderings_Oorder(_1397665), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1397665, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1397665, _1397667, _1397669)), c_SetInterval_Oord__class_OatLeastAtMost(_1397665, _1397669, _1397671)) = c_Orderings_Obot__class_Obot(tc_fun(_1397665, tc_HOL_Obool)))], (33212 ^ _777081) ^ [_1397801, _1397803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397801), _1397803)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1397803, _1397801) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (33218 ^ _777081) ^ [_1397890, _1397892] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397890), _1397892))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1397892, _1397890) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1397892), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1397892), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1397890)))], (33224 ^ _777081) ^ [_1397953, _1397955] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1397953, _1397955)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1397955), _1397953)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (33226 ^ _777081) ^ [_1398000, _1398002, _1398004] : [class_Orderings_Olinorder(_1398000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1398000), _1398002), _1398004)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1398000, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1398000), _1398002), c_Orderings_Obot__class_Obot(tc_fun(_1398000, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1398000, _1398002, _1398004)) = c_SetInterval_Oord__class_OatLeastAtMost(_1398000, _1398002, _1398004))], (33236 ^ _777081) ^ [_1398209, _1398211, _1398213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1398209)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1398211), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1398213)), 33243 ^ _777081 : [(33244 ^ _777081) ^ [_1398417] : [33246 ^ _777081 : [(33247 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33245 ^ [_1398209, _1398211, _1398213, _1398417]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1398209))))], (33250 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33248 ^ [_1398209, _1398211, _1398213, _1398417]), _1398213)))], (33252 ^ _777081) ^ [] : [-(_1398417 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33248 ^ [_1398209, _1398211, _1398213, _1398417]), 33245 ^ [_1398209, _1398211, _1398213, _1398417]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1398211), _1398417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1398211), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1398417), _1398209))))]]], (33260 ^ _777081) ^ [_1398693, _1398695, _1398697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1398693)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1398695), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1398697)), 33267 ^ _777081 : [(33268 ^ _777081) ^ [_1398901] : [33270 ^ _777081 : [(33271 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33269 ^ [_1398693, _1398695, _1398697, _1398901]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1398693))))], (33274 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33272 ^ [_1398693, _1398695, _1398697, _1398901]), _1398697)))], (33276 ^ _777081) ^ [] : [-(_1398901 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33272 ^ [_1398693, _1398695, _1398697, _1398901]), 33269 ^ [_1398693, _1398695, _1398697, _1398901]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1398901), _1398695)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1398901), _1398693)), _1398695)))]]], (33284 ^ _777081) ^ [_1399177, _1399179, _1399181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1399177)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1399179), _1399181)), 33291 ^ _777081 : [(33292 ^ _777081) ^ [_1399367] : [33294 ^ _777081 : [(33295 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33293 ^ [_1399177, _1399179, _1399181, _1399367]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1399177))))], (33298 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33296 ^ [_1399177, _1399179, _1399181, _1399367]), _1399181)))], (33300 ^ _777081) ^ [] : [-(_1399367 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33296 ^ [_1399177, _1399179, _1399181, _1399367]), 33293 ^ [_1399177, _1399179, _1399181, _1399367]))]], -(_1399367 = _1399179), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1399367), _1399177) = _1399179]]], (33308 ^ _777081) ^ [_1399642, _1399644] : [33310 ^ _777081 : [(33311 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 33309 ^ [_1399642, _1399644]), _1399642)))], (33313 ^ _777081) ^ [] : [hBOOL(hAPP(_1399644, 33309 ^ [_1399642, _1399644]))]], 33314 ^ _777081 : [(33315 ^ _777081) ^ [_1399793] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1399793), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1399642))), -(hBOOL(hAPP(_1399644, _1399793)))]]], (33321 ^ _777081) ^ [_1399896, _1399898] : [33323 ^ _777081 : [(33324 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 33322 ^ [_1399896, _1399898]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1399896))))], (33326 ^ _777081) ^ [] : [hBOOL(hAPP(_1399898, 33322 ^ [_1399896, _1399898]))]], 33327 ^ _777081 : [(33328 ^ _777081) ^ [_1400051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1400051), _1399896)), -(hBOOL(hAPP(_1399898, _1400051)))]]], (33334 ^ _777081) ^ [_1400167, _1400169] : [33342 ^ _777081 : [(33343 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 33341 ^ [_1400167, _1400169]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1400167))))], (33345 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1400169, 33341 ^ [_1400167, _1400169])))]], 33335 ^ _777081 : [(33336 ^ _777081) ^ [_1400236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1400236), _1400167)), hBOOL(hAPP(_1400169, _1400236))]]], (33347 ^ _777081) ^ [_1400397, _1400399] : [33355 ^ _777081 : [(33356 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 33354 ^ [_1400397, _1400399]), _1400397)))], (33358 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1400399, 33354 ^ [_1400397, _1400399])))]], 33348 ^ _777081 : [(33349 ^ _777081) ^ [_1400466] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1400466), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1400397))), hBOOL(hAPP(_1400399, _1400466))]]], (33360 ^ _777081) ^ [_1400655, _1400657, _1400659] : [hBOOL(hAPP(c_Predicate_OPowp(_1400655, hAPP(hAPP(c_COMBC(_1400655, tc_fun(_1400655, tc_HOL_Obool), tc_HOL_Obool), c_member(_1400655)), _1400657)), _1400659)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1400655, tc_HOL_Obool)), _1400659), hAPP(c_Set_OPow(_1400655), _1400657))))], (33366 ^ _777081) ^ [_1400800, _1400802, _1400804] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1400800, tc_HOL_Obool)), _1400804), hAPP(c_Set_OPow(_1400800), _1400802))), -(hBOOL(hAPP(c_Predicate_OPowp(_1400800, hAPP(hAPP(c_COMBC(_1400800, tc_fun(_1400800, tc_HOL_Obool), tc_HOL_Obool), c_member(_1400800)), _1400802)), _1400804)))], (33372 ^ _777081) ^ [_1400951, _1400953, _1400955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1400951, tc_HOL_Obool)), _1400953), _1400955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1400951, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1400951, _1400953)), c_Predicate_OPowp(_1400951, _1400955))))], (33378 ^ _777081) ^ [_1401088, _1401090, _1401092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1401088)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1401090), _1401092)), 33385 ^ _777081 : [(33386 ^ _777081) ^ [_1401278] : [33388 ^ _777081 : [(33389 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33387 ^ [_1401088, _1401090, _1401092, _1401278]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1401088))))], (33392 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33390 ^ [_1401088, _1401090, _1401092, _1401278]), _1401092)))], (33394 ^ _777081) ^ [] : [-(_1401278 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33390 ^ [_1401088, _1401090, _1401092, _1401278]), 33387 ^ [_1401088, _1401090, _1401092, _1401278]))]], -(_1401278 = _1401090), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1401278), _1401088) = _1401090]]], (33402 ^ _777081) ^ [_1401538, _1401540, _1401542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1401538)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1401540), _1401542)), 33409 ^ _777081 : [(33410 ^ _777081) ^ [_1401734] : [33412 ^ _777081 : [(33413 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33411 ^ [_1401538, _1401540, _1401542, _1401734]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1401538))))], (33416 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33414 ^ [_1401538, _1401540, _1401542, _1401734]), _1401542)))], (33418 ^ _777081) ^ [] : [-(_1401734 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33414 ^ [_1401538, _1401540, _1401542, _1401734]), 33411 ^ [_1401538, _1401540, _1401542, _1401734]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1401540), _1401734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1401540), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1401734), _1401538))))]]], (33426 ^ _777081) ^ [_1402010, _1402012, _1402014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1402010)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1402012), _1402014)), 33433 ^ _777081 : [(33434 ^ _777081) ^ [_1402206] : [33436 ^ _777081 : [(33437 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33435 ^ [_1402010, _1402012, _1402014, _1402206]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1402010))))], (33440 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33438 ^ [_1402010, _1402012, _1402014, _1402206]), _1402014)))], (33442 ^ _777081) ^ [] : [-(_1402206 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33438 ^ [_1402010, _1402012, _1402014, _1402206]), 33435 ^ [_1402010, _1402012, _1402014, _1402206]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1402206), _1402012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1402206), _1402010)), _1402012)))]]], (33450 ^ _777081) ^ [_1402482, _1402484, _1402486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1402482)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1402484), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1402486)), 33460 ^ _777081 : [(33461 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33459 ^ [_1402482, _1402484, _1402486]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1402482))))], (33464 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33462 ^ [_1402482, _1402484, _1402486]), _1402486)))], (33466 ^ _777081) ^ [] : [-(_1402484 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33462 ^ [_1402482, _1402484, _1402486]), 33459 ^ [_1402482, _1402484, _1402486]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1402484), _1402482) = _1402484)], (33470 ^ _777081) ^ [_1402821, _1402823, _1402825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1402821)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1402823), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1402825)), 33480 ^ _777081 : [(33481 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33479 ^ [_1402821, _1402823, _1402825]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1402821))))], (33484 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33482 ^ [_1402821, _1402823, _1402825]), _1402825)))], (33486 ^ _777081) ^ [] : [-(_1402823 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33482 ^ [_1402821, _1402823, _1402825]), 33479 ^ [_1402821, _1402823, _1402825]))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1402823), _1402821) = _1402823)], (33490 ^ _777081) ^ [_1403160, _1403162, _1403164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403160)), 33493 ^ _777081 : [(33494 ^ _777081) ^ [_1403294] : [33496 ^ _777081 : [(33497 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33495 ^ [_1403160, _1403162, _1403164, _1403294]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1403160))))], (33500 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33498 ^ [_1403160, _1403162, _1403164, _1403294]), _1403162)))], (33502 ^ _777081) ^ [] : [-(_1403294 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33498 ^ [_1403160, _1403162, _1403164, _1403294]), 33495 ^ [_1403160, _1403162, _1403164, _1403294]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1403164), _1403294)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1403164), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1403294), _1403160))))]]], (33510 ^ _777081) ^ [_1403568, _1403570, _1403572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403568)), 33513 ^ _777081 : [(33514 ^ _777081) ^ [_1403702] : [33516 ^ _777081 : [(33517 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33515 ^ [_1403568, _1403570, _1403572, _1403702]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1403568))))], (33520 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33518 ^ [_1403568, _1403570, _1403572, _1403702]), _1403570)))], (33522 ^ _777081) ^ [] : [-(_1403702 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33518 ^ [_1403568, _1403570, _1403572, _1403702]), 33515 ^ [_1403568, _1403570, _1403572, _1403702]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1403702), _1403572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1403702), _1403568)), _1403572)))]]], (33530 ^ _777081) ^ [_1403976, _1403978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403976)), 33539 ^ _777081 : [(33540 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1403978, 33535 ^ [_1403976, _1403978])))], (33542 ^ _777081) ^ [] : [hBOOL(hAPP(_1403978, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33535 ^ [_1403976, _1403978]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 33536 ^ [_1403976, _1403978]), _1403976))))]], 33543 ^ _777081 : [(33544 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1403978, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33535 ^ [_1403976, _1403978]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 33536 ^ [_1403976, _1403978]), _1403976)))))], (33546 ^ _777081) ^ [] : [hBOOL(hAPP(_1403978, 33535 ^ [_1403976, _1403978]))]], 33547 ^ _777081 : [(33548 ^ _777081) ^ [] : [33549 ^ _777081 : [(33550 ^ _777081) ^ [_1404408] : [hBOOL(hAPP(_1403978, _1404408))]], 33552 ^ _777081 : [(33553 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33551 ^ [_1403976, _1403978]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1403976))))], (33555 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1403978, 33551 ^ [_1403976, _1403978])))]]], (33557 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1403978, 33564 ^ [_1403976, _1403978]))), 33558 ^ _777081 : [(33559 ^ _777081) ^ [_1404523] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1404523), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1403976))), hBOOL(hAPP(_1403978, _1404523))]]]]], (33568 ^ _777081) ^ [_1404670, _1404672, _1404674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1404670)), 33571 ^ _777081 : [(33572 ^ _777081) ^ [_1404804] : [33574 ^ _777081 : [(33575 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33573 ^ [_1404670, _1404672, _1404674, _1404804]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1404670))))], (33578 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33576 ^ [_1404670, _1404672, _1404674, _1404804]), _1404672)))], (33580 ^ _777081) ^ [] : [-(_1404804 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 33576 ^ [_1404670, _1404672, _1404674, _1404804]), 33573 ^ [_1404670, _1404672, _1404674, _1404804]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1404804), _1404674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1404804), _1404670)), _1404674)))]]], (33588 ^ _777081) ^ [_1405078, _1405080, _1405082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1405078)), 33591 ^ _777081 : [(33592 ^ _777081) ^ [_1405212] : [33594 ^ _777081 : [(33595 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33593 ^ [_1405078, _1405080, _1405082, _1405212]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1405078))))], (33598 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 33596 ^ [_1405078, _1405080, _1405082, _1405212]), _1405080)))], (33600 ^ _777081) ^ [] : [-(_1405212 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 33596 ^ [_1405078, _1405080, _1405082, _1405212]), 33593 ^ [_1405078, _1405080, _1405082, _1405212]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405082), _1405212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405082), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1405212), _1405078))))]]], (33608 ^ _777081) ^ [_1405498, _1405500, _1405502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1405498), _1405500)), -(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)), _1405498)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1405502), _1405500)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1405502), _1405498)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1405500), _1405498)))], (33614 ^ _777081) ^ [_1405650, _1405652, _1405654] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1405650), _1405652))), 33617 ^ _777081 : [(33618 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1405654), _1405652)), -(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)), _1405650)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1405654), _1405652)) = 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))))], (33624 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1405654), _1405652))), -(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)), _1405650)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1405654), _1405652)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (33630 ^ _777081) ^ [_1405919] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1405919) = 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), _1405919))))], (33632 ^ _777081) ^ [_1405955, _1405957] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1405955), _1405957))))], (33634 ^ _777081) ^ [_1405988] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1405988))))], (33636 ^ _777081) ^ [_1406016, _1406018, _1406020] : [class_Orderings_Olinorder(_1406016), 33639 ^ _777081 : [(33640 ^ _777081) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1406016), _1406018) = hAPP(c_SetInterval_Oord__class_OatMost(_1406016), _1406020), -(_1406018 = _1406020)], (33646 ^ _777081) ^ [] : [_1406018 = _1406020, -(hAPP(c_SetInterval_Oord__class_OatMost(_1406016), _1406018) = hAPP(c_SetInterval_Oord__class_OatMost(_1406016), _1406020))]]], (33652 ^ _777081) ^ [_1406257, _1406259, _1406261, _1406263, _1406265] : [class_Orderings_Olinorder(_1406257), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406257), _1406259), _1406261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406257), _1406263), _1406265)), 33663 ^ _777081 : [(33664 ^ _777081) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1406257, _1406259), _1406261) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1406257, _1406263), _1406265), 33667 ^ _777081 : [(33668 ^ _777081) ^ [] : [-(_1406259 = _1406263)], (33670 ^ _777081) ^ [] : [-(_1406261 = _1406265)]]], (33672 ^ _777081) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1406257, _1406259), _1406261) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1406257, _1406263), _1406265)), _1406259 = _1406263, _1406261 = _1406265]]], (33682 ^ _777081) ^ [_1406738, _1406740, _1406742, _1406744, _1406746] : [class_Orderings_Olinorder(_1406738), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1406738, _1406740), _1406742) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1406738, _1406744), _1406746), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406738), _1406740), _1406742)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1406738), _1406744), _1406746)), -(_1406740 = _1406744)], (33700 ^ _777081) ^ [_1407045, _1407047, _1407049, _1407051, _1407053] : [class_Orderings_Olinorder(_1407045), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1407045, _1407047), _1407049) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1407045, _1407051), _1407053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407045), _1407047), _1407049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1407045), _1407051), _1407053)), -(_1407049 = _1407053)], (33718 ^ _777081) ^ [_1407367, _1407369] : [33720 ^ _777081 : [(33721 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 33719 ^ [_1407367, _1407369]), _1407367)))], (33723 ^ _777081) ^ [] : [hBOOL(hAPP(_1407369, 33719 ^ [_1407367, _1407369]))]], 33724 ^ _777081 : [(33725 ^ _777081) ^ [_1407517] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1407517), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1407367))), -(hBOOL(hAPP(_1407369, _1407517)))]]], (33731 ^ _777081) ^ [_1407618, _1407620] : [33733 ^ _777081 : [(33734 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 33732 ^ [_1407618, _1407620]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1407618))))], (33736 ^ _777081) ^ [] : [hBOOL(hAPP(_1407620, 33732 ^ [_1407618, _1407620]))]], 33737 ^ _777081 : [(33738 ^ _777081) ^ [_1407771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1407771), _1407618)), -(hBOOL(hAPP(_1407620, _1407771)))]]], (33744 ^ _777081) ^ [_1407887, _1407889] : [33752 ^ _777081 : [(33753 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 33751 ^ [_1407887, _1407889]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1407887))))], (33755 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1407889, 33751 ^ [_1407887, _1407889])))]], 33745 ^ _777081 : [(33746 ^ _777081) ^ [_1407955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1407955), _1407887)), hBOOL(hAPP(_1407889, _1407955))]]], (33757 ^ _777081) ^ [_1408115, _1408117] : [33765 ^ _777081 : [(33766 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 33764 ^ [_1408115, _1408117]), _1408115)))], (33768 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1408117, 33764 ^ [_1408115, _1408117])))]], 33758 ^ _777081 : [(33759 ^ _777081) ^ [_1408183] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1408183), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1408115))), hBOOL(hAPP(_1408117, _1408183))]]], (33770 ^ _777081) ^ [_1408352, _1408354] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408352), hAPP(c_Nat_OSuc, _1408354)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1408352, _1408354))], (33772 ^ _777081) ^ [_1408390] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408390), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (33774 ^ _777081) ^ [_1408419, _1408421] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408419), _1408421)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1408421), _1408419))], (33776 ^ _777081) ^ [_1408459, _1408461] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1408459), _1408461)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1408459)), hAPP(c_Nat_OSuc, _1408461)))], (33778 ^ _777081) ^ [_1408505, _1408507, _1408509] : [class_Orderings_Oorder(_1408505), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408505), _1408507), _1408509)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1408505, _1408509), _1408507) = c_Orderings_Obot__class_Obot(tc_fun(_1408505, tc_HOL_Obool)))], (33788 ^ _777081) ^ [_1408672, _1408674, _1408676] : [class_Orderings_Oorder(_1408672), 33791 ^ _777081 : [(33792 ^ _777081) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1408672, _1408674), _1408676) = c_Orderings_Obot__class_Obot(tc_fun(_1408672, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408672), _1408674), _1408676))], (33798 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408672), _1408674), _1408676))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1408672, _1408674), _1408676) = c_Orderings_Obot__class_Obot(tc_fun(_1408672, tc_HOL_Obool)))]]], (33804 ^ _777081) ^ [_1408897, _1408899, _1408901] : [class_Orderings_Oorder(_1408897), 33807 ^ _777081 : [(33808 ^ _777081) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1408897, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1408897, _1408899), _1408901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408897), _1408899), _1408901))], (33814 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408897), _1408899), _1408901))), -(c_Orderings_Obot__class_Obot(tc_fun(_1408897, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1408897, _1408899), _1408901))]]], (33820 ^ _777081) ^ [_1409122, _1409124, _1409126, _1409128, _1409130] : [class_Orderings_Olinorder(_1409122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1409122, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409122, _1409124), _1409126)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409122, _1409128), _1409130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409122), _1409126), _1409124))), 33831 ^ _777081 : [(33832 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409122), _1409128), _1409124)))], (33834 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409122), _1409126), _1409130)))]]], (33836 ^ _777081) ^ [_1409403, _1409405, _1409407, _1409409] : [class_Orderings_Olinorder(_1409403), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409403), _1409405), _1409407)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409403), _1409407), _1409409)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1409403, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409403, _1409405), _1409407)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409403, _1409407), _1409409)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409403, _1409405), _1409409))], (33850 ^ _777081) ^ [_1409680, _1409682, _1409684, _1409686] : [class_Orderings_Olinorder(_1409680), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409680), _1409682), _1409684)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1409680, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409680, _1409682), _1409686)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409680, _1409682), _1409684)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409680, _1409684), _1409686))], (33860 ^ _777081) ^ [_1409887, _1409889, _1409891, _1409893] : [class_Orderings_Oorder(_1409887), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409887, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409887, _1409889), _1409891)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1409887, _1409891), _1409893)) = c_Orderings_Obot__class_Obot(tc_fun(_1409887, tc_HOL_Obool)))], (33866 ^ _777081) ^ [_1410022, _1410024] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1410022)), _1410024) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1410022, _1410024))], (33868 ^ _777081) ^ [_1410060] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1410060) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1410060))], (33870 ^ _777081) ^ [_1410090, _1410092, _1410094] : [-(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)), _1410090)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1410092), _1410094)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1410092), _1410090)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1410094), _1410090)))], (33872 ^ _777081) ^ [_1410151] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1410151)) = hAPP(c_Nat_OSuc, _1410151))], (33874 ^ _777081) ^ [_1410183] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410183)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410183)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1410183)))], (33876 ^ _777081) ^ [_1410224, _1410226, _1410228] : [class_Orderings_Oord(_1410224), 33879 ^ _777081 : [(33880 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1410224), _1410226), hAPP(c_SetInterval_Oord__class_OatMost(_1410224), _1410228))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410224), _1410226), _1410228)))], (33886 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410224), _1410226), _1410228)), -(hBOOL(hAPP(hAPP(c_member(_1410224), _1410226), hAPP(c_SetInterval_Oord__class_OatMost(_1410224), _1410228))))]]], (33892 ^ _777081) ^ [_1410492, _1410494, _1410496] : [class_Orderings_Oorder(_1410492), 33895 ^ _777081 : [(33896 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1410492, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1410492), _1410494)), hAPP(c_SetInterval_Oord__class_OatMost(_1410492), _1410496))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410492), _1410494), _1410496)))], (33902 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410492), _1410494), _1410496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1410492, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1410492), _1410494)), hAPP(c_SetInterval_Oord__class_OatMost(_1410492), _1410496))))]]], (33908 ^ _777081) ^ [_1410784] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1410784), hAPP(c_Nat_OSuc, _1410784)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1410784), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (33910 ^ _777081) ^ [_1410822, _1410824, _1410826, _1410828] : [class_Orderings_Olinorder(_1410822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410822), _1410824), _1410826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410822), _1410826), _1410828)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410822, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1410822, _1410824), _1410826)), c_SetInterval_Oord__class_OatLeastAtMost(_1410822, _1410826, _1410828)) = c_SetInterval_Oord__class_OatLeastAtMost(_1410822, _1410824, _1410828))], (33924 ^ _777081) ^ [_1411091, _1411093, _1411095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1411091), _1411093)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1411091), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1411093), _1411095)) = 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, _1411091), _1411093)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1411093), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1411093), _1411095))))], (33930 ^ _777081) ^ [_1411252, _1411254, _1411256, _1411258] : [class_Orderings_Oorder(_1411252), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411252, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1411252, _1411254), _1411256)), c_SetInterval_Oord__class_OatLeastAtMost(_1411252, _1411256, _1411258)) = c_Orderings_Obot__class_Obot(tc_fun(_1411252, tc_HOL_Obool)))], (33936 ^ _777081) ^ [_1411383, _1411385, _1411387, _1411389, _1411391] : [class_Orderings_Olinorder(_1411383), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411383, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1411383, _1411385), _1411387)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1411383, _1411389), _1411391)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1411383, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1411383), _1411385), _1411389)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1411383), _1411387), _1411391)))], (33942 ^ _777081) ^ [_1411554, _1411556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1411554), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1411556), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1411556), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1411554))))), -(_1411554 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1411556), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1411556), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1411554))))], (33948 ^ _777081) ^ [_1411701, _1411703, _1411705, _1411707] : [class_Orderings_Oorder(_1411701), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1411701, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1411701, _1411703, _1411705)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1411701, _1411705), _1411707)) = c_Orderings_Obot__class_Obot(tc_fun(_1411701, tc_HOL_Obool)))], (33954 ^ _777081) ^ [_1411832, _1411834, _1411836] : [class_Groups_Oordered__ab__group__add(_1411832), -(hAPP(c_Set_Oimage(_1411832, _1411832, c_Groups_Ouminus__class_Ouminus(_1411832)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1411832, _1411834), _1411836)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1411832, hAPP(c_Groups_Ouminus__class_Ouminus(_1411832), _1411836), hAPP(c_Groups_Ouminus__class_Ouminus(_1411832), _1411834)))], (33960 ^ _777081) ^ [_1411967, _1411969, _1411971] : [class_Groups_Oordered__ab__group__add(_1411967), -(hAPP(c_Set_Oimage(_1411967, _1411967, c_Groups_Ouminus__class_Ouminus(_1411967)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1411967, _1411969, _1411971)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1411967, hAPP(c_Groups_Ouminus__class_Ouminus(_1411967), _1411971)), hAPP(c_Groups_Ouminus__class_Ouminus(_1411967), _1411969)))], (33966 ^ _777081) ^ [_1412111, _1412113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1412111), _1412113)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1412111), hAPP(c_Nat_OSuc, _1412113)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1412113), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1412111), _1412113)))], (33972 ^ _777081) ^ [_1412234, _1412236] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1412234), _1412236))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1412234), hAPP(c_Nat_OSuc, _1412236)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (33978 ^ _777081) ^ [] : [-(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))))], (33980 ^ _777081) ^ [_1412304, _1412306, _1412308, _1412310] : [class_Orderings_Olinorder(_1412304), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412304, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1412304), _1412306)), c_SetInterval_Oord__class_OatLeastAtMost(_1412304, _1412308, _1412310)) = c_SetInterval_Oord__class_OatLeastAtMost(_1412304, _1412308, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1412304), _1412306), _1412310)))], (33986 ^ _777081) ^ [_1412447, _1412449, _1412451, _1412453] : [class_Orderings_Olinorder(_1412447), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412447, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1412447, _1412449, _1412451)), hAPP(c_SetInterval_Oord__class_OatMost(_1412447), _1412453)) = c_SetInterval_Oord__class_OatLeastAtMost(_1412447, _1412449, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1412447), _1412451), _1412453)))], (33992 ^ _777081) ^ [_1412590, _1412592, _1412594] : [class_Orderings_Olinorder(_1412590), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412590), _1412592), _1412594)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1412590, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1412590), _1412592)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1412590, _1412592, _1412594)) = hAPP(c_SetInterval_Oord__class_OatMost(_1412590), _1412594))], (34002 ^ _777081) ^ [_1412785, _1412787, _1412789] : [class_Orderings_Oorder(_1412785), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412785, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1412785), _1412787)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1412785, _1412787, _1412789)) = c_Orderings_Obot__class_Obot(tc_fun(_1412785, tc_HOL_Obool)))], (34008 ^ _777081) ^ [_1412912, _1412914, _1412916] : [class_Orderings_Oorder(_1412912), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1412912, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1412912), _1412914)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1412912, _1412914, _1412916)) = c_Orderings_Obot__class_Obot(tc_fun(_1412912, tc_HOL_Obool)))], (34014 ^ _777081) ^ [_1413039, _1413041, _1413043, _1413045] : [class_Orderings_Olinorder(_1413039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1413039), _1413041), _1413043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413039), _1413043), _1413045)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413039, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1413039, _1413041, _1413043)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1413039, _1413043), _1413045)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1413039, _1413041, _1413045))], (34028 ^ _777081) ^ [_1413308, _1413310, _1413312] : [class_Orderings_Olinorder(_1413308), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413308), _1413310), _1413312)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413308, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1413308, _1413310), _1413312)), hAPP(hAPP(c_Set_Oinsert(_1413308), _1413312), c_Orderings_Obot__class_Obot(tc_fun(_1413308, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1413308, _1413310, _1413312))], (34038 ^ _777081) ^ [_1413521, _1413523, _1413525] : [class_Orderings_Olinorder(_1413521), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1413521), _1413523), _1413525)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413521, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1413521), _1413523), c_Orderings_Obot__class_Obot(tc_fun(_1413521, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1413521, _1413523, _1413525)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1413521, _1413523), _1413525))], (34048 ^ _777081) ^ [_1413734, _1413736, _1413738, _1413740] : [class_Orderings_Olinorder(_1413734), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1413734), _1413736), _1413738)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1413734), _1413738), _1413740)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1413734, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1413734, _1413736, _1413738)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1413734, _1413738, _1413740)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1413734, _1413736), _1413740))], (34062 ^ _777081) ^ [] : [-(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))))], (34064 ^ _777081) ^ [_1414021, _1414023, _1414025] : [class_Orderings_Olinorder(_1414021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1414021), _1414023), _1414025)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414021, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1414021), _1414023)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1414021, _1414023, _1414025)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1414021), _1414025))], (34074 ^ _777081) ^ [_1414216, _1414218, _1414220, _1414222, _1414224] : [c_Finite__Set_Ofolding__one__idem(_1414216, _1414218, _1414220), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414216), _1414222)), -(_1414222 = c_Orderings_Obot__class_Obot(tc_fun(_1414216, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1414216), _1414224)), -(_1414224 = c_Orderings_Obot__class_Obot(tc_fun(_1414216, tc_HOL_Obool))), -(hAPP(_1414220, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1414216, tc_HOL_Obool)), _1414222), _1414224)) = hAPP(hAPP(_1414218, hAPP(_1414220, _1414222)), hAPP(_1414220, _1414224)))], (34096 ^ _777081) ^ [_1414581] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1414581))))], (34098 ^ _777081) ^ [_1414609, _1414611] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1414609), _1414611))))], (34100 ^ _777081) ^ [_1414642] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1414642)) = _1414642)], (34102 ^ _777081) ^ [_1414671, _1414673, _1414675] : [class_Orderings_Olinorder(_1414671), 34105 ^ _777081 : [(34106 ^ _777081) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1414671), _1414673) = hAPP(c_SetInterval_Oord__class_OlessThan(_1414671), _1414675), -(_1414673 = _1414675)], (34112 ^ _777081) ^ [] : [_1414673 = _1414675, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1414671), _1414673) = hAPP(c_SetInterval_Oord__class_OlessThan(_1414671), _1414675))]]], (34118 ^ _777081) ^ [_1414912, _1414914, _1414916] : [class_Orderings_Olinorder(_1414912), 34121 ^ _777081 : [(34122 ^ _777081) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1414912), _1414914) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1414912), _1414916), -(_1414914 = _1414916)], (34128 ^ _777081) ^ [] : [_1414914 = _1414916, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1414912), _1414914) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1414912), _1414916))]]], (34134 ^ _777081) ^ [_1415153, _1415155, _1415157, _1415159] : [c_Finite__Set_Ofolding__one__idem(_1415153, _1415155, _1415157), -(hAPP(hAPP(_1415155, _1415159), _1415159) = _1415159)], (34140 ^ _777081) ^ [_1415248, _1415250] : [class_Groups_Oordered__ab__group__add(_1415248), -(hAPP(c_Set_Oimage(_1415248, _1415248, c_Groups_Ouminus__class_Ouminus(_1415248)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1415248), _1415250)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1415248), hAPP(c_Groups_Ouminus__class_Ouminus(_1415248), _1415250)))], (34146 ^ _777081) ^ [_1415371, _1415373] : [class_Groups_Oordered__ab__group__add(_1415371), -(hAPP(c_Set_Oimage(_1415371, _1415371, c_Groups_Ouminus__class_Ouminus(_1415371)), hAPP(c_SetInterval_Oord__class_OlessThan(_1415371), _1415373)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1415371), hAPP(c_Groups_Ouminus__class_Ouminus(_1415371), _1415373)))], (34152 ^ _777081) ^ [_1415494] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1415494) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1415494))], (34154 ^ _777081) ^ [] : [-(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)))], (34156 ^ _777081) ^ [_1415541] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415541)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1415541), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1415541)))], (34158 ^ _777081) ^ [_1415579] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415579)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1415579))], (34160 ^ _777081) ^ [_1415611] : [-(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)), _1415611))))], (34162 ^ _777081) ^ [_1415639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1415639)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1415639) = 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, _1415639))))], (34168 ^ _777081) ^ [_1415742, _1415744, _1415746] : [class_Orderings_Oord(_1415742), 34171 ^ _777081 : [(34172 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1415742), _1415744), hAPP(c_SetInterval_Oord__class_OlessThan(_1415742), _1415746))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415742), _1415744), _1415746)))], (34178 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415742), _1415744), _1415746)), -(hBOOL(hAPP(hAPP(c_member(_1415742), _1415744), hAPP(c_SetInterval_Oord__class_OlessThan(_1415742), _1415746))))]]], (34184 ^ _777081) ^ [_1416010, _1416012, _1416014] : [class_Orderings_Olinorder(_1416010), 34187 ^ _777081 : [(34188 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1416010, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1416010), _1416012)), hAPP(c_SetInterval_Oord__class_OlessThan(_1416010), _1416014))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1416010), _1416012), _1416014)))], (34194 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1416010), _1416012), _1416014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1416010, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1416010), _1416012)), hAPP(c_SetInterval_Oord__class_OlessThan(_1416010), _1416014))))]]], (34200 ^ _777081) ^ [_1416302, _1416304, _1416306] : [class_Orderings_Oord(_1416302), 34203 ^ _777081 : [(34204 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1416302), _1416304), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1416302), _1416306))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416302), _1416306), _1416304)))], (34210 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416302), _1416306), _1416304)), -(hBOOL(hAPP(hAPP(c_member(_1416302), _1416304), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1416302), _1416306))))]]], (34216 ^ _777081) ^ [_1416570, _1416572, _1416574] : [class_Orderings_Olinorder(_1416570), 34219 ^ _777081 : [(34220 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1416570, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1416570), _1416572)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1416570), _1416574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1416570), _1416574), _1416572)))], (34226 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1416570), _1416574), _1416572)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1416570, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1416570), _1416572)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1416570), _1416574))))]]], (34232 ^ _777081) ^ [_1416862, _1416864, _1416866] : [class_Orderings_Olinorder(_1416862), 34235 ^ _777081 : [(34236 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1416862, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1416862), _1416864)), hAPP(c_SetInterval_Oord__class_OlessThan(_1416862), _1416866))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416862), _1416864), _1416866)))], (34242 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416862), _1416864), _1416866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1416862, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1416862), _1416864)), hAPP(c_SetInterval_Oord__class_OlessThan(_1416862), _1416866))))]]], (34248 ^ _777081) ^ [_1417154, _1417156] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1417154), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1417156), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1417154, _1417156))], (34250 ^ _777081) ^ [_1417195, _1417197] : [class_Orderings_Olinorder(_1417195), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1417195, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1417195), _1417197)) = hAPP(c_SetInterval_Oord__class_OatMost(_1417195), _1417197))], (34256 ^ _777081) ^ [_1417306, _1417308] : [class_Orderings_Olinorder(_1417306), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1417306, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1417306), _1417308)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1417306), _1417308))], (34262 ^ _777081) ^ [_1417417, _1417419] : [-(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)), _1417417)), 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), _1417419), _1417417))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1417417), _1417419))], (34264 ^ _777081) ^ [_1417467] : [-(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)), _1417467)) = hAPP(c_Int_Onat, _1417467))], (34266 ^ _777081) ^ [_1417499, _1417501] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1417499), _1417501)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1417501), _1417499)))], (34268 ^ _777081) ^ [_1417542, _1417544, _1417546, _1417548, _1417550] : [c_Finite__Set_Ofolding__one__idem(_1417542, _1417544, _1417546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1417542), _1417548)), hBOOL(hAPP(hAPP(c_member(_1417542), _1417550), _1417548)), -(hAPP(hAPP(_1417544, _1417550), hAPP(_1417546, _1417548)) = hAPP(_1417546, _1417548))], (34282 ^ _777081) ^ [_1417789, _1417791] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1417789), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1417791) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1417789, _1417791))], (34284 ^ _777081) ^ [_1417830, _1417832] : [class_Orderings_Oorder(_1417830), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1417830, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1417830), _1417832), c_Orderings_Obot__class_Obot(tc_fun(_1417830, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1417830), _1417832)) = hAPP(hAPP(c_Set_Oinsert(_1417830), _1417832), c_Orderings_Obot__class_Obot(tc_fun(_1417830, tc_HOL_Obool))))], (34290 ^ _777081) ^ [_1417989, _1417991, _1417993] : [class_Orderings_Olinorder(_1417989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1417989), _1417991), _1417993)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1417989, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1417989), _1417991)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1417989, _1417991), _1417993)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1417989), _1417993))], (34300 ^ _777081) ^ [_1418188, _1418190, _1418192] : [class_Orderings_Oorder(_1418188), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418188, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1418188), _1418190)), c_SetInterval_Oord__class_OatLeastAtMost(_1418188, _1418190, _1418192)) = c_Orderings_Obot__class_Obot(tc_fun(_1418188, tc_HOL_Obool)))], (34306 ^ _777081) ^ [_1418315, _1418317, _1418319] : [class_Orderings_Oorder(_1418315), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418315, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1418315), _1418317)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1418315, _1418317), _1418319)) = c_Orderings_Obot__class_Obot(tc_fun(_1418315, tc_HOL_Obool)))], (34312 ^ _777081) ^ [_1418446, _1418448, _1418450] : [class_Orderings_Oorder(_1418446), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418446, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1418446, _1418448, _1418450)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1418446), _1418450)) = c_Orderings_Obot__class_Obot(tc_fun(_1418446, tc_HOL_Obool)))], (34318 ^ _777081) ^ [_1418573, _1418575, _1418577] : [class_Orderings_Olinorder(_1418573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1418573), _1418575), _1418577)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1418573, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1418573, _1418575, _1418577)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1418573), _1418577)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1418573), _1418575))], (34328 ^ _777081) ^ [_1418768, _1418770, _1418772] : [class_Orderings_Oorder(_1418768), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1418768, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1418768, _1418770, _1418772)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1418768), _1418772)) = c_Orderings_Obot__class_Obot(tc_fun(_1418768, tc_HOL_Obool)))], (34334 ^ _777081) ^ [_1418895] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1418895)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1418895)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1418895)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (34336 ^ _777081) ^ [_1418942] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1418942)) = 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), _1418942))))], (34338 ^ _777081) ^ [_1418980, _1418982] : [class_Orderings_Olinorder(_1418980), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1418980, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1418980), _1418982)), hAPP(hAPP(c_Set_Oinsert(_1418980), _1418982), c_Orderings_Obot__class_Obot(tc_fun(_1418980, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1418980), _1418982))], (34344 ^ _777081) ^ [_1419123, _1419125, _1419127, _1419129, _1419131] : [c_Finite__Set_Ofolding__one__idem(_1419123, _1419125, _1419127), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419123), _1419129)), -(_1419129 = c_Orderings_Obot__class_Obot(tc_fun(_1419123, tc_HOL_Obool))), -(hAPP(_1419127, hAPP(hAPP(c_Set_Oinsert(_1419123), _1419131), _1419129)) = hAPP(hAPP(_1419125, _1419131), hAPP(_1419127, _1419129)))], (34358 ^ _777081) ^ [_1419339, _1419341, _1419343, _1419345, _1419347] : [c_Finite__Set_Ofolding__one__idem(_1419339, _1419341, _1419343), hBOOL(hAPP(c_Finite__Set_Ofinite(_1419339), _1419345)), -(_1419347 = c_Orderings_Obot__class_Obot(tc_fun(_1419339, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1419339, tc_HOL_Obool)), _1419347), _1419345)), -(hAPP(hAPP(_1419341, hAPP(_1419343, _1419347)), hAPP(_1419343, _1419345)) = hAPP(_1419343, _1419345))], (34376 ^ _777081) ^ [_1419669, _1419671, _1419673] : [class_Orderings_Olinorder(_1419669), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1419669), _1419671), _1419673)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1419669, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1419669), _1419671)), c_SetInterval_Oord__class_OatLeastAtMost(_1419669, _1419671, _1419673)) = hAPP(c_SetInterval_Oord__class_OatMost(_1419669), _1419673))], (34386 ^ _777081) ^ [_1419864, _1419866, _1419868] : [-(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), _1419864)), 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))), _1419866))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1419868))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1419868)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1419864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1419864), 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), _1419868), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1419866)))))], (34388 ^ _777081) ^ [_1419951, _1419953, _1419955] : [class_Orderings_Olinorder(_1419951), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1419951), _1419953), _1419955)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1419951, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1419951, _1419953, _1419955)), hAPP(c_SetInterval_Oord__class_OatLeast(_1419951), _1419955)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1419951), _1419953))], (34398 ^ _777081) ^ [_1420146, _1420148, _1420150] : [class_Orderings_Olinorder(_1420146), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420146), _1420148), _1420150)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1420146, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1420146, _1420148, _1420150)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1420146), _1420150)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1420146), _1420148))], (34408 ^ _777081) ^ [_1420341, _1420343, _1420345, _1420347] : [class_Groups_Oordered__ab__group__add__abs(_1420341), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420341), hAPP(c_Groups_Oabs__class_Oabs(_1420341), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1420343, _1420341), _1420345), _1420347))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1420343, _1420341), hAPP(hAPP(c_COMBB(_1420341, _1420341, _1420343), c_Groups_Oabs__class_Oabs(_1420341)), _1420345)), _1420347))))], (34414 ^ _777081) ^ [_1420504, _1420506, _1420508, _1420510] : [class_Groups_Oordered__ab__group__add__abs(_1420504), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420504), c_Groups_Ozero__class_Ozero(_1420504)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1420506, _1420504), hAPP(hAPP(c_COMBB(_1420504, _1420504, _1420506), c_Groups_Oabs__class_Oabs(_1420504)), _1420508)), _1420510))))], (34420 ^ _777081) ^ [_1420643, _1420645, _1420647, _1420649, _1420651] : [class_Fields_Ofield(_1420643), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420643), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1420645, _1420643), _1420647), _1420649)), _1420651) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1420645, _1420643), hAPP(hAPP(c_COMBC(_1420645, _1420643, _1420643), hAPP(hAPP(c_COMBB(_1420643, tc_fun(_1420643, _1420643), _1420645), c_Rings_Oinverse__class_Odivide(_1420643)), _1420647)), _1420651)), _1420649))], (34426 ^ _777081) ^ [_1420826, _1420828, _1420830, _1420832] : [class_Groups_Oordered__ab__group__add__abs(_1420826), -(hAPP(c_Groups_Oabs__class_Oabs(_1420826), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1420828, _1420826), hAPP(hAPP(c_COMBB(_1420826, _1420826, _1420828), c_Groups_Oabs__class_Oabs(_1420826)), _1420830)), _1420832)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1420828, _1420826), hAPP(hAPP(c_COMBB(_1420826, _1420826, _1420828), c_Groups_Oabs__class_Oabs(_1420826)), _1420830)), _1420832))], (34432 ^ _777081) ^ [_1420999, _1421001, _1421003] : [class_Groups_Ocomm__monoid__add(_1420999), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421001, _1420999), hAPP(c_COMBK(_1420999, _1421001), c_Groups_Ozero__class_Ozero(_1420999))), _1421003) = c_Groups_Ozero__class_Ozero(_1420999))], (34438 ^ _777081) ^ [_1421114, _1421116, _1421118, _1421120, _1421122] : [class_Groups_Ocomm__monoid__add(_1421114), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421116, _1421114), hAPP(hAPP(c_COMBS(_1421116, _1421114, _1421114), hAPP(hAPP(c_COMBB(_1421114, tc_fun(_1421114, _1421114), _1421116), c_Groups_Oplus__class_Oplus(_1421114)), _1421118)), _1421120)), _1421122) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1421114), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421116, _1421114), _1421118), _1421122)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421116, _1421114), _1421120), _1421122)))], (34444 ^ _777081) ^ [_1421315, _1421317, _1421319, _1421321, _1421323] : [class_Rings_Osemiring__0(_1421315), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421315), _1421317), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421319, _1421315), _1421321), _1421323)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421319, _1421315), hAPP(hAPP(c_COMBB(_1421315, _1421315, _1421319), hAPP(c_Groups_Otimes__class_Otimes(_1421315), _1421317)), _1421321)), _1421323))], (34450 ^ _777081) ^ [_1421478, _1421480, _1421482, _1421484, _1421486] : [class_Rings_Osemiring__0(_1421478), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421478), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421480, _1421478), _1421482), _1421484)), _1421486) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421480, _1421478), hAPP(hAPP(c_COMBC(_1421480, _1421478, _1421478), hAPP(hAPP(c_COMBB(_1421478, tc_fun(_1421478, _1421478), _1421480), c_Groups_Otimes__class_Otimes(_1421478)), _1421482)), _1421486)), _1421484))], (34456 ^ _777081) ^ [_1421661, _1421663, _1421665, _1421667, _1421669, _1421671, _1421673] : [class_Rings_Osemiring__0(_1421661), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421661), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421663, _1421661), _1421665), _1421667)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421669, _1421661), _1421671), _1421673)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421663, _1421661), hAPP(hAPP(c_COMBC(_1421663, tc_fun(_1421669, tc_HOL_Obool), _1421661), hAPP(hAPP(c_COMBB(tc_fun(_1421669, _1421661), tc_fun(tc_fun(_1421669, tc_HOL_Obool), _1421661), _1421663), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1421669, _1421661)), hAPP(hAPP(c_COMBC(_1421663, tc_fun(_1421669, _1421661), tc_fun(_1421669, _1421661)), hAPP(hAPP(c_COMBB(tc_fun(_1421661, _1421661), tc_fun(tc_fun(_1421669, _1421661), tc_fun(_1421669, _1421661)), _1421663), c_COMBB(_1421661, _1421661, _1421669)), hAPP(hAPP(c_COMBB(_1421661, tc_fun(_1421661, _1421661), _1421663), c_Groups_Otimes__class_Otimes(_1421661)), _1421665))), _1421671))), _1421673)), _1421667))], (34462 ^ _777081) ^ [_1422000, _1422002, _1422004, _1422006] : [class_Groups_Oab__group__add(_1422000), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422002, _1422000), hAPP(hAPP(c_COMBB(_1422000, _1422000, _1422002), c_Groups_Ouminus__class_Ouminus(_1422000)), _1422004)), _1422006) = hAPP(c_Groups_Ouminus__class_Ouminus(_1422000), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422002, _1422000), _1422004), _1422006)))], (34468 ^ _777081) ^ [_1422149, _1422151, _1422153, _1422155, _1422157, _1422159] : [class_Groups_Ocomm__monoid__add(_1422149), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422151, _1422149), hAPP(hAPP(c_COMBC(_1422151, tc_fun(_1422153, tc_HOL_Obool), _1422149), hAPP(hAPP(c_COMBB(tc_fun(_1422153, _1422149), tc_fun(tc_fun(_1422153, tc_HOL_Obool), _1422149), _1422151), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422153, _1422149)), _1422155)), _1422157)), _1422159) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422153, _1422149), hAPP(hAPP(c_COMBC(_1422153, tc_fun(_1422151, tc_HOL_Obool), _1422149), hAPP(hAPP(c_COMBB(tc_fun(_1422151, _1422149), tc_fun(tc_fun(_1422151, tc_HOL_Obool), _1422149), _1422153), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422151, _1422149)), hAPP(c_COMBC(_1422151, _1422153, _1422149), _1422155))), _1422159)), _1422157))], (34474 ^ _777081) ^ [_1422422, _1422424, _1422426, _1422428] : [class_Rings_Oring__1(_1422422), -(hAPP(c_Int_Oring__1__class_Oof__int(_1422422), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422424, tc_Int_Oint), _1422426), _1422428)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422424, _1422422), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1422422, _1422424), c_Int_Oring__1__class_Oof__int(_1422422)), _1422426)), _1422428))], (34480 ^ _777081) ^ [_1422571, _1422573, _1422575, _1422577] : [class_Rings_Osemiring__1(_1422571), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1422571), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422573, tc_Nat_Onat), _1422575), _1422577)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422573, _1422571), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1422571, _1422573), c_Nat_Osemiring__1__class_Oof__nat(_1422571)), _1422575)), _1422577))], (34486 ^ _777081) ^ [_1422720, _1422722, _1422724, _1422726, _1422728] : [class_Groups_Oab__group__add(_1422720), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422722, _1422720), hAPP(hAPP(c_COMBS(_1422722, _1422720, _1422720), hAPP(hAPP(c_COMBB(_1422720, tc_fun(_1422720, _1422720), _1422722), c_Groups_Ominus__class_Ominus(_1422720)), _1422724)), _1422726)), _1422728) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1422720), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422722, _1422720), _1422724), _1422728)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1422722, _1422720), _1422726), _1422728)))], (34492 ^ _777081) ^ [_1422921, _1422923, _1422925] : [class_Orderings_Olinorder(_1422921), 34495 ^ _777081 : [(34496 ^ _777081) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1422921), _1422923) = hAPP(c_SetInterval_Oord__class_OatLeast(_1422921), _1422925), -(_1422923 = _1422925)], (34502 ^ _777081) ^ [] : [_1422923 = _1422925, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1422921), _1422923) = hAPP(c_SetInterval_Oord__class_OatLeast(_1422921), _1422925))]]], (34508 ^ _777081) ^ [_1423162, _1423164, _1423166] : [class_Groups_Ocomm__monoid__add(_1423162), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423164, _1423162), _1423166), c_Orderings_Obot__class_Obot(tc_fun(_1423164, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1423162))], (34514 ^ _777081) ^ [_1423271, _1423273, _1423275] : [class_Groups_Ocomm__monoid__add(_1423271), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423273, _1423271), _1423275), c_Orderings_Obot__class_Obot(tc_fun(_1423273, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1423271))], (34520 ^ _777081) ^ [_1423380, _1423382, _1423384, _1423386] : [class_Groups_Ocomm__monoid__add(_1423380), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1423382), _1423384))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423382, _1423380), _1423386), _1423384) = c_Groups_Ozero__class_Ozero(_1423380))], (34530 ^ _777081) ^ [_1423504, _1423506, _1423508, _1423510] : [class_Groups_Ocomm__monoid__add(_1423504), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1423506), _1423508))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423506, _1423504), _1423510), _1423508) = c_Groups_Ozero__class_Ozero(_1423504))], (34540 ^ _777081) ^ [_1423628, _1423630, _1423632, _1423634, _1423636] : [class_Groups_Ocomm__monoid__add(_1423628), hBOOL(hAPP(c_Finite__Set_Ofinite(_1423630), _1423632)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423630, _1423628), hAPP(hAPP(c_COMBS(_1423630, _1423628, _1423628), hAPP(hAPP(c_COMBB(_1423628, tc_fun(_1423628, _1423628), _1423630), c_Groups_Oplus__class_Oplus(_1423628)), _1423634)), _1423636)), _1423632) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1423628), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423630, _1423628), _1423634), _1423632)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1423630, _1423628), _1423636), _1423632)))], (34550 ^ _777081) ^ [_1423895, _1423897, _1423899] : [class_Groups_Ocomm__monoid__add(_1423895), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1423895), _1423897), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1423899))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1423895), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1423895), _1423897), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1423899))), hAPP(_1423897, _1423899)))], (34556 ^ _777081) ^ [_1424048, _1424050, _1424052, _1424054] : [class_Groups_Ocomm__monoid__add(_1424048), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424048), _1424050), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1424052)), hAPP(c_Nat_OSuc, _1424054))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424048), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1424048, tc_Nat_Onat), _1424050), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1424052), _1424054)))], (34562 ^ _777081) ^ [_1424219, _1424221, _1424223, _1424225, _1424227] : [class_Groups_Ocomm__monoid__add(_1424219), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424219), _1424221), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1424223), _1424225)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1424227), _1424225))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424219), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1424219, tc_Nat_Onat), _1424221), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1424225))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1424223), _1424227)))], (34568 ^ _777081) ^ [_1424410, _1424412, _1424414, _1424416] : [class_Groups_Ocomm__monoid__add(_1424410), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424410), _1424412), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1424414), hAPP(c_Nat_OSuc, _1424416))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424410), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1424410, tc_Nat_Onat), _1424412), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1424414, _1424416)))], (34574 ^ _777081) ^ [_1424573, _1424575, _1424577, _1424579, _1424581] : [class_Groups_Ocomm__monoid__add(_1424573), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424573), _1424575), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1424577), _1424579), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1424581), _1424579))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424573), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1424573, tc_Nat_Onat), _1424575), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1424579))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1424577, _1424581)))], (34580 ^ _777081) ^ [_1424756, _1424758, _1424760, _1424762, _1424764] : [class_Groups_Ocomm__monoid__add(_1424756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1424758), _1424760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1424760), _1424762)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1424756), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424756), _1424764), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1424758), _1424760))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424756), _1424764), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1424760), _1424762))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1424756), _1424764), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1424758), _1424762)))], (34594 ^ _777081) ^ [_1425079, _1425081, _1425083, _1425085, _1425087] : [class_Groups_Oab__group__add(_1425079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1425081), _1425083)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1425083), _1425085)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1425079), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1425079), _1425087), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1425081), _1425085))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1425079), _1425087), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1425081), _1425083))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1425079), _1425087), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1425083), _1425085)))], (34608 ^ _777081) ^ [_1425402, _1425404, _1425406] : [class_Orderings_Oord(_1425402), 34611 ^ _777081 : [(34612 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1425402), _1425404), hAPP(c_SetInterval_Oord__class_OatLeast(_1425402), _1425406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425402), _1425406), _1425404)))], (34618 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425402), _1425406), _1425404)), -(hBOOL(hAPP(hAPP(c_member(_1425402), _1425404), hAPP(c_SetInterval_Oord__class_OatLeast(_1425402), _1425406))))]]], (34624 ^ _777081) ^ [_1425670, _1425672, _1425674, _1425676, _1425678] : [class_Groups_Ocomm__monoid__add(_1425670), hBOOL(hAPP(c_Finite__Set_Ofinite(_1425672), _1425674)), 34631 ^ _777081 : [(34632 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1425672), _1425676), _1425674)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1425672, _1425670), hAPP(hAPP(c_COMBC(_1425672, _1425670, _1425670), hAPP(hAPP(c_COMBS(_1425672, _1425670, tc_fun(_1425670, _1425670)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1425670, tc_fun(_1425670, _1425670)), _1425672), c_If(_1425670)), hAPP(hAPP(c_COMBC(_1425672, _1425672, tc_HOL_Obool), c_fequal), _1425676))), _1425678)), c_Groups_Ozero__class_Ozero(_1425670))), _1425674) = hAPP(_1425678, _1425676))], (34638 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1425672), _1425676), _1425674))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1425672, _1425670), hAPP(hAPP(c_COMBC(_1425672, _1425670, _1425670), hAPP(hAPP(c_COMBS(_1425672, _1425670, tc_fun(_1425670, _1425670)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1425670, tc_fun(_1425670, _1425670)), _1425672), c_If(_1425670)), hAPP(hAPP(c_COMBC(_1425672, _1425672, tc_HOL_Obool), c_fequal), _1425676))), _1425678)), c_Groups_Ozero__class_Ozero(_1425670))), _1425674) = c_Groups_Ozero__class_Ozero(_1425670))]]], (34644 ^ _777081) ^ [_1426208, _1426210, _1426212, _1426214, _1426216] : [class_Groups_Ocomm__monoid__add(_1426208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1426210), _1426212)), 34651 ^ _777081 : [(34652 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1426210), _1426214), _1426212)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426210, _1426208), hAPP(hAPP(c_COMBC(_1426210, _1426208, _1426208), hAPP(hAPP(c_COMBS(_1426210, _1426208, tc_fun(_1426208, _1426208)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1426208, tc_fun(_1426208, _1426208)), _1426210), c_If(_1426208)), hAPP(c_fequal, _1426214))), _1426216)), c_Groups_Ozero__class_Ozero(_1426208))), _1426212) = hAPP(_1426216, _1426214))], (34658 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1426210), _1426214), _1426212))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1426210, _1426208), hAPP(hAPP(c_COMBC(_1426210, _1426208, _1426208), hAPP(hAPP(c_COMBS(_1426210, _1426208, tc_fun(_1426208, _1426208)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1426208, tc_fun(_1426208, _1426208)), _1426210), c_If(_1426208)), hAPP(c_fequal, _1426214))), _1426216)), c_Groups_Ozero__class_Ozero(_1426208))), _1426212) = c_Groups_Ozero__class_Ozero(_1426208))]]], (34664 ^ _777081) ^ [_1426718, _1426720, _1426722] : [class_Orderings_Oorder(_1426718), 34667 ^ _777081 : [(34668 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1426718, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1426718), _1426720)), hAPP(c_SetInterval_Oord__class_OatLeast(_1426718), _1426722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1426718), _1426722), _1426720)))], (34674 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1426718), _1426722), _1426720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1426718, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1426718), _1426720)), hAPP(c_SetInterval_Oord__class_OatLeast(_1426718), _1426722))))]]], (34680 ^ _777081) ^ [] : [-(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)))], (34682 ^ _777081) ^ [_1427028, _1427030, _1427032, _1427034] : [class_Rings_Osemiring__1(_1427028), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427030, _1427028), hAPP(c_COMBK(_1427028, _1427030), _1427032)), _1427034) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1427028), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1427028), hAPP(c_Finite__Set_Ocard(_1427030), _1427034))), _1427032))], (34688 ^ _777081) ^ [_1427173, _1427175, _1427177] : [class_Groups_Ocomm__monoid__add(_1427173), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1427173), _1427175), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1427177))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427173), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1427173), _1427175), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1427177))), hAPP(_1427175, hAPP(c_Nat_OSuc, _1427177))))], (34694 ^ _777081) ^ [_1427332, _1427334] : [class_Orderings_Olinorder(_1427332), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1427332, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1427332), _1427334)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1427332), _1427334))], (34700 ^ _777081) ^ [_1427443, _1427445] : [class_Orderings_Olinorder(_1427443), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1427443, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1427443), _1427445)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1427443), _1427445))], (34706 ^ _777081) ^ [_1427554, _1427556, _1427558, _1427560, _1427562] : [class_Groups_Ocomm__monoid__add(_1427554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427556), _1427558)), -(hBOOL(hAPP(hAPP(c_member(_1427556), _1427560), _1427558))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427556, _1427554), _1427562), hAPP(hAPP(c_Set_Oinsert(_1427556), _1427560), _1427558)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427554), hAPP(_1427562, _1427560)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427556, _1427554), _1427562), _1427558)))], (34720 ^ _777081) ^ [_1427804, _1427806, _1427808, _1427810, _1427812] : [class_Groups_Ocomm__monoid__add(_1427804), hBOOL(hAPP(c_Finite__Set_Ofinite(_1427806), _1427808)), -(hBOOL(hAPP(hAPP(c_member(_1427806), _1427810), _1427808))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427806, _1427804), _1427812), hAPP(hAPP(c_Set_Oinsert(_1427806), _1427810), _1427808)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427804), hAPP(_1427812, _1427810)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1427806, _1427804), _1427812), _1427808)))], (34734 ^ _777081) ^ [_1428054] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1428054)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1428054))], (34736 ^ _777081) ^ [_1428086, _1428088, _1428090, _1428092, _1428094] : [class_Groups_Ocomm__monoid__add(_1428086), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428088), _1428090)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428088), _1428092)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1428086), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428088, _1428086), _1428094), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1428088, tc_HOL_Obool)), _1428090), _1428092))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428088, _1428086), _1428094), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428088, tc_HOL_Obool)), _1428090), _1428092))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1428086), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428088, _1428086), _1428094), _1428090)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428088, _1428086), _1428094), _1428092)))], (34750 ^ _777081) ^ [_1428447, _1428449, _1428451, _1428453, _1428455] : [class_Groups_Oab__group__add(_1428447), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428449), _1428451)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428449, tc_HOL_Obool)), _1428453), _1428451)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428449, _1428447), _1428455), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1428449, tc_HOL_Obool)), _1428451), _1428453)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1428447), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428449, _1428447), _1428455), _1428451)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428449, _1428447), _1428455), _1428453)))], (34764 ^ _777081) ^ [_1428764, _1428766, _1428768, _1428770] : [class_Groups_Ocomm__monoid__add(_1428764), hBOOL(hAPP(c_Finite__Set_Ofinite(_1428766), _1428768)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428766, _1428764), _1428770), _1428768) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1428764, _1428766, c_Groups_Oplus__class_Oplus(_1428764)), _1428770), c_Groups_Ozero__class_Ozero(_1428764)), _1428768))], (34774 ^ _777081) ^ [_1428959, _1428961, _1428963, _1428965] : [class_Groups_Ocomm__monoid__add(_1428959), 34777 ^ _777081 : [(34778 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1428961), _1428963)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428961, _1428959), _1428965), _1428963) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1428959, _1428961, c_Groups_Oplus__class_Oplus(_1428959)), _1428965), c_Groups_Ozero__class_Ozero(_1428959)), _1428963))], (34784 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1428961), _1428963))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1428961, _1428959), _1428965), _1428963) = c_Groups_Ozero__class_Ozero(_1428959))]]], (34790 ^ _777081) ^ [_1429231, _1429233, _1429235] : [class_Groups_Ocomm__monoid__add(_1429231), hAPP(_1429233, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1429231), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429231), _1429233), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1429235)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429231), _1429233), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1429235)))], (34800 ^ _777081) ^ [_1429420, _1429422, _1429424, _1429426] : [class_Groups_Ocomm__monoid__add(_1429420), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1429422), _1429424)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429420), _1429426), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1429422), _1429424)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1429420), hAPP(_1429426, _1429422)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429420), _1429426), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1429422)), _1429424))))], (34810 ^ _777081) ^ [_1429653, _1429655, _1429657, _1429659] : [class_Groups_Ocomm__monoid__add(_1429653), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1429655), _1429657)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429653), _1429659), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1429655, _1429657)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1429653), hAPP(_1429659, _1429655)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1429653), _1429659), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1429655), _1429657))))], (34820 ^ _777081) ^ [_1429878, _1429880, _1429882, _1429884, _1429886] : [class_Groups_Ocomm__monoid__add(_1429878), hBOOL(hAPP(c_Finite__Set_Ofinite(_1429880), _1429882)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1429880, _1429878), _1429884), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429880, tc_HOL_Obool)), _1429882), _1429886)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1429880, _1429878), hAPP(hAPP(c_COMBC(_1429880, _1429878, _1429878), hAPP(hAPP(c_COMBS(_1429880, _1429878, tc_fun(_1429878, _1429878)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1429878, tc_fun(_1429878, _1429878)), _1429880), c_If(_1429878)), hAPP(hAPP(c_COMBC(_1429880, tc_fun(_1429880, tc_HOL_Obool), tc_HOL_Obool), c_member(_1429880)), _1429886))), _1429884)), c_Groups_Ozero__class_Ozero(_1429878))), _1429882))], (34830 ^ _777081) ^ [_1430199, _1430201, _1430203, _1430205, _1430207] : [class_Groups_Ocomm__monoid__add(_1430199), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430201), _1430203)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430201, _1430199), _1430205), hAPP(hAPP(c_Set_Oinsert(_1430201), _1430207), _1430203)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1430199), hAPP(_1430205, _1430207)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430201, _1430199), _1430205), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430201, tc_HOL_Obool)), _1430203), hAPP(hAPP(c_Set_Oinsert(_1430201), _1430207), c_Orderings_Obot__class_Obot(tc_fun(_1430201, tc_HOL_Obool)))))))], (34840 ^ _777081) ^ [_1430468, _1430470, _1430472, _1430474, _1430476] : [class_Groups_Ocomm__monoid__add(_1430468), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430470), _1430472)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430470), _1430474)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430470, tc_HOL_Obool)), _1430472), _1430474) = c_Orderings_Obot__class_Obot(tc_fun(_1430470, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430470, _1430468), _1430476), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430470, tc_HOL_Obool)), _1430472), _1430474)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1430468), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430470, _1430468), _1430476), _1430472)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430470, _1430468), _1430476), _1430474)))], (34858 ^ _777081) ^ [_1430863, _1430865, _1430867, _1430869, _1430871] : [class_Groups_Oab__group__add(_1430863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430865), _1430867)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1430865), _1430869)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430865, _1430863), _1430871), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430865, tc_HOL_Obool)), _1430867), _1430869)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1430863), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1430863), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430865, _1430863), _1430871), _1430867)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430865, _1430863), _1430871), _1430869))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1430865, _1430863), _1430871), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430865, tc_HOL_Obool)), _1430867), _1430869))))], (34872 ^ _777081) ^ [_1431224, _1431226, _1431228] : [class_Orderings_Olinorder(_1431224), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431224), _1431226), _1431228)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431224, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1431224, _1431226), _1431228)), hAPP(c_SetInterval_Oord__class_OatLeast(_1431224), _1431228)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1431224), _1431226))], (34882 ^ _777081) ^ [_1431423, _1431425, _1431427] : [class_Orderings_Oorder(_1431423), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431423, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1431423, _1431425), _1431427)), hAPP(c_SetInterval_Oord__class_OatLeast(_1431423), _1431427)) = c_Orderings_Obot__class_Obot(tc_fun(_1431423, tc_HOL_Obool)))], (34888 ^ _777081) ^ [_1431554, _1431556, _1431558, _1431560] : [class_Orderings_Olinorder(_1431554), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431554, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1431554), _1431556)), c_SetInterval_Oord__class_OatLeastAtMost(_1431554, _1431558, _1431560)) = c_SetInterval_Oord__class_OatLeastAtMost(_1431554, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1431554), _1431556), _1431558), _1431560))], (34894 ^ _777081) ^ [_1431697, _1431699, _1431701, _1431703] : [class_Orderings_Olinorder(_1431697), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1431697, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1431697, _1431699, _1431701)), hAPP(c_SetInterval_Oord__class_OatLeast(_1431697), _1431703)) = c_SetInterval_Oord__class_OatLeastAtMost(_1431697, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1431697), _1431699), _1431703), _1431701))], (34900 ^ _777081) ^ [_1431840, _1431842, _1431844, _1431846] : [class_Groups_Ocomm__monoid__add(_1431840), 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hAPP(c_Nat_OSuc, _1432172))))]]], (34932 ^ _777081) ^ [_1432506, _1432508, _1432510, _1432512] : [class_Groups_Ocomm__monoid__add(_1432506), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1432508), _1432510)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1432506), _1432512), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1432508, _1432510)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432506), hAPP(_1432512, _1432508)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1432506), _1432512), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1432508, _1432510))))], (34942 ^ _777081) ^ [_1432725, _1432727, _1432729] : [class_Orderings_Oorder(_1432725), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1432725, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1432725, _1432727, _1432729)), hAPP(c_SetInterval_Oord__class_OatLeast(_1432725), _1432729)) = c_Orderings_Obot__class_Obot(tc_fun(_1432725, tc_HOL_Obool)))], (34948 ^ _777081) ^ [_1432852, _1432854] : [class_Groups_Oordered__ab__group__add(_1432852), -(hAPP(c_Set_Oimage(_1432852, _1432852, c_Groups_Ouminus__class_Ouminus(_1432852)), hAPP(c_SetInterval_Oord__class_OatMost(_1432852), _1432854)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1432852), hAPP(c_Groups_Ouminus__class_Ouminus(_1432852), _1432854)))], (34954 ^ _777081) ^ [_1432975, _1432977] : [class_Groups_Oordered__ab__group__add(_1432975), -(hAPP(c_Set_Oimage(_1432975, _1432975, c_Groups_Ouminus__class_Ouminus(_1432975)), hAPP(c_SetInterval_Oord__class_OatLeast(_1432975), _1432977)) = hAPP(c_SetInterval_Oord__class_OatMost(_1432975), hAPP(c_Groups_Ouminus__class_Ouminus(_1432975), _1432977)))], (34960 ^ _777081) ^ [_1433098] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1433098)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1433098)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1433098), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (34962 ^ _777081) ^ [_1433142, _1433144, _1433146, _1433148, _1433150] : [class_Groups_Ocomm__monoid__add(_1433142), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1433144), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1433146), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1433142), _1433148), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1433144, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1433146), _1433150))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1433142), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1433142), _1433148), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1433144, _1433146))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1433142), _1433148), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1433146), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1433146), _1433150)))))], (34972 ^ _777081) ^ [_1433433, _1433435, _1433437, _1433439, _1433441] : [class_Groups_Ocomm__monoid__add(_1433433), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433435), _1433437)), hBOOL(hAPP(hAPP(c_member(_1433435), _1433439), _1433437)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1433435, _1433433), _1433441), _1433437) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1433433), hAPP(_1433441, _1433439)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1433435, _1433433), _1433441), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1433435, tc_HOL_Obool)), _1433437), hAPP(hAPP(c_Set_Oinsert(_1433435), _1433439), c_Orderings_Obot__class_Obot(tc_fun(_1433435, tc_HOL_Obool)))))))], (34986 ^ _777081) ^ [_1433758, _1433760, _1433762, _1433764, _1433766] : [class_Groups_Ocomm__monoid__add(_1433758), hBOOL(hAPP(c_Finite__Set_Ofinite(_1433760), _1433762)), hBOOL(hAPP(hAPP(c_member(_1433760), _1433764), _1433762)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1433760, _1433758), _1433766), _1433762) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1433758), hAPP(_1433766, _1433764)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1433760, _1433758), _1433766), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1433760, tc_HOL_Obool)), _1433762), hAPP(hAPP(c_Set_Oinsert(_1433760), _1433764), c_Orderings_Obot__class_Obot(tc_fun(_1433760, tc_HOL_Obool)))))))], (35000 ^ _777081) ^ [_1434083, _1434085, _1434087, _1434089, _1434091] : [class_Rings_Oring(_1434083), hBOOL(hAPP(c_Finite__Set_Ofinite(_1434085), _1434087)), hBOOL(hAPP(hAPP(c_member(_1434085), _1434089), _1434087)), 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c_Orderings_Obot__class_Obot(tc_fun(_1434410, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1434408), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434410, _1434408), _1434416), _1434412)), hAPP(_1434416, _1434414)))], (35028 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1434410), _1434414), _1434412))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434410, _1434408), _1434416), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1434410, tc_HOL_Obool)), _1434412), hAPP(hAPP(c_Set_Oinsert(_1434410), _1434414), c_Orderings_Obot__class_Obot(tc_fun(_1434410, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1434410, _1434408), _1434416), _1434412))]]], (35034 ^ _777081) ^ [_1434878, _1434880, _1434882, _1434884] : [class_Rings_Ocomm__semiring__1(_1434878), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434878), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434878), c_Groups_Oone__class_Oone(_1434878)), c_Groups_Oone__class_Oone(_1434878))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1434878), hAPP(hAPP(c_COMBB(_1434878, _1434878, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1434878), _1434880)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1434878, _1434878), hAPP(hAPP(c_COMBB(_1434878, tc_fun(_1434878, _1434878), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1434878)), c_Nat_Osemiring__1__class_Oof__nat(_1434878))), _1434882))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1434884))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434878), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1434878), _1434884)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434878), _1434880), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434878), _1434880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434878), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1434878), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1434884), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1434882)))))], (35040 ^ 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hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1435403), c_Nat_Osemiring__1__class_Oof__nat(_1435403)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1435405))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435403), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1435403), _1435405)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1435403), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1435403), _1435405)), c_Groups_Oone__class_Oone(_1435403))))], (35056 ^ _777081) ^ [_1435604, _1435606, _1435608, _1435610] : [class_Groups_Oab__group__add(_1435604), 35059 ^ _777081 : [(35060 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1435606), _1435608)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1435604), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1435604, _1435604), hAPP(hAPP(c_COMBB(_1435604, tc_fun(_1435604, _1435604), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1435604)), 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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, _1435606, _1435608)) = c_Groups_Ozero__class_Ozero(_1435604))]]], (35072 ^ _777081) ^ [_1436042, _1436044] : [class_Orderings_Oorder(_1436042), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1436042, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1436042), _1436044)), hAPP(c_SetInterval_Oord__class_OatLeast(_1436042), _1436044)) = hAPP(hAPP(c_Set_Oinsert(_1436042), _1436044), c_Orderings_Obot__class_Obot(tc_fun(_1436042, tc_HOL_Obool))))], (35078 ^ _777081) ^ [_1436185, _1436187] : [class_Orderings_Olinorder(_1436185), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1436185, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1436185), _1436187), c_Orderings_Obot__class_Obot(tc_fun(_1436185, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1436185), _1436187)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1436185), _1436187))], (35084 ^ _777081) ^ [_1436328, _1436330, _1436332, _1436334, _1436336] : [class_Groups_Oordered__comm__monoid__add(_1436328), hBOOL(hAPP(c_Finite__Set_Ofinite(_1436330), _1436332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1436330, tc_HOL_Obool)), _1436334), _1436332)), 35098 ^ _777081 : [(35099 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1436330), 35097 ^ [_1436328, _1436330, _1436332, _1436334, _1436336]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1436330, tc_HOL_Obool)), _1436332), _1436334))))], (35101 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436328), c_Groups_Ozero__class_Ozero(_1436328)), hAPP(_1436336, 35097 ^ [_1436328, _1436330, _1436332, _1436334, _1436336])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436328), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1436330, _1436328), _1436336), _1436334)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1436330, _1436328), _1436336), _1436332))))], (35105 ^ _777081) ^ [_1436814, _1436816, _1436818, _1436820, _1436822] : [class_Groups_Oordered__ab__semigroup__add(_1436814), class_Rings_Osemiring__1(_1436814), 35115 ^ _777081 : [(35116 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1436816), 35114 ^ [_1436814, _1436816, _1436818, _1436820, _1436822]), _1436818)))], (35118 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436814), hAPP(_1436820, 35114 ^ [_1436814, _1436816, _1436818, _1436820, _1436822])), _1436822))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436814), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1436816, _1436814), _1436820), _1436818)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1436814), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1436814), hAPP(c_Finite__Set_Ocard(_1436816), _1436818))), _1436822))))], (35122 ^ _777081) ^ [_1437204, _1437206, _1437208, 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hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437206, _1437204), _1437212), _1437210)))], (35143 ^ _777081) ^ [_1437699, _1437701, _1437703] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1437699), _1437701)), 35146 ^ _777081 : [(35157 ^ _777081) ^ [] : [35159 ^ _777081 : [(35160 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1437699), 35158 ^ [_1437699, _1437701, _1437703]), _1437701)))], (35162 ^ _777081) ^ [] : [hAPP(_1437703, 35158 ^ [_1437699, _1437701, _1437703]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437699, tc_Nat_Onat), _1437703), _1437701) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35147 ^ _777081) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1437699, tc_Nat_Onat), _1437703), _1437701) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 35150 ^ _777081 : [(35151 ^ _777081) ^ [_1437861] : [hBOOL(hAPP(hAPP(c_member(_1437699), _1437861), _1437701)), -(hAPP(_1437703, _1437861) = 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[hBOOL(hAPP(c_Finite__Set_Ofinite(_1440071), _1440073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1440071, tc_HOL_Obool)), _1440073), _1440075)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440071, tc_Nat_Onat), _1440077), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1440071, tc_HOL_Obool)), _1440075), _1440073)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440071, tc_Nat_Onat), _1440077), _1440075)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440071, tc_Nat_Onat), _1440077), _1440073)))], (35272 ^ _777081) ^ [_1440324, _1440326, _1440328] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1440324), _1440326), _1440328) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1440324), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1440324, tc_Int_Oint), _1440326), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1440328))), class_Groups_Ocomm__monoid__add(_1440324), class_Groups_Ocomm__monoid__mult(_1440324)], (35282 ^ _777081) ^ [_1440530, _1440532, _1440534, _1440536] : [hBOOL(hAPP(hAPP(c_member(_1440530), _1440532), _1440534)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440530, tc_Nat_Onat), _1440536), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1440530, tc_HOL_Obool)), _1440534), hAPP(hAPP(c_Set_Oinsert(_1440530), _1440532), c_Orderings_Obot__class_Obot(tc_fun(_1440530, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440530, tc_Nat_Onat), _1440536), _1440534)), hAPP(_1440536, _1440532)))], (35288 ^ _777081) ^ [_1440721, _1440723, _1440725, _1440727] : [-(hBOOL(hAPP(hAPP(c_member(_1440721), _1440723), _1440725))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440721, tc_Nat_Onat), _1440727), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1440721, tc_HOL_Obool)), _1440725), hAPP(hAPP(c_Set_Oinsert(_1440721), _1440723), c_Orderings_Obot__class_Obot(tc_fun(_1440721, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440721, tc_Nat_Onat), _1440727), _1440725))], (35294 ^ _777081) ^ [_1440812, _1440814, _1440816, _1440818] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1440812), _1440814)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1440812), _1440816)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440812, tc_Nat_Onat), _1440818), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1440812, tc_HOL_Obool)), _1440814), _1440816)) = 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(_1440812, tc_Nat_Onat), _1440818), _1440814)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1440812, tc_Nat_Onat), _1440818), 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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), _1441350)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1441352))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1441354))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1441354), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1441350), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1441350), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1441354), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1441352)))))], (35320 ^ _777081) ^ [_1441431, _1441433, _1441435] : [35322 ^ _777081 : [(35323 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1441431), 35321 ^ [_1441431, _1441433, _1441435]), _1441433)))], (35325 ^ _777081) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1441435, 35321 ^ [_1441431, _1441433, _1441435]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1441431, tc_Int_Oint), _1441435), _1441433) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1441431, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1441431), c_Int_Onat), _1441435)), _1441433)))], (35329 ^ _777081) ^ [_1441661, _1441663, _1441665, _1441667, _1441669] : [class_Groups_Ocomm__monoid__add(_1441661), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441663), _1441665)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1441663), _1441667)), 35343 ^ _777081 : [(35344 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1441663), 35342 ^ [_1441661, _1441663, _1441665, _1441667, _1441669]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1441663, tc_HOL_Obool)), _1441665), _1441667))))], (35346 ^ _777081) ^ [] : [hAPP(_1441669, 35342 ^ [_1441661, _1441663, _1441665, _1441667, _1441669]) = c_Groups_Ozero__class_Ozero(_1441661)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1441663, _1441661), _1441669), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1441663, tc_HOL_Obool)), _1441665), _1441667)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1441661), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1441663, _1441661), _1441669), _1441665)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1441663, _1441661), _1441669), _1441667)))], (35350 ^ _777081) ^ [_1442156, _1442158, _1442160, _1442162, _1442164] : [class_Groups_Ocomm__monoid__add(_1442156), class_Groups_Oordered__ab__semigroup__add(_1442156), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442158), _1442160)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1442158, tc_HOL_Obool)), _1442162), _1442160)), 35368 ^ _777081 : [(35369 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1442158), 35367 ^ [_1442156, _1442158, _1442160, _1442162, _1442164]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1442158, tc_HOL_Obool)), _1442160), _1442162))))], (35371 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442156), c_Groups_Ozero__class_Ozero(_1442156)), hAPP(_1442164, 35367 ^ [_1442156, _1442158, _1442160, _1442162, _1442164])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442156), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1442158, _1442156), _1442164), _1442162)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1442158, _1442156), _1442164), _1442160))))], (35375 ^ _777081) ^ [_1442700, _1442702, _1442704, _1442706, _1442708, _1442710] : [class_Groups_Oordered__ab__group__add(_1442700), hBOOL(hAPP(c_Finite__Set_Ofinite(_1442702), _1442704)), 35385 ^ _777081 : [(35386 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1442702), 35384 ^ [_1442700, _1442702, _1442704, _1442706, _1442708, _1442710]), _1442704)))], (35388 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442700), c_Groups_Ozero__class_Ozero(_1442700)), hAPP(_1442706, 35384 ^ [_1442700, _1442702, _1442704, _1442706, _1442708, _1442710])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1442702, _1442700), _1442706), _1442704) = _1442708, hBOOL(hAPP(hAPP(c_member(_1442702), _1442710), _1442704)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442700), hAPP(_1442706, _1442710)), _1442708)))], (35400 ^ _777081) ^ [_1443220, _1443222, _1443224, _1443226, _1443228] : [class_Groups_Oordered__ab__group__add(_1443220), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443222), _1443224)), 35410 ^ _777081 : [(35411 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1443222), 35409 ^ [_1443220, _1443222, _1443224, _1443226, _1443228]), _1443224)))], (35413 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1443220), c_Groups_Ozero__class_Ozero(_1443220)), hAPP(_1443226, 35409 ^ [_1443220, _1443222, _1443224, _1443226, _1443228])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443222, _1443220), _1443226), _1443224) = c_Groups_Ozero__class_Ozero(_1443220), hBOOL(hAPP(hAPP(c_member(_1443222), _1443228), _1443224)), -(hAPP(_1443226, _1443228) = c_Groups_Ozero__class_Ozero(_1443220))], (35425 ^ _777081) ^ [_1443718, _1443720, _1443722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1443718, 35426 ^ [_1443718, _1443720, _1443722])), hAPP(_1443720, 35426 ^ [_1443718, _1443720, _1443722]))), -(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), _1443720), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1443722))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1443718), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1443722))) = 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)), _1443720)), _1443718)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1443722)))], (35432 ^ _777081) ^ [_1443951, _1443953, _1443955, _1443957, _1443959] : [class_Groups_Ocomm__monoid__add(_1443951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1443953), _1443955)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1443953, tc_HOL_Obool)), _1443957), _1443955)), 35446 ^ _777081 : [(35447 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1443953), 35445 ^ [_1443951, _1443953, _1443955, _1443957, _1443959]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1443953, tc_HOL_Obool)), _1443955), _1443957))))], (35449 ^ _777081) ^ [] : [hAPP(_1443959, 35445 ^ [_1443951, _1443953, _1443955, _1443957, _1443959]) = c_Groups_Ozero__class_Ozero(_1443951)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443953, _1443951), _1443959), _1443957) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1443953, _1443951), _1443959), _1443955))], (35453 ^ _777081) ^ [_1444402, _1444404, _1444406, _1444408, _1444410] : [class_Groups_Ocomm__monoid__add(_1444402), hBOOL(hAPP(c_Finite__Set_Ofinite(_1444404), _1444406)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1444404, tc_HOL_Obool)), _1444408), _1444406)), 35467 ^ _777081 : [(35468 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1444404), 35466 ^ [_1444402, _1444404, _1444406, _1444408, _1444410]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1444404, tc_HOL_Obool)), _1444406), _1444408))))], (35470 ^ _777081) ^ [] : [hAPP(_1444410, 35466 ^ [_1444402, _1444404, _1444406, _1444408, _1444410]) = c_Groups_Ozero__class_Ozero(_1444402)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444404, _1444402), _1444410), _1444406) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1444404, _1444402), _1444410), _1444408))], (35474 ^ _777081) ^ [_1444853, _1444855, _1444857, _1444859] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1444853), _1444855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1444853, tc_HOL_Obool)), _1444855), _1444857)), hBOOL(hAPP(_1444859, c_Orderings_Obot__class_Obot(tc_fun(_1444853, tc_HOL_Obool)))), 35489 ^ _777081 : [(35490 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1444853), 35488 ^ [_1444853, _1444855, _1444857, _1444859])))], (35492 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1444853), 35487 ^ [_1444853, _1444855, _1444857, _1444859]), _1444857)))], (35494 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1444853), 35487 ^ [_1444853, _1444855, _1444857, _1444859]), 35488 ^ [_1444853, _1444855, _1444857, _1444859]))], (35496 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1444859, 35488 ^ [_1444853, _1444855, _1444857, _1444859])))], (35498 ^ _777081) ^ [] : [hBOOL(hAPP(_1444859, hAPP(hAPP(c_Set_Oinsert(_1444853), 35487 ^ [_1444853, _1444855, _1444857, _1444859]), 35488 ^ [_1444853, _1444855, _1444857, _1444859])))]], -(hBOOL(hAPP(_1444859, _1444855)))], (35502 ^ _777081) ^ [_1445518, _1445520, _1445522, _1445524, _1445526] : [class_Groups_Ocomm__monoid__add(_1445518), class_Groups_Oordered__cancel__ab__semigroup__add(_1445518), hBOOL(hAPP(c_Finite__Set_Ofinite(_1445520), _1445522)), -(_1445522 = c_Orderings_Obot__class_Obot(tc_fun(_1445520, tc_HOL_Obool))), 35520 ^ _777081 : [(35521 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1445520), 35519 ^ [_1445518, _1445520, _1445522, _1445524, _1445526]), _1445522)))], (35523 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1445518), hAPP(_1445524, 35519 ^ [_1445518, _1445520, _1445522, _1445524, _1445526])), hAPP(_1445526, 35519 ^ [_1445518, _1445520, _1445522, _1445524, _1445526])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1445518), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1445520, _1445518), _1445524), _1445522)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1445520, _1445518), _1445526), _1445522))))], (35527 ^ _777081) ^ [_1446049, _1446051, _1446053] : [class_Fields_Olinordered__field__inverse__zero(_1446049), 35533 ^ _777081 : [(35534 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446049), c_Groups_Ozero__class_Ozero(_1446049)), 35532 ^ [_1446049, _1446051, _1446053])))], (35536 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1446049), 35532 ^ [_1446049, _1446051, _1446053]), c_Groups_Oone__class_Oone(_1446049))))], (35538 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1446049), 35532 ^ [_1446049, _1446051, _1446053]), _1446051)), _1446053))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1446049), _1446051), _1446053)))], (35542 ^ _777081) ^ [_1446398, _1446400, _1446402, _1446404, _1446406, _1446408] : [class_Groups_Ocomm__monoid__add(_1446398), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446400), _1446402)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1446404), _1446406)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_sum(_1446400, _1446404), _1446398), _1446408), c_Sum__Type_OPlus(_1446400, _1446404, _1446402, _1446406)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1446398), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1446400, _1446398), hAPP(c_Fun_Ocomp(tc_sum(_1446400, _1446404), _1446398, _1446400, _1446408), c_Sum__Type_OInl(_1446400, _1446404))), _1446402)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1446404, _1446398), hAPP(c_Fun_Ocomp(tc_sum(_1446400, _1446404), _1446398, _1446404, _1446408), c_Sum__Type_OInr(_1446404, _1446400))), _1446406)))], (35556 ^ _777081) ^ [_1446759, _1446761, _1446763, _1446765, _1446767, _1446769] : [-(hAPP(c_Set_Oimage(_1446759, _1446761, hAPP(c_Fun_Ocomp(_1446763, _1446761, _1446759, _1446765), _1446767)), _1446769) = hAPP(c_Set_Oimage(_1446763, _1446761, _1446765), hAPP(c_Set_Oimage(_1446759, _1446763, _1446767), _1446769)))], (35558 ^ _777081) ^ [_1446821, _1446823, _1446825, _1446827, _1446829, _1446831, _1446833] : [-(hAPP(c_Product__Type_Oapfst(_1446821, _1446823, _1446825, _1446827), hAPP(c_Product__Type_Oapfst(_1446829, _1446821, _1446825, _1446831), _1446833)) = hAPP(c_Product__Type_Oapfst(_1446829, _1446823, _1446825, hAPP(c_Fun_Ocomp(_1446821, _1446823, _1446829, _1446827), _1446831)), _1446833))], (35560 ^ _777081) ^ [_1446888, _1446890, _1446892, _1446894, _1446896, _1446898, _1446900] : [-(hAPP(c_Fun_Ocomp(_1446888, _1446890, _1446892, _1446894), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1446892, _1446888), _1446896), _1446898), _1446900)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1446892, _1446890), hAPP(c_Fun_Ocomp(_1446888, _1446890, _1446892, _1446894), _1446896)), _1446898), hAPP(_1446894, _1446900)))], (35562 ^ _777081) ^ [_1446966, _1446968, _1446970, _1446972, _1446974, _1446976] : [-(hAPP(c_Set_Ovimage(_1446966, _1446968, hAPP(c_Fun_Ocomp(_1446970, _1446968, _1446966, _1446972), _1446974)), _1446976) = hAPP(c_Set_Ovimage(_1446966, _1446970, _1446974), hAPP(c_Set_Ovimage(_1446970, _1446968, _1446972), _1446976)))], (35564 ^ _777081) ^ [_1447028, _1447030, _1447032, _1447034, _1447036, _1447038] : [-(hAPP(hAPP(c_Fun_Ocomp(_1447028, _1447030, _1447032, _1447034), _1447036), _1447038) = hAPP(_1447034, hAPP(_1447036, _1447038)))], (35566 ^ _777081) ^ [_1447078, _1447080, _1447082, _1447084, _1447086] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1447078), tc_Option_Ooption(_1447080), tc_Option_Ooption(_1447082), hAPP(c_Option_Omap(_1447078, _1447080), _1447084)), hAPP(c_Option_Omap(_1447082, _1447078), _1447086)) = hAPP(c_Option_Omap(_1447082, _1447080), hAPP(c_Fun_Ocomp(_1447078, _1447080, _1447082, _1447084), _1447086)))], (35568 ^ _777081) ^ [_1447149, _1447151, _1447153, _1447155, _1447157, _1447159, _1447161] : [-(hAPP(c_Fun_Ocomp(_1447149, _1447151, _1447153, _1447155), hAPP(c_Fun_Ocomp(_1447157, _1447149, _1447153, _1447159), _1447161)) = hAPP(c_Fun_Ocomp(_1447157, _1447151, _1447153, hAPP(c_Fun_Ocomp(_1447149, _1447151, _1447157, _1447155), _1447159)), _1447161))], (35570 ^ _777081) ^ [_1447216, _1447218, _1447220, _1447222, _1447224, _1447226] : [-(hAPP(hAPP(c_Fun_Ocomp(_1447216, _1447218, _1447220, _1447222), _1447224), _1447226) = hAPP(_1447222, hAPP(_1447224, _1447226)))], (35572 ^ _777081) ^ [_1447266, _1447268, _1447270, _1447272, _1447274, _1447276, _1447278, _1447280, _1447282] : [hAPP(c_Fun_Ocomp(_1447266, _1447268, _1447270, _1447272), _1447274) = hAPP(c_Fun_Ocomp(_1447276, _1447268, _1447270, _1447278), _1447280), -(hAPP(_1447272, hAPP(_1447274, _1447282)) = hAPP(_1447278, hAPP(_1447280, _1447282)))], (35578 ^ _777081) ^ [_1447413, _1447415, _1447417, _1447419, _1447421, _1447423, _1447425, _1447427] : [hAPP(c_Fun_Ocomp(_1447413, _1447415, _1447417, _1447419), _1447421) = hAPP(c_Fun_Ocomp(_1447423, _1447415, _1447417, _1447425), _1447427), 35581 ^ _777081 : [(35582 ^ _777081) ^ [_1447528] : [-(hAPP(_1447419, hAPP(_1447421, _1447528)) = hAPP(_1447425, hAPP(_1447427, _1447528)))]]], (35584 ^ _777081) ^ [_1447567, _1447569, _1447571, _1447573, _1447575, _1447577, _1447579, _1447581, _1447583, _1447585, _1447587] : [hAPP(_1447567, hAPP(_1447569, _1447571)) = hAPP(_1447573, hAPP(_1447575, _1447577)), -(hAPP(hAPP(c_Fun_Ocomp(_1447579, _1447581, _1447583, _1447567), _1447569), _1447571) = hAPP(hAPP(c_Fun_Ocomp(_1447585, _1447581, _1447587, _1447573), _1447575), _1447577))], (35590 ^ _777081) ^ [_1447730, _1447732, _1447734, _1447736, _1447738, _1447740, _1447742] : [hAPP(c_Fun_Ocomp(_1447730, _1447732, _1447734, _1447736), _1447738) = _1447740, -(hAPP(_1447736, hAPP(_1447738, _1447742)) = hAPP(_1447740, _1447742))], (35596 ^ _777081) ^ [_1447851, _1447853, _1447855, _1447857, _1447859, _1447861] : [-(hAPP(hAPP(c_Fun_Ocomp(_1447851, _1447853, _1447855, hAPP(c_COMBK(_1447853, _1447851), _1447857)), _1447859), _1447861) = _1447857)], (35598 ^ _777081) ^ [_1447901, _1447903, _1447905, _1447907, _1447909, _1447911] : [-(hAPP(hAPP(c_Option_Omap(_1447901, _1447903), _1447905), hAPP(hAPP(c_Option_Omap(_1447907, _1447901), _1447909), _1447911)) = hAPP(hAPP(c_Option_Omap(_1447907, _1447903), hAPP(c_Fun_Ocomp(_1447901, _1447903, _1447907, _1447905), _1447909)), _1447911))], (35600 ^ _777081) ^ [_1447969, _1447971, _1447973, _1447975, _1447977, _1447979] : [-(hAPP(hAPP(c_Option_Omap(_1447969, _1447971), _1447973), hAPP(hAPP(c_Option_Omap(_1447975, _1447969), _1447977), _1447979)) = hAPP(hAPP(c_Option_Omap(_1447975, _1447971), hAPP(c_Fun_Ocomp(_1447969, _1447971, _1447975, _1447973), _1447977)), _1447979))], (35602 ^ _777081) ^ [_1448037, _1448039, _1448041, _1448043, _1448045, _1448047] : [c_Fun_Oinj__on(_1448037, _1448039, hAPP(c_Fun_Ocomp(_1448041, _1448039, _1448037, _1448043), _1448045), _1448047), -(c_Fun_Oinj__on(_1448037, _1448041, _1448045, _1448047))], (35608 ^ _777081) ^ [_1448146, _1448148, _1448150, _1448152, _1448154, _1448156, _1448158] : [-(hAPP(c_Product__Type_Oapsnd(_1448146, _1448148, _1448150, _1448152), hAPP(c_Product__Type_Oapsnd(_1448154, _1448146, _1448150, _1448156), _1448158)) = hAPP(c_Product__Type_Oapsnd(_1448154, _1448148, _1448150, hAPP(c_Fun_Ocomp(_1448146, _1448148, _1448154, _1448152), _1448156)), _1448158))], (35610 ^ _777081) ^ [_1448213, _1448215, _1448217, _1448219, _1448221] : [hAPP(c_Set_Oimage(_1448213, _1448215, _1448217), c_Orderings_Otop__class_Otop(tc_fun(_1448213, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1448215, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1448215, _1448219, _1448221), c_Orderings_Otop__class_Otop(tc_fun(_1448215, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1448219, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1448213, _1448219, hAPP(c_Fun_Ocomp(_1448215, _1448219, _1448213, _1448221), _1448217)), c_Orderings_Otop__class_Otop(tc_fun(_1448213, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1448219, tc_HOL_Obool)))], (35620 ^ _777081) ^ [_1448472, _1448474, _1448476, _1448478, _1448480, _1448482] : [c_Fun_Oinj__on(_1448472, _1448474, _1448476, _1448478), 35623 ^ _777081 : [(35624 ^ _777081) ^ [] : [c_Fun_Oinj__on(_1448474, _1448480, _1448482, hAPP(c_Set_Oimage(_1448472, _1448474, _1448476), _1448478)), -(c_Fun_Oinj__on(_1448472, _1448480, hAPP(c_Fun_Ocomp(_1448474, _1448480, _1448472, _1448482), _1448476), _1448478))], (35630 ^ _777081) ^ [] : [c_Fun_Oinj__on(_1448472, _1448480, hAPP(c_Fun_Ocomp(_1448474, _1448480, _1448472, _1448482), _1448476), _1448478), -(c_Fun_Oinj__on(_1448474, _1448480, _1448482, hAPP(c_Set_Oimage(_1448472, _1448474, _1448476), _1448478)))]]], (35636 ^ _777081) ^ [_1448764, _1448766, _1448768, _1448770, _1448772, _1448774] : [c_Fun_Oinj__on(_1448764, _1448766, _1448768, _1448770), c_Fun_Oinj__on(_1448766, _1448772, _1448774, hAPP(c_Set_Oimage(_1448764, _1448766, _1448768), _1448770)), -(c_Fun_Oinj__on(_1448764, _1448772, hAPP(c_Fun_Ocomp(_1448766, _1448772, _1448764, _1448774), _1448768), _1448770))], (35646 ^ _777081) ^ [_1448951, _1448953, _1448955, _1448957, _1448959, _1448961] : [c_Fun_Oinj__on(_1448951, _1448953, hAPP(c_Fun_Ocomp(_1448955, _1448953, _1448951, _1448957), _1448959), _1448961), -(c_Fun_Oinj__on(_1448955, _1448953, _1448957, hAPP(c_Set_Oimage(_1448951, _1448955, _1448959), _1448961)))], (35652 ^ _777081) ^ [_1449074, _1449076, _1449078, _1449080, _1449082] : [c_Fun_Oinj__on(_1449074, _1449076, _1449078, c_Orderings_Otop__class_Otop(tc_fun(_1449074, tc_HOL_Obool))), c_Fun_Oinj__on(_1449080, _1449074, _1449082, c_Orderings_Otop__class_Otop(tc_fun(_1449080, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1449080, _1449076, hAPP(c_Fun_Ocomp(_1449074, _1449076, _1449080, _1449078), _1449082), c_Orderings_Otop__class_Otop(tc_fun(_1449080, tc_HOL_Obool))))], (35662 ^ _777081) ^ [_1449273, _1449275, _1449277, _1449279, _1449281, _1449283] : [class_Groups_Ocomm__monoid__add(_1449273), c_Fun_Oinj__on(_1449275, _1449277, _1449279, _1449281), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1449277, _1449273), _1449283), hAPP(c_Set_Oimage(_1449275, _1449277, _1449279), _1449281)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1449275, _1449273), hAPP(c_Fun_Ocomp(_1449277, _1449273, _1449275, _1449283), _1449279)), _1449281))], (35672 ^ _777081) ^ [_1449486, _1449488, _1449490, _1449492, _1449494, _1449496] : [class_Groups_Ocomm__monoid__mult(_1449486), c_Fun_Oinj__on(_1449488, _1449490, _1449492, _1449494), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1449490, _1449486), _1449496), hAPP(c_Set_Oimage(_1449488, _1449490, _1449492), _1449494)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1449488, _1449486), hAPP(c_Fun_Ocomp(_1449490, _1449486, _1449488, _1449496), _1449492)), _1449494))], (35682 ^ _777081) ^ [_1449699, _1449701, _1449703, _1449705, _1449707, _1449709, _1449711, _1449713] : [class_Groups_Ocomm__monoid__mult(_1449699), c_Fun_Oinj__on(_1449701, _1449703, _1449705, _1449707), _1449709 = hAPP(c_Set_Oimage(_1449701, _1449703, _1449705), _1449707), _1449711 = hAPP(c_Fun_Ocomp(_1449703, _1449699, _1449701, _1449713), _1449705), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1449703, _1449699), _1449713), _1449709) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1449701, _1449699), _1449711), _1449707))], (35700 ^ _777081) ^ [_1450048, _1450050, _1450052, _1450054, _1450056] : [class_Groups_Ocomm__monoid__add(_1450048), hBOOL(hAPP(c_Finite__Set_Ofinite(_1450050), _1450052)), c_Fun_Oinj__on(_1450050, _1450050, _1450054, _1450052), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1450050, _1450048), _1450056), hAPP(c_Set_Oimage(_1450050, _1450050, _1450054), _1450052)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1450050, _1450048), hAPP(c_Fun_Ocomp(_1450050, _1450048, _1450050, _1450056), _1450054)), _1450052))], (35714 ^ _777081) ^ [_1450323, _1450325, _1450327, _1450329, _1450331] : [class_Groups_Ocomm__monoid__mult(_1450323), hBOOL(hAPP(c_Finite__Set_Ofinite(_1450325), _1450327)), c_Fun_Oinj__on(_1450325, _1450325, _1450329, _1450327), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1450325, _1450323), _1450331), hAPP(c_Set_Oimage(_1450325, _1450325, _1450329), _1450327)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1450325, _1450323), hAPP(c_Fun_Ocomp(_1450325, _1450323, _1450325, _1450331), _1450329)), _1450327))], (35728 ^ _777081) ^ [_1450598, _1450600, _1450602, _1450604, _1450606, _1450608, _1450610] : [c_Fun_Oinj__on(_1450598, _1450600, _1450602, hAPP(c_Set_Oimage(_1450604, _1450598, _1450606), _1450608)), c_Fun_Oinj__on(_1450604, _1450598, _1450606, _1450608), hBOOL(hAPP(hAPP(c_member(_1450600), _1450610), hAPP(c_Set_Oimage(_1450598, _1450600, _1450602), hAPP(c_Set_Oimage(_1450604, _1450598, _1450606), _1450608)))), -(hAPP(c_Fun_Othe__inv__into(_1450604, _1450600, _1450608, hAPP(c_Fun_Ocomp(_1450598, _1450600, _1450604, _1450602), _1450606)), _1450610) = hAPP(hAPP(c_Fun_Ocomp(_1450598, _1450604, _1450600, c_Fun_Othe__inv__into(_1450604, _1450598, _1450608, _1450606)), c_Fun_Othe__inv__into(_1450598, _1450600, hAPP(c_Set_Oimage(_1450604, _1450598, _1450606), _1450608), _1450602)), _1450610))], (35742 ^ _777081) ^ [_1450961, _1450963, _1450965, _1450967, _1450969, _1450971, _1450973] : [class_Groups_Oab__semigroup__mult(_1450961), hBOOL(hAPP(c_Finite__Set_Ofinite(_1450963), _1450965)), c_Fun_Oinj__on(_1450963, _1450967, _1450969, _1450965), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1450961, _1450967, c_Groups_Otimes__class_Otimes(_1450961)), _1450971), _1450973), hAPP(c_Set_Oimage(_1450963, _1450967, _1450969), _1450965)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1450961, _1450963, c_Groups_Otimes__class_Otimes(_1450961)), hAPP(c_Fun_Ocomp(_1450967, _1450961, _1450963, _1450971), _1450969)), _1450973), _1450965))], (35756 ^ _777081) ^ [_1451272, _1451274, _1451276, _1451278, _1451280, _1451282] : [c_Finite__Set_Ofolding(_1451272, _1451274, _1451276, _1451278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451272), _1451280)), hBOOL(hAPP(hAPP(c_member(_1451272), _1451282), _1451280)), -(hAPP(_1451278, _1451280) = hAPP(c_Fun_Ocomp(_1451274, _1451274, _1451274, hAPP(_1451278, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1451272, tc_HOL_Obool)), _1451280), hAPP(hAPP(c_Set_Oinsert(_1451272), _1451282), c_Orderings_Obot__class_Obot(tc_fun(_1451272, tc_HOL_Obool)))))), hAPP(_1451276, _1451282)))], (35770 ^ _777081) ^ [_1451585, _1451587, _1451589, _1451591, _1451593, _1451595, _1451597, _1451599] : [c_Finite__Set_Ofolding__image(_1451585, _1451587, _1451589, _1451591, _1451593), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451587), _1451595)), c_Fun_Oinj__on(_1451587, _1451587, _1451597, _1451595), -(hAPP(hAPP(_1451593, _1451599), hAPP(c_Set_Oimage(_1451587, _1451587, _1451597), _1451595)) = hAPP(hAPP(_1451593, hAPP(c_Fun_Ocomp(_1451587, _1451585, _1451587, _1451599), _1451597)), _1451595))], (35784 ^ _777081) ^ [_1451874, _1451876, _1451878, _1451880, _1451882, _1451884] : [c_Finite__Set_Ofolding(_1451874, _1451876, _1451878, _1451880), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451874), _1451882)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1451874), _1451884)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1451874, tc_HOL_Obool)), _1451882), _1451884) = c_Orderings_Obot__class_Obot(tc_fun(_1451874, tc_HOL_Obool)), -(hAPP(_1451880, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451874, tc_HOL_Obool)), _1451882), _1451884)) = hAPP(c_Fun_Ocomp(_1451876, _1451876, _1451876, hAPP(_1451880, _1451882)), hAPP(_1451880, _1451884)))], (35802 ^ _777081) ^ [_1452247, _1452249, _1452251, _1452253, _1452255, _1452257, _1452259] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1452247), tc_Option_Ooption(_1452249), tc_sum(_1452251, _1452253), hAPP(c_Option_Omap(_1452247, _1452249), _1452255)), c_Sum__Type_Osum_Osum__case(_1452251, tc_Option_Ooption(_1452247), _1452253, _1452257, _1452259)) = c_Sum__Type_Osum_Osum__case(_1452251, tc_Option_Ooption(_1452249), _1452253, hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1452247), tc_Option_Ooption(_1452249), _1452251, hAPP(c_Option_Omap(_1452247, _1452249), _1452255)), _1452257), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1452247), tc_Option_Ooption(_1452249), _1452253, hAPP(c_Option_Omap(_1452247, _1452249), _1452255)), _1452259)))], (35804 ^ _777081) ^ [_1452355, _1452357, _1452359, _1452361, _1452363, _1452365, _1452367, _1452369, _1452371, _1452373, _1452375] : [c_Finite__Set_Ofolding(_1452355, _1452357, _1452359, _1452361), -(hAPP(c_Fun_Ocomp(_1452363, _1452365, _1452367, _1452369), hAPP(c_Fun_Ocomp(_1452371, _1452363, _1452367, _1452373), _1452375)) = hAPP(c_Fun_Ocomp(_1452371, _1452365, _1452367, hAPP(c_Fun_Ocomp(_1452363, _1452365, _1452371, _1452369), _1452373)), _1452375))], (35810 ^ _777081) ^ [_1452518, _1452520, _1452522, _1452524, _1452526, _1452528] : [c_Finite__Set_Ofolding(_1452518, _1452520, _1452522, _1452524), -(hAPP(c_Fun_Ocomp(_1452520, _1452520, _1452520, hAPP(_1452522, _1452526)), hAPP(_1452522, _1452528)) = hAPP(c_Fun_Ocomp(_1452520, _1452520, _1452520, hAPP(_1452522, _1452528)), hAPP(_1452522, _1452526)))], (35816 ^ _777081) ^ [_1452663, _1452665, _1452667, _1452669, _1452671, _1452673, _1452675, _1452677] : [c_Finite__Set_Ofolding(_1452663, _1452665, _1452667, _1452669), -(hAPP(c_Fun_Ocomp(_1452665, _1452665, _1452671, hAPP(_1452667, _1452673)), hAPP(c_Fun_Ocomp(_1452665, _1452665, _1452671, hAPP(_1452667, _1452675)), _1452677)) = hAPP(c_Fun_Ocomp(_1452665, _1452665, _1452671, hAPP(_1452667, _1452675)), hAPP(c_Fun_Ocomp(_1452665, _1452665, _1452671, hAPP(_1452667, _1452673)), _1452677)))], (35822 ^ _777081) ^ [_1452844, _1452846, _1452848, _1452850, _1452852] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1452844), tc_Option_Ooption(_1452846), _1452848, hAPP(c_Option_Omap(_1452844, _1452846), _1452850)), hAPP(c_COMBK(tc_Option_Ooption(_1452844), _1452848), c_Option_Ooption_ONone(_1452844))), _1452852) = c_Option_Ooption_ONone(_1452846))], (35824 ^ _777081) ^ [_1452908, _1452910, _1452912, _1452914, _1452916, _1452918, _1452920, _1452922] : [c_Finite__Set_Ofolding__image(_1452908, _1452910, _1452912, _1452914, _1452916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1452910), _1452918)), -(hAPP(hAPP(_1452916, hAPP(hAPP(c_COMBS(_1452910, _1452908, _1452908), hAPP(hAPP(c_COMBB(_1452908, tc_fun(_1452908, _1452908), _1452910), _1452912), _1452920)), _1452922)), _1452918) = hAPP(hAPP(_1452912, hAPP(hAPP(_1452916, _1452920), _1452918)), hAPP(hAPP(_1452916, _1452922), _1452918)))], (35834 ^ _777081) ^ [_1453169, _1453171, _1453173, _1453175, _1453177, _1453179, _1453181] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1453169, _1453171, _1453173), hAPP(c_Fun_Ocomp(_1453175, tc_fun(_1453171, _1453173), _1453169, _1453177), _1453179)), _1453181) = hAPP(hAPP(_1453177, hAPP(_1453179, hAPP(c_Product__Type_Ofst(_1453169, _1453171), _1453181))), hAPP(c_Product__Type_Osnd(_1453169, _1453171), _1453181)))], (35836 ^ _777081) ^ [_1453246, _1453248, _1453250, _1453252, _1453254, _1453256, _1453258] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1453246), tc_Option_Ooption(_1453248), _1453250, hAPP(c_Option_Omap(_1453246, _1453248), _1453252)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1453250, tc_Option_Ooption(_1453246)), _1453254), _1453256), hAPP(c_Option_Ooption_OSome(_1453246), _1453258))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1453250, tc_Option_Ooption(_1453248)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1453246), tc_Option_Ooption(_1453248), _1453250, hAPP(c_Option_Omap(_1453246, _1453248), _1453252)), _1453254)), _1453256), hAPP(c_Option_Ooption_OSome(_1453248), hAPP(_1453252, _1453258))))], (35838 ^ _777081) ^ [_1453358, _1453360, _1453362, _1453364, _1453366, _1453368] : [c_Finite__Set_Ofolding(_1453358, _1453360, _1453362, _1453364), hBOOL(hAPP(c_Finite__Set_Ofinite(_1453358), _1453366)), -(hAPP(c_Fun_Ocomp(_1453360, _1453360, _1453360, hAPP(_1453362, _1453368)), hAPP(_1453364, _1453366)) = hAPP(c_Fun_Ocomp(_1453360, _1453360, _1453360, hAPP(_1453364, _1453366)), hAPP(_1453362, _1453368)))], (35848 ^ _777081) ^ [_1453571, _1453573, _1453575, _1453577, _1453579, _1453581, _1453583, _1453585] : [c_Finite__Set_Ofolding(_1453571, _1453573, _1453575, _1453577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1453571), _1453579)), -(hAPP(c_Fun_Ocomp(_1453573, _1453573, _1453581, hAPP(_1453575, _1453583)), hAPP(c_Fun_Ocomp(_1453573, _1453573, _1453581, hAPP(_1453577, _1453579)), _1453585)) = hAPP(c_Fun_Ocomp(_1453573, _1453573, _1453581, hAPP(_1453577, _1453579)), hAPP(c_Fun_Ocomp(_1453573, _1453573, _1453581, hAPP(_1453575, _1453583)), _1453585)))], (35858 ^ _777081) ^ [_1453824, _1453826, _1453828, _1453830, _1453832, _1453834] : [c_Finite__Set_Ofolding(_1453824, _1453826, _1453828, _1453830), hBOOL(hAPP(c_Finite__Set_Ofinite(_1453824), _1453832)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1453824), _1453834)), -(hAPP(c_Fun_Ocomp(_1453826, _1453826, _1453826, hAPP(_1453830, _1453834)), hAPP(_1453830, _1453832)) = hAPP(c_Fun_Ocomp(_1453826, _1453826, _1453826, hAPP(_1453830, _1453832)), hAPP(_1453830, _1453834)))], (35872 ^ _777081) ^ [_1454105, _1454107, _1454109, _1454111, _1454113, _1454115, _1454117, _1454119] : [c_Finite__Set_Ofolding(_1454105, _1454107, _1454109, _1454111), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454105), _1454113)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454105), _1454115)), -(hAPP(c_Fun_Ocomp(_1454107, _1454107, _1454117, hAPP(_1454111, _1454115)), hAPP(c_Fun_Ocomp(_1454107, _1454107, _1454117, hAPP(_1454111, _1454113)), _1454119)) = hAPP(c_Fun_Ocomp(_1454107, _1454107, _1454117, hAPP(_1454111, _1454113)), hAPP(c_Fun_Ocomp(_1454107, _1454107, _1454117, hAPP(_1454111, _1454115)), _1454119)))], (35886 ^ _777081) ^ [_1454430, _1454432, _1454434, _1454436, _1454438, _1454440, _1454442] : [c_Finite__Set_Ofolding__image(_1454430, _1454432, _1454434, _1454436, _1454438), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454432), _1454440)), -(hAPP(hAPP(_1454438, _1454442), _1454440) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1454430, _1454432, _1454434), _1454442), _1454436), _1454440))], (35896 ^ _777081) ^ [_1454631, _1454633, _1454635, _1454637, _1454639, _1454641] : [c_Finite__Set_Ofolding(_1454631, _1454633, _1454635, _1454637), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454631), _1454639)), -(hBOOL(hAPP(hAPP(c_member(_1454631), _1454641), _1454639))), -(hAPP(_1454637, hAPP(hAPP(c_Set_Oinsert(_1454631), _1454641), _1454639)) = hAPP(c_Fun_Ocomp(_1454633, _1454633, _1454633, hAPP(_1454637, _1454639)), hAPP(_1454635, _1454641)))], (35910 ^ _777081) ^ [_1454867, _1454869, _1454871, _1454873, _1454875, _1454877] : [c_Finite__Set_Ofolding(_1454867, _1454869, _1454871, _1454873), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454867), _1454875)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1454867), _1454877)), -(hAPP(c_Fun_Ocomp(_1454869, _1454869, _1454869, hAPP(_1454873, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1454867, tc_HOL_Obool)), _1454875), _1454877))), hAPP(_1454873, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454867, tc_HOL_Obool)), _1454875), _1454877))) = hAPP(c_Fun_Ocomp(_1454869, _1454869, _1454869, hAPP(_1454873, _1454875)), hAPP(_1454873, _1454877)))], (35924 ^ _777081) ^ [_1455192, _1455194, _1455196, _1455198, _1455200, _1455202] : [c_Finite__Set_Ofolding(_1455192, _1455194, _1455196, _1455198), hBOOL(hAPP(c_Finite__Set_Ofinite(_1455192), _1455200)), -(hAPP(_1455198, hAPP(hAPP(c_Set_Oinsert(_1455192), _1455202), _1455200)) = hAPP(c_Fun_Ocomp(_1455194, _1455194, _1455194, hAPP(_1455198, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1455192, tc_HOL_Obool)), _1455200), hAPP(hAPP(c_Set_Oinsert(_1455192), _1455202), c_Orderings_Obot__class_Obot(tc_fun(_1455192, tc_HOL_Obool)))))), hAPP(_1455196, _1455202)))], (35934 ^ _777081) ^ [_1455447, _1455449, _1455451, _1455453, _1455455] : [c_Hoare__Mirabelle_Ohoare__valids(_1455447, _1455449, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1455447)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1455447), c_Hoare__Mirabelle_Opeek__and(_1455447, _1455451, _1455453)), _1455455), _1455451)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1455447), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__valids(_1455447, _1455449, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1455447)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1455447), _1455451), c_Com_Ocom_OWhile(_1455453, _1455455)), c_Hoare__Mirabelle_Opeek__and(_1455447, _1455451, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1455453)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1455447), tc_HOL_Obool)))))], (35940 ^ _777081) ^ [_1455674, _1455676, _1455678, _1455680, _1455682, _1455684, _1455686] : [c_Hoare__Mirabelle_Ohoare__derivs(_1455674, _1455676, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1455674)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1455674), c_Hoare__Mirabelle_Opeek__and(_1455674, _1455678, _1455680)), _1455682), _1455684)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1455674), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1455674, _1455676, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1455674)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1455674), c_Hoare__Mirabelle_Opeek__and(_1455674, _1455678, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1455680))), _1455686), _1455684)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1455674), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1455674, _1455676, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1455674)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1455674), _1455678), c_Com_Ocom_OCond(_1455680, _1455682, _1455686)), _1455684)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1455674), tc_HOL_Obool)))))], (35950 ^ _777081) ^ [_1456027, _1456029, _1456031, _1456033, _1456035] : [c_Hoare__Mirabelle_Ohoare__derivs(_1456027, _1456029, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1456027)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1456027), c_Hoare__Mirabelle_Opeek__and(_1456027, _1456031, _1456033)), _1456035), _1456031)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1456027), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1456027, _1456029, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1456027)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1456027), _1456031), c_Com_Ocom_OWhile(_1456033, _1456035)), c_Hoare__Mirabelle_Opeek__and(_1456027, _1456031, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1456033)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1456027), tc_HOL_Obool)))))], (35956 ^ _777081) ^ [_1456278, _1456280, _1456282, _1456284, _1456286] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1456278, _1456280, _1456282), _1456284), _1456286)), 35959 ^ _777081 : [(35960 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1456280, _1456284), _1456286)))], (35962 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1456282, _1456286)))]]], (35964 ^ _777081) ^ [_1456415, _1456417, _1456419, _1456421, _1456423] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1456415, _1456417, _1456419), _1456421), _1456423))), hBOOL(hAPP(hAPP(_1456417, _1456421), _1456423)), hBOOL(hAPP(_1456419, _1456423))], (35974 ^ _777081) ^ [_1456590, _1456592, _1456594, _1456596, _1456598, _1456600] : [class_Groups_Ocomm__monoid__add(_1456590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1456592), _1456594)), 35984 ^ _777081 : [(35985 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456592), 35983 ^ [_1456590, _1456592, _1456594, _1456596, _1456598, _1456600]), _1456594)))], (35988 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1456592), 35986 ^ [_1456590, _1456592, _1456594, _1456596, _1456598, _1456600]), _1456594)))], (35990 ^ _777081) ^ [] : [35983 ^ [_1456590, _1456592, _1456594, _1456596, _1456598, _1456600] = 35986 ^ [_1456590, _1456592, _1456594, _1456596, _1456598, _1456600]], (35992 ^ _777081) ^ [] : [-(hAPP(_1456596, 35983 ^ [_1456590, _1456592, _1456594, _1456596, _1456598, _1456600]) = hAPP(_1456596, 35986 ^ [_1456590, _1456592, _1456594, _1456596, _1456598, _1456600]))], (35994 ^ _777081) ^ [] : [hAPP(_1456598, hAPP(_1456596, 35983 ^ [_1456590, _1456592, _1456594, _1456596, _1456598, _1456600])) = c_Groups_Ozero__class_Ozero(_1456590)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456600, _1456590), _1456598), hAPP(c_Set_Oimage(_1456592, _1456600, _1456596), _1456594)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1456592, _1456590), hAPP(c_Fun_Ocomp(_1456600, _1456590, _1456592, _1456598), _1456596)), _1456594))], (35998 ^ _777081) ^ [_1457327, _1457329, _1457331, _1457333, _1457335, _1457337] : [c_Finite__Set_Ofolding__idem(_1457327, _1457329, _1457331, _1457333), hBOOL(hAPP(c_Finite__Set_Ofinite(_1457327), _1457335)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1457327), _1457337)), -(hAPP(_1457333, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1457327, tc_HOL_Obool)), _1457335), _1457337)) = hAPP(c_Fun_Ocomp(_1457329, _1457329, _1457329, hAPP(_1457333, _1457335)), hAPP(_1457333, _1457337)))], (36012 ^ _777081) ^ [_1457608, _1457610, _1457612, _1457614, _1457616, _1457618] : [c_Finite__Set_Ofolding__idem(_1457608, _1457610, _1457612, _1457614), hBOOL(hAPP(c_Finite__Set_Ofinite(_1457608), _1457616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1457608, tc_HOL_Obool)), _1457618), _1457616)), -(hAPP(c_Fun_Ocomp(_1457610, _1457610, _1457610, hAPP(_1457614, _1457616)), hAPP(_1457614, _1457618)) = hAPP(_1457614, _1457616))], (36026 ^ _777081) ^ [_1457879, _1457881, _1457883, _1457885, _1457887, _1457889, _1457891] : [c_Finite__Set_Ofolding__idem(_1457879, _1457881, _1457883, _1457885), -(hAPP(c_Fun_Ocomp(_1457881, _1457881, _1457887, hAPP(_1457883, _1457889)), hAPP(c_Fun_Ocomp(_1457881, _1457881, _1457887, hAPP(_1457883, _1457889)), _1457891)) = hAPP(c_Fun_Ocomp(_1457881, _1457881, _1457887, hAPP(_1457883, _1457889)), _1457891))], (36032 ^ _777081) ^ [_1458036, _1458038, _1458040, _1458042, _1458044] : [c_Finite__Set_Ofolding__idem(_1458036, _1458038, _1458040, _1458042), -(hAPP(c_Fun_Ocomp(_1458038, _1458038, _1458038, hAPP(_1458040, _1458044)), hAPP(_1458040, _1458044)) = hAPP(_1458040, _1458044))], (36038 ^ _777081) ^ [_1458157, _1458159, _1458161, _1458163, _1458165, _1458167] : [c_Finite__Set_Ofolding__idem(_1458157, _1458159, _1458161, _1458163), hBOOL(hAPP(c_Finite__Set_Ofinite(_1458157), _1458165)), hBOOL(hAPP(hAPP(c_member(_1458157), _1458167), _1458165)), -(hAPP(c_Fun_Ocomp(_1458159, _1458159, _1458159, hAPP(_1458163, _1458165)), hAPP(_1458161, _1458167)) = hAPP(_1458163, _1458165))], (36052 ^ _777081) ^ [_1458422, _1458424, _1458426, _1458428, _1458430, _1458432] : [c_Finite__Set_Ofolding__idem(_1458422, _1458424, _1458426, _1458428), hBOOL(hAPP(c_Finite__Set_Ofinite(_1458422), _1458430)), -(hAPP(_1458428, hAPP(hAPP(c_Set_Oinsert(_1458422), _1458432), _1458430)) = hAPP(c_Fun_Ocomp(_1458424, _1458424, _1458424, hAPP(_1458428, _1458430)), hAPP(_1458426, _1458432)))], (36062 ^ _777081) ^ [_1458629, _1458631, _1458633, _1458635, _1458637, _1458639, _1458641, _1458643] : [class_Groups_Ocomm__monoid__mult(_1458629), c_Fun_Oinj__on(_1458631, _1458633, _1458635, _1458637), _1458639 = hAPP(c_Set_Oimage(_1458631, _1458633, _1458635), _1458637), 36076 ^ _777081 : [(36077 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1458631), 36075 ^ [_1458629, _1458631, _1458633, _1458635, _1458637, _1458639, _1458641, _1458643]), _1458637)))], (36079 ^ _777081) ^ [] : [hAPP(_1458641, 36075 ^ [_1458629, _1458631, _1458633, _1458635, _1458637, _1458639, _1458641, _1458643]) = hAPP(hAPP(c_Fun_Ocomp(_1458633, _1458629, _1458631, _1458643), _1458635), 36075 ^ [_1458629, _1458631, _1458633, _1458635, _1458637, _1458639, _1458641, _1458643])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1458633, _1458629), _1458643), _1458639) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1458631, _1458629), _1458641), _1458637))], (36083 ^ _777081) ^ [_1459137, _1459139, _1459141, _1459143, _1459145] : [class_Groups_Ocomm__monoid__add(_1459137), class_Groups_Ocomm__monoid__mult(_1459137), _1459139 = _1459141, c_Nat__Transfer_Onat__set(_1459141), 36101 ^ _777081 : [(36102 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36100 ^ [_1459137, _1459139, _1459141, _1459143, _1459145])))], (36104 ^ _777081) ^ [] : [hAPP(_1459143, 36100 ^ [_1459137, _1459139, _1459141, _1459143, _1459145]) = hAPP(_1459145, 36100 ^ [_1459137, _1459139, _1459141, _1459143, _1459145])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1459137), _1459143), _1459139) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1459137), _1459145), _1459141))], (36108 ^ _777081) ^ [_1459600, _1459602, _1459604, _1459606, _1459608, _1459610] : [c_Equiv__Relations_Oequiv(_1459600, _1459602, _1459604), hBOOL(hAPP(hAPP(c_member(_1459600), _1459606), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1459600, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1459600, _1459600, _1459604), hAPP(hAPP(c_Set_Oinsert(_1459600), _1459608), c_Orderings_Obot__class_Obot(tc_fun(_1459600, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1459600, _1459600, _1459604), hAPP(hAPP(c_Set_Oinsert(_1459600), _1459610), c_Orderings_Obot__class_Obot(tc_fun(_1459600, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1459600, _1459600)), hAPP(hAPP(c_Product__Type_OPair(_1459600, _1459600), _1459608), _1459610)), _1459604)))], (36118 ^ _777081) ^ [] : [-(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))], (36120 ^ _777081) ^ [_1459919, _1459921, _1459923, _1459925] : [c_Equiv__Relations_Oequiv(_1459919, _1459921, _1459923), hBOOL(hAPP(hAPP(c_member(_1459919), _1459925), _1459921)), -(hBOOL(hAPP(hAPP(c_member(_1459919), _1459925), hAPP(c_Relation_OImage(_1459919, _1459919, _1459923), hAPP(hAPP(c_Set_Oinsert(_1459919), _1459925), c_Orderings_Obot__class_Obot(tc_fun(_1459919, tc_HOL_Obool)))))))], (36130 ^ _777081) ^ [_1460126, _1460128, _1460130, _1460132, _1460134] : [c_Equiv__Relations_Oequiv(_1460126, _1460128, _1460130), hBOOL(hAPP(hAPP(c_member(tc_prod(_1460126, _1460126)), hAPP(hAPP(c_Product__Type_OPair(_1460126, _1460126), _1460132), _1460134)), _1460130)), -(hAPP(c_Relation_OImage(_1460126, _1460126, _1460130), hAPP(hAPP(c_Set_Oinsert(_1460126), _1460132), c_Orderings_Obot__class_Obot(tc_fun(_1460126, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1460126, _1460126, _1460130), hAPP(hAPP(c_Set_Oinsert(_1460126), _1460134), c_Orderings_Obot__class_Obot(tc_fun(_1460126, tc_HOL_Obool)))))], (36140 ^ _777081) ^ [_1460387, _1460389, _1460391, _1460393, _1460395] : [c_Equiv__Relations_Oequiv(_1460387, _1460389, _1460391), 36143 ^ _777081 : [(36144 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1460387, _1460387)), hAPP(hAPP(c_Product__Type_OPair(_1460387, _1460387), _1460393), _1460395)), _1460391)), 36147 ^ _777081 : [(36148 ^ _777081) ^ [] : [-(hAPP(c_Relation_OImage(_1460387, _1460387, _1460391), hAPP(hAPP(c_Set_Oinsert(_1460387), _1460393), c_Orderings_Obot__class_Obot(tc_fun(_1460387, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1460387, _1460387, _1460391), hAPP(hAPP(c_Set_Oinsert(_1460387), _1460395), c_Orderings_Obot__class_Obot(tc_fun(_1460387, tc_HOL_Obool)))))], (36150 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1460387), _1460393), _1460389)))], (36152 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1460387), _1460395), _1460389)))]]], (36154 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1460387, _1460387)), hAPP(hAPP(c_Product__Type_OPair(_1460387, _1460387), _1460393), _1460395)), _1460391))), hAPP(c_Relation_OImage(_1460387, _1460387, _1460391), hAPP(hAPP(c_Set_Oinsert(_1460387), _1460393), c_Orderings_Obot__class_Obot(tc_fun(_1460387, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1460387, _1460387, _1460391), hAPP(hAPP(c_Set_Oinsert(_1460387), _1460395), c_Orderings_Obot__class_Obot(tc_fun(_1460387, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1460387), _1460393), _1460389)), hBOOL(hAPP(hAPP(c_member(_1460387), _1460395), _1460389))]]], (36168 ^ _777081) ^ [_1460987, _1460989, _1460991, _1460993, _1460995] : [hAPP(c_Relation_OImage(_1460987, _1460987, _1460989), hAPP(hAPP(c_Set_Oinsert(_1460987), _1460991), c_Orderings_Obot__class_Obot(tc_fun(_1460987, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1460987, _1460987, _1460989), hAPP(hAPP(c_Set_Oinsert(_1460987), _1460993), c_Orderings_Obot__class_Obot(tc_fun(_1460987, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1460987, _1460995, _1460989), hBOOL(hAPP(hAPP(c_member(_1460987), _1460993), _1460995)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1460987, _1460987)), hAPP(hAPP(c_Product__Type_OPair(_1460987, _1460987), _1460991), _1460993)), _1460989)))], (36182 ^ _777081) ^ [_1461320, _1461322, _1461324, _1461326, _1461328] : [c_Equiv__Relations_Oequiv(_1461320, _1461322, _1461324), hBOOL(hAPP(hAPP(c_member(_1461320), _1461326), _1461322)), hBOOL(hAPP(hAPP(c_member(_1461320), _1461328), _1461322)), 36193 ^ _777081 : [(36194 ^ _777081) ^ [] : [hAPP(c_Relation_OImage(_1461320, _1461320, _1461324), hAPP(hAPP(c_Set_Oinsert(_1461320), _1461326), c_Orderings_Obot__class_Obot(tc_fun(_1461320, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1461320, _1461320, _1461324), hAPP(hAPP(c_Set_Oinsert(_1461320), _1461328), c_Orderings_Obot__class_Obot(tc_fun(_1461320, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1461320, _1461320)), hAPP(hAPP(c_Product__Type_OPair(_1461320, _1461320), _1461326), _1461328)), _1461324)))], (36200 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1461320, _1461320)), hAPP(hAPP(c_Product__Type_OPair(_1461320, _1461320), _1461326), _1461328)), _1461324)), -(hAPP(c_Relation_OImage(_1461320, _1461320, _1461324), hAPP(hAPP(c_Set_Oinsert(_1461320), _1461326), c_Orderings_Obot__class_Obot(tc_fun(_1461320, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1461320, _1461320, _1461324), hAPP(hAPP(c_Set_Oinsert(_1461320), _1461328), c_Orderings_Obot__class_Obot(tc_fun(_1461320, tc_HOL_Obool)))))]]], (36206 ^ _777081) ^ [_1461868, _1461870, _1461872, _1461874, _1461876] : [c_Equiv__Relations_Oequiv(_1461868, _1461870, _1461872), hBOOL(hAPP(hAPP(c_member(tc_prod(_1461868, _1461868)), hAPP(hAPP(c_Product__Type_OPair(_1461868, _1461868), _1461874), _1461876)), _1461872)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1461868, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1461868, _1461868, _1461872), hAPP(hAPP(c_Set_Oinsert(_1461868), _1461874), c_Orderings_Obot__class_Obot(tc_fun(_1461868, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1461868, _1461868, _1461872), hAPP(hAPP(c_Set_Oinsert(_1461868), _1461876), c_Orderings_Obot__class_Obot(tc_fun(_1461868, tc_HOL_Obool)))))))], (36216 ^ _777081) ^ [_1462149, _1462151, _1462153, _1462155, _1462157] : [c_Equiv__Relations_Oequiv(_1462149, _1462151, _1462153), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462149, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1462149, _1462149, _1462153), hAPP(hAPP(c_Set_Oinsert(_1462149), _1462155), c_Orderings_Obot__class_Obot(tc_fun(_1462149, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1462149, _1462149, _1462153), hAPP(hAPP(c_Set_Oinsert(_1462149), _1462157), c_Orderings_Obot__class_Obot(tc_fun(_1462149, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1462149), _1462155), _1462151)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1462149, _1462149)), hAPP(hAPP(c_Product__Type_OPair(_1462149, _1462149), _1462157), _1462155)), _1462153)))], (36230 ^ _777081) ^ [_1462502, _1462504, _1462506] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1462502), _1462504)), c_Fun_Oinj__on(_1462502, tc_fun(tc_fun(_1462502, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1462502, tc_fun(tc_prod(_1462502, _1462502), tc_HOL_Obool), tc_fun(tc_fun(_1462502, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1462502, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1462502, _1462502), tc_HOL_Obool), tc_fun(tc_fun(_1462502, tc_HOL_Obool), tc_HOL_Obool)), _1462502), c_Equiv__Relations_Oquotient(_1462502)), hAPP(hAPP(c_COMBC(_1462502, tc_fun(_1462502, tc_HOL_Obool), tc_fun(_1462502, tc_HOL_Obool)), c_Set_Oinsert(_1462502)), c_Orderings_Obot__class_Obot(tc_fun(_1462502, tc_HOL_Obool))))), _1462506), _1462504), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1462502, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462502), _1462504), _1462506)) = hAPP(c_Finite__Set_Ocard(_1462502), _1462504))], (36240 ^ _777081) ^ [_1462851, _1462853, _1462855, _1462857, _1462859] : [c_Equiv__Relations_Oequiv(_1462851, _1462853, _1462855), hBOOL(hAPP(hAPP(c_member(_1462851), _1462857), _1462853)), hBOOL(hAPP(hAPP(c_member(_1462851), _1462859), _1462853)), 36251 ^ _777081 : [(36252 ^ _777081) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462851), hAPP(hAPP(c_Set_Oinsert(_1462851), _1462857), c_Orderings_Obot__class_Obot(tc_fun(_1462851, tc_HOL_Obool)))), _1462855) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462851), hAPP(hAPP(c_Set_Oinsert(_1462851), _1462859), c_Orderings_Obot__class_Obot(tc_fun(_1462851, tc_HOL_Obool)))), _1462855), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1462851, _1462851)), hAPP(hAPP(c_Product__Type_OPair(_1462851, _1462851), _1462857), _1462859)), _1462855)))], (36258 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1462851, _1462851)), hAPP(hAPP(c_Product__Type_OPair(_1462851, _1462851), _1462857), _1462859)), _1462855)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462851), hAPP(hAPP(c_Set_Oinsert(_1462851), _1462857), c_Orderings_Obot__class_Obot(tc_fun(_1462851, tc_HOL_Obool)))), _1462855) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462851), hAPP(hAPP(c_Set_Oinsert(_1462851), _1462859), c_Orderings_Obot__class_Obot(tc_fun(_1462851, tc_HOL_Obool)))), _1462855))]]], (36264 ^ _777081) ^ [_1463405, _1463407, _1463409] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1463405), hAPP(hAPP(c_Set_Oinsert(_1463405), _1463407), c_Orderings_Obot__class_Obot(tc_fun(_1463405, tc_HOL_Obool)))), _1463409) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1463405, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1463405, _1463405, _1463409), hAPP(hAPP(c_Set_Oinsert(_1463405), _1463407), c_Orderings_Obot__class_Obot(tc_fun(_1463405, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1463405, tc_HOL_Obool), tc_HOL_Obool))))], (36266 ^ _777081) ^ [_1463492, _1463494] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1463492), c_Orderings_Obot__class_Obot(tc_fun(_1463492, tc_HOL_Obool))), _1463494) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1463492, tc_HOL_Obool), tc_HOL_Obool)))], (36268 ^ _777081) ^ [_1463556, _1463558, _1463560] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1463556, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1463556), _1463558), _1463560), -(_1463558 = c_Orderings_Obot__class_Obot(tc_fun(_1463556, tc_HOL_Obool)))], (36274 ^ _777081) ^ [_1463673, _1463675, _1463677] : [_1463675 = c_Orderings_Obot__class_Obot(tc_fun(_1463673, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1463673, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1463673), _1463675), _1463677))], (36280 ^ _777081) ^ [_1463814, _1463816, _1463818] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1463814), _1463816), _1463818) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1463814, tc_HOL_Obool), tc_HOL_Obool)), -(_1463816 = c_Orderings_Obot__class_Obot(tc_fun(_1463814, tc_HOL_Obool)))], (36286 ^ _777081) ^ [_1463931, _1463933, _1463935] : [_1463933 = c_Orderings_Obot__class_Obot(tc_fun(_1463931, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1463931), _1463933), _1463935) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1463931, tc_HOL_Obool), tc_HOL_Obool)))], (36292 ^ _777081) ^ [_1464054, _1464056, _1464058, _1464060, _1464062] : [c_Equiv__Relations_Oequiv(_1464054, _1464056, _1464058), hBOOL(hAPP(hAPP(c_member(tc_fun(_1464054, tc_HOL_Obool)), _1464060), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1464054), _1464056), _1464058))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1464054, tc_HOL_Obool)), _1464062), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1464054), _1464056), _1464058))), -(_1464060 = _1464062), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1464054, tc_HOL_Obool)), _1464060), _1464062) = c_Orderings_Obot__class_Obot(tc_fun(_1464054, tc_HOL_Obool)))], (36310 ^ _777081) ^ [_1464372, _1464374, _1464376, _1464378] : [c_Fun_Oinj__on(_1464372, tc_fun(tc_fun(_1464372, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1464372, tc_fun(tc_prod(_1464372, _1464372), tc_HOL_Obool), tc_fun(tc_fun(_1464372, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1464372, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1464372, _1464372), tc_HOL_Obool), tc_fun(tc_fun(_1464372, tc_HOL_Obool), tc_HOL_Obool)), _1464372), c_Equiv__Relations_Oquotient(_1464372)), hAPP(hAPP(c_COMBC(_1464372, tc_fun(_1464372, tc_HOL_Obool), tc_fun(_1464372, tc_HOL_Obool)), c_Set_Oinsert(_1464372)), c_Orderings_Obot__class_Obot(tc_fun(_1464372, tc_HOL_Obool))))), _1464374), _1464376), hBOOL(hAPP(hAPP(c_member(_1464372), _1464378), _1464376)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1464372), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1464372, tc_HOL_Obool)), _1464376), hAPP(hAPP(c_Set_Oinsert(_1464372), _1464378), c_Orderings_Obot__class_Obot(tc_fun(_1464372, tc_HOL_Obool))))), _1464374) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1464372, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1464372), _1464376), _1464374)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1464372), hAPP(hAPP(c_Set_Oinsert(_1464372), _1464378), c_Orderings_Obot__class_Obot(tc_fun(_1464372, tc_HOL_Obool)))), _1464374)))], (36320 ^ _777081) ^ [_1464839, _1464841, _1464843, _1464845] : [hBOOL(hAPP(hAPP(c_member(_1464839), _1464841), _1464843)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1464839, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1464839, _1464839, _1464845), hAPP(hAPP(c_Set_Oinsert(_1464839), _1464841), c_Orderings_Obot__class_Obot(tc_fun(_1464839, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1464839), _1464843), _1464845))))], (36326 ^ _777081) ^ [_1465010, _1465012, _1465014, _1465016, _1465018, _1465020, _1465022] : [c_Equiv__Relations_Oequiv(_1465010, _1465012, _1465014), hBOOL(hAPP(hAPP(c_member(tc_fun(_1465010, tc_HOL_Obool)), _1465016), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1465010), _1465012), _1465014))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1465010, tc_HOL_Obool)), _1465018), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1465010), _1465012), _1465014))), hBOOL(hAPP(hAPP(c_member(_1465010), _1465020), _1465016)), hBOOL(hAPP(hAPP(c_member(_1465010), _1465022), _1465018)), 36345 ^ _777081 : [(36346 ^ _777081) ^ [] : [_1465016 = _1465018, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1465010, _1465010)), hAPP(hAPP(c_Product__Type_OPair(_1465010, _1465010), _1465020), _1465022)), _1465014)))], (36352 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1465010, _1465010)), hAPP(hAPP(c_Product__Type_OPair(_1465010, _1465010), _1465020), _1465022)), _1465014)), -(_1465016 = _1465018)]]], (36358 ^ _777081) ^ [_1465654, _1465656, _1465658, _1465660, _1465662, _1465664, _1465666] : [c_Equiv__Relations_Oequiv(_1465654, _1465656, _1465658), hBOOL(hAPP(hAPP(c_member(tc_fun(_1465654, tc_HOL_Obool)), _1465660), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1465654), _1465656), _1465658))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1465654, tc_HOL_Obool)), _1465662), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1465654), _1465656), _1465658))), hBOOL(hAPP(hAPP(c_member(_1465654), _1465664), _1465660)), hBOOL(hAPP(hAPP(c_member(_1465654), _1465666), _1465662)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1465654, _1465654)), hAPP(hAPP(c_Product__Type_OPair(_1465654, _1465654), _1465664), _1465666)), _1465658)), -(_1465660 = _1465662)], (36384 ^ _777081) ^ [_1466191, _1466193, _1466195, _1466197] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1466191, tc_HOL_Obool)), _1466193), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1466191), _1466195), _1466197))), 36388 ^ _777081 : [(36389 ^ _777081) ^ [] : [-(_1466193 = hAPP(c_Relation_OImage(_1466191, _1466191, _1466197), hAPP(hAPP(c_Set_Oinsert(_1466191), 36387 ^ [_1466191, _1466193, _1466195, _1466197]), c_Orderings_Obot__class_Obot(tc_fun(_1466191, tc_HOL_Obool)))))], (36391 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1466191), 36387 ^ [_1466191, _1466193, _1466195, _1466197]), _1466195)))]]], (36393 ^ _777081) ^ [] : [-(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))], (36395 ^ _777081) ^ [_1466452, _1466454] : [c_Equiv__Relations_Oequiv(_1466452, c_Orderings_Otop__class_Otop(tc_fun(_1466452, tc_HOL_Obool)), _1466454), -(c_Equiv__Relations_Oequivp(_1466452, hAPP(hAPP(c_COMBC(_1466452, tc_fun(tc_prod(_1466452, _1466452), tc_HOL_Obool), tc_fun(_1466452, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1466452, tc_fun(tc_fun(tc_prod(_1466452, _1466452), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1466452, _1466452), tc_HOL_Obool), tc_fun(_1466452, tc_HOL_Obool)), _1466452), c_COMBC(_1466452, tc_fun(tc_prod(_1466452, _1466452), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1466452, tc_prod(_1466452, _1466452)), tc_fun(_1466452, tc_fun(tc_fun(tc_prod(_1466452, _1466452), tc_HOL_Obool), tc_HOL_Obool)), _1466452), hAPP(c_COMBB(tc_prod(_1466452, _1466452), tc_fun(tc_fun(tc_prod(_1466452, _1466452), tc_HOL_Obool), tc_HOL_Obool), _1466452), c_member(tc_prod(_1466452, _1466452)))), c_Product__Type_OPair(_1466452, _1466452)))), _1466454)))], (36401 ^ _777081) ^ [_1466773, _1466775] : [c_Equiv__Relations_Oequivp(_1466773, hAPP(hAPP(c_COMBC(_1466773, tc_fun(tc_prod(_1466773, _1466773), tc_HOL_Obool), tc_fun(_1466773, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1466773, tc_fun(tc_fun(tc_prod(_1466773, _1466773), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1466773, _1466773), tc_HOL_Obool), tc_fun(_1466773, tc_HOL_Obool)), _1466773), c_COMBC(_1466773, tc_fun(tc_prod(_1466773, _1466773), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1466773, tc_prod(_1466773, _1466773)), tc_fun(_1466773, tc_fun(tc_fun(tc_prod(_1466773, _1466773), tc_HOL_Obool), tc_HOL_Obool)), _1466773), hAPP(c_COMBB(tc_prod(_1466773, _1466773), tc_fun(tc_fun(tc_prod(_1466773, _1466773), tc_HOL_Obool), tc_HOL_Obool), _1466773), c_member(tc_prod(_1466773, _1466773)))), c_Product__Type_OPair(_1466773, _1466773)))), _1466775)), -(c_Equiv__Relations_Oequiv(_1466773, c_Orderings_Otop__class_Otop(tc_fun(_1466773, tc_HOL_Obool)), _1466775))], (36407 ^ _777081) ^ [_1467100] : [-(c_Equiv__Relations_Oequivp(_1467100, c_fequal))], (36425 ^ _777081) ^ [_1467436, _1467438] : [-(c_Equiv__Relations_Oequivp(_1467436, _1467438)), 36430 ^ _777081 : [(36431 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1467438, 36426 ^ [_1467436, _1467438]), 36427 ^ [_1467436, _1467438])))], (36433 ^ _777081) ^ [] : [hAPP(_1467438, 36426 ^ [_1467436, _1467438]) = hAPP(_1467438, 36427 ^ [_1467436, _1467438])]], 36434 ^ _777081 : [(36435 ^ _777081) ^ [] : [-(hAPP(_1467438, 36426 ^ [_1467436, _1467438]) = hAPP(_1467438, 36427 ^ [_1467436, _1467438]))], (36437 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1467438, 36426 ^ [_1467436, _1467438]), 36427 ^ [_1467436, _1467438]))]]], (36409 ^ _777081) ^ [_1467138, _1467140] : [c_Equiv__Relations_Oequivp(_1467138, _1467140), 36412 ^ _777081 : [(36413 ^ _777081) ^ [_1467232, _1467234] : [hBOOL(hAPP(hAPP(_1467140, _1467234), _1467232)), -(hAPP(_1467140, _1467234) = hAPP(_1467140, _1467232))], (36419 ^ _777081) ^ [_1467331, _1467333] : [hAPP(_1467140, _1467333) = hAPP(_1467140, _1467331), -(hBOOL(hAPP(hAPP(_1467140, _1467333), _1467331)))]]], (36441 ^ _777081) ^ [_1467765, _1467767, _1467769] : [c_Equiv__Relations_Oequivp(_1467765, _1467767), -(hBOOL(hAPP(hAPP(_1467767, _1467769), _1467769)))], (36447 ^ _777081) ^ [_1467854, _1467856, _1467858, _1467860] : [c_Equiv__Relations_Oequivp(_1467854, _1467856), hBOOL(hAPP(hAPP(_1467856, _1467858), _1467860)), -(hBOOL(hAPP(hAPP(_1467856, _1467860), _1467858)))], (36457 ^ _777081) ^ [_1468011, _1468013, _1468015, _1468017, _1468019] : [c_Equiv__Relations_Oequivp(_1468011, _1468013), hBOOL(hAPP(hAPP(_1468013, _1468015), _1468017)), hBOOL(hAPP(hAPP(_1468013, _1468017), _1468019)), -(hBOOL(hAPP(hAPP(_1468013, _1468015), _1468019)))], (36471 ^ _777081) ^ [_1468240, _1468242, _1468244] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1468240), _1468242), _1468244) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1468240, tc_fun(tc_fun(_1468240, tc_HOL_Obool), tc_HOL_Obool)), _1468242), hAPP(hAPP(c_COMBC(_1468240, tc_fun(tc_fun(_1468240, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1468240, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1468240, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1468240, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1468240, tc_HOL_Obool), tc_HOL_Obool)), _1468240), c_Set_Oinsert(tc_fun(_1468240, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1468240, tc_HOL_Obool), tc_fun(_1468240, tc_HOL_Obool), _1468240), c_Relation_OImage(_1468240, _1468240, _1468244)), hAPP(hAPP(c_COMBC(_1468240, tc_fun(_1468240, tc_HOL_Obool), tc_fun(_1468240, tc_HOL_Obool)), c_Set_Oinsert(_1468240)), c_Orderings_Obot__class_Obot(tc_fun(_1468240, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1468240, tc_HOL_Obool), tc_HOL_Obool)))))], (36473 ^ _777081) ^ [_1468396, _1468398, _1468400, _1468402, _1468404] : [class_Groups_Oab__semigroup__mult(_1468396), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1468396, _1468396, c_Groups_Otimes__class_Otimes(_1468396), _1468398, _1468400), _1468402)), hBOOL(hAPP(hAPP(c_member(_1468396), _1468404), _1468400)), -(hBOOL(hAPP(hAPP(c_member(_1468396), _1468398), _1468400))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1468396, _1468396, c_Groups_Otimes__class_Otimes(_1468396), _1468404, hAPP(hAPP(c_Set_Oinsert(_1468396), _1468398), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468396, tc_HOL_Obool)), _1468400), hAPP(hAPP(c_Set_Oinsert(_1468396), _1468404), c_Orderings_Obot__class_Obot(tc_fun(_1468396, tc_HOL_Obool)))))), _1468402)))], (36491 ^ _777081) ^ [_1468740, _1468742, _1468744, _1468746, _1468748] : [class_Groups_Ocomm__monoid__add(_1468740), class_Groups_Ocomm__monoid__mult(_1468740), _1468742 = _1468744, c_Nat__Transfer_Onat__set(_1468744), 36509 ^ _777081 : [(36510 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36508 ^ [_1468740, _1468742, _1468744, _1468746, _1468748])))], (36512 ^ _777081) ^ [] : [hAPP(_1468746, 36508 ^ [_1468740, _1468742, _1468744, _1468746, _1468748]) = hAPP(_1468748, 36508 ^ [_1468740, _1468742, _1468744, _1468746, _1468748])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1468740), _1468746), _1468742) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1468740), _1468748), _1468744))], (36516 ^ _777081) ^ [_1469203, _1469205, _1469207, _1469209, _1469211, _1469213] : [hBOOL(hAPP(hAPP(c_member(_1469203), _1469205), _1469207)), hBOOL(hAPP(hAPP(_1469209, _1469205), _1469211)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1469203, tc_fun(_1469213, tc_HOL_Obool)), _1469207), _1469209), _1469211)))], (36526 ^ _777081) ^ [_1469400, _1469402, _1469404, _1469406, _1469408, _1469410] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1469400, tc_fun(_1469402, tc_HOL_Obool)), _1469404), hAPP(c_Fun_Ocomp(_1469406, tc_fun(_1469402, tc_HOL_Obool), _1469400, _1469408), _1469410)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1469406, tc_fun(_1469402, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469400, _1469406, _1469410), _1469404)), _1469408))], (36528 ^ _777081) ^ [_1469475, _1469477, _1469479, _1469481] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1469475), _1469477)), 36531 ^ _777081 : [(36542 ^ _777081) ^ [] : [36544 ^ _777081 : [(36545 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1469475), 36543 ^ [_1469475, _1469477, _1469479, _1469481]), _1469477)))], (36547 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1469479), hAPP(_1469481, 36543 ^ [_1469475, _1469477, _1469479, _1469481])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1469479), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1469475, tc_fun(_1469479, tc_HOL_Obool)), _1469477), _1469481))))], (36532 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1469479), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1469475, tc_fun(_1469479, tc_HOL_Obool)), _1469477), _1469481))), 36535 ^ _777081 : [(36536 ^ _777081) ^ [_1469659] : [hBOOL(hAPP(hAPP(c_member(_1469475), _1469659), _1469477)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1469479), hAPP(_1469481, _1469659))))]]]]], (36551 ^ _777081) ^ [_1469950, _1469952, _1469954, _1469956, _1469958, _1469960] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1469950, _1469952, _1469954, _1469956, _1469958), _1469960)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1469950), _1469958)))], (36557 ^ _777081) ^ [_1470059, _1470061, _1470063, _1470065, _1470067] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1470059, _1470061, _1470063, _1470065, c_Orderings_Obot__class_Obot(tc_fun(_1470059, tc_HOL_Obool))), _1470067)), -(_1470067 = _1470065)], (36563 ^ _777081) ^ [_1470168, _1470170, _1470172, _1470174] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1470168, _1470170, _1470172, _1470174, c_Orderings_Obot__class_Obot(tc_fun(_1470168, tc_HOL_Obool))), _1470174)))], (36565 ^ _777081) ^ [_1470210, _1470212, _1470214, _1470216] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1470210, _1470212, _1470214, _1470216, c_Orderings_Obot__class_Obot(tc_fun(_1470210, tc_HOL_Obool))), _1470216)))], (36567 ^ _777081) ^ [_1470252, _1470254, _1470256, _1470258, _1470260, _1470262] : [-(hAPP(c_Relation_OImage(_1470252, _1470254, _1470256), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1470258, tc_fun(_1470252, tc_HOL_Obool)), _1470260), _1470262)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1470258, tc_fun(_1470254, tc_HOL_Obool)), _1470260), hAPP(hAPP(c_COMBB(tc_fun(_1470252, tc_HOL_Obool), tc_fun(_1470254, tc_HOL_Obool), _1470258), c_Relation_OImage(_1470252, _1470254, _1470256)), _1470262)))], (36569 ^ _777081) ^ [_1470360, _1470362, _1470364, _1470366, _1470368] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1470360, tc_fun(_1470362, tc_HOL_Obool)), _1470364), _1470366), _1470368)), 36573 ^ _777081 : [(36574 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1470360), 36572 ^ [_1470360, _1470362, _1470364, _1470366, _1470368]), _1470364)))], (36576 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1470366, 36572 ^ [_1470360, _1470362, _1470364, _1470366, _1470368]), _1470368)))]]], (36578 ^ _777081) ^ [_1470548, _1470550, _1470552, _1470554, _1470556] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1470548, tc_fun(_1470550, tc_HOL_Obool)), _1470552), _1470554), _1470556))), 36579 ^ _777081 : [(36580 ^ _777081) ^ [_1470620] : [hBOOL(hAPP(hAPP(c_member(_1470548), _1470620), _1470552)), hBOOL(hAPP(hAPP(_1470554, _1470620), _1470556))]]], (36588 ^ _777081) ^ [_1470793, _1470795, _1470797, _1470799] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1470793, tc_fun(_1470795, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1470793, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1470795, tc_HOL_Obool), tc_fun(_1470795, tc_HOL_Obool), _1470793), hAPP(c_COMBC(_1470795, tc_fun(_1470795, tc_HOL_Obool), tc_HOL_Obool), c_member(_1470795))), _1470797)), _1470799)), -(hBOOL(hAPP(hAPP(c_member(_1470795), _1470799), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1470793, tc_fun(_1470795, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1470793, tc_HOL_Obool))), _1470797))))], (36594 ^ _777081) ^ [_1471012, _1471014, _1471016, _1471018] : [hBOOL(hAPP(hAPP(c_member(_1471014), _1471018), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1471012, tc_fun(_1471014, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1471012, tc_HOL_Obool))), _1471016))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1471012, tc_fun(_1471014, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1471012, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1471014, tc_HOL_Obool), tc_fun(_1471014, tc_HOL_Obool), _1471012), hAPP(c_COMBC(_1471014, tc_fun(_1471014, tc_HOL_Obool), tc_HOL_Obool), c_member(_1471014))), _1471016)), _1471018)))], (36600 ^ _777081) ^ [_1471236, _1471238, _1471240, _1471242, _1471244, _1471246, _1471248] : [-(hBOOL(hAPP(hAPP(c_member(_1471236), _1471238), _1471240))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1471236, _1471242, _1471244, _1471246, _1471240), _1471248)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1471236, _1471242, _1471244, _1471246, hAPP(hAPP(c_Set_Oinsert(_1471236), _1471238), _1471240)), hAPP(hAPP(_1471244, _1471238), _1471248))))], (36610 ^ _777081) ^ [_1471450, _1471452, _1471454, _1471456] : [-(hAPP(c_Relation_OImage(_1471450, _1471452, _1471454), _1471456) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1471450, tc_fun(_1471452, tc_HOL_Obool)), _1471456), hAPP(hAPP(c_COMBB(tc_fun(_1471450, tc_HOL_Obool), tc_fun(_1471452, tc_HOL_Obool), _1471450), c_Relation_OImage(_1471450, _1471452, _1471454)), hAPP(hAPP(c_COMBC(_1471450, tc_fun(_1471450, tc_HOL_Obool), tc_fun(_1471450, tc_HOL_Obool)), c_Set_Oinsert(_1471450)), c_Orderings_Obot__class_Obot(tc_fun(_1471450, tc_HOL_Obool))))))], (36612 ^ _777081) ^ [_1471541, _1471543, _1471545, _1471547, _1471549] : [class_Groups_Oab__semigroup__mult(_1471541), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1471541, _1471541, c_Groups_Otimes__class_Otimes(_1471541), _1471543, _1471545), _1471547)), -(hBOOL(hAPP(hAPP(c_member(_1471541), _1471543), _1471545))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1471541, _1471541, c_Groups_Otimes__class_Otimes(_1471541), _1471549, hAPP(hAPP(c_Set_Oinsert(_1471541), _1471543), _1471545)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1471541), _1471549), _1471547))))], (36626 ^ _777081) ^ [_1471781, _1471783, _1471785, _1471787, _1471789, _1471791, _1471793] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1471781, _1471783, _1471785, _1471787, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1471781, tc_HOL_Obool)), _1471789), hAPP(hAPP(c_Set_Oinsert(_1471781), _1471791), c_Orderings_Obot__class_Obot(tc_fun(_1471781, tc_HOL_Obool))))), _1471793)), hBOOL(hAPP(hAPP(c_member(_1471781), _1471791), _1471789)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1471781, _1471783, _1471785, _1471787, _1471789), hAPP(hAPP(_1471785, _1471791), _1471793))))], (36636 ^ _777081) ^ [_1472036, _1472038, _1472040, _1472042, _1472044, _1472046] : [hBOOL(hAPP(hAPP(c_member(_1472036), _1472038), _1472040)), hBOOL(hAPP(hAPP(c_member(_1472042), _1472044), hAPP(_1472046, _1472038))), -(hBOOL(hAPP(hAPP(c_member(_1472042), _1472044), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1472036, tc_fun(_1472042, tc_HOL_Obool)), _1472040), _1472046))))], (36646 ^ _777081) ^ [_1472253, _1472255, _1472257, _1472259] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1472253, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1472255, tc_fun(tc_fun(_1472253, tc_HOL_Obool), tc_HOL_Obool)), _1472257), hAPP(hAPP(c_COMBB(tc_fun(_1472253, tc_HOL_Obool), tc_fun(tc_fun(_1472253, tc_HOL_Obool), tc_HOL_Obool), _1472255), c_Set_OPow(_1472253)), _1472259))), hAPP(c_Set_OPow(_1472253), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1472255, tc_fun(_1472253, tc_HOL_Obool)), _1472257), _1472259)))))], (36648 ^ _777081) ^ [_1472348, _1472350, _1472352, _1472354] : [-(hAPP(c_Set_Ovimage(_1472348, _1472350, _1472352), _1472354) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1472350, tc_fun(_1472348, tc_HOL_Obool)), _1472354), hAPP(hAPP(c_COMBB(tc_fun(_1472350, tc_HOL_Obool), tc_fun(_1472348, tc_HOL_Obool), _1472350), c_Set_Ovimage(_1472348, _1472350, _1472352)), hAPP(hAPP(c_COMBC(_1472350, tc_fun(_1472350, tc_HOL_Obool), tc_fun(_1472350, tc_HOL_Obool)), c_Set_Oinsert(_1472350)), c_Orderings_Obot__class_Obot(tc_fun(_1472350, tc_HOL_Obool))))))], (36650 ^ _777081) ^ [] : [-(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)))], (36652 ^ _777081) ^ [] : [-(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)))], (36654 ^ _777081) ^ [] : [-(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)))], (36656 ^ _777081) ^ [_1472493, _1472495] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472493, 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(_1472493, tc_HOL_Obool)), tc_fun(_1472493, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1472493, tc_HOL_Obool)), tc_fun(_1472493, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472493, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1472495)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1472493, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1472495))], (36675 ^ _777081) ^ [_1473049, _1473051, _1473053, _1473055, _1473057] : [36677 ^ _777081 : [(36678 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473051), 36676 ^ [_1473049, _1473051, _1473053, _1473055, _1473057]), _1473053)))], (36681 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1473049), 36679 ^ [_1473049, _1473051, _1473053, _1473055, _1473057]), hAPP(_1473055, 36676 ^ [_1473049, _1473051, _1473053, _1473055, _1473057]))))], (36683 ^ _777081) ^ [] : [hBOOL(hAPP(_1473057, 36679 ^ [_1473049, _1473051, _1473053, _1473055, _1473057]))]], 36684 ^ _777081 : [(36685 ^ _777081) ^ [_1473359] : [hBOOL(hAPP(hAPP(c_member(_1473049), _1473359), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473051, tc_fun(_1473049, tc_HOL_Obool)), _1473053), _1473055))), -(hBOOL(hAPP(_1473057, _1473359)))]]], (36658 ^ _777081) ^ [_1472613, _1472615, _1472617, _1472619, _1472621] : [36660 ^ _777081 : [(36661 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1472613), 36659 ^ [_1472613, _1472615, _1472617, _1472619, _1472621]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1472615, tc_fun(_1472613, tc_HOL_Obool)), _1472617), _1472619))))], (36663 ^ _777081) ^ [] : [hBOOL(hAPP(_1472621, 36659 ^ [_1472613, _1472615, _1472617, _1472619, _1472621]))]], 36664 ^ _777081 : [(36665 ^ _777081) ^ [_1472835] : [hBOOL(hAPP(hAPP(c_member(_1472615), _1472835), _1472617)), 36668 ^ _777081 : [(36669 ^ _777081) ^ [_1472932] : [hBOOL(hAPP(hAPP(c_member(_1472613), _1472932), hAPP(_1472619, _1472835))), -(hBOOL(hAPP(_1472621, _1472932)))]]]]], (36691 ^ _777081) ^ [_1473494, _1473496, _1473498, _1473500] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1473494, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1473496)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1473494, tc_HOL_Obool), tc_Nat_Onat), _1473498), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1473500))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1473494, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1473500, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1473496), _1473500))), _1473498))], (36693 ^ _777081) ^ [_1473576, _1473578, _1473580, _1473582, _1473584, _1473586] : [class_Complete__Lattice_Ocomplete__lattice(_1473576), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473578, _1473576), _1473580), hAPP(hAPP(c_COMBB(tc_fun(_1473582, _1473576), _1473576, _1473578), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473582, _1473576), _1473584)), _1473586)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473582, _1473576), _1473584), hAPP(hAPP(c_COMBB(tc_fun(_1473578, _1473576), _1473576, _1473582), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473578, _1473576), _1473580)), hAPP(c_COMBC(_1473578, _1473582, _1473576), _1473586))))], (36699 ^ _777081) ^ [_1473785, _1473787, _1473789, _1473791, _1473793, _1473795] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473785, tc_fun(_1473787, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473789, tc_fun(_1473785, tc_HOL_Obool)), _1473791), _1473793)), _1473795) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473789, tc_fun(_1473787, tc_HOL_Obool)), _1473791), hAPP(hAPP(c_COMBC(_1473789, tc_fun(_1473785, tc_fun(_1473787, tc_HOL_Obool)), tc_fun(_1473787, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473785, tc_HOL_Obool), tc_fun(tc_fun(_1473785, tc_fun(_1473787, tc_HOL_Obool)), tc_fun(_1473787, tc_HOL_Obool)), _1473789), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473785, tc_fun(_1473787, tc_HOL_Obool))), _1473793)), _1473795)))], (36701 ^ _777081) ^ [_1473904, _1473906, _1473908, _1473910, _1473912, _1473914] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473904, tc_fun(_1473906, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473908, tc_fun(_1473904, tc_HOL_Obool)), _1473910), _1473912)), _1473914) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473908, tc_fun(_1473906, tc_HOL_Obool)), _1473910), hAPP(hAPP(c_COMBC(_1473908, tc_fun(_1473904, tc_fun(_1473906, tc_HOL_Obool)), tc_fun(_1473906, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473904, tc_HOL_Obool), tc_fun(tc_fun(_1473904, tc_fun(_1473906, tc_HOL_Obool)), tc_fun(_1473906, tc_HOL_Obool)), _1473908), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1473904, tc_fun(_1473906, tc_HOL_Obool))), _1473912)), _1473914)))], (36703 ^ _777081) ^ [_1474023, _1474025, _1474027, _1474029, _1474031, _1474033] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474023, tc_fun(_1474025, tc_HOL_Obool)), _1474027), hAPP(hAPP(c_COMBC(_1474023, tc_fun(_1474029, tc_fun(_1474025, tc_HOL_Obool)), tc_fun(_1474025, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1474029, tc_HOL_Obool), tc_fun(tc_fun(_1474029, tc_fun(_1474025, tc_HOL_Obool)), tc_fun(_1474025, tc_HOL_Obool)), _1474023), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474029, tc_fun(_1474025, tc_HOL_Obool))), _1474031)), _1474033)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474029, tc_fun(_1474025, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474023, tc_fun(_1474029, tc_HOL_Obool)), _1474027), _1474031)), _1474033))], (36705 ^ _777081) ^ [_1474142, _1474144, _1474146] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1474142, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1474144)), _1474146) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1474142, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1474142, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1474144)), _1474146)), hAPP(_1474146, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36707 ^ _777081) ^ [_1474214, _1474216, _1474218, _1474220, _1474222] : [class_Complete__Lattice_Ocomplete__lattice(_1474214), 36710 ^ _777081 : [(36721 ^ _777081) ^ [] : [36723 ^ _777081 : [(36724 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1474216), 36722 ^ [_1474214, _1474216, _1474218, _1474220, _1474222]), _1474218)))], (36726 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1474214), hAPP(_1474220, 36722 ^ [_1474214, _1474216, _1474218, _1474220, _1474222])), _1474222))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1474214), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474216, _1474214), _1474218), _1474220)), _1474222)))], (36711 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1474214), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474216, _1474214), _1474218), _1474220)), _1474222)), 36714 ^ _777081 : [(36715 ^ _777081) ^ [_1474395] : [hBOOL(hAPP(hAPP(c_member(_1474216), _1474395), _1474218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1474214), hAPP(_1474220, _1474395)), _1474222)))]]]]], (36730 ^ _777081) ^ [_1474708, _1474710, _1474712, _1474714, _1474716] : [class_Complete__Lattice_Ocomplete__lattice(_1474708), class_Orderings_Olinorder(_1474708), 36737 ^ _777081 : [(36738 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1474708), _1474710), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474712, _1474708), _1474714), _1474716))), 36742 ^ _777081 : [(36743 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1474712), 36741 ^ [_1474708, _1474710, _1474712, _1474714, _1474716]), _1474714)))], (36745 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1474708), _1474710), hAPP(_1474716, 36741 ^ [_1474708, _1474710, _1474712, _1474714, _1474716]))))]]], (36747 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1474708), _1474710), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1474712, _1474708), _1474714), _1474716)))), 36748 ^ _777081 : [(36749 ^ _777081) ^ [_1475056] : [hBOOL(hAPP(hAPP(c_member(_1474712), _1475056), _1474714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1474708), _1474710), hAPP(_1474716, _1475056)))]]]]], (36757 ^ _777081) ^ [_1475250, _1475252, _1475254, _1475256, _1475258] : [hBOOL(hAPP(hAPP(c_member(_1475250), _1475252), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1475254, tc_fun(_1475250, tc_HOL_Obool)), _1475256), _1475258))), 36761 ^ _777081 : [(36762 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475254), 36760 ^ [_1475250, _1475252, _1475254, _1475256, _1475258]), _1475256)))], (36764 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475250), _1475252), hAPP(_1475258, 36760 ^ [_1475250, _1475252, _1475254, _1475256, _1475258]))))]]], (36766 ^ _777081) ^ [_1475458, _1475460, _1475462, _1475464, _1475466] : [-(hBOOL(hAPP(hAPP(c_member(_1475458), _1475460), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1475462, tc_fun(_1475458, tc_HOL_Obool)), _1475464), _1475466)))), 36767 ^ _777081 : [(36768 ^ _777081) ^ [_1475540] : [hBOOL(hAPP(hAPP(c_member(_1475462), _1475540), _1475464)), hBOOL(hAPP(hAPP(c_member(_1475458), _1475460), hAPP(_1475466, _1475540)))]]], (36776 ^ _777081) ^ [_1475707, _1475709, _1475711, _1475713] : [class_Complete__Lattice_Ocomplete__lattice(_1475707), -(_1475709 = c_Orderings_Obot__class_Obot(tc_fun(_1475711, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1475711, _1475707), _1475709), hAPP(c_COMBK(_1475707, _1475711), _1475713)) = _1475713)], (36796 ^ _777081) ^ [_1476091, _1476093, _1476095, _1476097] : [36798 ^ _777081 : [(36799 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476091), 36797 ^ [_1476091, _1476093, _1476095, _1476097]), _1476095)))], (36801 ^ _777081) ^ [] : [hAPP(_1476097, 36797 ^ [_1476091, _1476093, _1476095, _1476097]) = c_Orderings_Obot__class_Obot(tc_fun(_1476093, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476091, tc_fun(_1476093, tc_HOL_Obool)), _1476095), _1476097) = c_Orderings_Obot__class_Obot(tc_fun(_1476093, tc_HOL_Obool)))], (36786 ^ _777081) ^ [_1475862, _1475864, _1475866, _1475868] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1475862, tc_fun(_1475864, tc_HOL_Obool)), _1475866), _1475868) = c_Orderings_Obot__class_Obot(tc_fun(_1475864, tc_HOL_Obool)), 36789 ^ _777081 : [(36790 ^ _777081) ^ [_1475978] : [hBOOL(hAPP(hAPP(c_member(_1475862), _1475978), _1475866)), -(hAPP(_1475868, _1475978) = c_Orderings_Obot__class_Obot(tc_fun(_1475864, tc_HOL_Obool)))]]], (36805 ^ _777081) ^ [_1476336, _1476338, _1476340, _1476342] : [_1476336 = c_Orderings_Obot__class_Obot(tc_fun(_1476338, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476338, tc_fun(_1476340, tc_HOL_Obool)), _1476336), hAPP(c_COMBK(tc_fun(_1476340, tc_HOL_Obool), _1476338), _1476342)) = c_Orderings_Obot__class_Obot(tc_fun(_1476340, tc_HOL_Obool)))], (36811 ^ _777081) ^ [_1476473, _1476475, _1476477, _1476479] : [-(_1476473 = c_Orderings_Obot__class_Obot(tc_fun(_1476475, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476475, tc_fun(_1476477, tc_HOL_Obool)), _1476473), hAPP(c_COMBK(tc_fun(_1476477, tc_HOL_Obool), _1476475), _1476479)) = _1476479)], (36817 ^ _777081) ^ [_1476541, _1476543, _1476545] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476541, tc_fun(_1476543, tc_HOL_Obool)), _1476545), hAPP(c_COMBK(tc_fun(_1476543, tc_HOL_Obool), _1476541), c_Orderings_Obot__class_Obot(tc_fun(_1476543, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1476543, tc_HOL_Obool)))], (36829 ^ _777081) ^ [_1476849, _1476851, _1476853, _1476855] : [36831 ^ _777081 : [(36832 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476851), 36830 ^ [_1476849, _1476851, _1476853, _1476855]), _1476853)))], (36834 ^ _777081) ^ [] : [hAPP(_1476855, 36830 ^ [_1476849, _1476851, _1476853, _1476855]) = c_Orderings_Obot__class_Obot(tc_fun(_1476849, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1476849, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476851, tc_fun(_1476849, tc_HOL_Obool)), _1476853), _1476855))], (36819 ^ _777081) ^ [_1476620, _1476622, _1476624, _1476626] : [c_Orderings_Obot__class_Obot(tc_fun(_1476620, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476622, tc_fun(_1476620, tc_HOL_Obool)), _1476624), _1476626), 36822 ^ _777081 : [(36823 ^ _777081) ^ [_1476736] : [hBOOL(hAPP(hAPP(c_member(_1476622), _1476736), _1476624)), -(hAPP(_1476626, _1476736) = c_Orderings_Obot__class_Obot(tc_fun(_1476620, tc_HOL_Obool)))]]], (36848 ^ _777081) ^ [_1477361, _1477363, _1477365, _1477367, _1477369] : [36850 ^ _777081 : [(36851 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1477363), 36849 ^ [_1477361, _1477363, _1477365, _1477367, _1477369]), _1477365)))], (36853 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477361, tc_HOL_Obool)), hAPP(_1477367, 36849 ^ [_1477361, _1477363, _1477365, _1477367, _1477369])), _1477369))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477361, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477363, tc_fun(_1477361, tc_HOL_Obool)), _1477365), _1477367)), _1477369)))], (36838 ^ _777081) ^ [_1477103, _1477105, _1477107, _1477109, _1477111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477103, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477105, tc_fun(_1477103, tc_HOL_Obool)), _1477107), _1477109)), _1477111)), 36841 ^ _777081 : [(36842 ^ _777081) ^ [_1477236] : [hBOOL(hAPP(hAPP(c_member(_1477105), _1477236), _1477107)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477103, tc_HOL_Obool)), hAPP(_1477109, _1477236)), _1477111)))]]], (36857 ^ _777081) ^ [_1477624, _1477626, _1477628, _1477630, _1477632, _1477634] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477624, tc_fun(_1477626, tc_HOL_Obool)), _1477628), hAPP(hAPP(c_COMBB(_1477630, tc_fun(_1477626, tc_HOL_Obool), _1477624), _1477632), _1477634)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477630, tc_fun(_1477626, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1477624, _1477630, _1477634), _1477628)), _1477632))], (36859 ^ _777081) ^ [_1477701, _1477703, _1477705, _1477707, _1477709, _1477711] : [-(hAPP(c_Set_Oimage(_1477701, _1477703, _1477705), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477707, tc_fun(_1477701, tc_HOL_Obool)), _1477709), _1477711)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477707, tc_fun(_1477703, tc_HOL_Obool)), _1477709), hAPP(hAPP(c_COMBB(tc_fun(_1477701, tc_HOL_Obool), tc_fun(_1477703, tc_HOL_Obool), _1477707), c_Set_Oimage(_1477701, _1477703, _1477705)), _1477711)))], (36861 ^ _777081) ^ [_1477785, _1477787, _1477789, _1477791, _1477793, _1477795] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477785, tc_fun(_1477787, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1477789, _1477785, _1477791), _1477793)), _1477795) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477789, tc_fun(_1477787, tc_HOL_Obool)), _1477793), hAPP(hAPP(c_COMBB(_1477785, tc_fun(_1477787, tc_HOL_Obool), _1477789), _1477795), _1477791)))], (36863 ^ _777081) ^ [_1477862, _1477864, _1477866, _1477868, _1477870] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477862, tc_fun(_1477864, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477862, tc_HOL_Obool)), _1477866), _1477868)), _1477870) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477864, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477862, tc_fun(_1477864, tc_HOL_Obool)), _1477866), _1477870)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477862, tc_fun(_1477864, tc_HOL_Obool)), _1477868), _1477870)))], (36865 ^ _777081) ^ [_1477951, _1477953, _1477955, _1477957, _1477959] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477951, tc_fun(_1477953, tc_HOL_Obool)), _1477955), hAPP(hAPP(c_COMBS(_1477951, tc_fun(_1477953, tc_HOL_Obool), tc_fun(_1477953, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477953, tc_HOL_Obool), tc_fun(tc_fun(_1477953, tc_HOL_Obool), tc_fun(_1477953, tc_HOL_Obool)), _1477951), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477953, tc_HOL_Obool))), _1477957)), _1477959)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1477953, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477951, tc_fun(_1477953, tc_HOL_Obool)), _1477955), _1477957)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1477951, tc_fun(_1477953, tc_HOL_Obool)), _1477955), _1477959)))], (36867 ^ _777081) ^ [_1478072, _1478074, _1478076, _1478078, _1478080] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478072, tc_fun(_1478074, tc_HOL_Obool)), _1478076), hAPP(hAPP(c_COMBB(tc_fun(_1478074, tc_HOL_Obool), tc_fun(_1478074, tc_HOL_Obool), _1478072), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478074, tc_HOL_Obool)), _1478078)), _1478080)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478074, tc_HOL_Obool)), _1478078), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478072, tc_fun(_1478074, tc_HOL_Obool)), _1478076), _1478080)))], (36869 ^ _777081) ^ [_1478162, _1478164, _1478166, _1478168, _1478170] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478162, tc_fun(_1478164, tc_HOL_Obool)), _1478166), hAPP(hAPP(c_COMBC(_1478162, tc_fun(_1478164, tc_HOL_Obool), tc_fun(_1478164, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478164, tc_HOL_Obool), tc_fun(tc_fun(_1478164, tc_HOL_Obool), tc_fun(_1478164, tc_HOL_Obool)), _1478162), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478164, tc_HOL_Obool))), _1478168)), _1478170)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478164, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478162, tc_fun(_1478164, tc_HOL_Obool)), _1478166), _1478168)), _1478170))], (36871 ^ _777081) ^ [_1478271, _1478273, _1478275, _1478277, _1478279] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478271, tc_HOL_Obool)), _1478273), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478275, tc_fun(_1478271, tc_HOL_Obool)), _1478277), _1478279)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478275, tc_fun(_1478271, tc_HOL_Obool)), _1478277), hAPP(hAPP(c_COMBB(tc_fun(_1478271, tc_HOL_Obool), tc_fun(_1478271, tc_HOL_Obool), _1478275), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478271, tc_HOL_Obool)), _1478273)), _1478279)))], (36873 ^ _777081) ^ [_1478361, _1478363, _1478365, _1478367, _1478369] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478361, tc_HOL_Obool)), _1478363), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478365, tc_fun(_1478361, tc_HOL_Obool)), _1478367), _1478369)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478365, tc_fun(_1478361, tc_HOL_Obool)), _1478367), hAPP(hAPP(c_COMBB(tc_fun(_1478361, tc_HOL_Obool), tc_fun(_1478361, tc_HOL_Obool), _1478365), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478361, tc_HOL_Obool)), _1478363)), _1478369)))], (36875 ^ _777081) ^ [_1478451, _1478453, _1478455, _1478457, _1478459] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478451, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478453, tc_fun(_1478451, tc_HOL_Obool)), _1478455), _1478457)), _1478459) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478453, tc_fun(_1478451, tc_HOL_Obool)), _1478455), hAPP(hAPP(c_COMBC(_1478453, tc_fun(_1478451, tc_HOL_Obool), tc_fun(_1478451, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478451, tc_HOL_Obool), tc_fun(tc_fun(_1478451, tc_HOL_Obool), tc_fun(_1478451, tc_HOL_Obool)), _1478453), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478451, tc_HOL_Obool))), _1478457)), _1478459)))], (36877 ^ _777081) ^ [_1478560, _1478562, _1478564, _1478566, _1478568, _1478570, _1478572] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478560, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478562, tc_fun(_1478560, tc_HOL_Obool)), _1478564), _1478566)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478568, tc_fun(_1478560, tc_HOL_Obool)), _1478570), _1478572)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478562, tc_fun(_1478560, tc_HOL_Obool)), _1478564), hAPP(hAPP(c_COMBB(tc_fun(_1478568, tc_fun(_1478560, tc_HOL_Obool)), tc_fun(_1478560, tc_HOL_Obool), _1478562), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478568, tc_fun(_1478560, tc_HOL_Obool)), _1478570)), hAPP(hAPP(c_COMBC(_1478562, tc_fun(_1478568, tc_fun(_1478560, tc_HOL_Obool)), tc_fun(_1478568, tc_fun(_1478560, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1478560, tc_HOL_Obool), tc_fun(_1478560, tc_HOL_Obool)), tc_fun(tc_fun(_1478568, tc_fun(_1478560, tc_HOL_Obool)), tc_fun(_1478568, tc_fun(_1478560, tc_HOL_Obool))), _1478562), c_COMBB(tc_fun(_1478560, tc_HOL_Obool), tc_fun(_1478560, tc_HOL_Obool), _1478568)), hAPP(hAPP(c_COMBB(tc_fun(_1478560, tc_HOL_Obool), tc_fun(tc_fun(_1478560, tc_HOL_Obool), tc_fun(_1478560, tc_HOL_Obool)), _1478562), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1478560, tc_HOL_Obool))), _1478566))), _1478572))))], (36879 ^ _777081) ^ [_1478763, _1478765, _1478767, _1478769, _1478771, _1478773] : [class_Complete__Lattice_Ocomplete__lattice(_1478763), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478765, tc_fun(_1478767, _1478763)), _1478769), _1478771), _1478773) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478765, _1478763), _1478769), hAPP(hAPP(c_COMBC(_1478765, _1478767, _1478763), _1478771), _1478773)))], (36885 ^ _777081) ^ [_1478914, _1478916, _1478918, _1478920, _1478922] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478914, tc_fun(_1478916, tc_HOL_Obool)), _1478918), hAPP(hAPP(c_COMBC(_1478914, tc_fun(_1478916, tc_HOL_Obool), tc_fun(_1478916, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1478916, tc_HOL_Obool), tc_fun(tc_fun(_1478916, tc_HOL_Obool), tc_fun(_1478916, tc_HOL_Obool)), _1478914), c_Groups_Ominus__class_Ominus(tc_fun(_1478916, tc_HOL_Obool))), _1478920)), _1478922)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1478916, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478914, tc_fun(_1478916, tc_HOL_Obool)), _1478918), _1478920)), _1478922))], (36887 ^ _777081) ^ [_1479023, _1479025, _1479027, _1479029, _1479031] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1479023, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479025, tc_fun(_1479023, tc_HOL_Obool)), _1479027), _1479029)), _1479031) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479025, tc_fun(_1479023, tc_HOL_Obool)), _1479027), hAPP(hAPP(c_COMBC(_1479025, tc_fun(_1479023, tc_HOL_Obool), tc_fun(_1479023, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1479023, tc_HOL_Obool), tc_fun(tc_fun(_1479023, tc_HOL_Obool), tc_fun(_1479023, tc_HOL_Obool)), _1479025), c_Groups_Ominus__class_Ominus(tc_fun(_1479023, tc_HOL_Obool))), _1479029)), _1479031)))], (36889 ^ _777081) ^ [_1479132, _1479134, _1479136, _1479138, _1479140, _1479142] : [-(hAPP(c_Set_Ovimage(_1479132, _1479134, _1479136), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479138, tc_fun(_1479134, tc_HOL_Obool)), _1479140), _1479142)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479138, tc_fun(_1479132, tc_HOL_Obool)), _1479140), hAPP(hAPP(c_COMBB(tc_fun(_1479134, tc_HOL_Obool), tc_fun(_1479132, tc_HOL_Obool), _1479138), c_Set_Ovimage(_1479132, _1479134, _1479136)), _1479142)))], (36891 ^ _777081) ^ [_1479216, _1479218, _1479220, _1479222, _1479224] : [class_Complete__Lattice_Ocomplete__lattice(_1479216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479218, tc_HOL_Obool)), _1479220), _1479222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1479216), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479218, _1479216), _1479220), _1479224)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479218, _1479216), _1479222), _1479224))))], (36901 ^ _777081) ^ [_1479425, _1479427, _1479429, _1479431, _1479433] : [class_Complete__Lattice_Ocomplete__lattice(_1479425), hBOOL(hAPP(hAPP(c_member(_1479427), _1479429), _1479431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1479425), hAPP(_1479433, _1479429)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479427, _1479425), _1479431), _1479433))))], (36911 ^ _777081) ^ [_1479616, _1479618, _1479620, _1479622, _1479624, _1479626] : [hBOOL(hAPP(hAPP(c_member(_1479616), _1479618), _1479620)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479616, tc_fun(_1479622, tc_HOL_Obool)), _1479620), hAPP(hAPP(c_COMBB(tc_fun(_1479622, tc_HOL_Obool), tc_fun(_1479622, tc_HOL_Obool), _1479616), hAPP(c_Set_Oinsert(_1479622), _1479624)), _1479626)) = hAPP(hAPP(c_Set_Oinsert(_1479622), _1479624), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479616, tc_fun(_1479622, tc_HOL_Obool)), _1479620), _1479626)))], (36917 ^ _777081) ^ [_1479821, _1479823, _1479825, _1479827, _1479829] : [hBOOL(hAPP(hAPP(c_member(_1479821), _1479823), _1479825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1479827, tc_HOL_Obool)), hAPP(_1479829, _1479823)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479821, tc_fun(_1479827, tc_HOL_Obool)), _1479825), _1479829))))], (36923 ^ _777081) ^ [_1479968, _1479970, _1479972, _1479974, _1479976] : [hBOOL(hAPP(hAPP(c_member(_1479968), _1479970), _1479972)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1479974, tc_HOL_Obool)), hAPP(_1479976, _1479970)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479968, tc_fun(_1479974, tc_HOL_Obool)), _1479972), _1479976)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1479968, tc_fun(_1479974, tc_HOL_Obool)), _1479972), _1479976))], (36929 ^ _777081) ^ [_1480159, _1480161, _1480163, _1480165, _1480167] : [_1480159 = c_Orderings_Obot__class_Obot(tc_fun(_1480161, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480161, tc_fun(_1480163, tc_HOL_Obool)), _1480159), hAPP(hAPP(c_COMBB(tc_fun(_1480163, tc_HOL_Obool), tc_fun(_1480163, tc_HOL_Obool), _1480161), hAPP(c_Set_Oinsert(_1480163), _1480165)), _1480167)) = c_Orderings_Obot__class_Obot(tc_fun(_1480163, tc_HOL_Obool)))], (36935 ^ _777081) ^ [_1480322, _1480324, _1480326, _1480328, _1480330] : [-(_1480322 = c_Orderings_Obot__class_Obot(tc_fun(_1480324, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480324, tc_fun(_1480326, tc_HOL_Obool)), _1480322), hAPP(hAPP(c_COMBB(tc_fun(_1480326, tc_HOL_Obool), tc_fun(_1480326, tc_HOL_Obool), _1480324), hAPP(c_Set_Oinsert(_1480326), _1480328)), _1480330)) = hAPP(hAPP(c_Set_Oinsert(_1480326), _1480328), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480324, tc_fun(_1480326, tc_HOL_Obool)), _1480322), _1480330)))], (36941 ^ _777081) ^ [_1480424, _1480426] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480424, tc_fun(_1480424, tc_HOL_Obool)), _1480426), hAPP(hAPP(c_COMBC(_1480424, tc_fun(_1480424, tc_HOL_Obool), tc_fun(_1480424, tc_HOL_Obool)), c_Set_Oinsert(_1480424)), c_Orderings_Obot__class_Obot(tc_fun(_1480424, tc_HOL_Obool)))) = _1480426)], (36943 ^ _777081) ^ [_1480502, _1480504, _1480506, _1480508, _1480510] : [_1480502 = c_Orderings_Obot__class_Obot(tc_fun(_1480504, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1480506), _1480508), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480504, tc_fun(_1480506, tc_HOL_Obool)), _1480502), _1480510)) = hAPP(hAPP(c_Set_Oinsert(_1480506), _1480508), c_Orderings_Obot__class_Obot(tc_fun(_1480506, tc_HOL_Obool))))], (36949 ^ _777081) ^ [_1480655, _1480657, _1480659, _1480661, _1480663] : [-(_1480655 = c_Orderings_Obot__class_Obot(tc_fun(_1480657, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1480659), _1480661), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480657, tc_fun(_1480659, tc_HOL_Obool)), _1480655), _1480663)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480657, tc_fun(_1480659, tc_HOL_Obool)), _1480655), hAPP(hAPP(c_COMBB(tc_fun(_1480659, tc_HOL_Obool), tc_fun(_1480659, tc_HOL_Obool), _1480657), hAPP(c_Set_Oinsert(_1480659), _1480661)), _1480663)))], (36955 ^ _777081) ^ [_1480775, _1480777, _1480779, _1480781, _1480783] : [_1480775 = c_Orderings_Obot__class_Obot(tc_fun(_1480777, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480777, tc_fun(_1480779, tc_HOL_Obool)), _1480775), hAPP(hAPP(c_COMBB(tc_fun(_1480779, tc_HOL_Obool), tc_fun(_1480779, tc_HOL_Obool), _1480777), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480779, tc_HOL_Obool)), _1480781)), _1480783)) = c_Orderings_Obot__class_Obot(tc_fun(_1480779, tc_HOL_Obool)))], (36961 ^ _777081) ^ [_1480944, _1480946, _1480948, _1480950, _1480952] : [-(_1480944 = c_Orderings_Obot__class_Obot(tc_fun(_1480946, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480946, tc_fun(_1480948, tc_HOL_Obool)), _1480944), hAPP(hAPP(c_COMBB(tc_fun(_1480948, tc_HOL_Obool), tc_fun(_1480948, tc_HOL_Obool), _1480946), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480948, tc_HOL_Obool)), _1480950)), _1480952)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480948, tc_HOL_Obool)), _1480950), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1480946, tc_fun(_1480948, tc_HOL_Obool)), _1480944), _1480952)))], (36967 ^ _777081) ^ [_1481070, _1481072, _1481074, _1481076, _1481078] : [_1481070 = c_Orderings_Obot__class_Obot(tc_fun(_1481072, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481072, tc_fun(_1481074, tc_HOL_Obool)), _1481070), hAPP(hAPP(c_COMBC(_1481072, tc_fun(_1481074, tc_HOL_Obool), tc_fun(_1481074, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1481074, tc_HOL_Obool), tc_fun(tc_fun(_1481074, tc_HOL_Obool), tc_fun(_1481074, tc_HOL_Obool)), _1481072), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481074, tc_HOL_Obool))), _1481076)), _1481078)) = c_Orderings_Obot__class_Obot(tc_fun(_1481074, tc_HOL_Obool)))], (36973 ^ _777081) ^ [_1481277, _1481279, _1481281, _1481283, _1481285] : [-(_1481277 = c_Orderings_Obot__class_Obot(tc_fun(_1481279, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481279, tc_fun(_1481281, tc_HOL_Obool)), _1481277), hAPP(hAPP(c_COMBC(_1481279, tc_fun(_1481281, tc_HOL_Obool), tc_fun(_1481281, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1481281, tc_HOL_Obool), tc_fun(tc_fun(_1481281, tc_HOL_Obool), tc_fun(_1481281, tc_HOL_Obool)), _1481279), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481281, tc_HOL_Obool))), _1481283)), _1481285)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481281, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481279, tc_fun(_1481281, tc_HOL_Obool)), _1481277), _1481283)), _1481285))], (36979 ^ _777081) ^ [_1481422, _1481424, _1481426, _1481428, _1481430] : [_1481422 = c_Orderings_Obot__class_Obot(tc_fun(_1481424, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481426, tc_HOL_Obool)), _1481428), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481424, tc_fun(_1481426, tc_HOL_Obool)), _1481422), _1481430)) = _1481428)], (36985 ^ _777081) ^ [_1481555, _1481557, _1481559, _1481561, _1481563] : [-(_1481555 = c_Orderings_Obot__class_Obot(tc_fun(_1481557, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481559, tc_HOL_Obool)), _1481561), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481557, tc_fun(_1481559, tc_HOL_Obool)), _1481555), _1481563)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481557, tc_fun(_1481559, tc_HOL_Obool)), _1481555), hAPP(hAPP(c_COMBB(tc_fun(_1481559, tc_HOL_Obool), tc_fun(_1481559, tc_HOL_Obool), _1481557), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481559, tc_HOL_Obool)), _1481561)), _1481563)))], (36991 ^ _777081) ^ [_1481681, _1481683, _1481685, _1481687, _1481689] : [_1481681 = c_Orderings_Obot__class_Obot(tc_fun(_1481683, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481685, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481683, tc_fun(_1481685, tc_HOL_Obool)), _1481681), _1481687)), _1481689) = _1481689)], (36997 ^ _777081) ^ [_1481814, _1481816, _1481818, _1481820, _1481822] : [-(_1481814 = c_Orderings_Obot__class_Obot(tc_fun(_1481816, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481818, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481816, tc_fun(_1481818, tc_HOL_Obool)), _1481814), _1481820)), _1481822) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481816, tc_fun(_1481818, tc_HOL_Obool)), _1481814), hAPP(hAPP(c_COMBC(_1481816, tc_fun(_1481818, tc_HOL_Obool), tc_fun(_1481818, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1481818, tc_HOL_Obool), tc_fun(tc_fun(_1481818, tc_HOL_Obool), tc_fun(_1481818, tc_HOL_Obool)), _1481816), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481818, tc_HOL_Obool))), _1481820)), _1481822)))], (37003 ^ _777081) ^ [_1481941, _1481943, _1481945, _1481947, _1481949] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481941, tc_fun(_1481943, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1481941), _1481945), _1481947)), _1481949) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481943, tc_HOL_Obool)), hAPP(_1481949, _1481945)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481941, tc_fun(_1481943, tc_HOL_Obool)), _1481947), _1481949)))], (37005 ^ _777081) ^ [_1482018, _1482020, _1482022, _1482024] : [-(hAPP(c_Set_Oimage(_1482018, _1482020, _1482022), _1482024) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482018, tc_fun(_1482020, tc_HOL_Obool)), _1482024), hAPP(hAPP(c_COMBC(_1482018, tc_fun(_1482020, tc_HOL_Obool), tc_fun(_1482020, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1482020, tc_fun(tc_fun(_1482020, tc_HOL_Obool), tc_fun(_1482020, tc_HOL_Obool)), _1482018), c_Set_Oinsert(_1482020)), _1482022)), c_Orderings_Obot__class_Obot(tc_fun(_1482020, tc_HOL_Obool)))))], (37007 ^ _777081) ^ [_1482108] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1482108) = 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, _1482108)), 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))))))))], (37009 ^ _777081) ^ [_1482146, _1482148, _1482150, _1482152, _1482154, _1482156] : [c_Equiv__Relations_Oequiv(_1482146, _1482148, _1482150), c_Equiv__Relations_Ocongruent(_1482146, tc_fun(_1482152, tc_HOL_Obool), _1482150, _1482154), hBOOL(hAPP(hAPP(c_member(_1482146), _1482156), _1482148)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482146, tc_fun(_1482152, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1482146, _1482146, _1482150), hAPP(hAPP(c_Set_Oinsert(_1482146), _1482156), c_Orderings_Obot__class_Obot(tc_fun(_1482146, tc_HOL_Obool))))), _1482154) = hAPP(_1482154, _1482156))], (37023 ^ _777081) ^ [_1482447, _1482449, _1482451, _1482453, _1482455, _1482457, _1482459, _1482461, _1482463, _1482465] : [c_Equiv__Relations_Oequiv(_1482447, _1482449, _1482451), c_Equiv__Relations_Oequiv(_1482453, _1482455, _1482457), c_Equiv__Relations_Ocongruent2(_1482447, _1482453, tc_fun(_1482459, tc_HOL_Obool), _1482451, _1482457, _1482461), hBOOL(hAPP(hAPP(c_member(_1482447), _1482463), _1482449)), hBOOL(hAPP(hAPP(c_member(_1482453), _1482465), _1482455)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482447, tc_fun(_1482459, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1482447, _1482447, _1482451), hAPP(hAPP(c_Set_Oinsert(_1482447), _1482463), c_Orderings_Obot__class_Obot(tc_fun(_1482447, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1482453, tc_fun(_1482459, tc_HOL_Obool)), tc_fun(_1482459, tc_HOL_Obool), _1482447), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1482453, tc_fun(_1482459, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1482453, _1482453, _1482457), hAPP(hAPP(c_Set_Oinsert(_1482453), _1482465), c_Orderings_Obot__class_Obot(tc_fun(_1482453, tc_HOL_Obool)))))), _1482461)) = hAPP(hAPP(_1482461, _1482463), _1482465))], (37045 ^ _777081) ^ [_1483030, _1483032, _1483034, _1483036, _1483038, _1483040, _1483042, _1483044] : [hBOOL(hAPP(hAPP(c_member(_1483030), _1483032), _1483034)), hBOOL(hAPP(hAPP(hAPP(_1483036, _1483032), _1483038), _1483040)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1483030, tc_fun(_1483042, tc_fun(_1483044, tc_HOL_Obool))), _1483034), _1483036), _1483038), _1483040)))], (37055 ^ _777081) ^ [_1483268, _1483270] : [hAPP(c_Int_ORep__Integ, _1483268) = hAPP(c_Int_ORep__Integ, _1483270), -(_1483268 = _1483270)], (37061 ^ _777081) ^ [_1483353, _1483355] : [_1483353 = _1483355, -(hAPP(c_Int_ORep__Integ, _1483353) = hAPP(c_Int_ORep__Integ, _1483355))], (37067 ^ _777081) ^ [_1483444] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1483444)) = _1483444)], (37069 ^ _777081) ^ [_1483473, _1483475, _1483477, _1483479, _1483481, _1483483, _1483485, _1483487] : [c_Equiv__Relations_Oequiv(_1483473, _1483475, _1483477), c_Equiv__Relations_Ocongruent2(_1483473, _1483479, _1483481, _1483477, _1483483, _1483485), hBOOL(hAPP(hAPP(c_member(_1483473), _1483487), _1483475)), -(c_Equiv__Relations_Ocongruent(_1483479, _1483481, _1483483, hAPP(_1483485, _1483487)))], (37083 ^ _777081) ^ [_1483724] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1483724)), c_Int_OInteg)))], (37085 ^ _777081) ^ [_1483782, _1483784, _1483786, _1483788, _1483790, _1483792] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1483782, tc_fun(_1483784, tc_fun(_1483786, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1483782, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1483784, _1483786), tc_HOL_Obool), tc_fun(_1483784, tc_fun(_1483786, tc_HOL_Obool)), _1483782), hAPP(c_COMBC(_1483784, tc_fun(tc_prod(_1483784, _1483786), tc_HOL_Obool), tc_fun(_1483786, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483786, tc_fun(tc_fun(tc_prod(_1483784, _1483786), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1483784, _1483786), tc_HOL_Obool), tc_fun(_1483786, tc_HOL_Obool)), _1483784), c_COMBC(_1483786, tc_fun(tc_prod(_1483784, _1483786), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1483786, tc_prod(_1483784, _1483786)), tc_fun(_1483786, tc_fun(tc_fun(tc_prod(_1483784, _1483786), tc_HOL_Obool), tc_HOL_Obool)), _1483784), hAPP(c_COMBB(tc_prod(_1483784, _1483786), tc_fun(tc_fun(tc_prod(_1483784, _1483786), tc_HOL_Obool), tc_HOL_Obool), _1483786), c_member(tc_prod(_1483784, _1483786)))), c_Product__Type_OPair(_1483784, _1483786))))), _1483788)), _1483790), _1483792)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1483784, _1483786)), hAPP(hAPP(c_Product__Type_OPair(_1483784, _1483786), _1483790), _1483792)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1483782, tc_fun(tc_prod(_1483784, _1483786), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1483782, tc_HOL_Obool))), _1483788))))], (37091 ^ _777081) ^ [_1484265, _1484267, _1484269, _1484271, _1484273, _1484275] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1484267, _1484269)), hAPP(hAPP(c_Product__Type_OPair(_1484267, _1484269), _1484273), _1484275)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1484265, tc_fun(tc_prod(_1484267, _1484269), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1484265, tc_HOL_Obool))), _1484271))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1484265, tc_fun(_1484267, tc_fun(_1484269, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1484265, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1484267, _1484269), tc_HOL_Obool), tc_fun(_1484267, tc_fun(_1484269, tc_HOL_Obool)), _1484265), hAPP(c_COMBC(_1484267, tc_fun(tc_prod(_1484267, _1484269), tc_HOL_Obool), tc_fun(_1484269, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484269, tc_fun(tc_fun(tc_prod(_1484267, _1484269), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1484267, _1484269), tc_HOL_Obool), tc_fun(_1484269, tc_HOL_Obool)), _1484267), c_COMBC(_1484269, tc_fun(tc_prod(_1484267, _1484269), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1484269, tc_prod(_1484267, _1484269)), tc_fun(_1484269, tc_fun(tc_fun(tc_prod(_1484267, _1484269), tc_HOL_Obool), tc_HOL_Obool)), _1484267), hAPP(c_COMBB(tc_prod(_1484267, _1484269), tc_fun(tc_fun(tc_prod(_1484267, _1484269), tc_HOL_Obool), tc_HOL_Obool), _1484269), c_member(tc_prod(_1484267, _1484269)))), c_Product__Type_OPair(_1484267, _1484269))))), _1484271)), _1484273), _1484275)))], (37097 ^ _777081) ^ [_1484754, _1484756, _1484758, _1484760, _1484762, _1484764, _1484766, _1484768, _1484770, _1484772] : [c_Equiv__Relations_Ocongruent2(_1484754, _1484756, _1484758, _1484760, _1484762, _1484764), hBOOL(hAPP(hAPP(c_member(tc_prod(_1484754, _1484754)), hAPP(hAPP(c_Product__Type_OPair(_1484754, _1484754), _1484766), _1484768)), _1484760)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1484756, _1484756)), hAPP(hAPP(c_Product__Type_OPair(_1484756, _1484756), _1484770), _1484772)), _1484762)), -(hAPP(hAPP(_1484764, _1484766), _1484770) = hAPP(hAPP(_1484764, _1484768), _1484772))], (37111 ^ _777081) ^ [_1485091, _1485093, _1485095, _1485097, _1485099, _1485101] : [c_Equiv__Relations_Ocongruent(_1485091, _1485093, _1485095, _1485097), hBOOL(hAPP(hAPP(c_member(tc_prod(_1485091, _1485091)), hAPP(hAPP(c_Product__Type_OPair(_1485091, _1485091), _1485099), _1485101)), _1485095)), -(hAPP(_1485097, _1485099) = hAPP(_1485097, _1485101))], (37121 ^ _777081) ^ [_1485290, _1485292, _1485294, _1485296, _1485298, _1485300, _1485302, _1485304, _1485306] : [c_Equiv__Relations_Oequiv(_1485290, _1485292, _1485294), c_Equiv__Relations_Oequiv(_1485296, _1485298, _1485300), c_Equiv__Relations_Ocongruent2(_1485290, _1485296, tc_fun(_1485302, tc_HOL_Obool), _1485294, _1485300, _1485304), hBOOL(hAPP(hAPP(c_member(_1485296), _1485306), _1485298)), -(c_Equiv__Relations_Ocongruent(_1485290, tc_fun(_1485302, tc_HOL_Obool), _1485294, hAPP(hAPP(c_COMBB(tc_fun(_1485296, tc_fun(_1485302, tc_HOL_Obool)), tc_fun(_1485302, tc_HOL_Obool), _1485290), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485296, tc_fun(_1485302, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1485296, _1485296, _1485300), hAPP(hAPP(c_Set_Oinsert(_1485296), _1485306), c_Orderings_Obot__class_Obot(tc_fun(_1485296, tc_HOL_Obool)))))), _1485304)))], (37139 ^ _777081) ^ [_1485717] : [-(hAPP(c_Int_Onat, _1485717) = 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, _1485717)), 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)))))))], (37141 ^ _777081) ^ [_1485755, _1485757, _1485759, _1485761, _1485763, _1485765, _1485767] : [c_Equiv__Relations_Oequiv(_1485755, _1485757, _1485759), c_Equiv__Relations_Ocongruent(_1485755, tc_fun(_1485761, tc_HOL_Obool), _1485759, _1485763), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485755, tc_fun(_1485761, tc_HOL_Obool)), _1485765), _1485763) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485755, tc_fun(_1485761, tc_HOL_Obool)), _1485767), _1485763), hBOOL(hAPP(hAPP(c_member(tc_fun(_1485755, tc_HOL_Obool)), _1485765), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1485755), _1485757), _1485759))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1485755, tc_HOL_Obool)), _1485767), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1485755), _1485757), _1485759))), 37163 ^ _777081 : [(37164 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1485755), 37162 ^ [_1485755, _1485757, _1485759, _1485761, _1485763, _1485765, _1485767]), _1485757)))], (37167 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1485755), 37165 ^ [_1485755, _1485757, _1485759, _1485761, _1485763, _1485765, _1485767]), _1485757)))], (37169 ^ _777081) ^ [] : [-(hAPP(_1485763, 37162 ^ [_1485755, _1485757, _1485759, _1485761, _1485763, _1485765, _1485767]) = hAPP(_1485763, 37165 ^ [_1485755, _1485757, _1485759, _1485761, _1485763, _1485765, _1485767]))], (37171 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1485755, _1485755)), hAPP(hAPP(c_Product__Type_OPair(_1485755, _1485755), 37162 ^ [_1485755, _1485757, _1485759, _1485761, _1485763, _1485765, _1485767]), 37165 ^ [_1485755, _1485757, _1485759, _1485761, _1485763, _1485765, _1485767])), _1485759))]], -(_1485765 = _1485767)], (37175 ^ _777081) ^ [_1486725, _1486727, _1486729, _1486731, _1486733, _1486735, _1486737, _1486739, _1486741, _1486743, _1486745] : [c_Equiv__Relations_Oequiv(_1486725, _1486727, _1486729), c_Equiv__Relations_Oequiv(_1486731, _1486733, _1486735), c_Equiv__Relations_Ocongruent2(_1486725, _1486731, tc_fun(_1486737, tc_HOL_Obool), _1486729, _1486735, _1486739), hBOOL(hAPP(hAPP(c_member(tc_fun(_1486725, tc_HOL_Obool)), _1486741), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1486725), _1486727), _1486729))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1486731, tc_HOL_Obool)), _1486743), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1486731), _1486733), _1486735))), 37197 ^ _777081 : [(37198 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486725), 37196 ^ [_1486725, _1486727, _1486729, _1486731, _1486733, _1486735, _1486737, _1486739, _1486741, _1486743, _1486745]), _1486727)))], (37201 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486731), 37199 ^ [_1486725, _1486727, _1486729, _1486731, _1486733, _1486735, _1486737, _1486739, _1486741, _1486743, _1486745]), _1486733)))], (37203 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1486737, tc_HOL_Obool)), hAPP(hAPP(_1486739, 37196 ^ [_1486725, _1486727, _1486729, _1486731, _1486733, _1486735, _1486737, _1486739, _1486741, _1486743, _1486745]), 37199 ^ [_1486725, _1486727, _1486729, _1486731, _1486733, _1486735, _1486737, _1486739, _1486741, _1486743, _1486745])), _1486745))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1486737, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486725, tc_fun(_1486737, tc_HOL_Obool)), _1486741), hAPP(hAPP(c_COMBB(tc_fun(_1486731, tc_fun(_1486737, tc_HOL_Obool)), tc_fun(_1486737, tc_HOL_Obool), _1486725), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1486731, tc_fun(_1486737, tc_HOL_Obool)), _1486743)), _1486739))), _1486745)))], (37207 ^ _777081) ^ [_1487727, _1487729, _1487731, _1487733, _1487735, _1487737, _1487739] : [c_Equiv__Relations_Oequiv(_1487727, _1487729, _1487731), c_Equiv__Relations_Ocongruent(_1487727, tc_fun(_1487733, tc_HOL_Obool), _1487731, _1487735), hBOOL(hAPP(hAPP(c_member(tc_fun(_1487727, tc_HOL_Obool)), _1487737), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1487727), _1487729), _1487731))), 37221 ^ _777081 : [(37222 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1487727), 37220 ^ [_1487727, _1487729, _1487731, _1487733, _1487735, _1487737, _1487739]), _1487729)))], (37224 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1487733, tc_HOL_Obool)), hAPP(_1487735, 37220 ^ [_1487727, _1487729, _1487731, _1487733, _1487735, _1487737, _1487739])), _1487739))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1487733, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1487727, tc_fun(_1487733, tc_HOL_Obool)), _1487737), _1487735)), _1487739)))], (37228 ^ _777081) ^ [_1488268, _1488270, _1488272, _1488274, _1488276, _1488278, _1488280] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1488268, tc_fun(_1488270, tc_fun(_1488272, tc_HOL_Obool))), _1488274), _1488276), _1488278), _1488280)), 37232 ^ _777081 : [(37233 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1488268), 37231 ^ [_1488268, _1488270, _1488272, _1488274, _1488276, _1488278, _1488280]), _1488274)))], (37235 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1488276, 37231 ^ [_1488268, _1488270, _1488272, _1488274, _1488276, _1488278, _1488280]), _1488278), _1488280)))]]], (37237 ^ _777081) ^ [_1488486, _1488488, _1488490, _1488492, _1488494, _1488496, _1488498] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1488486, tc_fun(_1488488, tc_fun(_1488490, tc_HOL_Obool))), _1488492), _1488494), _1488496), _1488498))), 37238 ^ _777081 : [(37239 ^ _777081) ^ [_1488571] : [hBOOL(hAPP(hAPP(c_member(_1488486), _1488571), _1488492)), hBOOL(hAPP(hAPP(hAPP(_1488494, _1488571), _1488496), _1488498))]]], (37247 ^ _777081) ^ [_1488739, _1488741, _1488743, _1488745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488739, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1488739, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37248 ^ [_1488739, _1488741, _1488743, _1488745])), _1488741)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1488739, 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), 37248 ^ [_1488739, _1488741, _1488743, _1488745]), _1488743))), _1488745))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1488739, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1488739, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1488741)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1488739, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1488745))))], (37254 ^ _777081) ^ [_1489069, _1489071, _1489073, _1489075, _1489077] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1489069, _1489069, _1489071, _1489073, _1489075), _1489077)), -(hBOOL(hAPP(hAPP(c_member(_1489069), _1489073), _1489075))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1489069, _1489071, hAPP(hAPP(c_Set_Oinsert(_1489069), _1489073), _1489075)), _1489077)))], (37264 ^ _777081) ^ [_1489225, _1489227, _1489229, _1489231] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1489225, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37265 ^ [_1489225, _1489227, _1489229, _1489231])), _1489227) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1489225, 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), 37265 ^ [_1489225, _1489227, _1489229, _1489231]), _1489229))), _1489231), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1489225, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1489227) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1489225, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1489231))], (37271 ^ _777081) ^ [_1489520, _1489522, _1489524] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1489520, _1489522, c_Orderings_Obot__class_Obot(tc_fun(_1489520, tc_HOL_Obool))), _1489524))], (37273 ^ _777081) ^ [_1489558, _1489560, _1489562, _1489564] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1489558, _1489560, _1489562), _1489564)), _1489562 = c_Orderings_Obot__class_Obot(tc_fun(_1489558, tc_HOL_Obool))], (37279 ^ _777081) ^ [_1489683, _1489685, _1489687, _1489689] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1489683, _1489685, hAPP(hAPP(c_Set_Oinsert(_1489683), _1489687), c_Orderings_Obot__class_Obot(tc_fun(_1489683, tc_HOL_Obool)))), _1489689)), -(_1489687 = _1489689)], (37285 ^ _777081) ^ [_1489798, _1489800, _1489802, _1489804] : [_1489802 = _1489804, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1489798, _1489800, hAPP(hAPP(c_Set_Oinsert(_1489798), _1489802), c_Orderings_Obot__class_Obot(tc_fun(_1489798, tc_HOL_Obool)))), _1489804)))], (37291 ^ _777081) ^ [_1489919, _1489921, _1489923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489919, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1489919, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37292 ^ [_1489919, _1489921, _1489923])), _1489921)), _1489923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489919, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1489919, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1489921)), _1489923)))], (37298 ^ _777081) ^ [_1490145, _1490147] : [-(c_Relation_OId__on(_1490145, _1490147) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1490145, tc_fun(tc_prod(_1490145, _1490145), tc_HOL_Obool)), _1490147), hAPP(hAPP(c_COMBC(_1490145, tc_fun(tc_prod(_1490145, _1490145), tc_HOL_Obool), tc_fun(tc_prod(_1490145, _1490145), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1490145, _1490145), tc_fun(tc_fun(tc_prod(_1490145, _1490145), tc_HOL_Obool), tc_fun(tc_prod(_1490145, _1490145), tc_HOL_Obool)), _1490145), c_Set_Oinsert(tc_prod(_1490145, _1490145))), hAPP(hAPP(c_COMBS(_1490145, _1490145, tc_prod(_1490145, _1490145)), c_Product__Type_OPair(_1490145, _1490145)), c_COMBI(_1490145)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490145, _1490145), tc_HOL_Obool)))))], (37300 ^ _777081) ^ [] : [-(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))], (37302 ^ _777081) ^ [_1490287, _1490289] : [-(c_Relation_OId__on(_1490287, _1490289) = hAPP(c_Product__Type_Oprod_Oprod__case(_1490287, _1490287, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1490287, tc_HOL_Obool, tc_fun(_1490287, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490287, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1490287, tc_HOL_Obool)), _1490287), c_COMBC(_1490287, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490287, tc_HOL_Obool), tc_fun(_1490287, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1490287), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1490287), c_fconj)), c_fequal))), _1490289)))], (37304 ^ _777081) ^ [_1490381] : [-(c_Relation_OId__on(_1490381, c_Orderings_Obot__class_Obot(tc_fun(_1490381, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490381, _1490381), tc_HOL_Obool)))], (37306 ^ _777081) ^ [_1490420, _1490422, _1490424] : [-(hAPP(c_Relation_OImage(_1490420, _1490420, c_Relation_OId__on(_1490420, _1490422)), _1490424) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490420, tc_HOL_Obool)), _1490422), _1490424))], (37308 ^ _777081) ^ [_1490468, _1490470, _1490472, _1490474] : [_1490468 = _1490470, hBOOL(hAPP(hAPP(c_member(_1490472), _1490468), _1490474)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1490472, _1490472)), hAPP(hAPP(c_Product__Type_OPair(_1490472, _1490472), _1490468), _1490470)), c_Relation_OId__on(_1490472, _1490474))))], (37318 ^ _777081) ^ [_1490684, _1490686, _1490688, _1490690] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1490684, _1490684)), hAPP(hAPP(c_Product__Type_OPair(_1490684, _1490684), _1490686), _1490688)), c_Relation_OId__on(_1490684, _1490690))), 37321 ^ _777081 : [(37322 ^ _777081) ^ [] : [-(_1490686 = _1490688)], (37324 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490684), _1490686), _1490690)))]]], (37326 ^ _777081) ^ [_1490845, _1490847, _1490849, _1490851] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1490845, _1490845)), hAPP(hAPP(c_Product__Type_OPair(_1490845, _1490845), _1490847), _1490849)), c_Relation_OId__on(_1490845, _1490851)))), _1490847 = _1490849, hBOOL(hAPP(hAPP(c_member(_1490845), _1490847), _1490851))], (37336 ^ _777081) ^ [_1491042, _1491044, _1491046, _1491048, _1491050] : [c_Typedef_Otype__definition(_1491042, _1491044, _1491046, _1491048, _1491050), -(hAPP(c_Set_Oimage(_1491042, _1491044, _1491046), c_Orderings_Otop__class_Otop(tc_fun(_1491042, tc_HOL_Obool))) = _1491050)], (37342 ^ _777081) ^ [_1491155, _1491157, _1491159, _1491161, _1491163] : [c_Typedef_Otype__definition(_1491155, _1491157, _1491159, _1491161, _1491163), -(hAPP(c_Set_Oimage(_1491157, _1491155, _1491161), _1491163) = c_Orderings_Otop__class_Otop(tc_fun(_1491155, tc_HOL_Obool)))], (37348 ^ _777081) ^ [_1491268, _1491270, _1491272, _1491274, _1491276, _1491278, _1491280] : [c_Typedef_Otype__definition(_1491268, _1491270, _1491272, _1491274, _1491276), hBOOL(hAPP(hAPP(c_member(_1491270), _1491278), _1491276)), hBOOL(hAPP(hAPP(c_member(_1491270), _1491280), _1491276)), 37359 ^ _777081 : [(37360 ^ _777081) ^ [] : [hAPP(_1491274, _1491278) = hAPP(_1491274, _1491280), -(_1491278 = _1491280)], (37366 ^ _777081) ^ [] : [_1491278 = _1491280, -(hAPP(_1491274, _1491278) = hAPP(_1491274, _1491280))]]], (37372 ^ _777081) ^ [_1491681, _1491683, _1491685, _1491687, _1491689, _1491691] : [c_Typedef_Otype__definition(_1491681, _1491683, _1491685, _1491687, _1491689), -(hAPP(_1491687, hAPP(_1491685, _1491691)) = _1491691)], (37378 ^ _777081) ^ [_1491784, _1491786, _1491788, _1491790, _1491792, _1491794, _1491796] : [c_Typedef_Otype__definition(_1491784, _1491786, _1491788, _1491790, _1491792), 37381 ^ _777081 : [(37382 ^ _777081) ^ [] : [hAPP(_1491788, _1491794) = hAPP(_1491788, _1491796), -(_1491794 = _1491796)], (37388 ^ _777081) ^ [] : [_1491794 = _1491796, -(hAPP(_1491788, _1491794) = hAPP(_1491788, _1491796))]]], (37394 ^ _777081) ^ [_1492045, _1492047, _1492049, _1492051, _1492053, _1492055] : [c_Typedef_Otype__definition(_1492045, _1492047, _1492049, _1492051, _1492053), -(hBOOL(hAPP(hAPP(c_member(_1492047), hAPP(_1492049, _1492055)), _1492053)))], (37400 ^ _777081) ^ [_1492156, _1492158, _1492160, _1492162, _1492164, _1492166] : [c_Typedef_Otype__definition(_1492156, _1492158, _1492160, _1492162, _1492164), hBOOL(hAPP(hAPP(c_member(_1492158), _1492166), _1492164)), -(hAPP(_1492160, hAPP(_1492162, _1492166)) = _1492166)], (37410 ^ _777081) ^ [_1492333, _1492335, _1492337] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492333, _1492333)), _1492335), c_Relation_OId__on(_1492333, _1492337))), 37414 ^ _777081 : [(37415 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492333), 37413 ^ [_1492333, _1492335, _1492337]), _1492337)))], (37417 ^ _777081) ^ [] : [-(_1492335 = hAPP(hAPP(c_Product__Type_OPair(_1492333, _1492333), 37413 ^ [_1492333, _1492335, _1492337]), 37413 ^ [_1492333, _1492335, _1492337]))]]], (37419 ^ _777081) ^ [_1492553, _1492555, _1492557, _1492559] : [c_Wellfounded_Omax__extp(_1492553, _1492555, _1492557, _1492559), 37422 ^ _777081 : [(37423 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1492553), _1492557)))], (37425 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1492553), _1492559)))], (37427 ^ _777081) ^ [] : [_1492559 = c_Orderings_Obot__class_Obot(tc_fun(_1492553, tc_HOL_Obool))], (37429 ^ _777081) ^ [_1492769] : [hBOOL(hAPP(hAPP(c_member(_1492553), _1492769), _1492557)), 37433 ^ _777081 : [(37434 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492553), 37432 ^ [_1492553, _1492555, _1492557, _1492559, _1492769]), _1492559)))], (37436 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1492555, _1492769), 37432 ^ [_1492553, _1492555, _1492557, _1492559, _1492769])))]]]]], (37438 ^ _777081) ^ [_1492953, _1492955, _1492957, _1492959] : [-(c_Wellfounded_Omax__extp(_1492953, _1492955, _1492957, _1492959)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492953), _1492957)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492953), _1492959)), -(_1492959 = c_Orderings_Obot__class_Obot(tc_fun(_1492953, tc_HOL_Obool))), 37452 ^ _777081 : [(37453 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492953), 37451 ^ [_1492953, _1492955, _1492957, _1492959]), _1492957)))], (37455 ^ _777081) ^ [_1493298] : [hBOOL(hAPP(hAPP(c_member(_1492953), _1493298), _1492959)), hBOOL(hAPP(hAPP(_1492955, 37451 ^ [_1492953, _1492955, _1492957, _1492959]), _1493298))]]], (37463 ^ _777081) ^ [_1493466, _1493468, _1493470, _1493472] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1493466), _1493468)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493466), _1493470)), -(_1493470 = c_Orderings_Obot__class_Obot(tc_fun(_1493466, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1493466, tc_HOL_Obool), tc_fun(_1493466, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1493466, tc_HOL_Obool), tc_fun(_1493466, tc_HOL_Obool)), _1493468), _1493470)), c_Wellfounded_Omax__ext(_1493466, _1493472)))), 37477 ^ _777081 : [(37478 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493466), 37476 ^ [_1493466, _1493468, _1493470, _1493472]), _1493468)))], (37480 ^ _777081) ^ [_1493871] : [hBOOL(hAPP(hAPP(c_member(_1493466), _1493871), _1493470)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1493466, _1493466)), hAPP(hAPP(c_Product__Type_OPair(_1493466, _1493466), 37476 ^ [_1493466, _1493468, _1493470, _1493472]), _1493871)), _1493472))]]], (37488 ^ _777081) ^ [_1494097] : [-(c_Nitpick_Ozero__frac(_1494097) = c_Nitpick_OAbs__Frac(_1494097, 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))))], (37490 ^ _777081) ^ [_1494149, _1494151, _1494153, _1494155, _1494157] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1494149, _1494151, hAPP(hAPP(c_Set_Oinsert(_1494149), _1494153), _1494155)), _1494157)), 37495 ^ _777081 : [(37496 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1494149), _1494153), _1494155) = hAPP(hAPP(c_Set_Oinsert(_1494149), 37493 ^ [_1494149, _1494151, _1494153, _1494155, _1494157]), 37494 ^ [_1494149, _1494151, _1494153, _1494155, _1494157]))], (37498 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1494149, _1494149, _1494151, 37493 ^ [_1494149, _1494151, _1494153, _1494155, _1494157], 37494 ^ [_1494149, _1494151, _1494153, _1494155, _1494157]), _1494157)))], (37500 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1494149), 37493 ^ [_1494149, _1494151, _1494153, _1494155, _1494157]), 37494 ^ [_1494149, _1494151, _1494153, _1494155, _1494157]))]]], (37502 ^ _777081) ^ [_1494540, _1494542, _1494544, _1494546, _1494548] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1494540, _1494542, hAPP(hAPP(c_Set_Oinsert(_1494540), _1494544), _1494546)), _1494548))), 37503 ^ _777081 : [(37504 ^ _777081) ^ [_1494644, _1494646] : [hAPP(hAPP(c_Set_Oinsert(_1494540), _1494544), _1494546) = hAPP(hAPP(c_Set_Oinsert(_1494540), _1494646), _1494644), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1494540, _1494540, _1494542, _1494646, _1494644), _1494548)), -(hBOOL(hAPP(hAPP(c_member(_1494540), _1494646), _1494644)))]]], (37516 ^ _777081) ^ [_1494901, _1494903, _1494905, _1494907, _1494909] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1494901, _1494903, hAPP(hAPP(c_Set_Oinsert(_1494901), _1494905), _1494907)), _1494909)), 37521 ^ _777081 : [(37522 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1494901), _1494905), _1494907) = hAPP(hAPP(c_Set_Oinsert(_1494901), 37519 ^ [_1494901, _1494903, _1494905, _1494907, _1494909]), 37520 ^ [_1494901, _1494903, _1494905, _1494907, _1494909]))], (37524 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1494901, _1494901, _1494903, 37519 ^ [_1494901, _1494903, _1494905, _1494907, _1494909], 37520 ^ [_1494901, _1494903, _1494905, _1494907, _1494909]), _1494909)))], (37526 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1494901), 37519 ^ [_1494901, _1494903, _1494905, _1494907, _1494909]), 37520 ^ [_1494901, _1494903, _1494905, _1494907, _1494909]))]]], (37528 ^ _777081) ^ [_1495294] : [-(c_Nitpick_Oone__frac(_1495294) = c_Nitpick_OAbs__Frac(_1495294, 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))))], (37530 ^ _777081) ^ [_1495322, _1495324] : [-(c_Nitpick_Onumber__of__frac(_1495322, _1495324) = c_Nitpick_OAbs__Frac(_1495322, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1495324), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (37532 ^ _777081) ^ [_1495359, _1495361, _1495363] : [-(c_Nitpick_Ofrac(_1495359, _1495361, _1495363) = c_Nitpick_OAbs__Frac(_1495359, c_Nitpick_Onorm__frac(_1495361, _1495363)))], (37534 ^ _777081) ^ [_1495396, _1495398, _1495400, _1495402, _1495404, _1495406] : [-(hAPP(c_Set_Oimage(_1495396, tc_prod(_1495398, _1495400), hAPP(hAPP(c_COMBS(_1495396, _1495400, tc_prod(_1495398, _1495400)), hAPP(hAPP(c_COMBB(_1495398, tc_fun(_1495400, tc_prod(_1495398, _1495400)), _1495396), c_Product__Type_OPair(_1495398, _1495400)), _1495402)), _1495404)), _1495406) = hAPP(hAPP(c_Product__Type_OSigma(_1495398, _1495400), hAPP(c_Set_Oimage(_1495396, _1495398, _1495402), _1495406)), hAPP(hAPP(c_COMBB(tc_fun(_1495396, tc_HOL_Obool), tc_fun(_1495400, tc_HOL_Obool), _1495398), c_Set_Oimage(_1495396, _1495400, _1495404)), hAPP(hAPP(c_COMBC(_1495398, tc_fun(_1495396, tc_HOL_Obool), tc_fun(_1495396, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495396, tc_HOL_Obool), tc_fun(tc_fun(_1495396, tc_HOL_Obool), tc_fun(_1495396, tc_HOL_Obool)), _1495398), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1495396, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1495398, tc_HOL_Obool), tc_fun(_1495396, tc_HOL_Obool), _1495398), c_Set_Ovimage(_1495396, _1495398, _1495402)), hAPP(hAPP(c_COMBC(_1495398, tc_fun(_1495398, tc_HOL_Obool), tc_fun(_1495398, tc_HOL_Obool)), c_Set_Oinsert(_1495398)), c_Orderings_Obot__class_Obot(tc_fun(_1495398, tc_HOL_Obool)))))), _1495406))))], (37536 ^ _777081) ^ [_1495593, _1495595, _1495597] : [class_Groups_Oab__semigroup__mult(_1495593), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495593), _1495595)), -(_1495595 = c_Orderings_Obot__class_Obot(tc_fun(_1495593, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495593), _1495597)), -(_1495597 = c_Orderings_Obot__class_Obot(tc_fun(_1495593, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1495593, tc_HOL_Obool)), _1495595), _1495597) = c_Orderings_Obot__class_Obot(tc_fun(_1495593, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1495593, c_Groups_Otimes__class_Otimes(_1495593)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1495593, tc_HOL_Obool)), _1495595), _1495597)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1495593), hAPP(c_Finite__Set_Ofold1(_1495593, c_Groups_Otimes__class_Otimes(_1495593)), _1495595)), hAPP(c_Finite__Set_Ofold1(_1495593, c_Groups_Otimes__class_Otimes(_1495593)), _1495597)))], (37562 ^ _777081) ^ [_1496100, _1496102, _1496104] : [class_Orderings_Olinorder(_1496100), -(_1496102 = c_Orderings_Obot__class_Obot(tc_fun(_1496100, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496100, tc_HOL_Obool)), _1496102), _1496104)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1496100), _1496104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1496100), hAPP(c_Finite__Set_Ofold1(_1496100, c_Orderings_Oord__class_Omin(_1496100)), _1496104)), hAPP(c_Finite__Set_Ofold1(_1496100, c_Orderings_Oord__class_Omin(_1496100)), _1496102))))], (37580 ^ _777081) ^ [_1496426, _1496428, _1496430, _1496432, _1496434, _1496436] : [hBOOL(hAPP(hAPP(c_member(_1496426), _1496428), _1496430)), hBOOL(hAPP(hAPP(c_member(_1496432), _1496434), hAPP(_1496436, _1496428))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1496426, _1496432)), hAPP(hAPP(c_Product__Type_OPair(_1496426, _1496432), _1496428), _1496434)), hAPP(hAPP(c_Product__Type_OSigma(_1496426, _1496432), _1496430), _1496436))))], (37590 ^ _777081) ^ [_1496661, _1496663, _1496665, _1496667, _1496669, _1496671] : [hBOOL(hAPP(hAPP(c_member(_1496661), _1496663), _1496665)), 37593 ^ _777081 : [(37594 ^ _777081) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1496667, _1496661), _1496669), hAPP(c_COMBK(tc_fun(_1496661, tc_HOL_Obool), _1496667), _1496665)) = hAPP(hAPP(c_Product__Type_OSigma(_1496667, _1496661), _1496671), hAPP(c_COMBK(tc_fun(_1496661, tc_HOL_Obool), _1496667), _1496665)), -(_1496669 = _1496671)], (37600 ^ _777081) ^ [] : [_1496669 = _1496671, -(hAPP(hAPP(c_Product__Type_OSigma(_1496667, _1496661), _1496669), hAPP(c_COMBK(tc_fun(_1496661, tc_HOL_Obool), _1496667), _1496665)) = hAPP(hAPP(c_Product__Type_OSigma(_1496667, _1496661), _1496671), hAPP(c_COMBK(tc_fun(_1496661, tc_HOL_Obool), _1496667), _1496665)))]]], (37606 ^ _777081) ^ [_1497014, _1497016, _1497018, _1497020, _1497022] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1497014, _1497016), _1497018), hAPP(hAPP(c_COMBS(_1497014, tc_fun(_1497016, tc_HOL_Obool), tc_fun(_1497016, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1497016, tc_HOL_Obool), tc_fun(tc_fun(_1497016, tc_HOL_Obool), tc_fun(_1497016, tc_HOL_Obool)), _1497014), c_Groups_Ominus__class_Ominus(tc_fun(_1497016, tc_HOL_Obool))), _1497020)), _1497022)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1497014, _1497016), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1497014, _1497016), _1497018), _1497020)), hAPP(hAPP(c_Product__Type_OSigma(_1497014, _1497016), _1497018), _1497022)))], (37608 ^ _777081) ^ [_1497129, _1497131, _1497133, _1497135, _1497137] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1497129, _1497131), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1497129, tc_HOL_Obool)), _1497133), _1497135)), hAPP(c_COMBK(tc_fun(_1497131, tc_HOL_Obool), _1497129), _1497137)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1497129, _1497131), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1497129, _1497131), _1497133), hAPP(c_COMBK(tc_fun(_1497131, tc_HOL_Obool), _1497129), _1497137))), hAPP(hAPP(c_Product__Type_OSigma(_1497129, _1497131), _1497135), hAPP(c_COMBK(tc_fun(_1497131, tc_HOL_Obool), _1497129), _1497137))))], (37610 ^ _777081) ^ [_1497239, _1497241, _1497243, _1497245, _1497247] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1497239, _1497241), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1497239, tc_HOL_Obool)), _1497243), _1497245)), _1497247) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1497239, _1497241), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1497239, _1497241), _1497243), _1497247)), hAPP(hAPP(c_Product__Type_OSigma(_1497239, _1497241), _1497245), _1497247)))], (37612 ^ _777081) ^ [_1497322, _1497324, _1497326] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1497322, _1497324), c_Orderings_Obot__class_Obot(tc_fun(_1497322, tc_HOL_Obool))), _1497326) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1497322, _1497324), tc_HOL_Obool)))], (37614 ^ _777081) ^ [_1497371, _1497373, _1497375, _1497377] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1497371, _1497373)), hAPP(hAPP(c_Product__Type_OSigma(_1497371, _1497373), _1497375), hAPP(c_COMBK(tc_fun(_1497373, tc_HOL_Obool), _1497371), _1497377))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1497371), _1497375)), hAPP(c_Finite__Set_Ocard(_1497373), _1497377)))], (37616 ^ _777081) ^ [_1497442, _1497444, _1497446, _1497448, _1497450, _1497452] : [class_Groups_Ocomm__monoid__add(_1497442), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497444, _1497442), hAPP(hAPP(c_COMBC(_1497444, tc_fun(_1497446, tc_HOL_Obool), _1497442), hAPP(hAPP(c_COMBB(tc_fun(_1497446, _1497442), tc_fun(tc_fun(_1497446, tc_HOL_Obool), _1497442), _1497444), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497446, _1497442)), _1497448)), _1497450)), _1497452) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1497444, _1497446), _1497442), hAPP(c_Product__Type_Oprod_Oprod__case(_1497444, _1497446, _1497442), _1497448)), hAPP(hAPP(c_Product__Type_OSigma(_1497444, _1497446), _1497452), hAPP(c_COMBK(tc_fun(_1497446, tc_HOL_Obool), _1497444), _1497450))))], (37622 ^ _777081) ^ [_1497687, _1497689, _1497691] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1497687, _1497689), _1497691), hAPP(c_COMBK(tc_fun(_1497689, tc_HOL_Obool), _1497687), c_Orderings_Obot__class_Obot(tc_fun(_1497689, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1497687, _1497689), tc_HOL_Obool)))], (37634 ^ _777081) ^ [_1497928, _1497930, _1497932, _1497934] : [37635 ^ _777081 : [(37636 ^ _777081) ^ [] : [_1497932 = c_Orderings_Obot__class_Obot(tc_fun(_1497928, tc_HOL_Obool))], (37638 ^ _777081) ^ [] : [_1497934 = c_Orderings_Obot__class_Obot(tc_fun(_1497930, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1497928, _1497930), _1497932), hAPP(c_COMBK(tc_fun(_1497930, tc_HOL_Obool), _1497928), _1497934)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1497928, _1497930), tc_HOL_Obool)))], (37624 ^ _777081) ^ [_1497766, _1497768, _1497770, _1497772] : [hAPP(hAPP(c_Product__Type_OSigma(_1497766, _1497768), _1497770), hAPP(c_COMBK(tc_fun(_1497768, tc_HOL_Obool), _1497766), _1497772)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1497766, _1497768), tc_HOL_Obool)), -(_1497770 = c_Orderings_Obot__class_Obot(tc_fun(_1497766, tc_HOL_Obool))), -(_1497772 = c_Orderings_Obot__class_Obot(tc_fun(_1497768, tc_HOL_Obool)))], (37642 ^ _777081) ^ [_1498121, _1498123, _1498125] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1498121, _1498123), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1498121, _1498123), _1498125), hAPP(c_COMBK(tc_fun(_1498123, tc_HOL_Obool), _1498121), c_Orderings_Otop__class_Otop(tc_fun(_1498123, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1498121, _1498123), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1498121, tc_HOL_Obool)), _1498125)), hAPP(c_COMBK(tc_fun(_1498123, tc_HOL_Obool), _1498121), c_Orderings_Otop__class_Otop(tc_fun(_1498123, tc_HOL_Obool)))))], (37644 ^ _777081) ^ [_1498213, _1498215, _1498217] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1498213, _1498215), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1498213, _1498215), c_Orderings_Otop__class_Otop(tc_fun(_1498213, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1498215, tc_HOL_Obool), _1498213), _1498217))) = hAPP(hAPP(c_Product__Type_OSigma(_1498213, _1498215), c_Orderings_Otop__class_Otop(tc_fun(_1498213, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1498215, tc_HOL_Obool), _1498213), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1498215, tc_HOL_Obool)), _1498217))))], (37646 ^ _777081) ^ [_1498305, _1498307, _1498309, _1498311, _1498313, _1498315] : [class_Groups_Ocomm__monoid__mult(_1498305), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1498307, _1498305), hAPP(hAPP(c_COMBC(_1498307, tc_fun(_1498309, tc_HOL_Obool), _1498305), hAPP(hAPP(c_COMBB(tc_fun(_1498309, _1498305), tc_fun(tc_fun(_1498309, tc_HOL_Obool), _1498305), _1498307), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1498309, _1498305)), _1498311)), _1498313)), _1498315) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1498307, _1498309), _1498305), hAPP(c_Product__Type_Oprod_Oprod__case(_1498307, _1498309, _1498305), _1498311)), hAPP(hAPP(c_Product__Type_OSigma(_1498307, _1498309), _1498315), hAPP(c_COMBK(tc_fun(_1498309, tc_HOL_Obool), _1498307), _1498313))))], (37652 ^ _777081) ^ [_1498550, _1498552, _1498554, _1498556, _1498558] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1498550, _1498552), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1498550, tc_HOL_Obool)), _1498554), _1498556)), _1498558) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1498550, _1498552), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1498550, _1498552), _1498554), _1498558)), hAPP(hAPP(c_Product__Type_OSigma(_1498550, _1498552), _1498556), _1498558)))], (37654 ^ _777081) ^ [_1498633, _1498635, _1498637, _1498639, _1498641] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1498633, _1498635), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1498633, tc_HOL_Obool)), _1498637), _1498639)), hAPP(c_COMBK(tc_fun(_1498635, tc_HOL_Obool), _1498633), _1498641)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1498633, _1498635), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1498633, _1498635), _1498637), hAPP(c_COMBK(tc_fun(_1498635, tc_HOL_Obool), _1498633), _1498641))), hAPP(hAPP(c_Product__Type_OSigma(_1498633, _1498635), _1498639), hAPP(c_COMBK(tc_fun(_1498635, tc_HOL_Obool), _1498633), _1498641))))], (37656 ^ _777081) ^ [_1498743, _1498745, _1498747, _1498749, _1498751] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1498743, _1498745), _1498747), hAPP(hAPP(c_COMBS(_1498743, tc_fun(_1498745, tc_HOL_Obool), tc_fun(_1498745, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498745, tc_HOL_Obool), tc_fun(tc_fun(_1498745, tc_HOL_Obool), tc_fun(_1498745, tc_HOL_Obool)), _1498743), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1498745, tc_HOL_Obool))), _1498749)), _1498751)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1498743, _1498745), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1498743, _1498745), _1498747), _1498749)), hAPP(hAPP(c_Product__Type_OSigma(_1498743, _1498745), _1498747), _1498751)))], (37658 ^ _777081) ^ [_1498858, _1498860, _1498862, _1498864] : [-(hAPP(c_Set_Oimage(tc_prod(_1498858, _1498860), tc_prod(_1498860, _1498858), hAPP(c_Product__Type_Oprod_Oprod__case(_1498858, _1498860, tc_prod(_1498860, _1498858)), hAPP(c_COMBC(_1498860, _1498858, tc_prod(_1498860, _1498858)), c_Product__Type_OPair(_1498860, _1498858)))), hAPP(hAPP(c_Product__Type_OSigma(_1498858, _1498860), _1498862), hAPP(c_COMBK(tc_fun(_1498860, tc_HOL_Obool), _1498858), _1498864))) = hAPP(hAPP(c_Product__Type_OSigma(_1498860, _1498858), _1498864), hAPP(c_COMBK(tc_fun(_1498858, tc_HOL_Obool), _1498860), _1498862)))], (37660 ^ _777081) ^ [_1498959, _1498961, _1498963, _1498965] : [_1498959 = c_Finite__Set_Ofold1(_1498961, _1498963), -(hAPP(_1498959, hAPP(hAPP(c_Set_Oinsert(_1498961), _1498965), c_Orderings_Obot__class_Obot(tc_fun(_1498961, tc_HOL_Obool)))) = _1498965)], (37666 ^ _777081) ^ [_1499078, _1499080, _1499082] : [-(hAPP(c_Finite__Set_Ofold1(_1499078, _1499080), hAPP(hAPP(c_Set_Oinsert(_1499078), _1499082), c_Orderings_Obot__class_Obot(tc_fun(_1499078, tc_HOL_Obool)))) = _1499082)], (37668 ^ _777081) ^ [_1499124, _1499126, _1499128, _1499130] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1499124), _1499126)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499128), _1499130)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1499124, _1499128)), hAPP(hAPP(c_Product__Type_OSigma(_1499124, _1499128), _1499126), hAPP(c_COMBK(tc_fun(_1499128, tc_HOL_Obool), _1499124), _1499130)))))], (37678 ^ _777081) ^ [_1499327, _1499329, _1499331] : [c_Equiv__Relations_Oequiv(_1499327, _1499329, _1499331), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1499327, _1499327), tc_HOL_Obool)), _1499331), hAPP(hAPP(c_Product__Type_OSigma(_1499327, _1499327), _1499329), hAPP(c_COMBK(tc_fun(_1499327, tc_HOL_Obool), _1499327), _1499329)))))], (37684 ^ _777081) ^ [_1499470, _1499472, _1499474, _1499476, _1499478] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1499470, _1499472), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499470, tc_HOL_Obool)), _1499474), _1499476)), _1499478) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1499470, _1499472), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1499470, _1499472), _1499474), _1499478)), hAPP(hAPP(c_Product__Type_OSigma(_1499470, _1499472), _1499476), _1499478)))], (37686 ^ _777081) ^ [_1499553, _1499555, _1499557, _1499559, _1499561] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1499553, _1499555), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499553, tc_HOL_Obool)), _1499557), _1499559)), hAPP(c_COMBK(tc_fun(_1499555, tc_HOL_Obool), _1499553), _1499561)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1499553, _1499555), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1499553, _1499555), _1499557), hAPP(c_COMBK(tc_fun(_1499555, tc_HOL_Obool), _1499553), _1499561))), hAPP(hAPP(c_Product__Type_OSigma(_1499553, _1499555), _1499559), hAPP(c_COMBK(tc_fun(_1499555, tc_HOL_Obool), _1499553), _1499561))))], (37688 ^ _777081) ^ [_1499663, _1499665, _1499667, _1499669, _1499671] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1499663, _1499665), _1499667), hAPP(hAPP(c_COMBS(_1499663, tc_fun(_1499665, tc_HOL_Obool), tc_fun(_1499665, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1499665, tc_HOL_Obool), tc_fun(tc_fun(_1499665, tc_HOL_Obool), tc_fun(_1499665, tc_HOL_Obool)), _1499663), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499665, tc_HOL_Obool))), _1499669)), _1499671)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1499663, _1499665), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1499663, _1499665), _1499667), _1499669)), hAPP(hAPP(c_Product__Type_OSigma(_1499663, _1499665), _1499667), _1499671)))], (37690 ^ _777081) ^ [_1499778, _1499780] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1499778, _1499778), tc_HOL_Obool)), c_Relation_OId__on(_1499778, _1499780)), hAPP(hAPP(c_Product__Type_OSigma(_1499778, _1499778), _1499780), hAPP(c_COMBK(tc_fun(_1499778, tc_HOL_Obool), _1499778), _1499780)))))], (37692 ^ _777081) ^ [_1499837, _1499839] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1499837, _1499839), c_Orderings_Otop__class_Otop(tc_fun(_1499837, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1499839, tc_HOL_Obool), _1499837), c_Orderings_Otop__class_Otop(tc_fun(_1499839, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1499837, _1499839), tc_HOL_Obool)))], (37694 ^ _777081) ^ [_1499898, _1499900, _1499902, _1499904, _1499906, _1499908] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1499898, _1499900)), hAPP(hAPP(c_Product__Type_OPair(_1499898, _1499900), _1499902), _1499904)), hAPP(hAPP(c_Product__Type_OSigma(_1499898, _1499900), _1499906), _1499908))), 37697 ^ _777081 : [(37698 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1499898), _1499902), _1499906)))], (37700 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1499900), _1499904), hAPP(_1499908, _1499902))))]]], (37702 ^ _777081) ^ [_1500103, _1500105, _1500107, _1500109, _1500111, _1500113] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1500103, _1500105)), hAPP(hAPP(c_Product__Type_OPair(_1500103, _1500105), _1500107), _1500109)), hAPP(hAPP(c_Product__Type_OSigma(_1500103, _1500105), _1500111), _1500113))), -(hBOOL(hAPP(hAPP(c_member(_1500105), _1500109), hAPP(_1500113, _1500107))))], (37708 ^ _777081) ^ [_1500264, _1500266, _1500268, _1500270, _1500272, _1500274] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1500264, _1500266)), hAPP(hAPP(c_Product__Type_OPair(_1500264, _1500266), _1500268), _1500270)), hAPP(hAPP(c_Product__Type_OSigma(_1500264, _1500266), _1500272), _1500274))), -(hBOOL(hAPP(hAPP(c_member(_1500264), _1500268), _1500272)))], (37714 ^ _777081) ^ [_1500446, _1500448, _1500450, _1500452, _1500454, _1500456] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1500446, _1500448)), hAPP(hAPP(c_Product__Type_OPair(_1500446, _1500448), _1500450), _1500452)), hAPP(hAPP(c_Product__Type_OSigma(_1500446, _1500448), _1500454), _1500456))), 37717 ^ _777081 : [(37718 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1500446), _1500450), _1500454)))], (37720 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1500448), _1500452), hAPP(_1500456, _1500450))))]]], (37722 ^ _777081) ^ [_1500643, _1500645, _1500647, _1500649, _1500651, _1500653] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1500643, _1500645)), hAPP(hAPP(c_Product__Type_OPair(_1500643, _1500645), _1500647), _1500649)), hAPP(hAPP(c_Product__Type_OSigma(_1500643, _1500645), _1500651), _1500653)))), hBOOL(hAPP(hAPP(c_member(_1500643), _1500647), _1500651)), hBOOL(hAPP(hAPP(c_member(_1500645), _1500649), hAPP(_1500653, _1500647)))], (37732 ^ _777081) ^ [_1500880, _1500882, _1500884, _1500886] : [c_Finite__Set_Ofolding__one(_1500880, _1500882, _1500884), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500880), _1500886)), -(hAPP(_1500884, _1500886) = hAPP(c_Finite__Set_Ofold1(_1500880, _1500882), _1500886))], (37742 ^ _777081) ^ [_1501045, _1501047, _1501049, _1501051] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1501045, _1501047)), hAPP(hAPP(c_Product__Type_OSigma(_1501045, _1501047), hAPP(hAPP(c_Set_Oinsert(_1501045), _1501049), c_Orderings_Obot__class_Obot(tc_fun(_1501045, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1501047, tc_HOL_Obool), _1501045), _1501051))) = hAPP(c_Finite__Set_Ocard(_1501047), _1501051))], (37744 ^ _777081) ^ [_1501118, _1501120, _1501122, _1501124, _1501126, _1501128] : [hBOOL(hAPP(hAPP(c_member(_1501118), _1501120), _1501122)), 37747 ^ _777081 : [(37748 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501124, _1501118), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1501124, _1501118), _1501126), hAPP(c_COMBK(tc_fun(_1501118, tc_HOL_Obool), _1501124), _1501122))), hAPP(hAPP(c_Product__Type_OSigma(_1501124, _1501118), _1501128), hAPP(c_COMBK(tc_fun(_1501118, tc_HOL_Obool), _1501124), _1501122)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501124, tc_HOL_Obool)), _1501126), _1501128)))], (37754 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501124, tc_HOL_Obool)), _1501126), _1501128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501124, _1501118), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1501124, _1501118), _1501126), hAPP(c_COMBK(tc_fun(_1501118, tc_HOL_Obool), _1501124), _1501122))), hAPP(hAPP(c_Product__Type_OSigma(_1501124, _1501118), _1501128), hAPP(c_COMBK(tc_fun(_1501118, tc_HOL_Obool), _1501124), _1501122)))))]]], (37760 ^ _777081) ^ [_1501540, _1501542, _1501544, _1501546, _1501548, _1501550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1501540, _1501542), tc_HOL_Obool)), _1501544), hAPP(hAPP(c_Product__Type_OSigma(_1501540, _1501542), _1501546), hAPP(c_COMBK(tc_fun(_1501542, tc_HOL_Obool), _1501540), _1501548)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1501542, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1501540, _1501542, _1501544), _1501550)), _1501548)))], (37766 ^ _777081) ^ [_1501721, _1501723, _1501725, _1501727] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1501721, _1501723)), hAPP(hAPP(c_Product__Type_OSigma(_1501721, _1501723), _1501725), hAPP(c_COMBK(tc_fun(_1501723, tc_HOL_Obool), _1501721), _1501727)))), -(_1501727 = c_Orderings_Obot__class_Obot(tc_fun(_1501723, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1501721), _1501725)))], (37776 ^ _777081) ^ [_1501885, _1501887, _1501889, _1501891] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1501885, _1501887)), hAPP(hAPP(c_Product__Type_OSigma(_1501885, _1501887), _1501889), hAPP(c_COMBK(tc_fun(_1501887, tc_HOL_Obool), _1501885), _1501891)))), -(_1501889 = c_Orderings_Obot__class_Obot(tc_fun(_1501885, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1501887), _1501891)))], (37786 ^ _777081) ^ [_1502064, _1502066, _1502068, _1502070] : [_1502064 = c_Orderings_Obot__class_Obot(tc_fun(_1502066, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1502068, _1502066), _1502068, c_Product__Type_Ofst(_1502068, _1502066)), hAPP(hAPP(c_Product__Type_OSigma(_1502068, _1502066), _1502070), hAPP(c_COMBK(tc_fun(_1502066, tc_HOL_Obool), _1502068), _1502064))) = c_Orderings_Obot__class_Obot(tc_fun(_1502068, tc_HOL_Obool)))], (37792 ^ _777081) ^ [_1502221, _1502223, _1502225, _1502227] : [-(_1502221 = c_Orderings_Obot__class_Obot(tc_fun(_1502223, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1502225, _1502223), _1502225, c_Product__Type_Ofst(_1502225, _1502223)), hAPP(hAPP(c_Product__Type_OSigma(_1502225, _1502223), _1502227), hAPP(c_COMBK(tc_fun(_1502223, tc_HOL_Obool), _1502225), _1502221))) = _1502227)], (37798 ^ _777081) ^ [_1502314, _1502316, _1502318, _1502320] : [_1502314 = c_Orderings_Obot__class_Obot(tc_fun(_1502316, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1502316, _1502318), _1502318, c_Product__Type_Osnd(_1502316, _1502318)), hAPP(hAPP(c_Product__Type_OSigma(_1502316, _1502318), _1502314), hAPP(c_COMBK(tc_fun(_1502318, tc_HOL_Obool), _1502316), _1502320))) = c_Orderings_Obot__class_Obot(tc_fun(_1502318, tc_HOL_Obool)))], (37804 ^ _777081) ^ [_1502471, _1502473, _1502475, _1502477] : [-(_1502471 = c_Orderings_Obot__class_Obot(tc_fun(_1502473, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1502473, _1502475), _1502475, c_Product__Type_Osnd(_1502473, _1502475)), hAPP(hAPP(c_Product__Type_OSigma(_1502473, _1502475), _1502471), hAPP(c_COMBK(tc_fun(_1502475, tc_HOL_Obool), _1502473), _1502477))) = _1502477)], (37810 ^ _777081) ^ [_1502549, _1502551, _1502553] : [-(hAPP(c_Finite__Set_Ofold1(_1502549, _1502551), _1502553) = c_HOL_OThe(_1502549, c_Finite__Set_Ofold1Set(_1502549, _1502551, _1502553)))], (37812 ^ _777081) ^ [_1502589, _1502591] : [class_Lattices_Olattice(_1502589), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502589), _1502591)), -(c_Big__Operators_Olattice__class_OSup__fin(_1502589, _1502591) = hAPP(c_Finite__Set_Ofold1(_1502589, c_Lattices_Osemilattice__sup__class_Osup(_1502589)), _1502591))], (37822 ^ _777081) ^ [_1502746, _1502748] : [class_Lattices_Olattice(_1502746), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502746), _1502748)), -(c_Big__Operators_Olattice__class_OInf__fin(_1502746, _1502748) = hAPP(c_Finite__Set_Ofold1(_1502746, c_Lattices_Osemilattice__inf__class_Oinf(_1502746)), _1502748))], (37832 ^ _777081) ^ [_1502903, _1502905] : [class_Orderings_Olinorder(_1502903), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502903), _1502905)), -(c_Big__Operators_Olinorder__class_OMin(_1502903, _1502905) = hAPP(c_Finite__Set_Ofold1(_1502903, c_Orderings_Oord__class_Omin(_1502903)), _1502905))], (37842 ^ _777081) ^ [_1503060, _1503062] : [class_Orderings_Olinorder(_1503060), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503060), _1503062)), -(c_Big__Operators_Olinorder__class_OMax(_1503060, _1503062) = hAPP(c_Finite__Set_Ofold1(_1503060, c_Orderings_Oord__class_Omax(_1503060)), _1503062))], (37852 ^ _777081) ^ [_1503217, _1503219] : [class_Orderings_Olinorder(_1503217), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503217), _1503219)), -(c_Big__Operators_Olattice_OInf__fin(_1503217, c_Orderings_Oord__class_Omin(_1503217), _1503219) = hAPP(c_Finite__Set_Ofold1(_1503217, c_Orderings_Oord__class_Omin(_1503217)), _1503219))], (37862 ^ _777081) ^ [_1503380, _1503382] : [class_Orderings_Olinorder(_1503380), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503380), _1503382)), -(c_Big__Operators_Olattice_OSup__fin(_1503380, c_Orderings_Oord__class_Omax(_1503380), _1503382) = hAPP(c_Finite__Set_Ofold1(_1503380, c_Orderings_Oord__class_Omax(_1503380)), _1503382))], (37872 ^ _777081) ^ [_1503543, _1503545, _1503547, _1503549, _1503551, _1503553] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1503543, _1503545), hAPP(hAPP(c_Set_Oinsert(_1503543), _1503547), _1503549)), hAPP(c_COMBK(tc_fun(_1503545, tc_HOL_Obool), _1503543), hAPP(hAPP(c_Set_Oinsert(_1503545), _1503551), _1503553))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1503543, _1503545)), hAPP(hAPP(c_Product__Type_OPair(_1503543, _1503545), _1503547), _1503551)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1503543, _1503545), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1503543, _1503545), _1503549), hAPP(c_COMBK(tc_fun(_1503545, tc_HOL_Obool), _1503543), hAPP(hAPP(c_Set_Oinsert(_1503545), _1503551), _1503553)))), hAPP(hAPP(c_Product__Type_OSigma(_1503543, _1503545), hAPP(hAPP(c_Set_Oinsert(_1503543), _1503547), _1503549)), hAPP(c_COMBK(tc_fun(_1503545, tc_HOL_Obool), _1503543), _1503553)))))], (37874 ^ _777081) ^ [_1503696, _1503698, _1503700, _1503702] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503696), _1503698)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1503696, _1503696), tc_HOL_Obool)), _1503700), hAPP(hAPP(c_Product__Type_OSigma(_1503696, _1503696), _1503698), hAPP(c_COMBK(tc_fun(_1503696, tc_HOL_Obool), _1503696), _1503698)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1503696, tc_HOL_Obool)), _1503702), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1503696), _1503698), _1503700))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1503696), _1503702)))], (37888 ^ _777081) ^ [_1504003, _1504005, _1504007, _1504009, _1504011, _1504013] : [-(hAPP(c_Set_Ovimage(_1504003, tc_prod(_1504005, _1504007), _1504009), hAPP(hAPP(c_Product__Type_OSigma(_1504005, _1504007), _1504011), hAPP(c_COMBK(tc_fun(_1504007, tc_HOL_Obool), _1504005), _1504013))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1504003, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1504003, _1504005, hAPP(c_Fun_Ocomp(tc_prod(_1504005, _1504007), _1504005, _1504003, c_Product__Type_Ofst(_1504005, _1504007)), _1504009)), _1504011)), hAPP(c_Set_Ovimage(_1504003, _1504007, hAPP(c_Fun_Ocomp(tc_prod(_1504005, _1504007), _1504007, _1504003, c_Product__Type_Osnd(_1504005, _1504007)), _1504009)), _1504013)))], (37890 ^ _777081) ^ [_1504117, _1504119, _1504121, _1504123, _1504125, _1504127, _1504129, _1504131] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1504117, _1504119), tc_fun(tc_prod(_1504121, _1504123), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1504117, _1504119), _1504125), hAPP(c_COMBK(tc_fun(_1504119, tc_HOL_Obool), _1504117), _1504127))), hAPP(c_Product__Type_Oprod_Oprod__case(_1504117, _1504119, tc_fun(tc_prod(_1504121, _1504123), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1504117, tc_fun(_1504119, tc_fun(_1504121, tc_fun(_1504123, tc_HOL_Obool))), tc_fun(_1504119, tc_fun(tc_prod(_1504121, _1504123), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1504121, tc_fun(_1504123, tc_HOL_Obool)), tc_fun(tc_prod(_1504121, _1504123), tc_HOL_Obool)), tc_fun(tc_fun(_1504119, tc_fun(_1504121, tc_fun(_1504123, tc_HOL_Obool))), tc_fun(_1504119, tc_fun(tc_prod(_1504121, _1504123), tc_HOL_Obool))), _1504117), c_COMBB(tc_fun(_1504121, tc_fun(_1504123, tc_HOL_Obool)), tc_fun(tc_prod(_1504121, _1504123), tc_HOL_Obool), _1504119)), hAPP(hAPP(c_COMBB(tc_fun(_1504121, tc_HOL_Obool), tc_fun(tc_fun(_1504121, tc_fun(_1504123, tc_HOL_Obool)), tc_fun(tc_prod(_1504121, _1504123), tc_HOL_Obool)), _1504117), c_Product__Type_OSigma(_1504121, _1504123)), _1504129))), hAPP(hAPP(c_COMBB(tc_fun(_1504123, tc_HOL_Obool), tc_fun(_1504121, tc_fun(_1504123, tc_HOL_Obool)), _1504119), c_COMBK(tc_fun(_1504123, tc_HOL_Obool), _1504121)), _1504131)))) = hAPP(hAPP(c_Product__Type_OSigma(_1504121, _1504123), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1504117, tc_fun(_1504121, tc_HOL_Obool)), _1504125), _1504129)), hAPP(c_COMBK(tc_fun(_1504123, tc_HOL_Obool), _1504121), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1504119, tc_fun(_1504123, tc_HOL_Obool)), _1504127), _1504131))))], (37892 ^ _777081) ^ [_1504391, _1504393, _1504395, _1504397] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1504391, _1504393), _1504395), _1504397) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1504391, tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool)), _1504395), hAPP(hAPP(c_COMBS(_1504391, tc_fun(_1504393, tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool)), tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504393, tc_HOL_Obool), tc_fun(tc_fun(_1504393, tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool)), tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool)), _1504391), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1504393, tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool))), _1504397)), hAPP(hAPP(c_COMBC(_1504391, tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool), tc_fun(_1504393, tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1504393, tc_fun(tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool), tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool), tc_fun(_1504393, tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool))), _1504391), c_COMBC(_1504393, tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool), tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1504393, tc_prod(_1504391, _1504393)), tc_fun(_1504393, tc_fun(tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool), tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool))), _1504391), hAPP(c_COMBB(tc_prod(_1504391, _1504393), tc_fun(tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool), tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool)), _1504393), c_Set_Oinsert(tc_prod(_1504391, _1504393)))), c_Product__Type_OPair(_1504391, _1504393)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1504391, _1504393), tc_HOL_Obool))))))], (37894 ^ _777081) ^ [_1504671, _1504673, _1504675] : [class_Lattices_Osemilattice__inf(_1504671), hBOOL(hAPP(c_Finite__Set_Ofinite(_1504671), _1504673)), hBOOL(hAPP(hAPP(c_member(_1504671), _1504675), _1504673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1504671), hAPP(c_Finite__Set_Ofold1(_1504671, c_Lattices_Osemilattice__inf__class_Oinf(_1504671)), _1504673)), _1504675)))], (37908 ^ _777081) ^ [_1504908, _1504910, _1504912] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1504908), _1504910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1504908, _1504908), tc_HOL_Obool)), _1504912), hAPP(hAPP(c_Product__Type_OSigma(_1504908, _1504908), _1504910), hAPP(c_COMBK(tc_fun(_1504908, tc_HOL_Obool), _1504908), _1504910)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1504908, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1504908), _1504910), _1504912))))], (37918 ^ _777081) ^ [_1505141, _1505143, _1505145] : [class_Lattices_Osemilattice__inf(_1505141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505141), _1505143)), -(_1505143 = c_Orderings_Obot__class_Obot(tc_fun(_1505141, tc_HOL_Obool))), 37929 ^ _777081 : [(37940 ^ _777081) ^ [] : [37942 ^ _777081 : [(37943 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1505141), 37941 ^ [_1505141, _1505143, _1505145]), _1505143)))], (37945 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1505141), _1505145), 37941 ^ [_1505141, _1505143, _1505145]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1505141), _1505145), hAPP(c_Finite__Set_Ofold1(_1505141, c_Lattices_Osemilattice__inf__class_Oinf(_1505141)), _1505143))))], (37930 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1505141), _1505145), hAPP(c_Finite__Set_Ofold1(_1505141, c_Lattices_Osemilattice__inf__class_Oinf(_1505141)), _1505143))), 37933 ^ _777081 : [(37934 ^ _777081) ^ [_1505434] : [hBOOL(hAPP(hAPP(c_member(_1505141), _1505434), _1505143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1505141), _1505145), _1505434)))]]]]], (37949 ^ _777081) ^ [_1505719, _1505721, _1505723] : [class_Orderings_Olinorder(_1505719), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505719), _1505721)), hBOOL(hAPP(hAPP(c_member(_1505719), _1505723), _1505721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1505719), hAPP(c_Finite__Set_Ofold1(_1505719, c_Orderings_Oord__class_Omin(_1505719)), _1505721)), _1505723)))], (37963 ^ _777081) ^ [_1505956, _1505958, _1505960] : [class_Lattices_Oab__semigroup__idem__mult(_1505956), -(_1505958 = c_Orderings_Obot__class_Obot(tc_fun(_1505956, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505956), _1505958)), -(hAPP(c_Finite__Set_Ofold1(_1505956, c_Groups_Otimes__class_Otimes(_1505956)), hAPP(hAPP(c_Set_Oinsert(_1505956), _1505960), _1505958)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1505956), _1505960), hAPP(c_Finite__Set_Ofold1(_1505956, c_Groups_Otimes__class_Otimes(_1505956)), _1505958)))], (37977 ^ _777081) ^ [_1506226, _1506228, _1506230] : [class_Orderings_Olinorder(_1506226), hBOOL(hAPP(c_Finite__Set_Ofinite(_1506226), _1506228)), -(_1506228 = c_Orderings_Obot__class_Obot(tc_fun(_1506226, tc_HOL_Obool))), 37988 ^ _777081 : [(37999 ^ _777081) ^ [] : [38001 ^ _777081 : [(38002 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1506226), 38000 ^ [_1506226, _1506228, _1506230]), _1506228)))], (38004 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1506226), _1506230), 38000 ^ [_1506226, _1506228, _1506230]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1506226), _1506230), hAPP(c_Finite__Set_Ofold1(_1506226, c_Orderings_Oord__class_Omin(_1506226)), _1506228))))], (37989 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1506226), _1506230), hAPP(c_Finite__Set_Ofold1(_1506226, c_Orderings_Oord__class_Omin(_1506226)), _1506228))), 37992 ^ _777081 : [(37993 ^ _777081) ^ [_1506519] : [hBOOL(hAPP(hAPP(c_member(_1506226), _1506519), _1506228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1506226), _1506230), _1506519)))]]]]], (38008 ^ _777081) ^ [_1506804, _1506806, _1506808] : [class_Orderings_Olinorder(_1506804), hBOOL(hAPP(c_Finite__Set_Ofinite(_1506804), _1506806)), -(_1506806 = c_Orderings_Obot__class_Obot(tc_fun(_1506804, tc_HOL_Obool))), 38019 ^ _777081 : [(38020 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1506804), hAPP(c_Finite__Set_Ofold1(_1506804, c_Orderings_Oord__class_Omin(_1506804)), _1506806)), _1506808)), 38024 ^ _777081 : [(38025 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1506804), 38023 ^ [_1506804, _1506806, _1506808]), _1506806)))], (38027 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1506804), 38023 ^ [_1506804, _1506806, _1506808]), _1506808)))]]], (38029 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1506804), hAPP(c_Finite__Set_Ofold1(_1506804, c_Orderings_Oord__class_Omin(_1506804)), _1506806)), _1506808))), 38030 ^ _777081 : [(38031 ^ _777081) ^ [_1507193] : [hBOOL(hAPP(hAPP(c_member(_1506804), _1507193), _1506806)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1506804), _1507193), _1506808))]]]]], (38039 ^ _777081) ^ [_1507354, _1507356, _1507358] : [class_Lattices_Oab__semigroup__idem__mult(_1507354), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507354), _1507356)), -(_1507356 = c_Orderings_Obot__class_Obot(tc_fun(_1507354, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507354), _1507358)), -(_1507358 = c_Orderings_Obot__class_Obot(tc_fun(_1507354, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1507354, c_Groups_Otimes__class_Otimes(_1507354)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1507354, tc_HOL_Obool)), _1507356), _1507358)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1507354), hAPP(c_Finite__Set_Ofold1(_1507354, c_Groups_Otimes__class_Otimes(_1507354)), _1507356)), hAPP(c_Finite__Set_Ofold1(_1507354, c_Groups_Otimes__class_Otimes(_1507354)), _1507358)))], (38061 ^ _777081) ^ [_1507733, _1507735, _1507737] : [class_Orderings_Olinorder(_1507733), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507733), _1507735)), -(_1507735 = c_Orderings_Obot__class_Obot(tc_fun(_1507733, tc_HOL_Obool))), 38072 ^ _777081 : [(38083 ^ _777081) ^ [] : [38085 ^ _777081 : [(38086 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1507733), 38084 ^ [_1507733, _1507735, _1507737]), _1507735)))], (38088 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1507733), _1507737), 38084 ^ [_1507733, _1507735, _1507737]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1507733), _1507737), hAPP(c_Finite__Set_Ofold1(_1507733, c_Orderings_Oord__class_Omin(_1507733)), _1507735))))], (38073 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1507733), _1507737), hAPP(c_Finite__Set_Ofold1(_1507733, c_Orderings_Oord__class_Omin(_1507733)), _1507735))), 38076 ^ _777081 : [(38077 ^ _777081) ^ [_1508026] : [hBOOL(hAPP(hAPP(c_member(_1507733), _1508026), _1507735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1507733), _1507737), _1508026)))]]]]], (38092 ^ _777081) ^ [_1508311, _1508313, _1508315] : [class_Orderings_Olinorder(_1508311), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508311), _1508313)), -(_1508313 = c_Orderings_Obot__class_Obot(tc_fun(_1508311, tc_HOL_Obool))), 38103 ^ _777081 : [(38104 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1508311), hAPP(c_Finite__Set_Ofold1(_1508311, c_Orderings_Oord__class_Omin(_1508311)), _1508313)), _1508315)), 38108 ^ _777081 : [(38109 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508311), 38107 ^ [_1508311, _1508313, _1508315]), _1508313)))], (38111 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1508311), 38107 ^ [_1508311, _1508313, _1508315]), _1508315)))]]], (38113 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1508311), hAPP(c_Finite__Set_Ofold1(_1508311, c_Orderings_Oord__class_Omin(_1508311)), _1508313)), _1508315))), 38114 ^ _777081 : [(38115 ^ _777081) ^ [_1508700] : [hBOOL(hAPP(hAPP(c_member(_1508311), _1508700), _1508313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1508311), _1508700), _1508315))]]]]], (38123 ^ _777081) ^ [_1508861, _1508863, _1508865] : [class_Groups_Oab__semigroup__mult(_1508861), -(_1508863 = c_Orderings_Obot__class_Obot(tc_fun(_1508861, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508861), _1508863)), -(hBOOL(hAPP(hAPP(c_member(_1508861), _1508865), _1508863))), -(hAPP(c_Finite__Set_Ofold1(_1508861, c_Groups_Otimes__class_Otimes(_1508861)), hAPP(hAPP(c_Set_Oinsert(_1508861), _1508865), _1508863)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1508861), _1508865), hAPP(c_Finite__Set_Ofold1(_1508861, c_Groups_Otimes__class_Otimes(_1508861)), _1508863)))], (38141 ^ _777081) ^ [_1509160, _1509162, _1509164, _1509166] : [c_Big__Operators_Osemilattice__big(_1509160, _1509162, _1509164), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509160), _1509166)), -(hAPP(_1509164, _1509166) = hAPP(c_Finite__Set_Ofold1(_1509160, _1509162), _1509166))], (38152 ^ _777081) ^ [_1509323, _1509325, _1509327, _1509329] : [-(c_Fun_Oinj__on(_1509323, tc_prod(_1509325, _1509323), 38150 ^ [_1509323, _1509325, _1509327, _1509329], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1509325, tc_fun(_1509323, tc_HOL_Obool)), _1509327), _1509329)))], (38154 ^ _777081) ^ [_1509377, _1509379, _1509381, _1509383] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1509379, _1509377), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1509377, tc_prod(_1509379, _1509377), 38150 ^ [_1509377, _1509379, _1509381, _1509383]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1509379, tc_fun(_1509377, tc_HOL_Obool)), _1509381), _1509383))), hAPP(hAPP(c_Product__Type_OSigma(_1509379, _1509377), _1509381), _1509383))))], (38156 ^ _777081) ^ [_1509463, _1509465, _1509467, _1509469, _1509471, _1509473] : [class_Groups_Ocomm__monoid__mult(_1509463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509465), _1509467)), 38166 ^ _777081 : [(38167 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1509465), 38165 ^ [_1509463, _1509465, _1509467, _1509469, _1509471, _1509473]), _1509467)))], (38169 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1509469), hAPP(_1509471, 38165 ^ [_1509463, _1509465, _1509467, _1509469, _1509471, _1509473])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1509463, _1509465, c_Groups_Otimes__class_Otimes(_1509463)), hAPP(hAPP(c_COMBS(_1509465, tc_fun(_1509469, tc_HOL_Obool), _1509463), hAPP(hAPP(c_COMBC(_1509465, _1509463, tc_fun(tc_fun(_1509469, tc_HOL_Obool), _1509463)), hAPP(hAPP(c_COMBB(tc_fun(_1509469, _1509463), tc_fun(_1509463, tc_fun(tc_fun(_1509469, tc_HOL_Obool), _1509463)), _1509465), c_Finite__Set_Ofold__image(_1509463, _1509469, c_Groups_Otimes__class_Otimes(_1509463))), _1509473)), c_Groups_Oone__class_Oone(_1509463))), _1509471)), c_Groups_Oone__class_Oone(_1509463)), _1509467) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1509463, tc_prod(_1509465, _1509469), c_Groups_Otimes__class_Otimes(_1509463)), hAPP(c_Product__Type_Oprod_Oprod__case(_1509465, _1509469, _1509463), _1509473)), c_Groups_Oone__class_Oone(_1509463)), hAPP(hAPP(c_Product__Type_OSigma(_1509465, _1509469), _1509467), _1509471)))], (38173 ^ _777081) ^ [_1510020, _1510022, _1510024, _1510026, _1510028, _1510030] : [class_Groups_Ocomm__monoid__mult(_1510020), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510022), _1510024)), 38183 ^ _777081 : [(38184 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1510022), 38182 ^ [_1510020, _1510022, _1510024, _1510026, _1510028, _1510030]), _1510024)))], (38186 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1510026), hAPP(_1510028, 38182 ^ [_1510020, _1510022, _1510024, _1510026, _1510028, _1510030])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1510022, _1510020), hAPP(hAPP(c_COMBS(_1510022, tc_fun(_1510026, tc_HOL_Obool), _1510020), hAPP(hAPP(c_COMBB(tc_fun(_1510026, _1510020), tc_fun(tc_fun(_1510026, tc_HOL_Obool), _1510020), _1510022), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1510026, _1510020)), _1510030)), _1510028)), _1510024) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1510022, _1510026), _1510020), hAPP(c_Product__Type_Oprod_Oprod__case(_1510022, _1510026, _1510020), _1510030)), hAPP(hAPP(c_Product__Type_OSigma(_1510022, _1510026), _1510024), _1510028)))], (38190 ^ _777081) ^ [_1510497, _1510499, _1510501, _1510503, _1510505, _1510507] : [class_Groups_Ocomm__monoid__add(_1510497), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510499), _1510501)), 38200 ^ _777081 : [(38201 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1510499), 38199 ^ [_1510497, _1510499, _1510501, _1510503, _1510505, _1510507]), _1510501)))], (38203 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1510503), hAPP(_1510505, 38199 ^ [_1510497, _1510499, _1510501, _1510503, _1510505, _1510507])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510499, _1510497), hAPP(hAPP(c_COMBS(_1510499, tc_fun(_1510503, tc_HOL_Obool), _1510497), hAPP(hAPP(c_COMBB(tc_fun(_1510503, _1510497), tc_fun(tc_fun(_1510503, tc_HOL_Obool), _1510497), _1510499), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510503, _1510497)), _1510507)), _1510505)), _1510501) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1510499, _1510503), _1510497), hAPP(c_Product__Type_Oprod_Oprod__case(_1510499, _1510503, _1510497), _1510507)), hAPP(hAPP(c_Product__Type_OSigma(_1510499, _1510503), _1510501), _1510505)))], (38207 ^ _777081) ^ [_1510974, _1510976, _1510978, _1510980] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1510974), _1510976)), 38213 ^ _777081 : [(38214 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1510974), 38212 ^ [_1510974, _1510976, _1510978, _1510980]), _1510976)))], (38216 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1510978), hAPP(_1510980, 38212 ^ [_1510974, _1510976, _1510978, _1510980])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1510974, _1510978)), hAPP(hAPP(c_Product__Type_OSigma(_1510974, _1510978), _1510976), _1510980)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1510974, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1510978, tc_HOL_Obool), tc_Nat_Onat, _1510974), c_Finite__Set_Ocard(_1510978)), _1510980)), _1510976))], (38220 ^ _777081) ^ [_1511311, _1511313] : [class_Groups_Oab__semigroup__mult(_1511311), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511311), _1511313)), -(_1511313 = c_Orderings_Obot__class_Obot(tc_fun(_1511311, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1511311), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1511311), 38233 ^ [_1511311, _1511313]), 38234 ^ [_1511311, _1511313])), hAPP(hAPP(c_Set_Oinsert(_1511311), 38233 ^ [_1511311, _1511313]), hAPP(hAPP(c_Set_Oinsert(_1511311), 38234 ^ [_1511311, _1511313]), c_Orderings_Obot__class_Obot(tc_fun(_1511311, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1511311), hAPP(c_Finite__Set_Ofold1(_1511311, c_Groups_Otimes__class_Otimes(_1511311)), _1511313)), _1511313)))], (38240 ^ _777081) ^ [_1511765, _1511767, _1511769, _1511771] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1511765), _1511767)), 38246 ^ _777081 : [(38247 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1511765), 38245 ^ [_1511765, _1511767, _1511769, _1511771]), _1511767)))], (38249 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1511769), hAPP(_1511771, 38245 ^ [_1511765, _1511767, _1511769, _1511771])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1511765, _1511769)), hAPP(hAPP(c_Product__Type_OSigma(_1511765, _1511769), _1511767), _1511771))))], (38253 ^ _777081) ^ [_1512052, _1512054, _1512056] : [class_Lattices_Oab__semigroup__idem__mult(_1512052), hAPP(_1512054, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1512052), 38258 ^ [_1512052, _1512054, _1512056]), 38259 ^ [_1512052, _1512054, _1512056])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1512052), hAPP(_1512054, 38258 ^ [_1512052, _1512054, _1512056])), hAPP(_1512054, 38259 ^ [_1512052, _1512054, _1512056])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512052), _1512056)), -(_1512056 = c_Orderings_Obot__class_Obot(tc_fun(_1512052, tc_HOL_Obool))), -(hAPP(_1512054, hAPP(c_Finite__Set_Ofold1(_1512052, c_Groups_Otimes__class_Otimes(_1512052)), _1512056)) = hAPP(c_Finite__Set_Ofold1(_1512052, c_Groups_Otimes__class_Otimes(_1512052)), hAPP(c_Set_Oimage(_1512052, _1512052, _1512054), _1512056)))], (38273 ^ _777081) ^ [_1512475, _1512477, _1512479, _1512481, _1512483] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1512475, _1512477)), _1512479), hAPP(hAPP(c_Product__Type_OSigma(_1512475, _1512477), _1512481), _1512483))), 38277 ^ _777081 : [(38278 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512475), 38276 ^ [_1512475, _1512477, _1512479, _1512481, _1512483]), _1512481)))], (38281 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1512477), 38279 ^ [_1512475, _1512477, _1512479, _1512481, _1512483]), hAPP(_1512483, 38276 ^ [_1512475, _1512477, _1512479, _1512481, _1512483]))))], (38283 ^ _777081) ^ [] : [-(_1512479 = hAPP(hAPP(c_Product__Type_OPair(_1512475, _1512477), 38276 ^ [_1512475, _1512477, _1512479, _1512481, _1512483]), 38279 ^ [_1512475, _1512477, _1512479, _1512481, _1512483]))]]], (38285 ^ _777081) ^ [_1512777, _1512779, _1512781, _1512783, _1512785, _1512787] : [hAPP(c_Set_Oimage(_1512777, _1512779, _1512781), c_Orderings_Otop__class_Otop(tc_fun(_1512777, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1512779, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1512783, _1512785, _1512787), c_Orderings_Otop__class_Otop(tc_fun(_1512783, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1512785, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1512777, _1512783), tc_prod(_1512779, _1512785), c_Product__Type_Omap__pair(_1512777, _1512779, _1512783, _1512785, _1512781, _1512787)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1512777, _1512783), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1512779, _1512785), tc_HOL_Obool)))], (38295 ^ _777081) ^ [_1513062, _1513064, _1513066, _1513068, _1513070, _1513072, _1513074, _1513076] : [c_Fun_Oinj__on(_1513062, _1513064, _1513066, _1513068), c_Fun_Oinj__on(_1513070, _1513072, _1513074, _1513076), -(c_Fun_Oinj__on(tc_prod(_1513062, _1513070), tc_prod(_1513064, _1513072), c_Product__Type_Omap__pair(_1513062, _1513064, _1513070, _1513072, _1513066, _1513074), hAPP(hAPP(c_Product__Type_OSigma(_1513062, _1513070), _1513068), hAPP(c_COMBK(tc_fun(_1513070, tc_HOL_Obool), _1513062), _1513076))))], (38305 ^ _777081) ^ [_1513289, _1513291, _1513293, _1513295, _1513297, _1513299, _1513301, _1513303, _1513305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1513289, _1513291)), hAPP(hAPP(c_Product__Type_OPair(_1513289, _1513291), _1513293), _1513295)), _1513297)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1513299, _1513301)), hAPP(hAPP(c_Product__Type_OPair(_1513299, _1513301), hAPP(_1513303, _1513293)), hAPP(_1513305, _1513295))), hAPP(c_Set_Oimage(tc_prod(_1513289, _1513291), tc_prod(_1513299, _1513301), c_Product__Type_Omap__pair(_1513289, _1513299, _1513291, _1513301, _1513303, _1513305)), _1513297))))], (38311 ^ _777081) ^ [_1513508, _1513510, _1513512, _1513514, _1513516, _1513518] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1513508, _1513510), _1513508, tc_prod(_1513512, _1513514), c_Product__Type_Ofst(_1513508, _1513510)), c_Product__Type_Omap__pair(_1513512, _1513508, _1513514, _1513510, _1513516, _1513518)) = hAPP(c_Fun_Ocomp(_1513512, _1513508, tc_prod(_1513512, _1513514), _1513516), c_Product__Type_Ofst(_1513512, _1513514)))], (38313 ^ _777081) ^ [_1513579, _1513581, _1513583, _1513585, _1513587, _1513589, _1513591, _1513593, _1513595, _1513597] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1513579, _1513581), tc_prod(_1513583, _1513585), tc_prod(_1513587, _1513589), c_Product__Type_Omap__pair(_1513579, _1513583, _1513581, _1513585, _1513591, _1513593)), c_Product__Type_Omap__pair(_1513587, _1513579, _1513589, _1513581, _1513595, _1513597)) = c_Product__Type_Omap__pair(_1513587, _1513583, _1513589, _1513585, hAPP(c_Fun_Ocomp(_1513579, _1513583, _1513587, _1513591), _1513595), hAPP(c_Fun_Ocomp(_1513581, _1513585, _1513589, _1513593), _1513597)))], (38315 ^ _777081) ^ [_1513674, _1513676, _1513678, _1513680, _1513682, _1513684, _1513686, _1513688, _1513690, _1513692] : [-(c_Product__Type_Omap__pair(_1513674, _1513676, _1513678, _1513680, hAPP(c_Fun_Ocomp(_1513682, _1513676, _1513674, _1513684), _1513686), hAPP(c_Fun_Ocomp(_1513688, _1513680, _1513678, _1513690), _1513692)) = hAPP(c_Fun_Ocomp(tc_prod(_1513682, _1513688), tc_prod(_1513676, _1513680), tc_prod(_1513674, _1513678), c_Product__Type_Omap__pair(_1513682, _1513676, _1513688, _1513680, _1513684, _1513690)), c_Product__Type_Omap__pair(_1513674, _1513682, _1513678, _1513688, _1513686, _1513692)))], (38317 ^ _777081) ^ [_1513769, _1513771, _1513773, _1513775, _1513777, _1513779, _1513781, _1513783, _1513785, _1513787, _1513789] : [-(hAPP(c_Product__Type_Omap__pair(_1513769, _1513771, _1513773, _1513775, _1513777, _1513779), hAPP(c_Product__Type_Omap__pair(_1513781, _1513769, _1513783, _1513773, _1513785, _1513787), _1513789)) = hAPP(c_Product__Type_Omap__pair(_1513781, _1513771, _1513783, _1513775, hAPP(c_Fun_Ocomp(_1513769, _1513771, _1513781, _1513777), _1513785), hAPP(c_Fun_Ocomp(_1513773, _1513775, _1513783, _1513779), _1513787)), _1513789))], (38319 ^ _777081) ^ [_1513858, _1513860, _1513862, _1513864, _1513866, _1513868] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1513858, _1513860), _1513860, tc_prod(_1513862, _1513864), c_Product__Type_Osnd(_1513858, _1513860)), c_Product__Type_Omap__pair(_1513862, _1513858, _1513864, _1513860, _1513866, _1513868)) = hAPP(c_Fun_Ocomp(_1513864, _1513860, tc_prod(_1513862, _1513864), _1513868), c_Product__Type_Osnd(_1513862, _1513864)))], (38321 ^ _777081) ^ [_1513929, _1513931, _1513933, _1513935, _1513937, _1513939, _1513941] : [-(hAPP(c_Product__Type_Osnd(_1513929, _1513931), hAPP(c_Product__Type_Omap__pair(_1513933, _1513929, _1513935, _1513931, _1513937, _1513939), _1513941)) = hAPP(_1513939, hAPP(c_Product__Type_Osnd(_1513933, _1513935), _1513941)))], (38323 ^ _777081) ^ [_1513989, _1513991, _1513993] : [-(hAPP(c_Product__Type_Omap__pair(_1513989, _1513989, _1513991, _1513991, c_COMBI(_1513989), c_COMBI(_1513991)), _1513993) = _1513993)], (38325 ^ _777081) ^ [_1514030, _1514032, _1514034, _1514036, _1514038, _1514040, _1514042, _1514044] : [-(hAPP(c_Product__Type_Omap__pair(_1514030, _1514032, _1514034, _1514036, _1514038, _1514040), hAPP(hAPP(c_Product__Type_OPair(_1514030, _1514034), _1514042), _1514044)) = hAPP(hAPP(c_Product__Type_OPair(_1514032, _1514036), hAPP(_1514038, _1514042)), hAPP(_1514040, _1514044)))], (38327 ^ _777081) ^ [_1514101, _1514103, _1514105, _1514107, _1514109, _1514111, _1514113] : [-(hAPP(c_Product__Type_Ofst(_1514101, _1514103), hAPP(c_Product__Type_Omap__pair(_1514105, _1514101, _1514107, _1514103, _1514109, _1514111), _1514113)) = hAPP(_1514109, hAPP(c_Product__Type_Ofst(_1514105, _1514107), _1514113)))], (38329 ^ _777081) ^ [_1514161, _1514163, _1514165, _1514167, _1514169, _1514171] : [-(c_Product__Type_Omap__pair(_1514161, _1514163, _1514165, _1514167, _1514169, _1514171) = hAPP(c_Product__Type_Oprod_Oprod__case(_1514161, _1514165, tc_prod(_1514163, _1514167)), hAPP(hAPP(c_COMBC(_1514161, tc_fun(_1514165, _1514167), tc_fun(_1514165, tc_prod(_1514163, _1514167))), hAPP(hAPP(c_COMBB(tc_fun(_1514167, tc_prod(_1514163, _1514167)), tc_fun(tc_fun(_1514165, _1514167), tc_fun(_1514165, tc_prod(_1514163, _1514167))), _1514161), c_COMBB(_1514167, tc_prod(_1514163, _1514167), _1514165)), hAPP(hAPP(c_COMBB(_1514163, tc_fun(_1514167, tc_prod(_1514163, _1514167)), _1514161), c_Product__Type_OPair(_1514163, _1514167)), _1514169))), _1514171)))], (38331 ^ _777081) ^ [_1514284, _1514286, _1514288, _1514290, _1514292, _1514294, _1514296, _1514298, _1514300, _1514302] : [hAPP(c_Set_Oimage(_1514284, _1514286, _1514288), _1514290) = _1514292, hAPP(c_Set_Oimage(_1514294, _1514296, _1514298), _1514300) = _1514302, -(hAPP(c_Set_Oimage(tc_prod(_1514284, _1514294), tc_prod(_1514286, _1514296), c_Product__Type_Omap__pair(_1514284, _1514286, _1514294, _1514296, _1514288, _1514298)), hAPP(hAPP(c_Product__Type_OSigma(_1514284, _1514294), _1514290), hAPP(c_COMBK(tc_fun(_1514294, tc_HOL_Obool), _1514284), _1514300))) = hAPP(hAPP(c_Product__Type_OSigma(_1514286, _1514296), _1514292), hAPP(c_COMBK(tc_fun(_1514296, tc_HOL_Obool), _1514286), _1514302)))], (38341 ^ _777081) ^ [_1514585, _1514587, _1514589, _1514591, _1514593, _1514595, _1514597, _1514599] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1514585, _1514587)), _1514589), hAPP(c_Set_Oimage(tc_prod(_1514591, _1514593), tc_prod(_1514585, _1514587), c_Product__Type_Omap__pair(_1514591, _1514585, _1514593, _1514587, _1514595, _1514597)), _1514599))), 38346 ^ _777081 : [(38347 ^ _777081) ^ [] : [-(_1514589 = hAPP(hAPP(c_Product__Type_OPair(_1514585, _1514587), hAPP(_1514595, 38344 ^ [_1514585, _1514587, _1514589, _1514591, _1514593, _1514595, _1514597, _1514599])), hAPP(_1514597, 38345 ^ [_1514585, _1514587, _1514589, _1514591, _1514593, _1514595, _1514597, _1514599])))], (38349 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1514591, _1514593)), hAPP(hAPP(c_Product__Type_OPair(_1514591, _1514593), 38344 ^ [_1514585, _1514587, _1514589, _1514591, _1514593, _1514595, _1514597, _1514599]), 38345 ^ [_1514585, _1514587, _1514589, _1514591, _1514593, _1514595, _1514597, _1514599])), _1514599)))]]], (38351 ^ _777081) ^ [_1514936, _1514938, _1514940] : [c_Relation_Orefl__on(_1514936, _1514938, _1514940), 38354 ^ _777081 : [(38355 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1514936, _1514936), tc_HOL_Obool)), _1514940), hAPP(hAPP(c_Product__Type_OSigma(_1514936, _1514936), _1514938), hAPP(c_COMBK(tc_fun(_1514936, tc_HOL_Obool), _1514936), _1514938)))))], (38357 ^ _777081) ^ [_1515118] : [hBOOL(hAPP(hAPP(c_member(_1514936), _1515118), _1514938)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1514936, _1514936)), hAPP(hAPP(c_Product__Type_OPair(_1514936, _1514936), _1515118), _1515118)), _1514940)))]]], (38363 ^ _777081) ^ [_1515253, _1515255, _1515257] : [-(c_Relation_Orefl__on(_1515253, _1515255, _1515257)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1515253, _1515253), tc_HOL_Obool)), _1515257), hAPP(hAPP(c_Product__Type_OSigma(_1515253, _1515253), _1515255), hAPP(c_COMBK(tc_fun(_1515253, tc_HOL_Obool), _1515253), _1515255)))), 38369 ^ _777081 : [(38370 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515253), 38368 ^ [_1515253, _1515255, _1515257]), _1515255)))], (38372 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1515253, _1515253)), hAPP(hAPP(c_Product__Type_OPair(_1515253, _1515253), 38368 ^ [_1515253, _1515255, _1515257]), 38368 ^ [_1515253, _1515255, _1515257])), _1515257))]]], (38376 ^ _777081) ^ [_1515602, _1515604, _1515606] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515602), _1515604)), 38382 ^ _777081 : [(38383 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515602), 38381 ^ [_1515602, _1515604, _1515606]), _1515604)))], (38385 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1515606, 38381 ^ [_1515602, _1515604, _1515606])))]], -(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(_1515602, tc_Nat_Onat), _1515606), _1515604))))], (38389 ^ _777081) ^ [_1515863, _1515865] : [-(c_Relation_Orefl__on(_1515863, _1515865, c_Relation_OId__on(_1515863, _1515865)))], (38391 ^ _777081) ^ [_1515892] : [-(c_Relation_Orefl__on(_1515892, c_Orderings_Obot__class_Obot(tc_fun(_1515892, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1515892, _1515892), tc_HOL_Obool))))], (38393 ^ _777081) ^ [_1515929, _1515931, _1515933, _1515935, _1515937] : [c_Relation_Orefl__on(_1515929, _1515931, _1515933), c_Relation_Orefl__on(_1515929, _1515935, _1515937), -(c_Relation_Orefl__on(_1515929, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1515929, tc_HOL_Obool)), _1515931), _1515935), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1515929, _1515929), tc_HOL_Obool)), _1515933), _1515937)))], (38403 ^ _777081) ^ [_1516126, _1516128, _1516130, _1516132, _1516134] : [c_Relation_Orefl__on(_1516126, _1516128, _1516130), c_Relation_Orefl__on(_1516126, _1516132, _1516134), -(c_Relation_Orefl__on(_1516126, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1516126, tc_HOL_Obool)), _1516128), _1516132), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1516126, _1516126), tc_HOL_Obool)), _1516130), _1516134)))], (38413 ^ _777081) ^ [_1516323, _1516325, _1516327, _1516329] : [c_Relation_Orefl__on(_1516323, _1516325, _1516327), hBOOL(hAPP(hAPP(c_member(_1516323), _1516329), _1516325)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516323, _1516323)), hAPP(hAPP(c_Product__Type_OPair(_1516323, _1516323), _1516329), _1516329)), _1516327)))], (38423 ^ _777081) ^ [_1516514, _1516516, _1516518, _1516520, _1516522] : [c_Relation_Orefl__on(_1516514, _1516516, _1516518), hBOOL(hAPP(hAPP(c_member(tc_prod(_1516514, _1516514)), hAPP(hAPP(c_Product__Type_OPair(_1516514, _1516514), _1516520), _1516522)), _1516518)), -(hBOOL(hAPP(hAPP(c_member(_1516514), _1516522), _1516516)))], (38433 ^ _777081) ^ [_1516709, _1516711, _1516713, _1516715, _1516717] : [c_Relation_Orefl__on(_1516709, _1516711, _1516713), hBOOL(hAPP(hAPP(c_member(tc_prod(_1516709, _1516709)), hAPP(hAPP(c_Product__Type_OPair(_1516709, _1516709), _1516715), _1516717)), _1516713)), -(hBOOL(hAPP(hAPP(c_member(_1516709), _1516715), _1516711)))], (38443 ^ _777081) ^ [_1516904, _1516906, _1516908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1516904, _1516904), tc_HOL_Obool)), _1516906), hAPP(hAPP(c_Product__Type_OSigma(_1516904, _1516904), _1516908), hAPP(c_COMBK(tc_fun(_1516904, tc_HOL_Obool), _1516904), _1516908)))), 38449 ^ _777081 : [(38450 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1516904), 38448 ^ [_1516904, _1516906, _1516908]), _1516908)))], (38452 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1516904, _1516904)), hAPP(hAPP(c_Product__Type_OPair(_1516904, _1516904), 38448 ^ [_1516904, _1516906, _1516908]), 38448 ^ [_1516904, _1516906, _1516908])), _1516906))]], -(c_Relation_Orefl__on(_1516904, _1516908, _1516906))], (38456 ^ _777081) ^ [_1517251, _1517253, _1517255, _1517257, _1517259] : [c_Finite__Set_Ofolding__one__idem(_1517251, _1517253, _1517255), hAPP(_1517257, hAPP(hAPP(_1517253, 38461 ^ [_1517251, _1517253, _1517255, _1517257, _1517259]), 38462 ^ [_1517251, _1517253, _1517255, _1517257, _1517259])) = hAPP(hAPP(_1517253, hAPP(_1517257, 38461 ^ [_1517251, _1517253, _1517255, _1517257, _1517259])), hAPP(_1517257, 38462 ^ [_1517251, _1517253, _1517255, _1517257, _1517259])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517251), _1517259)), -(_1517259 = c_Orderings_Obot__class_Obot(tc_fun(_1517251, tc_HOL_Obool))), -(hAPP(_1517257, hAPP(_1517255, _1517259)) = hAPP(_1517255, hAPP(c_Set_Oimage(_1517251, _1517251, _1517257), _1517259)))], (38476 ^ _777081) ^ [_1517686] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1517686), c_Int_OInteg)), -(_1517686 = hAPP(c_Int_ORep__Integ, 38479 ^ [_1517686]))], (38483 ^ _777081) ^ [_1517791, _1517793] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1517791), c_Int_OInteg)), hBOOL(hAPP(_1517793, hAPP(c_Int_ORep__Integ, 38488 ^ [_1517791, _1517793]))), -(hBOOL(hAPP(_1517793, _1517791)))], (38494 ^ _777081) ^ [_1517973, _1517975, _1517977, _1517979, _1517981, _1517983, _1517985, _1517987] : [c_Finite__Set_Ofolding__image__simple(_1517973, _1517975, _1517977, _1517979, _1517981, _1517983), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517975), _1517985)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1517975), _1517987)), 38508 ^ _777081 : [(38509 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1517975), 38507 ^ [_1517973, _1517975, _1517977, _1517979, _1517981, _1517983, _1517985, _1517987]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1517975, tc_HOL_Obool)), _1517985), _1517987))))], (38511 ^ _777081) ^ [] : [hAPP(_1517981, 38507 ^ [_1517973, _1517975, _1517977, _1517979, _1517981, _1517983, _1517985, _1517987]) = _1517979]], -(hAPP(_1517983, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1517975, tc_HOL_Obool)), _1517985), _1517987)) = hAPP(hAPP(_1517977, hAPP(_1517983, _1517985)), hAPP(_1517983, _1517987)))], (38515 ^ _777081) ^ [_1518474] : [-(c_Finite__Set_Ofun__left__comm__idem(_1518474, tc_fun(_1518474, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1518474, tc_HOL_Obool), tc_fun(tc_fun(_1518474, tc_HOL_Obool), tc_fun(_1518474, tc_HOL_Obool)), _1518474), hAPP(c_COMBC(tc_fun(_1518474, tc_HOL_Obool), tc_fun(_1518474, tc_HOL_Obool), tc_fun(_1518474, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1518474, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1518474, tc_fun(_1518474, tc_HOL_Obool), tc_fun(_1518474, tc_HOL_Obool)), c_Set_Oinsert(_1518474)), c_Orderings_Obot__class_Obot(tc_fun(_1518474, tc_HOL_Obool))))))], (38517 ^ _777081) ^ [_1518567] : [class_Lattices_Osemilattice__sup(_1518567), -(c_Finite__Set_Ofun__left__comm__idem(_1518567, _1518567, c_Lattices_Osemilattice__sup__class_Osup(_1518567)))], (38523 ^ _777081) ^ [_1518646] : [class_Lattices_Osemilattice__inf(_1518646), -(c_Finite__Set_Ofun__left__comm__idem(_1518646, _1518646, c_Lattices_Osemilattice__inf__class_Oinf(_1518646)))], (38529 ^ _777081) ^ [_1518725, _1518727, _1518729, _1518731, _1518733] : [c_Finite__Set_Ofun__left__comm__idem(_1518725, _1518727, _1518729), -(hAPP(hAPP(_1518729, _1518731), hAPP(hAPP(_1518729, _1518731), _1518733)) = hAPP(hAPP(_1518729, _1518731), _1518733))], (38535 ^ _777081) ^ [_1518846, _1518848, _1518850, _1518852, _1518854] : [c_Finite__Set_Ofun__left__comm__idem(_1518846, _1518848, _1518850), -(c_Finite__Set_Ofun__left__comm__idem(_1518852, _1518848, hAPP(hAPP(c_COMBB(_1518846, tc_fun(_1518848, _1518848), _1518852), _1518850), _1518854)))], (38541 ^ _777081) ^ [_1518959] : [-(c_Finite__Set_Ofun__left__comm__idem(_1518959, tc_fun(_1518959, tc_HOL_Obool), c_Set_Oinsert(_1518959)))], (38543 ^ _777081) ^ [_1518988] : [class_Lattices_Oab__semigroup__idem__mult(_1518988), -(c_Finite__Set_Ofun__left__comm__idem(_1518988, _1518988, c_Groups_Otimes__class_Otimes(_1518988)))], (38549 ^ _777081) ^ [_1519067] : [class_Orderings_Olinorder(_1519067), -(c_Finite__Set_Ofun__left__comm__idem(_1519067, _1519067, c_Orderings_Oord__class_Omax(_1519067)))], (38555 ^ _777081) ^ [_1519146] : [class_Orderings_Olinorder(_1519146), -(c_Finite__Set_Ofun__left__comm__idem(_1519146, _1519146, c_Orderings_Oord__class_Omin(_1519146)))], (38561 ^ _777081) ^ [_1519225, _1519227, _1519229, _1519231] : [c_Finite__Set_Ofun__left__comm__idem(_1519225, _1519227, _1519229), -(hAPP(c_Fun_Ocomp(_1519227, _1519227, _1519227, hAPP(_1519229, _1519231)), hAPP(_1519229, _1519231)) = hAPP(_1519229, _1519231))], (38567 ^ _777081) ^ [_1519338, _1519340] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1519338))), -(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)), _1519338))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1519340)))) = 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)), _1519338))), 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, _1519340))))))], (38573 ^ _777081) ^ [_1519421, _1519423] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1519421)), 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)), _1519421))), 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, _1519423))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (38579 ^ _777081) ^ [_1519551, _1519553] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1519551)), -(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)), _1519551))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1519553))))) = 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)), _1519551))), 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, _1519553))))))], (38585 ^ _777081) ^ [_1519728, _1519730, _1519732] : [hBOOL(hAPP(_1519728, _1519730)), -(hBOOL(hAPP(hAPP(c_member(_1519732), _1519730), hAPP(c_Set_OCollect(_1519732), _1519728))))], (38591 ^ _777081) ^ [_1519835, _1519837, _1519839] : [38592 ^ _777081 : [(38593 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1519835), hAPP(c_Set_OCollect(_1519835), _1519837)))], (38595 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1519835), hAPP(c_Set_OCollect(_1519835), _1519839)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1519835), hAPP(c_Set_OCollect(_1519835), hAPP(hAPP(c_COMBS(_1519835, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519835), c_fconj), _1519837)), _1519839)))))], (38599 ^ _777081) ^ [_1520046] : [-(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)), _1520046)))))], (38601 ^ _777081) ^ [_1520077] : [-(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)), _1520077)))))], (38603 ^ _777081) ^ [_1520108, _1520110, _1520112, _1520114] : [-(hAPP(c_Set_OCollect(tc_prod(_1520108, _1520110)), hAPP(c_Product__Type_Oprod_Oprod__case(_1520108, _1520110, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1520108, tc_fun(_1520110, tc_HOL_Obool), tc_fun(_1520110, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1520110, tc_HOL_Obool), tc_fun(_1520110, tc_HOL_Obool)), _1520108), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1520110)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520108), c_fconj), _1520112))), _1520114))) = hAPP(hAPP(c_Product__Type_OSigma(_1520108, _1520110), hAPP(c_Set_OCollect(_1520108), _1520112)), hAPP(c_COMBK(tc_fun(_1520110, tc_HOL_Obool), _1520108), hAPP(c_Set_OCollect(_1520110), _1520114))))], (38605 ^ _777081) ^ [_1520229, _1520231, _1520233, _1520235] : [-(hAPP(c_Set_OCollect(tc_prod(_1520229, _1520231)), hAPP(c_Product__Type_Oprod_Oprod__case(_1520229, _1520231, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1520229, tc_fun(_1520231, tc_HOL_Obool), tc_fun(_1520231, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1520231, tc_HOL_Obool), tc_fun(_1520231, tc_HOL_Obool)), _1520229), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1520231)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520229), c_fconj), _1520233))), _1520235))) = hAPP(hAPP(c_Product__Type_OSigma(_1520229, _1520231), hAPP(c_Set_OCollect(_1520229), _1520233)), hAPP(hAPP(c_COMBB(tc_fun(_1520231, tc_HOL_Obool), tc_fun(_1520231, tc_HOL_Obool), _1520229), c_Set_OCollect(_1520231)), _1520235)))], (38607 ^ _777081) ^ [_1520354, _1520356] : [-(hAPP(c_Set_OCollect(_1520354), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1520354), c_fNot), _1520356)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1520354, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1520354), _1520356)))], (38609 ^ _777081) ^ [_1520407, _1520409, _1520411, _1520413] : [-(hAPP(c_Set_Ovimage(_1520407, _1520409, _1520411), hAPP(c_Set_OCollect(_1520409), _1520413)) = hAPP(c_Set_OCollect(_1520407), hAPP(hAPP(c_COMBB(_1520409, tc_HOL_Obool, _1520407), _1520413), _1520411)))], (38611 ^ _777081) ^ [_1520463, _1520465, _1520467] : [hBOOL(hAPP(hAPP(c_member(_1520463), _1520465), hAPP(c_Set_OCollect(_1520463), _1520467))), -(hBOOL(hAPP(_1520467, _1520465)))], (38617 ^ _777081) ^ [_1520570, _1520572, _1520574] : [hBOOL(hAPP(hAPP(c_member(_1520570), _1520572), hAPP(c_Set_OCollect(_1520570), _1520574))), -(hBOOL(hAPP(_1520574, _1520572)))], (38623 ^ _777081) ^ [_1520695, _1520697, _1520699] : [hBOOL(hAPP(hAPP(c_member(_1520695), _1520697), hAPP(c_Set_OCollect(_1520695), _1520699))), -(hBOOL(hAPP(_1520699, _1520697)))], (38629 ^ _777081) ^ [_1520798, _1520800, _1520802] : [hBOOL(hAPP(_1520802, _1520800)), -(hBOOL(hAPP(hAPP(c_member(_1520798), _1520800), hAPP(c_Set_OCollect(_1520798), _1520802))))], (38635 ^ _777081) ^ [_1520907, _1520909] : [-(hAPP(c_Set_OCollect(_1520907), hAPP(hAPP(c_COMBC(_1520907, tc_fun(_1520907, tc_HOL_Obool), tc_HOL_Obool), c_member(_1520907)), _1520909)) = _1520909)], (38637 ^ _777081) ^ [_1520952, _1520954, _1520956] : [-(hAPP(hAPP(c_Set_Oinsert(_1520952), _1520954), hAPP(c_Set_OCollect(_1520952), _1520956)) = hAPP(c_Set_OCollect(_1520952), hAPP(hAPP(c_COMBS(_1520952, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1520952), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1520952), c_fNot), hAPP(hAPP(c_COMBC(_1520952, _1520952, tc_HOL_Obool), c_fequal), _1520954)))), _1520956)))], (38639 ^ _777081) ^ [_1521055, _1521057, _1521059] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1521055), hAPP(c_Set_OCollect(_1521055), hAPP(hAPP(c_COMBS(_1521055, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521055), c_fdisj), _1521057)), _1521059)))), 38642 ^ _777081 : [(38643 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521055), hAPP(c_Set_OCollect(_1521055), _1521057))))], (38645 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521055), hAPP(c_Set_OCollect(_1521055), _1521059))))]]], (38647 ^ _777081) ^ [_1521250, _1521252, _1521254] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521250), hAPP(c_Set_OCollect(_1521250), hAPP(hAPP(c_COMBS(_1521250, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521250), c_fdisj), _1521252)), _1521254))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521250), hAPP(c_Set_OCollect(_1521250), _1521252))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1521250), hAPP(c_Set_OCollect(_1521250), _1521254)))], (38657 ^ _777081) ^ [_1521494, _1521496] : [c_Orderings_Obot__class_Obot(tc_fun(_1521494, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1521494), _1521496), 38660 ^ _777081 : [(38661 ^ _777081) ^ [_1521579] : [hBOOL(hAPP(_1521496, _1521579))]]], (38663 ^ _777081) ^ [_1521602, _1521604] : [-(hBOOL(hAPP(_1521604, 38664 ^ [_1521602, _1521604]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1521602, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1521602), _1521604))], (38670 ^ _777081) ^ [_1521674, _1521676] : [hAPP(c_Set_OCollect(_1521674), _1521676) = c_Orderings_Obot__class_Obot(tc_fun(_1521674, tc_HOL_Obool)), 38673 ^ _777081 : [(38674 ^ _777081) ^ [_1521759] : [hBOOL(hAPP(_1521676, _1521759))]]], (38676 ^ _777081) ^ [_1521782, _1521784] : [-(hBOOL(hAPP(_1521784, 38677 ^ [_1521782, _1521784]))), -(hAPP(c_Set_OCollect(_1521782), _1521784) = c_Orderings_Obot__class_Obot(tc_fun(_1521782, tc_HOL_Obool)))], (38683 ^ _777081) ^ [_1521839] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1521839, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1521839), hAPP(c_COMBK(tc_HOL_Obool, _1521839), c_fFalse)))], (38685 ^ _777081) ^ [_1521878, _1521880, _1521882] : [-(hAPP(c_Set_OCollect(_1521878), hAPP(hAPP(c_COMBS(_1521878, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521878), c_fdisj), _1521880)), _1521882)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521878, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1521878), _1521880)), hAPP(c_Set_OCollect(_1521878), _1521882)))], (38687 ^ _777081) ^ [_1521951, _1521953, _1521955] : [-(hAPP(c_Set_OCollect(_1521951), hAPP(hAPP(c_COMBS(_1521951, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1521951), c_fconj), _1521953)), _1521955)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1521951, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1521951), _1521953)), hAPP(c_Set_OCollect(_1521951), _1521955)))], (38689 ^ _777081) ^ [_1522024, _1522026] : [-(hAPP(c_Set_OCollect(_1522024), _1522026) = _1522026)], (38691 ^ _777081) ^ [_1522054] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1522054, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1522054), hAPP(c_COMBK(tc_HOL_Obool, _1522054), c_fTrue)))], (38693 ^ _777081) ^ [_1522093, _1522095, _1522097] : [-(hAPP(hAPP(c_Set_Oinsert(_1522093), _1522095), _1522097) = hAPP(c_Set_OCollect(_1522093), hAPP(hAPP(c_COMBS(_1522093, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522093), c_fdisj), hAPP(hAPP(c_COMBC(_1522093, _1522093, tc_HOL_Obool), c_fequal), _1522095))), hAPP(hAPP(c_COMBC(_1522093, tc_fun(_1522093, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522093)), _1522097))))], (38695 ^ _777081) ^ [_1522178, _1522180, _1522182] : [-(hAPP(hAPP(c_Set_Oinsert(_1522178), _1522180), _1522182) = hAPP(c_Set_OCollect(_1522178), hAPP(hAPP(c_COMBS(_1522178, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522178), c_fdisj), hAPP(hAPP(c_COMBC(_1522178, _1522178, tc_HOL_Obool), c_fequal), _1522180))), hAPP(hAPP(c_COMBC(_1522178, tc_fun(_1522178, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522178)), _1522182))))], (38697 ^ _777081) ^ [_1522263, _1522265, _1522267] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1522263, tc_HOL_Obool)), _1522265), _1522267) = hAPP(c_Set_OCollect(_1522263), hAPP(hAPP(c_COMBS(_1522263, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522263), c_fdisj), hAPP(hAPP(c_COMBC(_1522263, tc_fun(_1522263, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522263)), _1522265))), hAPP(hAPP(c_COMBC(_1522263, tc_fun(_1522263, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522263)), _1522267))))], (38699 ^ _777081) ^ [_1522377, _1522379, _1522381, _1522383] : [hBOOL(hAPP(hAPP(c_member(_1522377), _1522379), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522377, tc_HOL_Obool)), _1522381), hAPP(c_Set_OCollect(_1522377), _1522383)))), 38702 ^ _777081 : [(38703 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1522377), _1522379), _1522381)))], (38705 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1522383, _1522379)))]]], (38707 ^ _777081) ^ [_1522544, _1522546, _1522548, _1522550] : [-(hBOOL(hAPP(hAPP(c_member(_1522544), _1522546), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522544, tc_HOL_Obool)), _1522548), hAPP(c_Set_OCollect(_1522544), _1522550))))), hBOOL(hAPP(hAPP(c_member(_1522544), _1522546), _1522548)), hBOOL(hAPP(_1522550, _1522546))], (38717 ^ _777081) ^ [_1522747, _1522749, _1522751] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522747, tc_HOL_Obool)), _1522749), _1522751) = hAPP(c_Set_OCollect(_1522747), hAPP(hAPP(c_COMBS(_1522747, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522747), c_fconj), hAPP(hAPP(c_COMBC(_1522747, tc_fun(_1522747, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522747)), _1522749))), hAPP(hAPP(c_COMBC(_1522747, tc_fun(_1522747, tc_HOL_Obool), tc_HOL_Obool), c_member(_1522747)), _1522751))))], (38719 ^ _777081) ^ [_1522840, _1522842] : [-(hAPP(c_Set_OCollect(_1522840), hAPP(c_fequal, _1522842)) = hAPP(hAPP(c_Set_Oinsert(_1522840), _1522842), c_Orderings_Obot__class_Obot(tc_fun(_1522840, tc_HOL_Obool))))], (38721 ^ _777081) ^ [_1522886, _1522888] : [-(hAPP(c_Set_OCollect(_1522886), hAPP(hAPP(c_COMBC(_1522886, _1522886, tc_HOL_Obool), c_fequal), _1522888)) = hAPP(hAPP(c_Set_Oinsert(_1522886), _1522888), c_Orderings_Obot__class_Obot(tc_fun(_1522886, tc_HOL_Obool))))], (38723 ^ _777081) ^ [_1522951, _1522953, _1522955] : [hBOOL(hAPP(_1522951, _1522953)), -(hAPP(c_Set_OCollect(_1522955), hAPP(hAPP(c_COMBS(_1522955, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1522955), c_fconj), hAPP(c_fequal, _1522953))), _1522951)) = hAPP(hAPP(c_Set_Oinsert(_1522955), _1522953), c_Orderings_Obot__class_Obot(tc_fun(_1522955, tc_HOL_Obool))))], (38729 ^ _777081) ^ [_1523110, _1523112, _1523114] : [-(hBOOL(hAPP(_1523110, _1523112))), -(hAPP(c_Set_OCollect(_1523114), hAPP(hAPP(c_COMBS(_1523114, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523114), c_fconj), hAPP(c_fequal, _1523112))), _1523110)) = c_Orderings_Obot__class_Obot(tc_fun(_1523114, tc_HOL_Obool)))], (38735 ^ _777081) ^ [_1523197, _1523199, _1523201] : [hBOOL(hAPP(_1523197, _1523199)), -(hAPP(c_Set_OCollect(_1523201), hAPP(hAPP(c_COMBS(_1523201, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523201), c_fconj), hAPP(hAPP(c_COMBC(_1523201, _1523201, tc_HOL_Obool), c_fequal), _1523199))), _1523197)) = hAPP(hAPP(c_Set_Oinsert(_1523201), _1523199), c_Orderings_Obot__class_Obot(tc_fun(_1523201, tc_HOL_Obool))))], (38741 ^ _777081) ^ [_1523370, _1523372, _1523374] : [-(hBOOL(hAPP(_1523370, _1523372))), -(hAPP(c_Set_OCollect(_1523374), hAPP(hAPP(c_COMBS(_1523374, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523374), c_fconj), hAPP(hAPP(c_COMBC(_1523374, _1523374, tc_HOL_Obool), c_fequal), _1523372))), _1523370)) = c_Orderings_Obot__class_Obot(tc_fun(_1523374, tc_HOL_Obool)))], (38747 ^ _777081) ^ [_1523452, _1523454, _1523456] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1523452, tc_HOL_Obool)), _1523454), _1523456) = hAPP(c_Set_OCollect(_1523452), hAPP(hAPP(c_COMBS(_1523452, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1523452), c_fconj), hAPP(hAPP(c_COMBC(_1523452, tc_fun(_1523452, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523452)), _1523454))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1523452), c_fNot), hAPP(hAPP(c_COMBC(_1523452, tc_fun(_1523452, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523452)), _1523456)))))], (38749 ^ _777081) ^ [_1523555, _1523557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523555), hAPP(c_Set_OCollect(_1523555), _1523557))), 38752 ^ _777081 : [(38753 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523555), hAPP(c_Set_OCollect(_1523555), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1523555), c_fNot), _1523557)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523555), c_Orderings_Otop__class_Otop(tc_fun(_1523555, tc_HOL_Obool)))))], (38759 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523555), c_Orderings_Otop__class_Otop(tc_fun(_1523555, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523555), hAPP(c_Set_OCollect(_1523555), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1523555), c_fNot), _1523557)))))]]], (38765 ^ _777081) ^ [_1523864, _1523866, _1523868] : [-(hAPP(hAPP(c_Set_Oinsert(_1523864), _1523866), _1523868) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1523864, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1523864), hAPP(hAPP(c_COMBC(_1523864, _1523864, tc_HOL_Obool), c_fequal), _1523866))), _1523868))], (38767 ^ _777081) ^ [_1523925, _1523927] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1523925, tc_HOL_Obool)), _1523927) = hAPP(c_Set_OCollect(_1523925), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1523925), c_fNot), hAPP(hAPP(c_COMBC(_1523925, tc_fun(_1523925, tc_HOL_Obool), tc_HOL_Obool), c_member(_1523925)), _1523927))))], (38769 ^ _777081) ^ [_1523988, _1523990, _1523992, _1523994] : [-(hAPP(c_Set_Ovimage(_1523988, _1523990, _1523992), _1523994) = hAPP(c_Set_OCollect(_1523988), hAPP(hAPP(c_COMBC(_1523988, tc_fun(_1523990, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1523990, tc_fun(tc_fun(_1523990, tc_HOL_Obool), tc_HOL_Obool), _1523988), c_member(_1523990)), _1523992)), _1523994)))], (38771 ^ _777081) ^ [_1524060, _1524062, _1524064] : [-(hAPP(c_Set_OCollect(_1524060), hAPP(hAPP(c_COMBS(_1524060, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524060), c_fimplies), _1524062)), _1524064)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1524060, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1524060, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1524060), _1524062))), hAPP(c_Set_OCollect(_1524060), _1524064)))], (38773 ^ _777081) ^ [_1524141, _1524143, _1524145] : [-(c_Map_Odom(_1524141, _1524143, _1524145) = hAPP(c_Set_OCollect(_1524141), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1524141), c_fNot), hAPP(hAPP(c_COMBC(_1524141, tc_Option_Ooption(_1524143), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1524143), tc_fun(tc_Option_Ooption(_1524143), tc_HOL_Obool), _1524141), c_fequal), _1524145)), c_Option_Ooption_ONone(_1524143)))))], (38775 ^ _777081) ^ [_1524218, _1524220] : [-(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), _1524218)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1524220))))))], (38777 ^ _777081) ^ [_1524260, _1524262, _1524264, _1524266, _1524268, _1524270, _1524272] : [class_Groups_Ocomm__monoid__add(_1524260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524262), _1524264)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1524266), _1524268)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524262, _1524260), hAPP(hAPP(c_COMBS(_1524262, tc_fun(_1524266, tc_HOL_Obool), _1524260), hAPP(hAPP(c_COMBB(tc_fun(_1524266, _1524260), tc_fun(tc_fun(_1524266, tc_HOL_Obool), _1524260), _1524262), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524266, _1524260)), _1524270)), hAPP(hAPP(c_COMBB(tc_fun(_1524266, tc_HOL_Obool), tc_fun(_1524266, tc_HOL_Obool), _1524262), c_Set_OCollect(_1524266)), hAPP(hAPP(c_COMBB(tc_fun(_1524266, tc_HOL_Obool), tc_fun(_1524266, tc_HOL_Obool), _1524262), hAPP(c_COMBS(_1524266, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524266), c_fconj), hAPP(hAPP(c_COMBC(_1524266, tc_fun(_1524266, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524266)), _1524268)))), _1524272)))), _1524264) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524266, _1524260), hAPP(hAPP(c_COMBS(_1524266, tc_fun(_1524262, tc_HOL_Obool), _1524260), hAPP(hAPP(c_COMBB(tc_fun(_1524262, _1524260), tc_fun(tc_fun(_1524262, tc_HOL_Obool), _1524260), _1524266), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1524262, _1524260)), hAPP(c_COMBC(_1524262, _1524266, _1524260), _1524270))), hAPP(hAPP(c_COMBB(tc_fun(_1524262, tc_HOL_Obool), tc_fun(_1524262, tc_HOL_Obool), _1524266), c_Set_OCollect(_1524262)), hAPP(hAPP(c_COMBB(tc_fun(_1524262, tc_HOL_Obool), tc_fun(_1524262, tc_HOL_Obool), _1524266), hAPP(c_COMBS(_1524262, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524262), c_fconj), hAPP(hAPP(c_COMBC(_1524262, tc_fun(_1524262, tc_HOL_Obool), tc_HOL_Obool), c_member(_1524262)), _1524264)))), hAPP(c_COMBC(_1524262, _1524266, tc_HOL_Obool), _1524272))))), _1524268))], (38791 ^ _777081) ^ [_1524953, _1524955, _1524957, _1524959, _1524961, _1524963] : [-(hAPP(c_Set_Oimage(_1524953, _1524955, hAPP(hAPP(c_COMBS(_1524953, _1524955, _1524955), hAPP(hAPP(c_COMBS(_1524953, _1524955, tc_fun(_1524955, _1524955)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1524955, tc_fun(_1524955, _1524955)), _1524953), c_If(_1524955)), _1524957)), _1524959)), _1524961)), _1524963) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1524955, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1524953, _1524955, _1524959), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1524953, tc_HOL_Obool)), _1524963), hAPP(c_Set_OCollect(_1524953), _1524957)))), hAPP(c_Set_Oimage(_1524953, _1524955, _1524961), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1524953, tc_HOL_Obool)), _1524963), hAPP(c_Set_OCollect(_1524953), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1524953), c_fNot), _1524957))))))], (38793 ^ _777081) ^ [_1525101, _1525103, _1525105, _1525107, _1525109] : [-(c_Map_Odom(_1525101, _1525103, hAPP(hAPP(c_COMBS(_1525101, tc_Option_Ooption(_1525103), tc_Option_Ooption(_1525103)), hAPP(hAPP(c_COMBS(_1525101, tc_Option_Ooption(_1525103), tc_fun(tc_Option_Ooption(_1525103), tc_Option_Ooption(_1525103))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1525103), tc_fun(tc_Option_Ooption(_1525103), tc_Option_Ooption(_1525103))), _1525101), c_If(tc_Option_Ooption(_1525103))), _1525105)), _1525107)), _1525109)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525101, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1525101, tc_HOL_Obool)), c_Map_Odom(_1525101, _1525103, _1525107)), hAPP(c_Set_OCollect(_1525101), _1525105))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1525101, tc_HOL_Obool)), c_Map_Odom(_1525101, _1525103, _1525109)), hAPP(c_Set_OCollect(_1525101), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1525101), c_fNot), _1525105)))))], (38795 ^ _777081) ^ [_1525256, _1525258, _1525260, _1525262] : [_1525256 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1525258, _1525260), 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)), _1525262))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1525258), _1525256)))], (38801 ^ _777081) ^ [_1525371, _1525373, _1525375, _1525377, _1525379] : [class_Groups_Ocomm__monoid__add(_1525371), hBOOL(hAPP(c_Finite__Set_Ofinite(_1525373), _1525375)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525373, _1525371), _1525377), hAPP(c_Set_OCollect(_1525373), hAPP(hAPP(c_COMBS(_1525373, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525373), c_fconj), hAPP(hAPP(c_COMBC(_1525373, tc_fun(_1525373, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525373)), _1525375))), hAPP(hAPP(c_COMBC(_1525373, tc_fun(_1525373, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525373)), _1525379)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525373, _1525371), hAPP(hAPP(c_COMBC(_1525373, _1525371, _1525371), hAPP(hAPP(c_COMBS(_1525373, _1525371, tc_fun(_1525371, _1525371)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525371, tc_fun(_1525371, _1525371)), _1525373), c_If(_1525371)), hAPP(hAPP(c_COMBC(_1525373, tc_fun(_1525373, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525373)), _1525379))), _1525377)), c_Groups_Ozero__class_Ozero(_1525371))), _1525375))], (38811 ^ _777081) ^ [_1525780, _1525782, _1525784, _1525786, _1525788, _1525790] : [class_Groups_Ocomm__monoid__add(_1525780), hBOOL(hAPP(c_Finite__Set_Ofinite(_1525782), _1525784)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525782, _1525780), _1525786), _1525784) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525788, _1525780), hAPP(hAPP(c_COMBB(tc_fun(_1525782, tc_HOL_Obool), _1525780, _1525788), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1525782, _1525780), _1525786)), hAPP(hAPP(c_COMBB(tc_fun(_1525782, tc_HOL_Obool), tc_fun(_1525782, tc_HOL_Obool), _1525788), c_Set_OCollect(_1525782)), hAPP(hAPP(c_COMBB(tc_fun(_1525782, tc_HOL_Obool), tc_fun(_1525782, tc_HOL_Obool), _1525788), hAPP(c_COMBS(_1525782, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1525782), c_fconj), hAPP(hAPP(c_COMBC(_1525782, tc_fun(_1525782, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525782)), _1525784)))), hAPP(c_COMBC(_1525782, _1525788, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1525788, tc_fun(_1525788, tc_HOL_Obool), _1525782), c_fequal), _1525790)))))), hAPP(c_Set_Oimage(_1525782, _1525788, _1525790), _1525784)))], (38821 ^ _777081) ^ [_1526191, _1526193, _1526195, _1526197] : [-(hAPP(c_Relation_OImage(_1526191, _1526193, _1526195), hAPP(hAPP(c_Set_Oinsert(_1526191), _1526197), c_Orderings_Obot__class_Obot(tc_fun(_1526191, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1526193), hAPP(hAPP(c_COMBC(_1526193, tc_fun(tc_prod(_1526191, _1526193), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1526191, _1526193), tc_fun(tc_fun(tc_prod(_1526191, _1526193), tc_HOL_Obool), tc_HOL_Obool), _1526193), c_member(tc_prod(_1526191, _1526193))), hAPP(c_Product__Type_OPair(_1526191, _1526193), _1526197))), _1526195)))], (38823 ^ _777081) ^ [_1526294, _1526296, _1526298, _1526300, _1526302, _1526304] : [class_Groups_Ocomm__monoid__add(_1526294), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526296), _1526298)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526296, _1526294), hAPP(hAPP(c_COMBS(_1526296, _1526294, _1526294), hAPP(hAPP(c_COMBS(_1526296, _1526294, tc_fun(_1526294, _1526294)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1526294, tc_fun(_1526294, _1526294)), _1526296), c_If(_1526294)), _1526300)), _1526302)), _1526304)), _1526298) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1526294), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526296, _1526294), _1526302), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1526296, tc_HOL_Obool)), _1526298), hAPP(c_Set_OCollect(_1526296), _1526300)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526296, _1526294), _1526304), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1526296, tc_HOL_Obool)), _1526298), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1526296, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1526296), _1526300))))))], (38833 ^ _777081) ^ [_1526677, _1526679, _1526681, _1526683, _1526685] : [-(c_Map_Odom(_1526677, _1526679, c_Fun_Ooverride__on(_1526677, tc_Option_Ooption(_1526679), _1526681, _1526683, _1526685)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1526677, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1526677, tc_HOL_Obool)), c_Map_Odom(_1526677, _1526679, _1526681)), hAPP(c_Set_OCollect(_1526677), hAPP(hAPP(c_COMBC(_1526677, tc_fun(_1526677, tc_HOL_Obool), tc_HOL_Obool), c_member(_1526677)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1526677, tc_HOL_Obool)), _1526685), c_Map_Odom(_1526677, _1526679, _1526683)))))), hAPP(c_Set_OCollect(_1526677), hAPP(hAPP(c_COMBC(_1526677, tc_fun(_1526677, tc_HOL_Obool), tc_HOL_Obool), c_member(_1526677)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1526677, tc_HOL_Obool)), _1526685), c_Map_Odom(_1526677, _1526679, _1526683))))))], (38835 ^ _777081) ^ [_1526816, _1526818, _1526820, _1526822, _1526824, _1526826] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1526816), _1526818)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1526820), _1526822)), 38845 ^ _777081 : [(38846 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526820), 38844 ^ [_1526816, _1526818, _1526820, _1526822, _1526824, _1526826]), _1526822)))], (38848 ^ _777081) ^ [] : [hAPP(c_Finite__Set_Ocard(_1526816), hAPP(c_Set_OCollect(_1526816), hAPP(hAPP(c_COMBS(_1526816, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1526816), c_fconj), hAPP(hAPP(c_COMBC(_1526816, tc_fun(_1526816, tc_HOL_Obool), tc_HOL_Obool), c_member(_1526816)), _1526818))), hAPP(hAPP(c_COMBC(_1526816, _1526820, tc_HOL_Obool), _1526824), 38844 ^ [_1526816, _1526818, _1526820, _1526822, _1526824, _1526826])))) = _1526826]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1526816, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1526820, tc_HOL_Obool), tc_Nat_Onat, _1526816), c_Finite__Set_Ocard(_1526820)), hAPP(hAPP(c_COMBB(tc_fun(_1526820, tc_HOL_Obool), tc_fun(_1526820, tc_HOL_Obool), _1526816), c_Set_OCollect(_1526820)), hAPP(hAPP(c_COMBB(tc_fun(_1526820, tc_HOL_Obool), tc_fun(_1526820, tc_HOL_Obool), _1526816), hAPP(c_COMBS(_1526820, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1526820), c_fconj), hAPP(hAPP(c_COMBC(_1526820, tc_fun(_1526820, tc_HOL_Obool), tc_HOL_Obool), c_member(_1526820)), _1526822)))), _1526824)))), _1526818) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1526826), hAPP(c_Finite__Set_Ocard(_1526820), _1526822)))], (38852 ^ _777081) ^ [_1527506, _1527508, _1527510] : [class_Orderings_Olinorder(_1527506), hBOOL(hAPP(c_Finite__Set_Ofinite(_1527506), _1527508)), -(_1527508 = c_Orderings_Obot__class_Obot(tc_fun(_1527506, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1527506), _1527510)), -(_1527510 = c_Orderings_Obot__class_Obot(tc_fun(_1527506, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1527506), c_Big__Operators_Olattice_OSup__fin(_1527506, c_Orderings_Oord__class_Omax(_1527506), _1527508)), c_Big__Operators_Olattice_OSup__fin(_1527506, c_Orderings_Oord__class_Omax(_1527506), _1527510)) = c_Big__Operators_Olattice_OSup__fin(_1527506, c_Orderings_Oord__class_Omax(_1527506), hAPP(c_Set_OCollect(_1527506), hAPP(hAPP(c_COMBB(tc_fun(_1527506, tc_HOL_Obool), tc_HOL_Obool, _1527506), c_HOL_OEx(_1527506)), hAPP(hAPP(c_COMBB(tc_fun(_1527506, tc_fun(_1527506, tc_HOL_Obool)), tc_fun(_1527506, tc_HOL_Obool), _1527506), hAPP(c_COMBB(tc_fun(_1527506, tc_HOL_Obool), tc_HOL_Obool, _1527506), c_HOL_OEx(_1527506))), hAPP(hAPP(c_COMBC(_1527506, tc_fun(_1527506, tc_fun(_1527506, tc_HOL_Obool)), tc_fun(_1527506, tc_fun(_1527506, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1527506, tc_fun(tc_fun(_1527506, tc_HOL_Obool), tc_fun(_1527506, tc_HOL_Obool))), tc_fun(tc_fun(_1527506, tc_fun(_1527506, tc_HOL_Obool)), tc_fun(_1527506, tc_fun(_1527506, tc_HOL_Obool))), _1527506), c_COMBS(_1527506, tc_fun(_1527506, tc_HOL_Obool), tc_fun(_1527506, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1527506, tc_fun(_1527506, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1527506, tc_fun(tc_fun(_1527506, tc_HOL_Obool), tc_fun(_1527506, tc_HOL_Obool))), _1527506), hAPP(c_COMBB(tc_fun(_1527506, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1527506, tc_HOL_Obool), tc_fun(_1527506, tc_HOL_Obool)), _1527506), c_COMBS(_1527506, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1527506, tc_fun(_1527506, tc_HOL_Obool)), tc_fun(_1527506, tc_fun(_1527506, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1527506), hAPP(c_COMBB(tc_fun(_1527506, tc_HOL_Obool), tc_fun(_1527506, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1527506), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527506), c_fconj))), hAPP(hAPP(c_COMBC(_1527506, tc_fun(_1527506, tc_fun(_1527506, _1527506)), tc_fun(_1527506, tc_fun(_1527506, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1527506, _1527506), tc_fun(_1527506, tc_HOL_Obool)), tc_fun(tc_fun(_1527506, tc_fun(_1527506, _1527506)), tc_fun(_1527506, tc_fun(_1527506, tc_HOL_Obool))), _1527506), c_COMBB(tc_fun(_1527506, _1527506), tc_fun(_1527506, tc_HOL_Obool), _1527506)), hAPP(hAPP(c_COMBB(tc_fun(_1527506, tc_HOL_Obool), tc_fun(tc_fun(_1527506, _1527506), tc_fun(_1527506, tc_HOL_Obool)), _1527506), c_COMBB(_1527506, tc_HOL_Obool, _1527506)), c_fequal))), c_Orderings_Oord__class_Omin(_1527506)))))), hAPP(hAPP(c_COMBC(_1527506, tc_fun(_1527506, tc_HOL_Obool), tc_fun(_1527506, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1527506, tc_HOL_Obool), tc_fun(_1527506, tc_HOL_Obool)), _1527506), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1527506)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1527506), c_fconj), hAPP(hAPP(c_COMBC(_1527506, tc_fun(_1527506, tc_HOL_Obool), tc_HOL_Obool), c_member(_1527506)), _1527508)))), hAPP(hAPP(c_COMBC(_1527506, tc_fun(_1527506, tc_HOL_Obool), tc_HOL_Obool), c_member(_1527506)), _1527510))))))))], (38874 ^ _777081) ^ [_1528623, _1528625] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1528623), _1528625)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1528623, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1528623, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1528623, tc_HOL_Obool), tc_fun(_1528623, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1528623, tc_HOL_Obool))), _1528625)))))], (38880 ^ _777081) ^ [_1528780, _1528782] : [-(hAPP(c_Set_OPow(_1528780), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1528780, tc_HOL_Obool)), _1528782)) = hAPP(c_Set_OCollect(tc_fun(_1528780, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1528780, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1528780, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1528780, tc_HOL_Obool), tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1528780, tc_HOL_Obool)), c_COMBS(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1528780, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1528780, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1528780, tc_HOL_Obool), tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_fun(_1528780, tc_HOL_Obool)), tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_fun(_1528780, tc_HOL_Obool)), tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1528780, tc_HOL_Obool)), c_COMBB(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1528780, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1528780, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1528780, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1528780, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1528780, tc_HOL_Obool)), _1528782)), c_Set_OPow(_1528780))))))], (38882 ^ _777081) ^ [_1529060, _1529062] : [-(hAPP(c_Set_OPow(_1529060), _1529062) = hAPP(c_Set_OCollect(tc_fun(_1529060, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1529060, tc_HOL_Obool), tc_fun(_1529060, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1529060, tc_HOL_Obool))), _1529062)))], (38884 ^ _777081) ^ [_1529119, _1529121, _1529123, _1529125] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1529119), hAPP(c_Set_OCollect(_1529119), _1529121))), 38887 ^ _777081 : [(38898 ^ _777081) ^ [] : [38900 ^ _777081 : [(38901 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1529121, 38899 ^ [_1529119, _1529121, _1529123, _1529125])))], (38903 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1529123), hAPP(c_Set_OCollect(_1529123), hAPP(hAPP(c_COMBC(_1529123, _1529119, tc_HOL_Obool), _1529125), 38899 ^ [_1529119, _1529121, _1529123, _1529125]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1529123), hAPP(c_Set_OCollect(_1529123), hAPP(hAPP(c_COMBB(tc_fun(_1529119, tc_HOL_Obool), tc_HOL_Obool, _1529123), c_HOL_OEx(_1529119)), hAPP(hAPP(c_COMBB(tc_fun(_1529119, tc_HOL_Obool), tc_fun(_1529119, tc_HOL_Obool), _1529123), hAPP(c_COMBS(_1529119, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529119), c_fconj), _1529121))), _1529125))))))], (38888 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1529123), hAPP(c_Set_OCollect(_1529123), hAPP(hAPP(c_COMBB(tc_fun(_1529119, tc_HOL_Obool), tc_HOL_Obool, _1529123), c_HOL_OEx(_1529119)), hAPP(hAPP(c_COMBB(tc_fun(_1529119, tc_HOL_Obool), tc_fun(_1529119, tc_HOL_Obool), _1529123), hAPP(c_COMBS(_1529119, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529119), c_fconj), _1529121))), _1529125))))), 38891 ^ _777081 : [(38892 ^ _777081) ^ [_1529402] : [hBOOL(hAPP(_1529121, _1529402)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1529123), hAPP(c_Set_OCollect(_1529123), hAPP(hAPP(c_COMBC(_1529123, _1529119, tc_HOL_Obool), _1529125), _1529402)))))]]]]], (38907 ^ _777081) ^ [_1529767, _1529769, _1529771, _1529773] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1529767), hAPP(c_Set_OCollect(_1529767), _1529769))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1529771), hAPP(c_Set_OCollect(_1529771), hAPP(hAPP(c_COMBB(tc_fun(_1529767, tc_HOL_Obool), tc_HOL_Obool, _1529771), c_HOL_OEx(_1529767)), hAPP(hAPP(c_COMBC(_1529771, tc_fun(_1529767, tc_HOL_Obool), tc_fun(_1529767, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529767, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1529767, tc_HOL_Obool), tc_fun(_1529767, tc_HOL_Obool)), _1529771), c_COMBS(_1529767, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529767, tc_HOL_Obool), tc_fun(_1529767, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1529771), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529767), c_fconj)), hAPP(hAPP(c_COMBC(_1529771, tc_fun(_1529767, _1529771), tc_fun(_1529767, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529771, tc_HOL_Obool), tc_fun(tc_fun(_1529767, _1529771), tc_fun(_1529767, tc_HOL_Obool)), _1529771), c_COMBB(_1529771, tc_HOL_Obool, _1529767)), c_fequal)), _1529773)))), _1529769))))))], (38913 ^ _777081) ^ [_1530124, _1530126, _1530128, _1530130, _1530132, _1530134] : [-(hBOOL(hAPP(hAPP(c_member(_1530124), _1530126), _1530128))), -(hAPP(c_Fun_Ooverride__on(_1530124, _1530130, _1530132, _1530134, _1530128), _1530126) = hAPP(_1530132, _1530126))], (38919 ^ _777081) ^ [_1530187, _1530189, _1530191, _1530193, _1530195, _1530197] : [hBOOL(hAPP(hAPP(c_member(_1530187), _1530189), _1530191)), -(hAPP(c_Fun_Ooverride__on(_1530187, _1530193, _1530195, _1530197, _1530191), _1530189) = hAPP(_1530197, _1530189))], (38925 ^ _777081) ^ [_1530310, _1530312, _1530314, _1530316] : [-(c_Fun_Ooverride__on(_1530310, _1530312, _1530314, _1530316, c_Orderings_Obot__class_Obot(tc_fun(_1530310, tc_HOL_Obool))) = _1530314)], (38927 ^ _777081) ^ [_1530350, _1530352] : [-(c_Fun_Oinj__on(tc_fun(_1530350, _1530352), tc_fun(tc_prod(_1530350, _1530352), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1530350, _1530352), tc_HOL_Obool), tc_fun(tc_prod(_1530350, _1530352), tc_HOL_Obool), tc_fun(_1530350, _1530352)), c_Set_OCollect(tc_prod(_1530350, _1530352))), hAPP(hAPP(c_COMBB(tc_fun(_1530350, tc_fun(_1530352, tc_HOL_Obool)), tc_fun(tc_prod(_1530350, _1530352), tc_HOL_Obool), tc_fun(_1530350, _1530352)), c_Product__Type_Oprod_Oprod__case(_1530350, _1530352, tc_HOL_Obool)), hAPP(c_COMBB(_1530352, tc_fun(_1530352, tc_HOL_Obool), _1530350), hAPP(c_COMBC(_1530352, _1530352, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1530350, _1530352), tc_HOL_Obool))))], (38929 ^ _777081) ^ [_1530470] : [-(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)))), _1530470))))], (38931 ^ _777081) ^ [_1530519, _1530521, _1530523, _1530525, _1530527, _1530529] : [hBOOL(hAPP(hAPP(c_member(_1530519), _1530521), _1530523)), -(hAPP(c_Fun_Ooverride__on(_1530519, _1530525, _1530527, _1530529, _1530523), _1530521) = hAPP(_1530529, _1530521))], (38937 ^ _777081) ^ [_1530636, _1530638, _1530640, _1530642, _1530644, _1530646] : [-(hBOOL(hAPP(hAPP(c_member(_1530636), _1530638), _1530640))), -(hAPP(c_Fun_Ooverride__on(_1530636, _1530642, _1530644, _1530646, _1530640), _1530638) = hAPP(_1530644, _1530638))], (38943 ^ _777081) ^ [_1530701] : [-(c_Wellfounded_Ofinite__psubset(_1530701) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1530701, tc_HOL_Obool), tc_fun(_1530701, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1530701, tc_HOL_Obool), tc_fun(_1530701, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1530701, tc_HOL_Obool), tc_fun(tc_fun(_1530701, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1530701, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1530701, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1530701, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1530701, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1530701, tc_HOL_Obool)), c_COMBS(tc_fun(_1530701, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1530701, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1530701, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1530701, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1530701, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1530701, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1530701)))))], (38945 ^ _777081) ^ [_1530861, _1530863, _1530865] : [-(c_Map_Oran(_1530861, _1530863, _1530865) = hAPP(c_Set_OCollect(_1530863), hAPP(hAPP(c_COMBB(tc_fun(_1530861, tc_HOL_Obool), tc_HOL_Obool, _1530863), c_HOL_OEx(_1530861)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1530863), tc_fun(_1530861, tc_HOL_Obool), _1530863), hAPP(c_COMBC(_1530861, tc_Option_Ooption(_1530863), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1530863), tc_fun(tc_Option_Ooption(_1530863), tc_HOL_Obool), _1530861), c_fequal), _1530865))), c_Option_Ooption_OSome(_1530863)))))], (38947 ^ _777081) ^ [_1530955, _1530957, _1530959, _1530961] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1530955, _1530957), _1530959), _1530961) = hAPP(c_Set_OCollect(tc_prod(_1530957, _1530957)), hAPP(c_Product__Type_Oprod_Oprod__case(_1530957, _1530957, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1530957, tc_fun(tc_prod(_1530955, _1530955), tc_HOL_Obool), tc_fun(_1530957, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530957, tc_fun(tc_fun(tc_prod(_1530955, _1530955), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1530955, _1530955), tc_HOL_Obool), tc_fun(_1530957, tc_HOL_Obool)), _1530957), c_COMBC(_1530957, tc_fun(tc_prod(_1530955, _1530955), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530957, tc_prod(_1530955, _1530955)), tc_fun(_1530957, tc_fun(tc_fun(tc_prod(_1530955, _1530955), tc_HOL_Obool), tc_HOL_Obool)), _1530957), hAPP(c_COMBB(tc_prod(_1530955, _1530955), tc_fun(tc_fun(tc_prod(_1530955, _1530955), tc_HOL_Obool), tc_HOL_Obool), _1530957), c_member(tc_prod(_1530955, _1530955)))), hAPP(hAPP(c_COMBC(_1530957, tc_fun(_1530957, _1530955), tc_fun(_1530957, tc_prod(_1530955, _1530955))), hAPP(hAPP(c_COMBB(tc_fun(_1530955, tc_prod(_1530955, _1530955)), tc_fun(tc_fun(_1530957, _1530955), tc_fun(_1530957, tc_prod(_1530955, _1530955))), _1530957), c_COMBB(_1530955, tc_prod(_1530955, _1530955), _1530957)), hAPP(hAPP(c_COMBB(_1530955, tc_fun(_1530955, tc_prod(_1530955, _1530955)), _1530957), c_Product__Type_OPair(_1530955, _1530955)), _1530961))), _1530961)))), _1530959))))], (38949 ^ _777081) ^ [_1531196] : [-(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)))), _1531196)) = 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), _1531196), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (38951 ^ _777081) ^ [_1531237] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1531237) = 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), _1531237), c_Int_Onat)))))], (38953 ^ _777081) ^ [_1531278, _1531280, _1531282] : [class_Groups_Olinordered__ab__semigroup__add(_1531278), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531278), _1531280)), -(_1531280 = c_Orderings_Obot__class_Obot(tc_fun(_1531278, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1531278), _1531282), c_Big__Operators_Olinorder__class_OMin(_1531278, _1531280)) = c_Big__Operators_Olinorder__class_OMin(_1531278, hAPP(c_Set_OCollect(_1531278), hAPP(hAPP(c_COMBB(tc_fun(_1531278, tc_HOL_Obool), tc_HOL_Obool, _1531278), c_HOL_OEx(_1531278)), hAPP(hAPP(c_COMBC(_1531278, tc_fun(_1531278, tc_HOL_Obool), tc_fun(_1531278, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531278, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1531278, tc_HOL_Obool), tc_fun(_1531278, tc_HOL_Obool)), _1531278), c_COMBS(_1531278, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531278, tc_HOL_Obool), tc_fun(_1531278, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1531278), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1531278), c_fconj)), hAPP(hAPP(c_COMBC(_1531278, tc_fun(_1531278, _1531278), tc_fun(_1531278, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531278, tc_HOL_Obool), tc_fun(tc_fun(_1531278, _1531278), tc_fun(_1531278, tc_HOL_Obool)), _1531278), c_COMBB(_1531278, tc_HOL_Obool, _1531278)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1531278), _1531282))))), hAPP(hAPP(c_COMBC(_1531278, tc_fun(_1531278, tc_HOL_Obool), tc_HOL_Obool), c_member(_1531278)), _1531280))))))], (38967 ^ _777081) ^ [_1531764, _1531766, _1531768] : [class_Groups_Olinordered__ab__semigroup__add(_1531764), hBOOL(hAPP(c_Finite__Set_Ofinite(_1531764), _1531766)), -(_1531766 = c_Orderings_Obot__class_Obot(tc_fun(_1531764, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1531764), _1531768), c_Big__Operators_Olinorder__class_OMax(_1531764, _1531766)) = c_Big__Operators_Olinorder__class_OMax(_1531764, hAPP(c_Set_OCollect(_1531764), hAPP(hAPP(c_COMBB(tc_fun(_1531764, tc_HOL_Obool), tc_HOL_Obool, _1531764), c_HOL_OEx(_1531764)), hAPP(hAPP(c_COMBC(_1531764, tc_fun(_1531764, tc_HOL_Obool), tc_fun(_1531764, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531764, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1531764, tc_HOL_Obool), tc_fun(_1531764, tc_HOL_Obool)), _1531764), c_COMBS(_1531764, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531764, tc_HOL_Obool), tc_fun(_1531764, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1531764), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1531764), c_fconj)), hAPP(hAPP(c_COMBC(_1531764, tc_fun(_1531764, _1531764), tc_fun(_1531764, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1531764, tc_HOL_Obool), tc_fun(tc_fun(_1531764, _1531764), tc_fun(_1531764, tc_HOL_Obool)), _1531764), c_COMBB(_1531764, tc_HOL_Obool, _1531764)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1531764), _1531768))))), hAPP(hAPP(c_COMBC(_1531764, tc_fun(_1531764, tc_HOL_Obool), tc_HOL_Obool), c_member(_1531764)), _1531766))))))], (38981 ^ _777081) ^ [_1532250, _1532252, _1532254] : [class_Lattices_Odistrib__lattice(_1532250), hBOOL(hAPP(c_Finite__Set_Ofinite(_1532250), _1532252)), -(_1532252 = c_Orderings_Obot__class_Obot(tc_fun(_1532250, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1532250), _1532254), c_Big__Operators_Olattice__class_OInf__fin(_1532250, _1532252)) = c_Big__Operators_Olattice__class_OInf__fin(_1532250, hAPP(c_Set_OCollect(_1532250), hAPP(hAPP(c_COMBB(tc_fun(_1532250, tc_HOL_Obool), tc_HOL_Obool, _1532250), c_HOL_OEx(_1532250)), hAPP(hAPP(c_COMBC(_1532250, tc_fun(_1532250, tc_HOL_Obool), tc_fun(_1532250, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532250, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1532250, tc_HOL_Obool), tc_fun(_1532250, tc_HOL_Obool)), _1532250), c_COMBS(_1532250, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532250, tc_HOL_Obool), tc_fun(_1532250, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1532250), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532250), c_fconj)), hAPP(hAPP(c_COMBC(_1532250, tc_fun(_1532250, _1532250), tc_fun(_1532250, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1532250, tc_HOL_Obool), tc_fun(tc_fun(_1532250, _1532250), tc_fun(_1532250, tc_HOL_Obool)), _1532250), c_COMBB(_1532250, tc_HOL_Obool, _1532250)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1532250), _1532254))))), hAPP(hAPP(c_COMBC(_1532250, tc_fun(_1532250, tc_HOL_Obool), tc_HOL_Obool), c_member(_1532250)), _1532252))))))], (38995 ^ _777081) ^ [_1532736, _1532738, _1532740] : [class_Lattices_Odistrib__lattice(_1532736), hBOOL(hAPP(c_Finite__Set_Ofinite(_1532736), _1532738)), -(_1532738 = c_Orderings_Obot__class_Obot(tc_fun(_1532736, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1532736), _1532740)), -(_1532740 = c_Orderings_Obot__class_Obot(tc_fun(_1532736, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1532736), c_Big__Operators_Olattice__class_OInf__fin(_1532736, _1532738)), c_Big__Operators_Olattice__class_OInf__fin(_1532736, _1532740)) = c_Big__Operators_Olattice__class_OInf__fin(_1532736, hAPP(c_Set_OCollect(_1532736), hAPP(hAPP(c_COMBB(tc_fun(_1532736, tc_HOL_Obool), tc_HOL_Obool, _1532736), c_HOL_OEx(_1532736)), hAPP(hAPP(c_COMBB(tc_fun(_1532736, tc_fun(_1532736, tc_HOL_Obool)), tc_fun(_1532736, tc_HOL_Obool), _1532736), hAPP(c_COMBB(tc_fun(_1532736, tc_HOL_Obool), tc_HOL_Obool, _1532736), c_HOL_OEx(_1532736))), hAPP(hAPP(c_COMBC(_1532736, tc_fun(_1532736, tc_fun(_1532736, tc_HOL_Obool)), tc_fun(_1532736, tc_fun(_1532736, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1532736, tc_fun(tc_fun(_1532736, tc_HOL_Obool), tc_fun(_1532736, tc_HOL_Obool))), tc_fun(tc_fun(_1532736, tc_fun(_1532736, tc_HOL_Obool)), tc_fun(_1532736, tc_fun(_1532736, tc_HOL_Obool))), _1532736), c_COMBS(_1532736, tc_fun(_1532736, tc_HOL_Obool), tc_fun(_1532736, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1532736, tc_fun(_1532736, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1532736, tc_fun(tc_fun(_1532736, tc_HOL_Obool), tc_fun(_1532736, tc_HOL_Obool))), _1532736), hAPP(c_COMBB(tc_fun(_1532736, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1532736, tc_HOL_Obool), tc_fun(_1532736, tc_HOL_Obool)), _1532736), c_COMBS(_1532736, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1532736, tc_fun(_1532736, tc_HOL_Obool)), tc_fun(_1532736, tc_fun(_1532736, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1532736), hAPP(c_COMBB(tc_fun(_1532736, tc_HOL_Obool), tc_fun(_1532736, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1532736), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532736), c_fconj))), hAPP(hAPP(c_COMBC(_1532736, tc_fun(_1532736, tc_fun(_1532736, _1532736)), tc_fun(_1532736, tc_fun(_1532736, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1532736, _1532736), tc_fun(_1532736, tc_HOL_Obool)), tc_fun(tc_fun(_1532736, tc_fun(_1532736, _1532736)), tc_fun(_1532736, tc_fun(_1532736, tc_HOL_Obool))), _1532736), c_COMBB(tc_fun(_1532736, _1532736), tc_fun(_1532736, tc_HOL_Obool), _1532736)), hAPP(hAPP(c_COMBB(tc_fun(_1532736, tc_HOL_Obool), tc_fun(tc_fun(_1532736, _1532736), tc_fun(_1532736, tc_HOL_Obool)), _1532736), c_COMBB(_1532736, tc_HOL_Obool, _1532736)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1532736)))))), hAPP(hAPP(c_COMBC(_1532736, tc_fun(_1532736, tc_HOL_Obool), tc_fun(_1532736, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1532736, tc_HOL_Obool), tc_fun(_1532736, tc_HOL_Obool)), _1532736), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1532736)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532736), c_fconj), hAPP(hAPP(c_COMBC(_1532736, tc_fun(_1532736, tc_HOL_Obool), tc_HOL_Obool), c_member(_1532736)), _1532738)))), hAPP(hAPP(c_COMBC(_1532736, tc_fun(_1532736, tc_HOL_Obool), tc_HOL_Obool), c_member(_1532736)), _1532740))))))))], (39017 ^ _777081) ^ [_1533835, _1533837, _1533839] : [class_Lattices_Odistrib__lattice(_1533835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533835), _1533837)), -(_1533837 = c_Orderings_Obot__class_Obot(tc_fun(_1533835, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1533835), _1533839), c_Big__Operators_Olattice__class_OSup__fin(_1533835, _1533837)) = c_Big__Operators_Olattice__class_OSup__fin(_1533835, hAPP(c_Set_OCollect(_1533835), hAPP(hAPP(c_COMBB(tc_fun(_1533835, tc_HOL_Obool), tc_HOL_Obool, _1533835), c_HOL_OEx(_1533835)), hAPP(hAPP(c_COMBC(_1533835, tc_fun(_1533835, tc_HOL_Obool), tc_fun(_1533835, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533835, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1533835, tc_HOL_Obool), tc_fun(_1533835, tc_HOL_Obool)), _1533835), c_COMBS(_1533835, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533835, tc_HOL_Obool), tc_fun(_1533835, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1533835), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1533835), c_fconj)), hAPP(hAPP(c_COMBC(_1533835, tc_fun(_1533835, _1533835), tc_fun(_1533835, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1533835, tc_HOL_Obool), tc_fun(tc_fun(_1533835, _1533835), tc_fun(_1533835, tc_HOL_Obool)), _1533835), c_COMBB(_1533835, tc_HOL_Obool, _1533835)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1533835), _1533839))))), hAPP(hAPP(c_COMBC(_1533835, tc_fun(_1533835, tc_HOL_Obool), tc_HOL_Obool), c_member(_1533835)), _1533837))))))], (39031 ^ _777081) ^ [_1534321, _1534323, _1534325] : [class_Lattices_Odistrib__lattice(_1534321), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534321), _1534323)), -(_1534323 = c_Orderings_Obot__class_Obot(tc_fun(_1534321, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1534321), _1534325)), -(_1534325 = c_Orderings_Obot__class_Obot(tc_fun(_1534321, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1534321), c_Big__Operators_Olattice__class_OSup__fin(_1534321, _1534323)), c_Big__Operators_Olattice__class_OSup__fin(_1534321, _1534325)) = c_Big__Operators_Olattice__class_OSup__fin(_1534321, hAPP(c_Set_OCollect(_1534321), hAPP(hAPP(c_COMBB(tc_fun(_1534321, tc_HOL_Obool), tc_HOL_Obool, _1534321), c_HOL_OEx(_1534321)), hAPP(hAPP(c_COMBB(tc_fun(_1534321, tc_fun(_1534321, tc_HOL_Obool)), tc_fun(_1534321, tc_HOL_Obool), _1534321), hAPP(c_COMBB(tc_fun(_1534321, tc_HOL_Obool), tc_HOL_Obool, _1534321), c_HOL_OEx(_1534321))), hAPP(hAPP(c_COMBC(_1534321, tc_fun(_1534321, tc_fun(_1534321, tc_HOL_Obool)), tc_fun(_1534321, tc_fun(_1534321, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534321, tc_fun(tc_fun(_1534321, tc_HOL_Obool), tc_fun(_1534321, tc_HOL_Obool))), tc_fun(tc_fun(_1534321, tc_fun(_1534321, tc_HOL_Obool)), tc_fun(_1534321, tc_fun(_1534321, tc_HOL_Obool))), _1534321), c_COMBS(_1534321, tc_fun(_1534321, tc_HOL_Obool), tc_fun(_1534321, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534321, tc_fun(_1534321, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1534321, tc_fun(tc_fun(_1534321, tc_HOL_Obool), tc_fun(_1534321, tc_HOL_Obool))), _1534321), hAPP(c_COMBB(tc_fun(_1534321, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1534321, tc_HOL_Obool), tc_fun(_1534321, tc_HOL_Obool)), _1534321), c_COMBS(_1534321, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534321, tc_fun(_1534321, tc_HOL_Obool)), tc_fun(_1534321, tc_fun(_1534321, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1534321), hAPP(c_COMBB(tc_fun(_1534321, tc_HOL_Obool), tc_fun(_1534321, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1534321), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534321), c_fconj))), hAPP(hAPP(c_COMBC(_1534321, tc_fun(_1534321, tc_fun(_1534321, _1534321)), tc_fun(_1534321, tc_fun(_1534321, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1534321, _1534321), tc_fun(_1534321, tc_HOL_Obool)), tc_fun(tc_fun(_1534321, tc_fun(_1534321, _1534321)), tc_fun(_1534321, tc_fun(_1534321, tc_HOL_Obool))), _1534321), c_COMBB(tc_fun(_1534321, _1534321), tc_fun(_1534321, tc_HOL_Obool), _1534321)), hAPP(hAPP(c_COMBB(tc_fun(_1534321, tc_HOL_Obool), tc_fun(tc_fun(_1534321, _1534321), tc_fun(_1534321, tc_HOL_Obool)), _1534321), c_COMBB(_1534321, tc_HOL_Obool, _1534321)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1534321)))))), hAPP(hAPP(c_COMBC(_1534321, tc_fun(_1534321, tc_HOL_Obool), tc_fun(_1534321, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1534321, tc_HOL_Obool), tc_fun(_1534321, tc_HOL_Obool)), _1534321), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534321)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534321), c_fconj), hAPP(hAPP(c_COMBC(_1534321, tc_fun(_1534321, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534321)), _1534323)))), hAPP(hAPP(c_COMBC(_1534321, tc_fun(_1534321, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534321)), _1534325))))))))], (39053 ^ _777081) ^ [_1535420, _1535422, _1535424] : [class_Orderings_Olinorder(_1535420), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535420), _1535422)), -(_1535422 = c_Orderings_Obot__class_Obot(tc_fun(_1535420, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1535420), _1535424), c_Big__Operators_Olattice_OInf__fin(_1535420, c_Orderings_Oord__class_Omin(_1535420), _1535422)) = c_Big__Operators_Olattice_OInf__fin(_1535420, c_Orderings_Oord__class_Omin(_1535420), hAPP(c_Set_OCollect(_1535420), hAPP(hAPP(c_COMBB(tc_fun(_1535420, tc_HOL_Obool), tc_HOL_Obool, _1535420), c_HOL_OEx(_1535420)), hAPP(hAPP(c_COMBC(_1535420, tc_fun(_1535420, tc_HOL_Obool), tc_fun(_1535420, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535420, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1535420, tc_HOL_Obool), tc_fun(_1535420, tc_HOL_Obool)), _1535420), c_COMBS(_1535420, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535420, tc_HOL_Obool), tc_fun(_1535420, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1535420), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535420), c_fconj)), hAPP(hAPP(c_COMBC(_1535420, tc_fun(_1535420, _1535420), tc_fun(_1535420, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535420, tc_HOL_Obool), tc_fun(tc_fun(_1535420, _1535420), tc_fun(_1535420, tc_HOL_Obool)), _1535420), c_COMBB(_1535420, tc_HOL_Obool, _1535420)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1535420), _1535424))))), hAPP(hAPP(c_COMBC(_1535420, tc_fun(_1535420, tc_HOL_Obool), tc_HOL_Obool), c_member(_1535420)), _1535422))))))], (39067 ^ _777081) ^ [_1535918, _1535920, _1535922] : [class_Orderings_Olinorder(_1535918), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535918), _1535920)), -(_1535920 = c_Orderings_Obot__class_Obot(tc_fun(_1535918, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1535918), _1535922), c_Big__Operators_Olattice_OSup__fin(_1535918, c_Orderings_Oord__class_Omax(_1535918), _1535920)) = c_Big__Operators_Olattice_OSup__fin(_1535918, c_Orderings_Oord__class_Omax(_1535918), hAPP(c_Set_OCollect(_1535918), hAPP(hAPP(c_COMBB(tc_fun(_1535918, tc_HOL_Obool), tc_HOL_Obool, _1535918), c_HOL_OEx(_1535918)), hAPP(hAPP(c_COMBC(_1535918, tc_fun(_1535918, tc_HOL_Obool), tc_fun(_1535918, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535918, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1535918, tc_HOL_Obool), tc_fun(_1535918, tc_HOL_Obool)), _1535918), c_COMBS(_1535918, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535918, tc_HOL_Obool), tc_fun(_1535918, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1535918), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1535918), c_fconj)), hAPP(hAPP(c_COMBC(_1535918, tc_fun(_1535918, _1535918), tc_fun(_1535918, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535918, tc_HOL_Obool), tc_fun(tc_fun(_1535918, _1535918), tc_fun(_1535918, tc_HOL_Obool)), _1535918), c_COMBB(_1535918, tc_HOL_Obool, _1535918)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1535918), _1535922))))), hAPP(hAPP(c_COMBC(_1535918, tc_fun(_1535918, tc_HOL_Obool), tc_HOL_Obool), c_member(_1535918)), _1535920))))))], (39081 ^ _777081) ^ [_1536416, _1536418, _1536420] : [class_Orderings_Olinorder(_1536416), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536416), _1536418)), -(_1536418 = c_Orderings_Obot__class_Obot(tc_fun(_1536416, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536416), _1536420)), -(_1536420 = c_Orderings_Obot__class_Obot(tc_fun(_1536416, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1536416), c_Big__Operators_Olattice_OInf__fin(_1536416, c_Orderings_Oord__class_Omin(_1536416), _1536418)), c_Big__Operators_Olattice_OInf__fin(_1536416, c_Orderings_Oord__class_Omin(_1536416), _1536420)) = c_Big__Operators_Olattice_OInf__fin(_1536416, c_Orderings_Oord__class_Omin(_1536416), hAPP(c_Set_OCollect(_1536416), hAPP(hAPP(c_COMBB(tc_fun(_1536416, tc_HOL_Obool), tc_HOL_Obool, _1536416), c_HOL_OEx(_1536416)), hAPP(hAPP(c_COMBB(tc_fun(_1536416, tc_fun(_1536416, tc_HOL_Obool)), tc_fun(_1536416, tc_HOL_Obool), _1536416), hAPP(c_COMBB(tc_fun(_1536416, tc_HOL_Obool), tc_HOL_Obool, _1536416), c_HOL_OEx(_1536416))), hAPP(hAPP(c_COMBC(_1536416, tc_fun(_1536416, tc_fun(_1536416, tc_HOL_Obool)), tc_fun(_1536416, tc_fun(_1536416, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536416, tc_fun(tc_fun(_1536416, tc_HOL_Obool), tc_fun(_1536416, tc_HOL_Obool))), tc_fun(tc_fun(_1536416, tc_fun(_1536416, tc_HOL_Obool)), tc_fun(_1536416, tc_fun(_1536416, tc_HOL_Obool))), _1536416), c_COMBS(_1536416, tc_fun(_1536416, tc_HOL_Obool), tc_fun(_1536416, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536416, tc_fun(_1536416, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1536416, tc_fun(tc_fun(_1536416, tc_HOL_Obool), tc_fun(_1536416, tc_HOL_Obool))), _1536416), hAPP(c_COMBB(tc_fun(_1536416, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1536416, tc_HOL_Obool), tc_fun(_1536416, tc_HOL_Obool)), _1536416), c_COMBS(_1536416, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1536416, tc_fun(_1536416, tc_HOL_Obool)), tc_fun(_1536416, tc_fun(_1536416, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1536416), hAPP(c_COMBB(tc_fun(_1536416, tc_HOL_Obool), tc_fun(_1536416, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1536416), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536416), c_fconj))), hAPP(hAPP(c_COMBC(_1536416, tc_fun(_1536416, tc_fun(_1536416, _1536416)), tc_fun(_1536416, tc_fun(_1536416, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1536416, _1536416), tc_fun(_1536416, tc_HOL_Obool)), tc_fun(tc_fun(_1536416, tc_fun(_1536416, _1536416)), tc_fun(_1536416, tc_fun(_1536416, tc_HOL_Obool))), _1536416), c_COMBB(tc_fun(_1536416, _1536416), tc_fun(_1536416, tc_HOL_Obool), _1536416)), hAPP(hAPP(c_COMBB(tc_fun(_1536416, tc_HOL_Obool), tc_fun(tc_fun(_1536416, _1536416), tc_fun(_1536416, tc_HOL_Obool)), _1536416), c_COMBB(_1536416, tc_HOL_Obool, _1536416)), c_fequal))), c_Orderings_Oord__class_Omax(_1536416)))))), hAPP(hAPP(c_COMBC(_1536416, tc_fun(_1536416, tc_HOL_Obool), tc_fun(_1536416, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1536416, tc_HOL_Obool), tc_fun(_1536416, tc_HOL_Obool)), _1536416), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1536416)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536416), c_fconj), hAPP(hAPP(c_COMBC(_1536416, tc_fun(_1536416, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536416)), _1536418)))), hAPP(hAPP(c_COMBC(_1536416, tc_fun(_1536416, tc_HOL_Obool), tc_HOL_Obool), c_member(_1536416)), _1536420))))))))], (39103 ^ _777081) ^ [_1537533, _1537535, _1537537, _1537539] : [-(c_Nitpick_Oprod(_1537533, _1537535, _1537537, _1537539) = hAPP(c_Set_OCollect(tc_prod(_1537533, _1537535)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537533, _1537535, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1537533, tc_fun(_1537535, tc_HOL_Obool), tc_fun(_1537535, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1537535, tc_HOL_Obool), tc_fun(_1537535, tc_HOL_Obool)), _1537533), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1537535)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1537533), c_fconj), hAPP(hAPP(c_COMBC(_1537533, tc_fun(_1537533, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537533)), _1537537)))), hAPP(hAPP(c_COMBC(_1537535, tc_fun(_1537535, tc_HOL_Obool), tc_HOL_Obool), c_member(_1537535)), _1537539)))))], (39105 ^ _777081) ^ [_1537661] : [-(c_Int_Oint__ge__less__than(_1537661) = 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), _1537661)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (39107 ^ _777081) ^ [_1537707] : [-(c_Int_Oint__ge__less__than2(_1537707) = 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), _1537707)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (39109 ^ _777081) ^ [_1537768, _1537770] : [c_Predicate_Oreflp(_1537768, _1537770), -(c_Relation_Orefl__on(_1537768, c_Orderings_Otop__class_Otop(tc_fun(_1537768, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1537768, _1537768)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537768, _1537768, tc_HOL_Obool), _1537770))))], (39115 ^ _777081) ^ [_1537883, _1537885] : [c_Relation_Orefl__on(_1537883, c_Orderings_Otop__class_Otop(tc_fun(_1537883, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1537883, _1537883)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537883, _1537883, tc_HOL_Obool), _1537885))), -(c_Predicate_Oreflp(_1537883, _1537885))], (39121 ^ _777081) ^ [_1538004, _1538006, _1538008, _1538010, _1538012, _1538014, _1538016] : [class_Rings_Osemiring__0(_1538004), c_Fun_Oinj__on(tc_prod(_1538006, _1538008), _1538004, hAPP(c_Product__Type_Oprod_Oprod__case(_1538006, _1538008, _1538004), hAPP(hAPP(c_COMBC(_1538006, tc_fun(_1538008, _1538004), tc_fun(_1538008, _1538004)), hAPP(hAPP(c_COMBB(tc_fun(_1538004, _1538004), tc_fun(tc_fun(_1538008, _1538004), tc_fun(_1538008, _1538004)), _1538006), c_COMBB(_1538004, _1538004, _1538008)), hAPP(hAPP(c_COMBB(_1538004, tc_fun(_1538004, _1538004), _1538006), c_Groups_Otimes__class_Otimes(_1538004)), _1538010))), _1538012)), hAPP(hAPP(c_Product__Type_OSigma(_1538006, _1538008), _1538014), hAPP(c_COMBK(tc_fun(_1538008, tc_HOL_Obool), _1538006), _1538016))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1538004), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538006, _1538004), _1538010), _1538014)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538008, _1538004), _1538012), _1538016)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538004, _1538004), c_Fun_Oid(_1538004)), hAPP(c_Set_OCollect(_1538004), hAPP(hAPP(c_COMBB(tc_fun(_1538006, tc_HOL_Obool), tc_HOL_Obool, _1538004), c_HOL_OEx(_1538006)), hAPP(hAPP(c_COMBB(tc_fun(_1538006, tc_fun(_1538008, tc_HOL_Obool)), tc_fun(_1538006, tc_HOL_Obool), _1538004), hAPP(c_COMBB(tc_fun(_1538008, tc_HOL_Obool), tc_HOL_Obool, _1538006), c_HOL_OEx(_1538008))), hAPP(hAPP(c_COMBC(_1538004, tc_fun(_1538006, tc_fun(_1538008, tc_HOL_Obool)), tc_fun(_1538006, tc_fun(_1538008, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1538006, tc_fun(tc_fun(_1538008, tc_HOL_Obool), tc_fun(_1538008, tc_HOL_Obool))), tc_fun(tc_fun(_1538006, tc_fun(_1538008, tc_HOL_Obool)), tc_fun(_1538006, tc_fun(_1538008, tc_HOL_Obool))), _1538004), c_COMBS(_1538006, tc_fun(_1538008, tc_HOL_Obool), tc_fun(_1538008, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1538006, tc_fun(_1538008, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1538006, tc_fun(tc_fun(_1538008, tc_HOL_Obool), tc_fun(_1538008, tc_HOL_Obool))), _1538004), hAPP(c_COMBB(tc_fun(_1538008, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1538008, tc_HOL_Obool), tc_fun(_1538008, tc_HOL_Obool)), _1538006), c_COMBS(_1538008, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1538006, tc_fun(_1538008, tc_HOL_Obool)), tc_fun(_1538006, tc_fun(_1538008, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1538004), hAPP(c_COMBB(tc_fun(_1538008, tc_HOL_Obool), tc_fun(_1538008, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1538006), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538008), c_fconj))), hAPP(hAPP(c_COMBC(_1538004, tc_fun(_1538006, tc_fun(_1538008, _1538004)), tc_fun(_1538006, tc_fun(_1538008, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1538008, _1538004), tc_fun(_1538008, tc_HOL_Obool)), tc_fun(tc_fun(_1538006, tc_fun(_1538008, _1538004)), tc_fun(_1538006, tc_fun(_1538008, tc_HOL_Obool))), _1538004), c_COMBB(tc_fun(_1538008, _1538004), tc_fun(_1538008, tc_HOL_Obool), _1538006)), hAPP(hAPP(c_COMBB(tc_fun(_1538004, tc_HOL_Obool), tc_fun(tc_fun(_1538008, _1538004), tc_fun(_1538008, tc_HOL_Obool)), _1538004), c_COMBB(_1538004, tc_HOL_Obool, _1538008)), c_fequal))), hAPP(hAPP(c_COMBC(_1538006, tc_fun(_1538008, _1538004), tc_fun(_1538008, _1538004)), hAPP(hAPP(c_COMBB(tc_fun(_1538004, _1538004), tc_fun(tc_fun(_1538008, _1538004), tc_fun(_1538008, _1538004)), _1538006), c_COMBB(_1538004, _1538004, _1538008)), hAPP(hAPP(c_COMBB(_1538004, tc_fun(_1538004, _1538004), _1538006), c_Groups_Otimes__class_Otimes(_1538004)), _1538010))), _1538012)))))), hAPP(hAPP(c_COMBC(_1538006, tc_fun(_1538008, tc_HOL_Obool), tc_fun(_1538008, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1538008, tc_HOL_Obool), tc_fun(_1538008, tc_HOL_Obool)), _1538006), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1538008)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1538006), c_fconj), hAPP(hAPP(c_COMBC(_1538006, tc_fun(_1538006, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538006)), _1538014)))), hAPP(hAPP(c_COMBC(_1538008, tc_fun(_1538008, tc_HOL_Obool), tc_HOL_Obool), c_member(_1538008)), _1538016))))))))], (39131 ^ _777081) ^ [_1539281, _1539283, _1539285, _1539287, _1539289, _1539291] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539281), _1539283)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539285), _1539287)), 39141 ^ _777081 : [(39142 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539285), 39140 ^ [_1539281, _1539283, _1539285, _1539287, _1539289, _1539291]), _1539287)))], (39144 ^ _777081) ^ [] : [hAPP(c_Finite__Set_Ocard(_1539281), hAPP(c_Set_OCollect(_1539281), hAPP(hAPP(c_COMBS(_1539281, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539281), c_fconj), hAPP(hAPP(c_COMBC(_1539281, tc_fun(_1539281, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539281)), _1539283))), hAPP(hAPP(c_COMBC(_1539281, _1539285, tc_HOL_Obool), _1539289), 39140 ^ [_1539281, _1539283, _1539285, _1539287, _1539289, _1539291])))) = hAPP(_1539291, 39140 ^ [_1539281, _1539283, _1539285, _1539287, _1539289, _1539291])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539281, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1539285, tc_HOL_Obool), tc_Nat_Onat, _1539281), c_Finite__Set_Ocard(_1539285)), hAPP(hAPP(c_COMBB(tc_fun(_1539285, tc_HOL_Obool), tc_fun(_1539285, tc_HOL_Obool), _1539281), c_Set_OCollect(_1539285)), hAPP(hAPP(c_COMBB(tc_fun(_1539285, tc_HOL_Obool), tc_fun(_1539285, tc_HOL_Obool), _1539281), hAPP(c_COMBS(_1539285, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539285), c_fconj), hAPP(hAPP(c_COMBC(_1539285, tc_fun(_1539285, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539285)), _1539287)))), _1539289)))), _1539283) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1539285, tc_Nat_Onat), _1539291), _1539287))], (39148 ^ _777081) ^ [_1539991, _1539993] : [-(c_Fun_Oinj__on(_1539991, _1539991, c_Fun_Oid(_1539991), _1539993))], (39150 ^ _777081) ^ [_1540020, _1540022] : [-(c_Product__Type_Omap__pair(_1540020, _1540020, _1540022, _1540022, c_COMBI(_1540020), c_COMBI(_1540022)) = c_Fun_Oid(tc_prod(_1540020, _1540022)))], (39152 ^ _777081) ^ [_1540061, _1540063] : [-(c_Product__Type_Omap__pair(_1540061, _1540061, _1540063, _1540063, c_Fun_Oid(_1540061), c_Fun_Oid(_1540063)) = c_Fun_Oid(tc_prod(_1540061, _1540063)))], (39154 ^ _777081) ^ [_1540102, _1540104] : [-(c_Product__Type_Oapfst(_1540102, _1540102, _1540104, c_Fun_Oid(_1540102)) = c_Fun_Oid(tc_prod(_1540102, _1540104)))], (39156 ^ _777081) ^ [_1540139, _1540141] : [-(hAPP(c_Fun_Oid(_1540139), _1540141) = _1540141)], (39158 ^ _777081) ^ [_1540169, _1540171] : [-(hAPP(c_Fun_Oid(_1540169), _1540171) = _1540171)], (39160 ^ _777081) ^ [_1540199] : [-(hAPP(c_Option_Omap(_1540199, _1540199), c_Fun_Oid(_1540199)) = c_Fun_Oid(tc_Option_Ooption(_1540199)))], (39162 ^ _777081) ^ [_1540234, _1540236, _1540238] : [c_Predicate_Oreflp(_1540234, _1540236), -(hBOOL(hAPP(hAPP(_1540236, _1540238), _1540238)))], (39168 ^ _777081) ^ [_1540323, _1540325] : [-(c_Product__Type_Oapsnd(_1540323, _1540323, _1540325, c_Fun_Oid(_1540323)) = c_Fun_Oid(tc_prod(_1540325, _1540323)))], (39170 ^ _777081) ^ [_1540360] : [-(hAPP(c_Option_Omap(_1540360, _1540360), c_COMBI(_1540360)) = c_Fun_Oid(tc_Option_Ooption(_1540360)))], (39172 ^ _777081) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (39174 ^ _777081) ^ [_1540413, _1540415] : [-(hAPP(c_Set_Ovimage(_1540413, _1540413, c_Fun_Oid(_1540413)), _1540415) = _1540415)], (39176 ^ _777081) ^ [_1540447, _1540449, _1540451] : [-(hAPP(c_Fun_Ocomp(_1540447, _1540447, _1540449, c_Fun_Oid(_1540447)), _1540451) = _1540451)], (39178 ^ _777081) ^ [_1540484, _1540486, _1540488] : [-(hAPP(c_Fun_Ocomp(_1540484, _1540486, _1540484, _1540488), c_Fun_Oid(_1540484)) = _1540488)], (39180 ^ _777081) ^ [_1540521, _1540523, _1540525, _1540527, _1540529, _1540531, _1540533] : [hAPP(c_Fun_Ocomp(_1540521, _1540523, _1540525, _1540527), _1540529) = hAPP(c_Fun_Ocomp(_1540523, _1540523, _1540525, c_Fun_Oid(_1540523)), _1540531), -(hAPP(_1540527, hAPP(_1540529, _1540533)) = hAPP(_1540531, _1540533))], (39186 ^ _777081) ^ [_1540662, _1540664] : [-(hAPP(c_Set_Oimage(_1540662, _1540662, c_Fun_Oid(_1540662)), _1540664) = _1540664)], (39188 ^ _777081) ^ [_1540696] : [-(hAPP(c_Set_Oimage(_1540696, _1540696, c_Fun_Oid(_1540696)), c_Orderings_Otop__class_Otop(tc_fun(_1540696, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1540696, tc_HOL_Obool)))], (39190 ^ _777081) ^ [_1540738, _1540740, _1540742, _1540744] : [c_Finite__Set_Ofolding(_1540738, _1540740, _1540742, _1540744), -(hAPP(_1540744, c_Orderings_Obot__class_Obot(tc_fun(_1540738, tc_HOL_Obool))) = c_Fun_Oid(_1540740))], (39196 ^ _777081) ^ [_1540843, _1540845, _1540847, _1540849] : [-(c_Product__Type_Oapfst(_1540843, _1540845, _1540847, _1540849) = c_Product__Type_Omap__pair(_1540843, _1540845, _1540847, _1540847, _1540849, c_Fun_Oid(_1540847)))], (39198 ^ _777081) ^ [_1540886, _1540888, _1540890, _1540892] : [-(c_Product__Type_Oapsnd(_1540886, _1540888, _1540890, _1540892) = c_Product__Type_Omap__pair(_1540890, _1540890, _1540886, _1540888, c_Fun_Oid(_1540890), _1540892))], (39200 ^ _777081) ^ [_1540929, _1540931] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1540929, _1540931, tc_prod(_1540929, _1540931)), c_Product__Type_OPair(_1540929, _1540931)) = c_Fun_Oid(tc_prod(_1540929, _1540931)))], (39202 ^ _777081) ^ [_1540972, _1540974, _1540976, _1540978] : [class_Groups_Ocomm__monoid__add(_1540972), c_Fun_Oinj__on(_1540974, _1540972, _1540976, _1540978), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1540974, _1540972), _1540976), _1540978) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1540972, _1540972), c_Fun_Oid(_1540972)), hAPP(c_Set_Oimage(_1540974, _1540972, _1540976), _1540978)))], (39212 ^ _777081) ^ [_1541165, _1541167, _1541169, _1541171] : [class_Groups_Ocomm__monoid__mult(_1541165), c_Fun_Oinj__on(_1541167, _1541165, _1541169, _1541171), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1541167, _1541165), _1541169), _1541171) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1541165, _1541165), c_Fun_Oid(_1541165)), hAPP(c_Set_Oimage(_1541167, _1541165, _1541169), _1541171)))], (39222 ^ _777081) ^ [_1541373, _1541375] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1541373), _1541375)), -(_1541375 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1541373, 39226 ^ [_1541373, _1541375]), 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)), 39225 ^ [_1541373, _1541375]))))], (39230 ^ _777081) ^ [_1541504, _1541506] : [39231 ^ _777081 : [(39232 ^ _777081) ^ [_1541568, _1541570] : [_1541506 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1541504, _1541568), 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)), _1541570)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1541504), _1541506)))], (39236 ^ _777081) ^ [_1541640, _1541642, _1541644, _1541646, _1541648] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1541640, _1541642, _1541644), _1541646), _1541648) = hAPP(c_Set_OCollect(tc_prod(_1541640, _1541644)), hAPP(c_Product__Type_Oprod_Oprod__case(_1541640, _1541644, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1541644, tc_fun(_1541642, tc_HOL_Obool)), tc_fun(_1541644, tc_HOL_Obool), _1541640), hAPP(c_COMBB(tc_fun(_1541642, tc_HOL_Obool), tc_HOL_Obool, _1541644), c_HOL_OEx(_1541642))), hAPP(hAPP(c_COMBC(_1541640, tc_fun(_1541644, tc_fun(_1541642, tc_HOL_Obool)), tc_fun(_1541644, tc_fun(_1541642, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1541642, tc_HOL_Obool), tc_fun(_1541642, tc_HOL_Obool)), tc_fun(tc_fun(_1541644, tc_fun(_1541642, tc_HOL_Obool)), tc_fun(_1541644, tc_fun(_1541642, tc_HOL_Obool))), _1541640), c_COMBB(tc_fun(_1541642, tc_HOL_Obool), tc_fun(_1541642, tc_HOL_Obool), _1541644)), hAPP(hAPP(c_COMBB(tc_fun(_1541642, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1541642, tc_HOL_Obool), tc_fun(_1541642, tc_HOL_Obool)), _1541640), c_COMBS(_1541642, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541642, tc_HOL_Obool), tc_fun(_1541642, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1541640), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1541642), c_fconj)), hAPP(hAPP(c_COMBC(_1541640, tc_fun(tc_prod(_1541640, _1541642), tc_HOL_Obool), tc_fun(_1541642, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541642, tc_fun(tc_fun(tc_prod(_1541640, _1541642), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1541640, _1541642), tc_HOL_Obool), tc_fun(_1541642, tc_HOL_Obool)), _1541640), c_COMBC(_1541642, tc_fun(tc_prod(_1541640, _1541642), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541642, tc_prod(_1541640, _1541642)), tc_fun(_1541642, tc_fun(tc_fun(tc_prod(_1541640, _1541642), tc_HOL_Obool), tc_HOL_Obool)), _1541640), hAPP(c_COMBB(tc_prod(_1541640, _1541642), tc_fun(tc_fun(tc_prod(_1541640, _1541642), tc_HOL_Obool), tc_HOL_Obool), _1541642), c_member(tc_prod(_1541640, _1541642)))), c_Product__Type_OPair(_1541640, _1541642)))), _1541646))))), hAPP(hAPP(c_COMBC(_1541644, tc_fun(tc_prod(_1541642, _1541644), tc_HOL_Obool), tc_fun(_1541642, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541642, tc_fun(tc_fun(tc_prod(_1541642, _1541644), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1541642, _1541644), tc_HOL_Obool), tc_fun(_1541642, tc_HOL_Obool)), _1541644), c_COMBC(_1541642, tc_fun(tc_prod(_1541642, _1541644), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1541642, tc_prod(_1541642, _1541644)), tc_fun(_1541642, tc_fun(tc_fun(tc_prod(_1541642, _1541644), tc_HOL_Obool), tc_HOL_Obool)), _1541644), hAPP(c_COMBB(tc_prod(_1541642, _1541644), tc_fun(tc_fun(tc_prod(_1541642, _1541644), tc_HOL_Obool), tc_HOL_Obool), _1541642), c_member(tc_prod(_1541642, _1541644)))), hAPP(c_COMBC(_1541642, _1541644, tc_prod(_1541642, _1541644)), c_Product__Type_OPair(_1541642, _1541644))))), _1541648))))))], (39238 ^ _777081) ^ [_1542088, _1542090, _1542092] : [-(hAPP(c_Relation_ORange(_1542088, _1542090), hAPP(c_Set_OCollect(tc_prod(_1542088, _1542090)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542088, _1542090, tc_HOL_Obool), _1542092))) = hAPP(c_Set_OCollect(_1542090), hAPP(hAPP(c_COMBB(tc_fun(_1542088, tc_HOL_Obool), tc_HOL_Obool, _1542090), c_HOL_OEx(_1542088)), hAPP(c_COMBC(_1542088, _1542090, tc_HOL_Obool), _1542092))))], (39240 ^ _777081) ^ [_1542163, _1542165, _1542167, _1542169, _1542171, _1542173, _1542175, _1542177] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542163, _1542165)), hAPP(hAPP(c_Product__Type_OPair(_1542163, _1542165), _1542167), _1542169)), _1542171)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1542165, _1542173)), hAPP(hAPP(c_Product__Type_OPair(_1542165, _1542173), _1542169), _1542175)), _1542177)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542163, _1542173)), hAPP(hAPP(c_Product__Type_OPair(_1542163, _1542173), _1542167), _1542175)), hAPP(hAPP(c_Relation_Orel__comp(_1542163, _1542165, _1542173), _1542171), _1542177))))], (39250 ^ _777081) ^ [_1542450, _1542452, _1542454, _1542456, _1542458] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542450, _1542452)), hAPP(hAPP(c_Product__Type_OPair(_1542450, _1542452), _1542454), _1542456)), _1542458)), -(hBOOL(hAPP(hAPP(c_member(_1542452), _1542456), hAPP(c_Relation_ORange(_1542450, _1542452), _1542458))))], (39256 ^ _777081) ^ [_1542597, _1542599, _1542601, _1542603, _1542605, _1542607, _1542609] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1542597, _1542599, _1542601), _1542603), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542605, tc_fun(tc_prod(_1542599, _1542601), tc_HOL_Obool)), _1542607), _1542609)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542605, tc_fun(tc_prod(_1542597, _1542601), tc_HOL_Obool)), _1542607), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1542599, _1542601), tc_HOL_Obool), tc_fun(tc_prod(_1542597, _1542601), tc_HOL_Obool), _1542605), hAPP(c_Relation_Orel__comp(_1542597, _1542599, _1542601), _1542603)), _1542609)))], (39258 ^ _777081) ^ [_1542701, _1542703, _1542705, _1542707, _1542709, _1542711, _1542713] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1542701, _1542703, _1542705), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542707, tc_fun(tc_prod(_1542701, _1542703), tc_HOL_Obool)), _1542709), _1542711)), _1542713) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1542707, tc_fun(tc_prod(_1542701, _1542705), tc_HOL_Obool)), _1542709), hAPP(hAPP(c_COMBC(_1542707, tc_fun(tc_prod(_1542703, _1542705), tc_HOL_Obool), tc_fun(tc_prod(_1542701, _1542705), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1542701, _1542703), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1542703, _1542705), tc_HOL_Obool), tc_fun(tc_prod(_1542701, _1542705), tc_HOL_Obool)), _1542707), c_Relation_Orel__comp(_1542701, _1542703, _1542705)), _1542711)), _1542713)))], (39260 ^ _777081) ^ [_1542833, _1542835] : [-(hAPP(c_Relation_ORange(_1542833, _1542833), c_Relation_OId__on(_1542833, _1542835)) = _1542835)], (39262 ^ _777081) ^ [_1542867, _1542869, _1542871, _1542873, _1542875, _1542877, _1542879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542867, _1542869), tc_HOL_Obool)), _1542871), _1542873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542869, _1542875), tc_HOL_Obool)), _1542877), _1542879)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542867, _1542875), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1542867, _1542869, _1542875), _1542871), _1542877)), hAPP(hAPP(c_Relation_Orel__comp(_1542867, _1542869, _1542875), _1542873), _1542879))))], (39272 ^ _777081) ^ [_1543134, _1543136, _1543138, _1543140, _1543142, _1543144] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1543134, _1543136, _1543138), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1543134, _1543136), tc_HOL_Obool)), _1543140), _1543142)), _1543144) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1543134, _1543138), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1543134, _1543136, _1543138), _1543140), _1543144)), hAPP(hAPP(c_Relation_Orel__comp(_1543134, _1543136, _1543138), _1543142), _1543144)))], (39274 ^ _777081) ^ [_1543225, _1543227, _1543229, _1543231, _1543233, _1543235] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1543225, _1543227, _1543229), _1543231), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1543227, _1543229), tc_HOL_Obool)), _1543233), _1543235)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1543225, _1543229), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1543225, _1543227, _1543229), _1543231), _1543233)), hAPP(hAPP(c_Relation_Orel__comp(_1543225, _1543227, _1543229), _1543231), _1543235)))], (39276 ^ _777081) ^ [_1543316, _1543318, _1543320, _1543322] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1543316, _1543318, _1543320), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543316, _1543318), tc_HOL_Obool))), _1543322) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543316, _1543320), tc_HOL_Obool)))], (39278 ^ _777081) ^ [_1543371, _1543373, _1543375, _1543377] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1543371, _1543373, _1543375), _1543377), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543373, _1543375), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543371, _1543375), tc_HOL_Obool)))], (39280 ^ _777081) ^ [_1543426, _1543428, _1543430, _1543432, _1543434, _1543436, _1543438] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1543426, _1543428, _1543430), hAPP(hAPP(c_Relation_Orel__comp(_1543426, _1543432, _1543428), _1543434), _1543436)), _1543438) = hAPP(hAPP(c_Relation_Orel__comp(_1543426, _1543432, _1543430), _1543434), hAPP(hAPP(c_Relation_Orel__comp(_1543432, _1543428, _1543430), _1543436), _1543438)))], (39282 ^ _777081) ^ [_1543501, _1543503, _1543505, _1543507] : [hAPP(hAPP(c_Relation_Orel__comp(_1543501, _1543501, _1543501), _1543503), _1543505) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543501, _1543501), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1543501, _1543501, _1543501), _1543503), _1543507) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543501, _1543501), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1543501, _1543501, _1543501), _1543503), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1543501, _1543501), tc_HOL_Obool)), _1543505), _1543507)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543501, _1543501), tc_HOL_Obool)))], (39292 ^ _777081) ^ [_1543774, _1543776, _1543778, _1543780] : [hAPP(hAPP(c_Relation_Orel__comp(_1543774, _1543774, _1543774), _1543776), _1543778) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543774, _1543774), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1543774, _1543774, _1543774), _1543780), _1543778) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543774, _1543774), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1543774, _1543774, _1543774), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1543774, _1543774), tc_HOL_Obool)), _1543776), _1543780)), _1543778) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1543774, _1543774), tc_HOL_Obool)))], (39302 ^ _777081) ^ [_1544047, _1544049] : [-(hAPP(c_Relation_ORange(_1544047, _1544049), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544047, _1544049), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1544049, tc_HOL_Obool)))], (39304 ^ _777081) ^ [_1544109, _1544111, _1544113] : [hAPP(c_Relation_ORange(_1544109, _1544111), _1544113) = c_Orderings_Obot__class_Obot(tc_fun(_1544111, tc_HOL_Obool)), -(_1544113 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544109, _1544111), tc_HOL_Obool)))], (39310 ^ _777081) ^ [_1544222, _1544224, _1544226] : [_1544226 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544222, _1544224), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1544222, _1544224), _1544226) = c_Orderings_Obot__class_Obot(tc_fun(_1544224, tc_HOL_Obool)))], (39316 ^ _777081) ^ [_1544341, _1544343, _1544345, _1544347, _1544349, _1544351, _1544353, _1544355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1544341, _1544343), tc_HOL_Obool)), _1544345), hAPP(hAPP(c_Product__Type_OSigma(_1544341, _1544343), _1544347), hAPP(c_COMBK(tc_fun(_1544343, tc_HOL_Obool), _1544341), _1544349)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1544343, _1544351), tc_HOL_Obool)), _1544353), hAPP(hAPP(c_Product__Type_OSigma(_1544343, _1544351), _1544349), hAPP(c_COMBK(tc_fun(_1544351, tc_HOL_Obool), _1544343), _1544355)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1544341, _1544351), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1544341, _1544343, _1544351), _1544345), _1544353)), hAPP(hAPP(c_Product__Type_OSigma(_1544341, _1544351), _1544347), hAPP(c_COMBK(tc_fun(_1544351, tc_HOL_Obool), _1544341), _1544355)))))], (39326 ^ _777081) ^ [_1544700, _1544702, _1544704, _1544706] : [-(hAPP(c_Relation_ORange(_1544700, _1544702), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1544700, _1544702), tc_HOL_Obool)), _1544704), _1544706)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1544702, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1544700, _1544702), _1544704)), hAPP(c_Relation_ORange(_1544700, _1544702), _1544706)))], (39328 ^ _777081) ^ [_1544772, _1544774, _1544776] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1544772, _1544774)), _1544776)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544774), hAPP(c_Relation_ORange(_1544772, _1544774), _1544776))))], (39334 ^ _777081) ^ [_1544885, _1544887, _1544889] : [-(hAPP(c_Set_Oimage(tc_prod(_1544885, _1544887), _1544887, c_Product__Type_Osnd(_1544885, _1544887)), _1544889) = hAPP(c_Relation_ORange(_1544885, _1544887), _1544889))], (39336 ^ _777081) ^ [_1544952, _1544954, _1544956, _1544958] : [hBOOL(hAPP(hAPP(c_member(_1544952), _1544954), hAPP(c_Relation_ORange(_1544956, _1544952), _1544958))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1544956, _1544952)), hAPP(hAPP(c_Product__Type_OPair(_1544956, _1544952), 39339 ^ [_1544952, _1544954, _1544956, _1544958]), _1544954)), _1544958)))], (39343 ^ _777081) ^ [_1545109, _1545111, _1545113, _1545115] : [39344 ^ _777081 : [(39345 ^ _777081) ^ [_1545184] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545113, _1545109)), hAPP(hAPP(c_Product__Type_OPair(_1545113, _1545109), _1545184), _1545111)), _1545115))]], -(hBOOL(hAPP(hAPP(c_member(_1545109), _1545111), hAPP(c_Relation_ORange(_1545113, _1545109), _1545115))))], (39349 ^ _777081) ^ [_1545269, _1545271, _1545273, _1545275, _1545277] : [-(hAPP(c_Relation_ORange(_1545269, _1545271), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1545269, _1545271)), hAPP(hAPP(c_Product__Type_OPair(_1545269, _1545271), _1545273), _1545275)), _1545277)) = hAPP(hAPP(c_Set_Oinsert(_1545271), _1545275), hAPP(c_Relation_ORange(_1545269, _1545271), _1545277)))], (39351 ^ _777081) ^ [_1545340, _1545342, _1545344, _1545346] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1545340, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1545342, _1545340), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1545342, _1545340), tc_HOL_Obool)), _1545344), _1545346))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545340, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1545342, _1545340), _1545344)), hAPP(c_Relation_ORange(_1545342, _1545340), _1545346)))))], (39353 ^ _777081) ^ [_1545422, _1545424, _1545426, _1545428] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1545422, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1545422, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1545424, _1545422), _1545426)), hAPP(c_Relation_ORange(_1545424, _1545422), _1545428))), hAPP(c_Relation_ORange(_1545424, _1545422), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1545424, _1545422), tc_HOL_Obool)), _1545426), _1545428)))))], (39355 ^ _777081) ^ [_1545504, _1545506, _1545508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1545504, _1545504), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1545504, _1545504, _1545504), _1545506), _1545508)), _1545506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1545504, tc_HOL_Obool), tc_fun(_1545504, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1545504, tc_HOL_Obool), tc_fun(_1545504, tc_HOL_Obool), tc_fun(_1545504, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1545504, _1545506)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1545504, tc_HOL_Obool), tc_fun(_1545504, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1545504, _1545508)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1545504, tc_HOL_Obool), tc_fun(_1545504, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1545504, tc_HOL_Obool), tc_fun(_1545504, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1545504, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1545504, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1545504, tc_HOL_Obool), tc_fun(_1545504, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1545504, _1545506))))], (39361 ^ _777081) ^ [_1545875, _1545877, _1545879] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1545875, _1545875), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1545875, _1545875, _1545875), _1545877), _1545879)), _1545877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1545875, tc_HOL_Obool), tc_fun(_1545875, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1545875, tc_HOL_Obool), tc_fun(_1545875, tc_HOL_Obool), tc_fun(_1545875, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1545875, _1545877)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1545875, tc_HOL_Obool), tc_fun(_1545875, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1545875, _1545879)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1545875, tc_HOL_Obool), tc_fun(_1545875, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1545875, tc_HOL_Obool), tc_fun(_1545875, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1545875, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1545875, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1545875, tc_HOL_Obool), tc_fun(_1545875, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1545875, _1545877))))], (39367 ^ _777081) ^ [_1546267, _1546269, _1546271, _1546273] : [hBOOL(hAPP(c_Predicate_ORangeP(_1546267, _1546269, hAPP(hAPP(c_COMBC(_1546267, tc_fun(tc_prod(_1546267, _1546269), tc_HOL_Obool), tc_fun(_1546269, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546269, tc_fun(tc_fun(tc_prod(_1546267, _1546269), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1546267, _1546269), tc_HOL_Obool), tc_fun(_1546269, tc_HOL_Obool)), _1546267), c_COMBC(_1546269, tc_fun(tc_prod(_1546267, _1546269), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546269, tc_prod(_1546267, _1546269)), tc_fun(_1546269, tc_fun(tc_fun(tc_prod(_1546267, _1546269), tc_HOL_Obool), tc_HOL_Obool)), _1546267), hAPP(c_COMBB(tc_prod(_1546267, _1546269), tc_fun(tc_fun(tc_prod(_1546267, _1546269), tc_HOL_Obool), tc_HOL_Obool), _1546269), c_member(tc_prod(_1546267, _1546269)))), c_Product__Type_OPair(_1546267, _1546269)))), _1546271)), _1546273)), -(hBOOL(hAPP(hAPP(c_member(_1546269), _1546273), hAPP(c_Relation_ORange(_1546267, _1546269), _1546271))))], (39373 ^ _777081) ^ [_1546618, _1546620, _1546622, _1546624] : [hBOOL(hAPP(hAPP(c_member(_1546620), _1546624), hAPP(c_Relation_ORange(_1546618, _1546620), _1546622))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1546618, _1546620, hAPP(hAPP(c_COMBC(_1546618, tc_fun(tc_prod(_1546618, _1546620), tc_HOL_Obool), tc_fun(_1546620, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546620, tc_fun(tc_fun(tc_prod(_1546618, _1546620), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1546618, _1546620), tc_HOL_Obool), tc_fun(_1546620, tc_HOL_Obool)), _1546618), c_COMBC(_1546620, tc_fun(tc_prod(_1546618, _1546620), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1546620, tc_prod(_1546618, _1546620)), tc_fun(_1546620, tc_fun(tc_fun(tc_prod(_1546618, _1546620), tc_HOL_Obool), tc_HOL_Obool)), _1546618), hAPP(c_COMBB(tc_prod(_1546618, _1546620), tc_fun(tc_fun(tc_prod(_1546618, _1546620), tc_HOL_Obool), tc_HOL_Obool), _1546620), c_member(tc_prod(_1546618, _1546620)))), c_Product__Type_OPair(_1546618, _1546620)))), _1546622)), _1546624)))], (39379 ^ _777081) ^ [_1546975, _1546977, _1546979, _1546981] : [hBOOL(hAPP(hAPP(c_member(_1546975), _1546977), hAPP(c_Relation_ORange(_1546979, _1546975), _1546981))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546979, _1546975)), hAPP(hAPP(c_Product__Type_OPair(_1546979, _1546975), 39382 ^ [_1546975, _1546977, _1546979, _1546981]), _1546977)), _1546981)))], (39386 ^ _777081) ^ [_1547140, _1547142, _1547144, _1547146, _1547148] : [hBOOL(hAPP(hAPP(_1547140, _1547142), _1547144)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1547146, _1547148, _1547140), _1547144)))], (39392 ^ _777081) ^ [_1547266, _1547268, _1547270, _1547272] : [hBOOL(hAPP(c_Predicate_ORangeP(_1547266, _1547268, _1547270), _1547272)), -(hBOOL(hAPP(hAPP(_1547270, 39395 ^ [_1547266, _1547268, _1547270, _1547272]), _1547272)))], (39399 ^ _777081) ^ [_1547381, _1547383, _1547385, _1547387] : [39400 ^ _777081 : [(39401 ^ _777081) ^ [_1547435] : [hBOOL(hAPP(hAPP(_1547385, _1547435), _1547387))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1547381, _1547383, _1547385), _1547387)))], (39405 ^ _777081) ^ [_1547529, _1547531, _1547533, _1547535, _1547537, _1547539, _1547541] : [c_Predicate_Opred__comp(_1547529, _1547531, _1547533, hAPP(hAPP(c_COMBC(_1547529, tc_fun(tc_prod(_1547529, _1547531), tc_HOL_Obool), tc_fun(_1547531, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547531, tc_fun(tc_fun(tc_prod(_1547529, _1547531), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1547529, _1547531), tc_HOL_Obool), tc_fun(_1547531, tc_HOL_Obool)), _1547529), c_COMBC(_1547531, tc_fun(tc_prod(_1547529, _1547531), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547531, tc_prod(_1547529, _1547531)), tc_fun(_1547531, tc_fun(tc_fun(tc_prod(_1547529, _1547531), tc_HOL_Obool), tc_HOL_Obool)), _1547529), hAPP(c_COMBB(tc_prod(_1547529, _1547531), tc_fun(tc_fun(tc_prod(_1547529, _1547531), tc_HOL_Obool), tc_HOL_Obool), _1547531), c_member(tc_prod(_1547529, _1547531)))), c_Product__Type_OPair(_1547529, _1547531)))), _1547535), hAPP(hAPP(c_COMBC(_1547531, tc_fun(tc_prod(_1547531, _1547533), tc_HOL_Obool), tc_fun(_1547533, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547533, tc_fun(tc_fun(tc_prod(_1547531, _1547533), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1547531, _1547533), tc_HOL_Obool), tc_fun(_1547533, tc_HOL_Obool)), _1547531), c_COMBC(_1547533, tc_fun(tc_prod(_1547531, _1547533), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1547533, tc_prod(_1547531, _1547533)), tc_fun(_1547533, tc_fun(tc_fun(tc_prod(_1547531, _1547533), tc_HOL_Obool), tc_HOL_Obool)), _1547531), hAPP(c_COMBB(tc_prod(_1547531, _1547533), tc_fun(tc_fun(tc_prod(_1547531, _1547533), tc_HOL_Obool), tc_HOL_Obool), _1547533), c_member(tc_prod(_1547531, _1547533)))), c_Product__Type_OPair(_1547531, _1547533)))), _1547537), _1547539, _1547541), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547529, _1547533)), hAPP(hAPP(c_Product__Type_OPair(_1547529, _1547533), _1547539), _1547541)), hAPP(hAPP(c_Relation_Orel__comp(_1547529, _1547531, _1547533), _1547535), _1547537))))], (39411 ^ _777081) ^ [_1548152, _1548154, _1548156, _1548158, _1548160, _1548162, _1548164] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548152, _1548156)), hAPP(hAPP(c_Product__Type_OPair(_1548152, _1548156), _1548162), _1548164)), hAPP(hAPP(c_Relation_Orel__comp(_1548152, _1548154, _1548156), _1548158), _1548160))), -(c_Predicate_Opred__comp(_1548152, _1548154, _1548156, hAPP(hAPP(c_COMBC(_1548152, tc_fun(tc_prod(_1548152, _1548154), tc_HOL_Obool), tc_fun(_1548154, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548154, tc_fun(tc_fun(tc_prod(_1548152, _1548154), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1548152, _1548154), tc_HOL_Obool), tc_fun(_1548154, tc_HOL_Obool)), _1548152), c_COMBC(_1548154, tc_fun(tc_prod(_1548152, _1548154), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548154, tc_prod(_1548152, _1548154)), tc_fun(_1548154, tc_fun(tc_fun(tc_prod(_1548152, _1548154), tc_HOL_Obool), tc_HOL_Obool)), _1548152), hAPP(c_COMBB(tc_prod(_1548152, _1548154), tc_fun(tc_fun(tc_prod(_1548152, _1548154), tc_HOL_Obool), tc_HOL_Obool), _1548154), c_member(tc_prod(_1548152, _1548154)))), c_Product__Type_OPair(_1548152, _1548154)))), _1548158), hAPP(hAPP(c_COMBC(_1548154, tc_fun(tc_prod(_1548154, _1548156), tc_HOL_Obool), tc_fun(_1548156, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548156, tc_fun(tc_fun(tc_prod(_1548154, _1548156), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1548154, _1548156), tc_HOL_Obool), tc_fun(_1548156, tc_HOL_Obool)), _1548154), c_COMBC(_1548156, tc_fun(tc_prod(_1548154, _1548156), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548156, tc_prod(_1548154, _1548156)), tc_fun(_1548156, tc_fun(tc_fun(tc_prod(_1548154, _1548156), tc_HOL_Obool), tc_HOL_Obool)), _1548154), hAPP(c_COMBB(tc_prod(_1548154, _1548156), tc_fun(tc_fun(tc_prod(_1548154, _1548156), tc_HOL_Obool), tc_HOL_Obool), _1548156), c_member(tc_prod(_1548154, _1548156)))), c_Product__Type_OPair(_1548154, _1548156)))), _1548160), _1548162, _1548164))], (39417 ^ _777081) ^ [_1548781, _1548783, _1548785] : [c_Wellfounded_Owf(_1548781, _1548783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1548781, _1548781), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1548781, _1548781, _1548781), _1548783), _1548785)), _1548783)), -(c_FunDef_Oreduction__pair(_1548781, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1548781, _1548781), tc_HOL_Obool), tc_fun(tc_prod(_1548781, _1548781), tc_HOL_Obool)), _1548783), _1548785)))], (39427 ^ _777081) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (39429 ^ _777081) ^ [_1549020, _1549022, _1549024, _1549026, _1549028, _1549030, _1549032, _1549034] : [hBOOL(hAPP(hAPP(_1549020, _1549022), _1549024)), hBOOL(hAPP(hAPP(_1549026, _1549024), _1549028)), -(c_Predicate_Opred__comp(_1549030, _1549032, _1549034, _1549020, _1549026, _1549022, _1549028))], (39439 ^ _777081) ^ [_1549203] : [-(c_Wellfounded_Owf(_1549203, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1549203, _1549203), tc_HOL_Obool))))], (39441 ^ _777081) ^ [_1549234, _1549236, _1549238, _1549240] : [c_Wellfounded_Owf(_1549234, _1549236), -(c_Wellfounded_Owf(_1549238, hAPP(hAPP(c_Relation_Oinv__image(_1549234, _1549238), _1549236), _1549240)))], (39447 ^ _777081) ^ [_1549333, _1549335, _1549337, _1549339] : [c_Wellfounded_Owf(_1549333, _1549335), c_Wellfounded_Owf(_1549337, _1549339), -(c_Wellfounded_Owf(tc_prod(_1549333, _1549337), c_Wellfounded_Olex__prod(_1549333, _1549337, _1549335, _1549339)))], (39457 ^ _777081) ^ [_1549486, _1549488] : [-(c_Wellfounded_Owf(_1549486, hAPP(c_Wellfounded_Omeasure(_1549486), _1549488)))], (39459 ^ _777081) ^ [_1549531, _1549533] : [c_Wellfounded_Owf(_1549531, _1549533), -(c_Wellfounded_Owf(_1549531, hAPP(hAPP(c_Relation_Orel__comp(_1549531, _1549531, _1549531), _1549533), _1549533)))], (39465 ^ _777081) ^ [_1549624, _1549626] : [c_Wellfounded_Owf(_1549624, hAPP(hAPP(c_Relation_Orel__comp(_1549624, _1549624, _1549624), _1549626), _1549626)), -(c_Wellfounded_Owf(_1549624, _1549626))], (39471 ^ _777081) ^ [_1549723, _1549725] : [c_Wellfounded_Owf(_1549723, _1549725), -(c_Wellfounded_Owf(tc_fun(_1549723, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1549723, _1549725)))], (39477 ^ _777081) ^ [_1549812, _1549814, _1549816] : [c_Wellfounded_Owf(_1549812, _1549814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1549812, _1549812), tc_HOL_Obool)), _1549816), _1549814)), -(c_Wellfounded_Owf(_1549812, _1549816))], (39487 ^ _777081) ^ [_1549971, _1549973, _1549975] : [c_Wellfounded_Owf(_1549971, _1549973), -(hBOOL(hAPP(hAPP(c_member(_1549971), _1549975), c_Wellfounded_Oacc(_1549971, _1549973))))], (39493 ^ _777081) ^ [_1550085, _1550087] : [c_Wellfounded_Owf(_1550085, _1550087), 39496 ^ _777081 : [(39497 ^ _777081) ^ [_1550154] : [-(hBOOL(hAPP(hAPP(c_member(_1550085), _1550154), c_Wellfounded_Oacc(_1550085, _1550087))))]]], (39499 ^ _777081) ^ [_1550187, _1550189] : [hBOOL(hAPP(hAPP(c_member(_1550187), 39500 ^ [_1550187, _1550189]), c_Wellfounded_Oacc(_1550187, _1550189))), -(c_Wellfounded_Owf(_1550187, _1550189))], (39506 ^ _777081) ^ [_1550320] : [-(c_Wellfounded_Owf(tc_fun(_1550320, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1550320)))], (39508 ^ _777081) ^ [_1550348, _1550350, _1550352] : [c_Wellfounded_Owf(_1550348, _1550350), -(c_Wellfounded_Owf(_1550348, c_Wellfounded_Omlex__prod(_1550348, _1550352, _1550350)))], (39514 ^ _777081) ^ [_1550435, _1550437, _1550439] : [c_Wellfounded_Owf(_1550435, _1550437), -(c_Wellfounded_Owf(_1550435, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1550435, _1550435), tc_HOL_Obool)), _1550437), _1550439)))], (39520 ^ _777081) ^ [_1550542, _1550544, _1550546] : [c_Wellfounded_Owf(_1550542, _1550544), -(c_Wellfounded_Owf(_1550542, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1550542, _1550542), tc_HOL_Obool)), _1550546), _1550544)))], (39526 ^ _777081) ^ [_1550649, _1550651] : [c_Wellfounded_Owf(_1550649, _1550651), -(c_Wellfounded_Owf(tc_fun(_1550649, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1550649, _1550651)))], (39532 ^ _777081) ^ [_1550768, _1550770, _1550772, _1550774, _1550776, _1550778, _1550780] : [c_Predicate_Opred__comp(_1550768, _1550770, _1550772, _1550774, _1550776, _1550778, _1550780), 39536 ^ _777081 : [(39537 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1550774, _1550778), 39535 ^ [_1550768, _1550770, _1550772, _1550774, _1550776, _1550778, _1550780])))], (39539 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1550776, 39535 ^ [_1550768, _1550770, _1550772, _1550774, _1550776, _1550778, _1550780]), _1550780)))]]], (39541 ^ _777081) ^ [_1550946, _1550948, _1550950, _1550952, _1550954, _1550956, _1550958] : [-(c_Predicate_Opred__comp(_1550946, _1550948, _1550950, _1550952, _1550954, _1550956, _1550958)), 39542 ^ _777081 : [(39543 ^ _777081) ^ [_1551011] : [hBOOL(hAPP(hAPP(_1550952, _1550956), _1551011)), hBOOL(hAPP(hAPP(_1550954, _1551011), _1550958))]]], (39551 ^ _777081) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (39553 ^ _777081) ^ [_1551172, _1551174, _1551176] : [c_Wellfounded_Owf(_1551172, _1551174), hBOOL(hAPP(hAPP(c_member(tc_prod(_1551172, _1551172)), hAPP(hAPP(c_Product__Type_OPair(_1551172, _1551172), _1551176), _1551176)), _1551174))], (39559 ^ _777081) ^ [_1551290, _1551292, _1551294, _1551296] : [c_Wellfounded_Owf(_1551290, _1551292), hBOOL(hAPP(hAPP(c_member(tc_prod(_1551290, _1551290)), hAPP(hAPP(c_Product__Type_OPair(_1551290, _1551290), _1551294), _1551296)), _1551292)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1551290, _1551290)), hAPP(hAPP(c_Product__Type_OPair(_1551290, _1551290), _1551296), _1551294)), _1551292))], (39569 ^ _777081) ^ [_1551504, _1551506, _1551508, _1551510] : [c_Wellfounded_Owf(_1551504, _1551506), hBOOL(hAPP(hAPP(c_member(tc_prod(_1551504, _1551504)), hAPP(hAPP(c_Product__Type_OPair(_1551504, _1551504), _1551508), _1551510)), _1551506)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1551504, _1551504)), hAPP(hAPP(c_Product__Type_OPair(_1551504, _1551504), _1551510), _1551508)), _1551506))], (39579 ^ _777081) ^ [_1551718, _1551720, _1551722] : [c_Wellfounded_Owf(_1551718, _1551720), hBOOL(hAPP(hAPP(c_member(tc_prod(_1551718, _1551718)), hAPP(hAPP(c_Product__Type_OPair(_1551718, _1551718), _1551722), _1551722)), _1551720))], (39585 ^ _777081) ^ [_1551836] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1551836)))], (39587 ^ _777081) ^ [_1551861] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1551861)))], (39589 ^ _777081) ^ [] : [-(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)))))], (39591 ^ _777081) ^ [_1551904, _1551906] : [hAPP(hAPP(c_Relation_Orel__comp(_1551904, _1551904, _1551904), _1551906), _1551906) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551904, _1551904), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1551904, _1551906))], (39597 ^ _777081) ^ [_1552035, _1552037, _1552039] : [c_Wellfounded_Owf(_1552035, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552035, _1552035), tc_HOL_Obool)), _1552037), _1552039)), -(c_Wellfounded_Owf(_1552035, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552035, _1552035), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552035, _1552035), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1552035, _1552035, _1552035), _1552037), _1552037)), hAPP(hAPP(c_Relation_Orel__comp(_1552035, _1552035, _1552035), _1552039), _1552037))), _1552039)))], (39603 ^ _777081) ^ [_1552234, _1552236, _1552238] : [c_Wellfounded_Owf(_1552234, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552234, _1552234), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552234, _1552234), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1552234, _1552234, _1552234), _1552236), _1552236)), hAPP(hAPP(c_Relation_Orel__comp(_1552234, _1552234, _1552234), _1552238), _1552236))), _1552238)), -(c_Wellfounded_Owf(_1552234, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552234, _1552234), tc_HOL_Obool)), _1552236), _1552238)))], (39609 ^ _777081) ^ [_1552454, _1552456] : [c_Wellfounded_Owf(_1552454, _1552456), 39613 ^ _777081 : [(39614 ^ _777081) ^ [_1552590] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1552454, _1552454)), hAPP(hAPP(c_Product__Type_OPair(_1552454, _1552454), hAPP(_1552590, hAPP(c_Nat_OSuc, 39612 ^ [_1552454, _1552456, _1552590]))), hAPP(_1552590, 39612 ^ [_1552454, _1552456, _1552590]))), _1552456))]]], (39616 ^ _777081) ^ [_1552657, _1552659] : [39618 ^ _777081 : [(39619 ^ _777081) ^ [_1552682] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1552657, _1552657)), hAPP(hAPP(c_Product__Type_OPair(_1552657, _1552657), hAPP(39617 ^ [_1552657, _1552659], hAPP(c_Nat_OSuc, _1552682))), hAPP(39617 ^ [_1552657, _1552659], _1552682))), _1552659)))]], -(c_Wellfounded_Owf(_1552657, _1552659))], (39623 ^ _777081) ^ [_1552758, _1552760, _1552762] : [c_Wellfounded_Owf(_1552758, _1552760), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1552758, tc_HOL_Obool)), _1552762), hAPP(c_Relation_OImage(_1552758, _1552758, _1552760), _1552762))), -(_1552762 = c_Orderings_Obot__class_Obot(tc_fun(_1552758, tc_HOL_Obool)))], (39633 ^ _777081) ^ [_1552935, _1552937, _1552939] : [c_Wellfounded_Owf(_1552935, _1552937), c_Wellfounded_Owf(_1552935, _1552939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552935, _1552935), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1552935, _1552935, _1552935), _1552937), _1552939)), _1552937)), -(c_Wellfounded_Owf(_1552935, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552935, _1552935), tc_HOL_Obool)), _1552937), _1552939)))], (39647 ^ _777081) ^ [_1553196] : [class_Orderings_Owellorder(_1553196), -(c_Wellfounded_Owf(_1553196, hAPP(c_Set_OCollect(tc_prod(_1553196, _1553196)), hAPP(c_Product__Type_Oprod_Oprod__case(_1553196, _1553196, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1553196)))))], (39653 ^ _777081) ^ [_1553318, _1553320] : [c_FunDef_Oreduction__pair(_1553318, _1553320), 39656 ^ _777081 : [(39657 ^ _777081) ^ [] : [-(c_Wellfounded_Owf(_1553318, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1553318, _1553318), tc_HOL_Obool), tc_fun(tc_prod(_1553318, _1553318), tc_HOL_Obool)), _1553320)))], (39659 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1553318, _1553318), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1553318, _1553318, _1553318), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1553318, _1553318), tc_HOL_Obool), tc_fun(tc_prod(_1553318, _1553318), tc_HOL_Obool)), _1553320)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1553318, _1553318), tc_HOL_Obool), tc_fun(tc_prod(_1553318, _1553318), tc_HOL_Obool)), _1553320))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1553318, _1553318), tc_HOL_Obool), tc_fun(tc_prod(_1553318, _1553318), tc_HOL_Obool)), _1553320))))]]], (39661 ^ _777081) ^ [_1553607, _1553609] : [-(c_FunDef_Oreduction__pair(_1553607, _1553609)), c_Wellfounded_Owf(_1553607, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1553607, _1553607), tc_HOL_Obool), tc_fun(tc_prod(_1553607, _1553607), tc_HOL_Obool)), _1553609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1553607, _1553607), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1553607, _1553607, _1553607), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1553607, _1553607), tc_HOL_Obool), tc_fun(tc_prod(_1553607, _1553607), tc_HOL_Obool)), _1553609)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1553607, _1553607), tc_HOL_Obool), tc_fun(tc_prod(_1553607, _1553607), tc_HOL_Obool)), _1553609))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1553607, _1553607), tc_HOL_Obool), tc_fun(tc_prod(_1553607, _1553607), tc_HOL_Obool)), _1553609)))], (39671 ^ _777081) ^ [_1553928, _1553930, _1553932, _1553934] : [c_FunDef_Oreduction__pair(_1553928, _1553930), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1553928, _1553928), tc_HOL_Obool)), _1553932), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1553928, _1553928), tc_HOL_Obool), tc_fun(tc_prod(_1553928, _1553928), tc_HOL_Obool)), _1553930))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1553928, _1553928), tc_HOL_Obool)), _1553934), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1553928, _1553928), tc_HOL_Obool), tc_fun(tc_prod(_1553928, _1553928), tc_HOL_Obool)), _1553930))), c_Wellfounded_Owf(_1553928, _1553934), -(c_Wellfounded_Owf(_1553928, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1553928, _1553928), tc_HOL_Obool)), _1553932), _1553934)))], (39689 ^ _777081) ^ [_1554329, _1554331, _1554333, _1554335] : [c_Wellfounded_Owf(_1554329, _1554331), c_Fun_Oinj__on(_1554329, _1554333, _1554335, c_Orderings_Otop__class_Otop(tc_fun(_1554329, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1554333, hAPP(c_Set_Oimage(tc_prod(_1554329, _1554329), tc_prod(_1554333, _1554333), c_Product__Type_Omap__pair(_1554329, _1554333, _1554329, _1554333, _1554335, _1554335)), _1554331)))], (39699 ^ _777081) ^ [_1554520, _1554522] : [c_Wellfounded_Owf(_1554520, _1554522), -(c_Wellfounded_Owf(tc_List_Olist(_1554520), c_List_Olenlex(_1554520, _1554522)))], (39705 ^ _777081) ^ [_1554607, _1554609, _1554611] : [c_Wellfounded_Owf(_1554607, _1554609), c_Wellfounded_Owf(_1554607, _1554611), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1554607, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1554607, _1554607), _1554609)), hAPP(c_Relation_ORange(_1554607, _1554607), _1554611)) = c_Orderings_Obot__class_Obot(tc_fun(_1554607, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1554607, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1554607, _1554607), tc_HOL_Obool)), _1554609), _1554611)))], (39719 ^ _777081) ^ [_1554878, _1554880, _1554882, _1554884, _1554886] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554878, _1554880)), hAPP(hAPP(c_Product__Type_OPair(_1554878, _1554880), _1554882), _1554884)), _1554886)), -(hBOOL(hAPP(hAPP(c_member(_1554878), _1554882), hAPP(c_Relation_ODomain(_1554878, _1554880), _1554886))))], (39725 ^ _777081) ^ [_1555025, _1555027] : [-(hAPP(c_Relation_ODomain(_1555025, _1555025), c_Relation_OId__on(_1555025, _1555027)) = _1555027)], (39727 ^ _777081) ^ [_1555077, _1555079, _1555081] : [hAPP(c_Relation_ODomain(_1555077, _1555079), _1555081) = c_Orderings_Obot__class_Obot(tc_fun(_1555077, tc_HOL_Obool)), -(_1555081 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1555077, _1555079), tc_HOL_Obool)))], (39733 ^ _777081) ^ [_1555190, _1555192, _1555194] : [_1555194 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1555190, _1555192), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1555190, _1555192), _1555194) = c_Orderings_Obot__class_Obot(tc_fun(_1555190, tc_HOL_Obool)))], (39739 ^ _777081) ^ [_1555309, _1555311] : [-(hAPP(c_Relation_ODomain(_1555309, _1555311), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1555309, _1555311), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1555309, tc_HOL_Obool)))], (39741 ^ _777081) ^ [_1555353, _1555355, _1555357, _1555359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555353, _1555355), tc_HOL_Obool)), _1555357), _1555359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555353, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1555353, _1555355), _1555357)), hAPP(c_Relation_ODomain(_1555353, _1555355), _1555359))))], (39747 ^ _777081) ^ [_1555504, _1555506, _1555508, _1555510] : [-(hAPP(c_Relation_ODomain(_1555504, _1555506), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1555504, _1555506), tc_HOL_Obool)), _1555508), _1555510)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1555504, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1555504, _1555506), _1555508)), hAPP(c_Relation_ODomain(_1555504, _1555506), _1555510)))], (39749 ^ _777081) ^ [_1555576, _1555578, _1555580] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1555576, _1555578)), _1555580)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1555576), hAPP(c_Relation_ODomain(_1555576, _1555578), _1555580))))], (39755 ^ _777081) ^ [_1555689, _1555691, _1555693] : [-(hAPP(c_Set_Oimage(tc_prod(_1555689, _1555691), _1555689, c_Product__Type_Ofst(_1555689, _1555691)), _1555693) = hAPP(c_Relation_ODomain(_1555689, _1555691), _1555693))], (39757 ^ _777081) ^ [_1555756, _1555758, _1555760, _1555762] : [hBOOL(hAPP(hAPP(c_member(_1555756), _1555758), hAPP(c_Relation_ODomain(_1555756, _1555760), _1555762))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1555756, _1555760)), hAPP(hAPP(c_Product__Type_OPair(_1555756, _1555760), _1555758), 39760 ^ [_1555756, _1555758, _1555760, _1555762])), _1555762)))], (39764 ^ _777081) ^ [_1555913, _1555915, _1555917, _1555919] : [39765 ^ _777081 : [(39766 ^ _777081) ^ [_1555988] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1555913, _1555917)), hAPP(hAPP(c_Product__Type_OPair(_1555913, _1555917), _1555915), _1555988)), _1555919))]], -(hBOOL(hAPP(hAPP(c_member(_1555913), _1555915), hAPP(c_Relation_ODomain(_1555913, _1555917), _1555919))))], (39770 ^ _777081) ^ [_1556073, _1556075, _1556077, _1556079, _1556081] : [-(hAPP(c_Relation_ODomain(_1556073, _1556075), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1556073, _1556075)), hAPP(hAPP(c_Product__Type_OPair(_1556073, _1556075), _1556077), _1556079)), _1556081)) = hAPP(hAPP(c_Set_Oinsert(_1556073), _1556077), hAPP(c_Relation_ODomain(_1556073, _1556075), _1556081)))], (39772 ^ _777081) ^ [_1556144, _1556146, _1556148, _1556150] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1556144, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1556144, _1556146), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1556144, _1556146), tc_HOL_Obool)), _1556148), _1556150))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1556144, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1556144, _1556146), _1556148)), hAPP(c_Relation_ODomain(_1556144, _1556146), _1556150)))))], (39774 ^ _777081) ^ [_1556226, _1556228, _1556230, _1556232] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1556226, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1556226, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1556226, _1556228), _1556230)), hAPP(c_Relation_ODomain(_1556226, _1556228), _1556232))), hAPP(c_Relation_ODomain(_1556226, _1556228), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1556226, _1556228), tc_HOL_Obool)), _1556230), _1556232)))))], (39776 ^ _777081) ^ [_1556308, _1556310] : [-(hAPP(c_Relation_OField(_1556308), _1556310) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1556308, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1556308, _1556308), _1556310)), hAPP(c_Relation_ORange(_1556308, _1556308), _1556310)))], (39778 ^ _777081) ^ [_1556361, _1556363, _1556365] : [-(hAPP(c_Relation_ODomain(_1556361, _1556363), hAPP(c_Set_OCollect(tc_prod(_1556361, _1556363)), hAPP(c_Product__Type_Oprod_Oprod__case(_1556361, _1556363, tc_HOL_Obool), _1556365))) = hAPP(c_Set_OCollect(_1556361), hAPP(hAPP(c_COMBB(tc_fun(_1556363, tc_HOL_Obool), tc_HOL_Obool, _1556361), c_HOL_OEx(_1556363)), _1556365)))], (39780 ^ _777081) ^ [] : [-(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))))], (39782 ^ _777081) ^ [_1556468, _1556470, _1556472, _1556474] : [hBOOL(hAPP(c_Predicate_ODomainP(_1556468, _1556470, hAPP(hAPP(c_COMBC(_1556468, tc_fun(tc_prod(_1556468, _1556470), tc_HOL_Obool), tc_fun(_1556470, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1556470, tc_fun(tc_fun(tc_prod(_1556468, _1556470), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1556468, _1556470), tc_HOL_Obool), tc_fun(_1556470, tc_HOL_Obool)), _1556468), c_COMBC(_1556470, tc_fun(tc_prod(_1556468, _1556470), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1556470, tc_prod(_1556468, _1556470)), tc_fun(_1556470, tc_fun(tc_fun(tc_prod(_1556468, _1556470), tc_HOL_Obool), tc_HOL_Obool)), _1556468), hAPP(c_COMBB(tc_prod(_1556468, _1556470), tc_fun(tc_fun(tc_prod(_1556468, _1556470), tc_HOL_Obool), tc_HOL_Obool), _1556470), c_member(tc_prod(_1556468, _1556470)))), c_Product__Type_OPair(_1556468, _1556470)))), _1556472)), _1556474)), -(hBOOL(hAPP(hAPP(c_member(_1556468), _1556474), hAPP(c_Relation_ODomain(_1556468, _1556470), _1556472))))], (39788 ^ _777081) ^ [_1556819, _1556821, _1556823, _1556825] : [hBOOL(hAPP(hAPP(c_member(_1556819), _1556825), hAPP(c_Relation_ODomain(_1556819, _1556821), _1556823))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1556819, _1556821, hAPP(hAPP(c_COMBC(_1556819, tc_fun(tc_prod(_1556819, _1556821), tc_HOL_Obool), tc_fun(_1556821, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1556821, tc_fun(tc_fun(tc_prod(_1556819, _1556821), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1556819, _1556821), tc_HOL_Obool), tc_fun(_1556821, tc_HOL_Obool)), _1556819), c_COMBC(_1556821, tc_fun(tc_prod(_1556819, _1556821), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1556821, tc_prod(_1556819, _1556821)), tc_fun(_1556821, tc_fun(tc_fun(tc_prod(_1556819, _1556821), tc_HOL_Obool), tc_HOL_Obool)), _1556819), hAPP(c_COMBB(tc_prod(_1556819, _1556821), tc_fun(tc_fun(tc_prod(_1556819, _1556821), tc_HOL_Obool), tc_HOL_Obool), _1556821), c_member(tc_prod(_1556819, _1556821)))), c_Product__Type_OPair(_1556819, _1556821)))), _1556823)), _1556825)))], (39794 ^ _777081) ^ [_1557176, _1557178, _1557180, _1557182, _1557184] : [hBOOL(hAPP(hAPP(_1557176, _1557178), _1557180)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1557182, _1557184, _1557176), _1557178)))], (39800 ^ _777081) ^ [_1557302, _1557304, _1557306, _1557308] : [hBOOL(hAPP(c_Predicate_ODomainP(_1557302, _1557304, _1557306), _1557308)), -(hBOOL(hAPP(hAPP(_1557306, _1557308), 39803 ^ [_1557302, _1557304, _1557306, _1557308])))], (39807 ^ _777081) ^ [_1557417, _1557419, _1557421, _1557423] : [39808 ^ _777081 : [(39809 ^ _777081) ^ [_1557471] : [hBOOL(hAPP(hAPP(_1557421, _1557423), _1557471))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1557417, _1557419, _1557421), _1557423)))], (39813 ^ _777081) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (39815 ^ _777081) ^ [_1557553, _1557555] : [c_Wellfounded_Owf(_1557553, _1557555), -(c_Wellfounded_Owf(tc_List_Olist(_1557553), c_List_Olex(_1557553, _1557555)))], (39821 ^ _777081) ^ [_1557640, _1557642, _1557644] : [c_Wellfounded_Owf(_1557640, _1557642), -(c_Wellfounded_Owf(tc_List_Olist(_1557640), hAPP(c_List_Olexn(_1557640, _1557642), _1557644)))], (39827 ^ _777081) ^ [_1557735, _1557737] : [-(c_List_Olex(_1557735, _1557737) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1557735), tc_List_Olist(_1557735)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1557735, _1557737)))], (39829 ^ _777081) ^ [_1557785, _1557787] : [-(hAPP(c_List_Olexn(_1557785, _1557787), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1557785), tc_List_Olist(_1557785)), tc_HOL_Obool)))], (39831 ^ _777081) ^ [_1557828, _1557830, _1557832, _1557834] : [hBOOL(hAPP(hAPP(c_member(_1557828), _1557830), hAPP(c_Relation_ODomain(_1557828, _1557832), _1557834))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1557828, _1557832)), hAPP(hAPP(c_Product__Type_OPair(_1557828, _1557832), _1557830), 39834 ^ [_1557828, _1557830, _1557832, _1557834])), _1557834)))], (39838 ^ _777081) ^ [_1557993, _1557995, _1557997, _1557999] : [39840 ^ _777081 : [(39841 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1557993, 39839 ^ [_1557993, _1557995, _1557997, _1557999])))], (39843 ^ _777081) ^ [] : [c_Wellfounded_Owf(_1557995, hAPP(_1557997, 39839 ^ [_1557993, _1557995, _1557997, _1557999]))]], -(c_Wellfounded_Owf(tc_prod(_1557999, _1557995), c_Recdef_Osame__fst(_1557999, _1557995, _1557993, _1557997)))], (39847 ^ _777081) ^ [_1558178, _1558180, _1558182, _1558184] : [39849 ^ _777081 : [(39850 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1558178, 39848 ^ [_1558178, _1558180, _1558182, _1558184])))], (39852 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1558180, hAPP(_1558182, 39848 ^ [_1558178, _1558180, _1558182, _1558184]))), hAPP(_1558180, 39848 ^ [_1558178, _1558180, _1558182, _1558184])))]], -(c_Wellfounded_Owf(_1558184, hAPP(c_Set_OCollect(tc_prod(_1558184, _1558184)), hAPP(c_Product__Type_Oprod_Oprod__case(_1558184, _1558184, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1558184, tc_HOL_Obool), tc_fun(_1558184, tc_HOL_Obool), _1558184), hAPP(c_COMBS(_1558184, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1558184), c_fconj), _1558178))), hAPP(hAPP(c_COMBC(_1558184, tc_fun(_1558184, _1558184), tc_fun(_1558184, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1558184, tc_HOL_Obool), tc_fun(tc_fun(_1558184, _1558184), tc_fun(_1558184, tc_HOL_Obool)), _1558184), c_COMBB(_1558184, tc_HOL_Obool, _1558184)), c_fequal)), _1558182))))))], (39856 ^ _777081) ^ [_1558586, _1558588] : [c_Wellfounded_OwfP(_1558586, _1558588), -(c_Wellfounded_Owf(_1558586, hAPP(c_Set_OCollect(tc_prod(_1558586, _1558586)), hAPP(c_Product__Type_Oprod_Oprod__case(_1558586, _1558586, tc_HOL_Obool), _1558588))))], (39862 ^ _777081) ^ [_1558689, _1558691] : [c_Wellfounded_Owf(_1558689, hAPP(c_Set_OCollect(tc_prod(_1558689, _1558689)), hAPP(c_Product__Type_Oprod_Oprod__case(_1558689, _1558689, tc_HOL_Obool), _1558691))), -(c_Wellfounded_OwfP(_1558689, _1558691))], (39868 ^ _777081) ^ [_1558798] : [-(c_Wellfounded_OwfP(_1558798, hAPP(c_COMBK(tc_fun(_1558798, tc_HOL_Obool), _1558798), hAPP(c_COMBK(tc_HOL_Obool, _1558798), c_fFalse))))], (39870 ^ _777081) ^ [_1558836, _1558838, _1558840] : [c_Wellfounded_OwfP(_1558836, _1558838), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1558836, tc_fun(_1558836, tc_HOL_Obool))), _1558840), _1558838)), -(c_Wellfounded_OwfP(_1558836, _1558840))], (39880 ^ _777081) ^ [_1558995, _1558997, _1558999] : [c_Wellfounded_OwfP(_1558995, _1558997), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1558995, _1558997), _1558999)))], (39886 ^ _777081) ^ [_1559099, _1559101] : [c_Wellfounded_OwfP(_1559099, _1559101), 39889 ^ _777081 : [(39890 ^ _777081) ^ [_1559163] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1559099, _1559101), _1559163)))]]], (39892 ^ _777081) ^ [_1559191, _1559193] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1559191, _1559193), 39893 ^ [_1559191, _1559193])), -(c_Wellfounded_OwfP(_1559191, _1559193))], (39899 ^ _777081) ^ [_1559309, _1559311] : [c_Wellfounded_Owf(_1559309, _1559311), -(c_Wellfounded_OwfP(_1559309, c_FunDef_Oin__rel(_1559309, _1559309, _1559311)))], (39905 ^ _777081) ^ [_1559409, _1559411] : [c_Wellfounded_OwfP(_1559409, hAPP(hAPP(c_COMBC(_1559409, tc_fun(tc_prod(_1559409, _1559409), tc_HOL_Obool), tc_fun(_1559409, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559409, tc_fun(tc_fun(tc_prod(_1559409, _1559409), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1559409, _1559409), tc_HOL_Obool), tc_fun(_1559409, tc_HOL_Obool)), _1559409), c_COMBC(_1559409, tc_fun(tc_prod(_1559409, _1559409), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559409, tc_prod(_1559409, _1559409)), tc_fun(_1559409, tc_fun(tc_fun(tc_prod(_1559409, _1559409), tc_HOL_Obool), tc_HOL_Obool)), _1559409), hAPP(c_COMBB(tc_prod(_1559409, _1559409), tc_fun(tc_fun(tc_prod(_1559409, _1559409), tc_HOL_Obool), tc_HOL_Obool), _1559409), c_member(tc_prod(_1559409, _1559409)))), c_Product__Type_OPair(_1559409, _1559409)))), _1559411)), -(c_Wellfounded_Owf(_1559409, _1559411))], (39911 ^ _777081) ^ [_1559718, _1559720] : [c_Wellfounded_Owf(_1559718, _1559720), -(c_Wellfounded_OwfP(_1559718, hAPP(hAPP(c_COMBC(_1559718, tc_fun(tc_prod(_1559718, _1559718), tc_HOL_Obool), tc_fun(_1559718, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559718, tc_fun(tc_fun(tc_prod(_1559718, _1559718), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1559718, _1559718), tc_HOL_Obool), tc_fun(_1559718, tc_HOL_Obool)), _1559718), c_COMBC(_1559718, tc_fun(tc_prod(_1559718, _1559718), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559718, tc_prod(_1559718, _1559718)), tc_fun(_1559718, tc_fun(tc_fun(tc_prod(_1559718, _1559718), tc_HOL_Obool), tc_HOL_Obool)), _1559718), hAPP(c_COMBB(tc_prod(_1559718, _1559718), tc_fun(tc_fun(tc_prod(_1559718, _1559718), tc_HOL_Obool), tc_HOL_Obool), _1559718), c_member(tc_prod(_1559718, _1559718)))), c_Product__Type_OPair(_1559718, _1559718)))), _1559720)))], (39917 ^ _777081) ^ [_1560033, _1560035] : [c_Wellfounded_OwfP(_1560033, _1560035), -(c_Wellfounded_Oacyclic(_1560033, hAPP(c_Set_OCollect(tc_prod(_1560033, _1560033)), hAPP(c_Product__Type_Oprod_Oprod__case(_1560033, _1560033, tc_HOL_Obool), _1560035))))], (39923 ^ _777081) ^ [_1560139, _1560141, _1560143, _1560145] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1560139), _1560141))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560143), hAPP(c_Set_Oimage(_1560139, _1560143, _1560145), _1560141))), 39931 ^ _777081 : [(39932 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560139), 39930 ^ [_1560139, _1560141, _1560143, _1560145]), _1560141)))], (39934 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1560139), hAPP(c_Set_OCollect(_1560139), hAPP(hAPP(c_COMBS(_1560139, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1560139), c_fconj), hAPP(hAPP(c_COMBC(_1560139, tc_fun(_1560139, tc_HOL_Obool), tc_HOL_Obool), c_member(_1560139)), _1560141))), hAPP(hAPP(c_COMBC(_1560139, _1560143, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1560143, tc_fun(_1560143, tc_HOL_Obool), _1560139), c_fequal), _1560145)), hAPP(_1560145, 39930 ^ [_1560139, _1560141, _1560143, _1560145]))))))]]], (39936 ^ _777081) ^ [_1560604, _1560606] : [c_Wellfounded_Owf(_1560604, _1560606), -(c_Wellfounded_Oacyclic(_1560604, _1560606))], (39942 ^ _777081) ^ [_1560681, _1560683, _1560685] : [c_Wellfounded_Oacyclic(_1560681, _1560683), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1560681, _1560681), tc_HOL_Obool)), _1560685), _1560683)), -(c_Wellfounded_Oacyclic(_1560681, _1560685))], (39952 ^ _777081) ^ [_1560840, _1560842] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560840, _1560840)), _1560842)), c_Wellfounded_Oacyclic(_1560840, _1560842), -(c_Wellfounded_Owf(_1560840, _1560842))], (39962 ^ _777081) ^ [_1560983, _1560985] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1560983, _1560983)), _1560985)), 39965 ^ _777081 : [(39966 ^ _777081) ^ [] : [c_Wellfounded_Owf(_1560983, _1560985), -(c_Wellfounded_Oacyclic(_1560983, _1560985))], (39972 ^ _777081) ^ [] : [c_Wellfounded_Oacyclic(_1560983, _1560985), -(c_Wellfounded_Owf(_1560983, _1560985))]]], (39978 ^ _777081) ^ [_1561219, _1561221] : [c_Nitpick_Owf_H(_1561219, _1561221), 39981 ^ _777081 : [(39982 ^ _777081) ^ [] : [-(c_Wellfounded_Oacyclic(_1561219, _1561221))], (39984 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1561219, _1561219)), _1561221))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (39990 ^ _777081) ^ [_1561339, _1561341] : [-(c_Nitpick_Owf_H(_1561339, _1561341)), c_Wellfounded_Oacyclic(_1561339, _1561341), 39995 ^ _777081 : [(39996 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1561339, _1561339)), _1561341))], (39998 ^ _777081) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (40018 ^ _777081) ^ [_1562153, _1562155, _1562157] : [-(c_Relation_Orefl__on(_1562153, _1562155, _1562157)), 40022 ^ _777081 : [(40023 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562153, _1562153)), 40021 ^ [_1562153, _1562155, _1562157]), _1562157)))], (40025 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1562153, _1562153, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1562153, tc_fun(_1562153, tc_HOL_Obool), tc_fun(_1562153, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1562153, tc_HOL_Obool), tc_fun(_1562153, tc_HOL_Obool)), _1562153), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1562153)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1562153), c_fconj), hAPP(hAPP(c_COMBC(_1562153, tc_fun(_1562153, tc_HOL_Obool), tc_HOL_Obool), c_member(_1562153)), _1562155)))), hAPP(hAPP(c_COMBC(_1562153, tc_fun(_1562153, tc_HOL_Obool), tc_HOL_Obool), c_member(_1562153)), _1562155))), 40021 ^ [_1562153, _1562155, _1562157]))]], 40027 ^ _777081 : [(40028 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562153), 40026 ^ [_1562153, _1562155, _1562157]), _1562155)))], (40030 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562153, _1562153)), hAPP(hAPP(c_Product__Type_OPair(_1562153, _1562153), 40026 ^ [_1562153, _1562155, _1562157]), 40026 ^ [_1562153, _1562155, _1562157])), _1562157))]]], (40002 ^ _777081) ^ [_1561534, _1561536, _1561538] : [c_Relation_Orefl__on(_1561534, _1561536, _1561538), 40005 ^ _777081 : [(40006 ^ _777081) ^ [_1561745] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1561534, _1561534)), _1561745), _1561538)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1561534, _1561534, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1561534, tc_fun(_1561534, tc_HOL_Obool), tc_fun(_1561534, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1561534, tc_HOL_Obool), tc_fun(_1561534, tc_HOL_Obool)), _1561534), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1561534)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1561534), c_fconj), hAPP(hAPP(c_COMBC(_1561534, tc_fun(_1561534, tc_HOL_Obool), tc_HOL_Obool), c_member(_1561534)), _1561536)))), hAPP(hAPP(c_COMBC(_1561534, tc_fun(_1561534, tc_HOL_Obool), tc_HOL_Obool), c_member(_1561534)), _1561536))), _1561745)))], (40012 ^ _777081) ^ [_1562018] : [hBOOL(hAPP(hAPP(c_member(_1561534), _1562018), _1561536)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1561534, _1561534)), hAPP(hAPP(c_Product__Type_OPair(_1561534, _1561534), _1562018), _1562018)), _1561538)))]]], (40034 ^ _777081) ^ [_1562794, _1562796, _1562798] : [hBOOL(hAPP(hAPP(c_member(_1562796), _1562794), c_Orderings_Obot__class_Obot(tc_fun(_1562796, tc_HOL_Obool)))), -(hBOOL(hAPP(_1562798, _1562794)))], (40040 ^ _777081) ^ [_1562916, _1562918] : [40042 ^ _777081 : [(40043 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562916), 40041 ^ [_1562916, _1562918]), c_Orderings_Otop__class_Otop(tc_fun(_1562916, tc_HOL_Obool)))))], (40045 ^ _777081) ^ [] : [hBOOL(hAPP(_1562918, 40041 ^ [_1562916, _1562918]))]], 40046 ^ _777081 : [(40047 ^ _777081) ^ [_1563068] : [-(hBOOL(hAPP(_1562918, _1563068)))]]], (40049 ^ _777081) ^ [_1563095, _1563097] : [hBOOL(hAPP(_1563097, 40050 ^ [_1563095, _1563097])), 40053 ^ _777081 : [(40054 ^ _777081) ^ [_1563202] : [hBOOL(hAPP(hAPP(c_member(_1563095), _1563202), c_Orderings_Otop__class_Otop(tc_fun(_1563095, tc_HOL_Obool)))), -(hBOOL(hAPP(_1563097, _1563202)))]]], (40070 ^ _777081) ^ [_1563516, _1563518, _1563520] : [40072 ^ _777081 : [(40073 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1563516), 40071 ^ [_1563516, _1563518, _1563520]), _1563520)))], (40075 ^ _777081) ^ [] : [hBOOL(hAPP(_1563518, 40071 ^ [_1563516, _1563518, _1563520]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1563516, _1563518), _1563520)))], (40060 ^ _777081) ^ [_1563333, _1563335, _1563337] : [hBOOL(hAPP(c_Predicate_OPowp(_1563333, _1563335), _1563337)), 40063 ^ _777081 : [(40064 ^ _777081) ^ [_1563417] : [hBOOL(hAPP(hAPP(c_member(_1563333), _1563417), _1563337)), -(hBOOL(hAPP(_1563335, _1563417)))]]], (40089 ^ _777081) ^ [_1564093, _1564095, _1564097, _1564099] : [40091 ^ _777081 : [(40092 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564093, _1564093)), 40090 ^ [_1564093, _1564095, _1564097, _1564099]), _1564097)))], (40094 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1564093, _1564093, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1564093, tc_fun(_1564093, _1564095), tc_fun(_1564093, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1564095, tc_HOL_Obool), tc_fun(tc_fun(_1564093, _1564095), tc_fun(_1564093, tc_HOL_Obool)), _1564093), c_COMBB(_1564095, tc_HOL_Obool, _1564093)), hAPP(hAPP(c_COMBB(_1564095, tc_fun(_1564095, tc_HOL_Obool), _1564093), c_fequal), _1564099))), _1564099)), 40090 ^ [_1564093, _1564095, _1564097, _1564099]))]], -(c_Equiv__Relations_Ocongruent(_1564093, _1564095, _1564097, _1564099))], (40079 ^ _777081) ^ [_1563717, _1563719, _1563721, _1563723] : [c_Equiv__Relations_Ocongruent(_1563717, _1563719, _1563721, _1563723), 40082 ^ _777081 : [(40083 ^ _777081) ^ [_1563862] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563717, _1563717)), _1563862), _1563721)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1563717, _1563717, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1563717, tc_fun(_1563717, _1563719), tc_fun(_1563717, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1563719, tc_HOL_Obool), tc_fun(tc_fun(_1563717, _1563719), tc_fun(_1563717, tc_HOL_Obool)), _1563717), c_COMBB(_1563719, tc_HOL_Obool, _1563717)), hAPP(hAPP(c_COMBB(_1563719, tc_fun(_1563719, tc_HOL_Obool), _1563717), c_fequal), _1563723))), _1563723)), _1563862)))]]], (40098 ^ _777081) ^ [_1564468, _1564470] : [40100 ^ _777081 : [(40101 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40099 ^ [_1564468, _1564470]), c_Int_OInteg)))], (40103 ^ _777081) ^ [] : [hBOOL(hAPP(_1564468, hAPP(c_Int_OAbs__Integ, 40099 ^ [_1564468, _1564470])))]], -(hBOOL(hAPP(_1564468, _1564470)))], (40108 ^ _777081) ^ [_1564635] : [-(_1564635 = hAPP(c_Int_OAbs__Integ, 40106 ^ [_1564635]))], (40110 ^ _777081) ^ [_1564663] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40106 ^ [_1564663]), c_Int_OInteg)))], (40112 ^ _777081) ^ [_1564698, _1564700, _1564702] : [40114 ^ _777081 : [(40115 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1564698)), 40113 ^ [_1564698, _1564700, _1564702]), _1564700)))], (40117 ^ _777081) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1564698, hAPP(c_Nat_OSuc, _1564702), 40113 ^ [_1564698, _1564700, _1564702])]], 40118 ^ _777081 : [(40119 ^ _777081) ^ [_1564871] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1564698)), _1564871), _1564700)), -(c_Hoare__Mirabelle_Otriple__valid(_1564698, _1564702, _1564871))]]], (40142 ^ _777081) ^ [_1565386, _1565388, _1565390] : [-(c_Hoare__Mirabelle_Ohoare__valids(_1565386, _1565388, _1565390)), 40144 ^ _777081 : [(40152 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1565386)), 40150 ^ [_1565386, _1565388, _1565390]), _1565390)))], (40154 ^ _777081) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1565386, 40143 ^ [_1565386, _1565388, _1565390], 40150 ^ [_1565386, _1565388, _1565390])], (40145 ^ _777081) ^ [_1565532] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1565386)), _1565532), _1565388)), -(c_Hoare__Mirabelle_Otriple__valid(_1565386, 40143 ^ [_1565386, _1565388, _1565390], _1565532))]]], (40125 ^ _777081) ^ [_1564996, _1564998, _1565000] : [c_Hoare__Mirabelle_Ohoare__valids(_1564996, _1564998, _1565000), 40128 ^ _777081 : [(40129 ^ _777081) ^ [_1565105] : [40131 ^ _777081 : [(40132 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1564996)), 40130 ^ [_1564996, _1564998, _1565000, _1565105]), _1564998)))], (40134 ^ _777081) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1564996, _1565105, 40130 ^ [_1564996, _1564998, _1565000, _1565105])]], 40135 ^ _777081 : [(40136 ^ _777081) ^ [_1565277] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1564996)), _1565277), _1565000)), -(c_Hoare__Mirabelle_Otriple__valid(_1564996, _1565105, _1565277))]]]]], (40158 ^ _777081) ^ [_1565787, _1565789, _1565791, _1565793] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1565787)), hAPP(c_Set_Oimage(_1565789, tc_Option_Ooption(_1565787), _1565791), c_Orderings_Otop__class_Otop(tc_fun(_1565789, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1565787)), hAPP(c_Set_Oimage(_1565789, tc_Option_Ooption(_1565787), c_Map_Omap__add(_1565789, _1565787, _1565791, hAPP(c_Map_Omap__of(_1565789, _1565787), _1565793))), c_Orderings_Otop__class_Otop(tc_fun(_1565789, tc_HOL_Obool))))))], (40164 ^ _777081) ^ [_1565970, _1565972, _1565974, _1565976] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1565970), _1565972)), 40170 ^ _777081 : [(40171 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565970), 40169 ^ [_1565970, _1565972, _1565974, _1565976]), _1565972)))], (40173 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1565974), hAPP(_1565976, 40169 ^ [_1565970, _1565972, _1565974, _1565976])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1565974), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1565970, tc_fun(_1565974, tc_HOL_Obool)), _1565972), _1565976))))], (40177 ^ _777081) ^ [_1566257, _1566259, _1566261] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1566257), c_Map_Odom(_1566257, _1566259, hAPP(c_Map_Omap__of(_1566257, _1566259), _1566261)))))], (40179 ^ _777081) ^ [_1566298, _1566300, _1566302] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1566298)), hAPP(c_Set_Oimage(_1566300, tc_Option_Ooption(_1566298), hAPP(c_Map_Omap__of(_1566300, _1566298), _1566302)), c_Orderings_Otop__class_Otop(tc_fun(_1566300, tc_HOL_Obool))))))], (40181 ^ _777081) ^ [_1566351, _1566353, _1566355, _1566357] : [-(c_Map_Omap__add(_1566351, _1566353, _1566355, hAPP(c_Map_Omap__of(_1566351, _1566353), _1566357)) = c_List_Ofoldr(tc_prod(_1566351, _1566353), tc_fun(_1566351, tc_Option_Ooption(_1566353)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566351, _1566353, tc_fun(tc_fun(_1566351, tc_Option_Ooption(_1566353)), tc_fun(_1566351, tc_Option_Ooption(_1566353)))), hAPP(hAPP(c_COMBC(_1566351, tc_fun(_1566353, tc_Option_Ooption(_1566353)), tc_fun(_1566353, tc_fun(tc_fun(_1566351, tc_Option_Ooption(_1566353)), tc_fun(_1566351, tc_Option_Ooption(_1566353))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1566353), tc_fun(tc_fun(_1566351, tc_Option_Ooption(_1566353)), tc_fun(_1566351, tc_Option_Ooption(_1566353)))), tc_fun(tc_fun(_1566353, tc_Option_Ooption(_1566353)), tc_fun(_1566353, tc_fun(tc_fun(_1566351, tc_Option_Ooption(_1566353)), tc_fun(_1566351, tc_Option_Ooption(_1566353))))), _1566351), c_COMBB(tc_Option_Ooption(_1566353), tc_fun(tc_fun(_1566351, tc_Option_Ooption(_1566353)), tc_fun(_1566351, tc_Option_Ooption(_1566353))), _1566353)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1566351, tc_Option_Ooption(_1566353)), tc_fun(tc_Option_Ooption(_1566353), tc_fun(_1566351, tc_Option_Ooption(_1566353)))), tc_fun(tc_Option_Ooption(_1566353), tc_fun(tc_fun(_1566351, tc_Option_Ooption(_1566353)), tc_fun(_1566351, tc_Option_Ooption(_1566353)))), _1566351), c_COMBC(tc_fun(_1566351, tc_Option_Ooption(_1566353)), tc_Option_Ooption(_1566353), tc_fun(_1566351, tc_Option_Ooption(_1566353)))), hAPP(c_COMBC(tc_fun(_1566351, tc_Option_Ooption(_1566353)), _1566351, tc_fun(tc_Option_Ooption(_1566353), tc_fun(_1566351, tc_Option_Ooption(_1566353)))), c_Fun_Ofun__upd(_1566351, tc_Option_Ooption(_1566353)))))), c_Option_Ooption_OSome(_1566353))), _1566357, _1566355))], (40183 ^ _777081) ^ [_1566618, _1566620, _1566622, _1566624, _1566626, _1566628, _1566630] : [c_Fun_Oinj__on(_1566618, _1566620, _1566622, c_Orderings_Otop__class_Otop(tc_fun(_1566618, tc_HOL_Obool))), hAPP(hAPP(c_Map_Omap__of(_1566618, _1566624), _1566626), _1566628) = hAPP(c_Option_Ooption_OSome(_1566624), _1566630), -(hAPP(hAPP(c_Map_Omap__of(_1566620, _1566624), hAPP(hAPP(c_List_Omap(tc_prod(_1566618, _1566624), tc_prod(_1566620, _1566624)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566618, _1566624, tc_prod(_1566620, _1566624)), hAPP(hAPP(c_COMBB(_1566620, tc_fun(_1566624, tc_prod(_1566620, _1566624)), _1566618), c_Product__Type_OPair(_1566620, _1566624)), _1566622))), _1566626)), hAPP(_1566622, _1566628)) = hAPP(c_Option_Ooption_OSome(_1566624), _1566630))], (40193 ^ _777081) ^ [_1566931, _1566933, _1566935] : [c_Fun_Oinj__on(_1566931, _1566933, _1566935, c_Orderings_Otop__class_Otop(tc_fun(_1566931, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1566931), tc_List_Olist(_1566933), hAPP(c_List_Omap(_1566931, _1566933), _1566935), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1566931), tc_HOL_Obool))))], (40199 ^ _777081) ^ [_1567080, _1567082, _1567084] : [c_Fun_Oinj__on(tc_List_Olist(_1567080), tc_List_Olist(_1567082), hAPP(c_List_Omap(_1567080, _1567082), _1567084), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1567080), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1567080, _1567082, _1567084, c_Orderings_Otop__class_Otop(tc_fun(_1567080, tc_HOL_Obool))))], (40205 ^ _777081) ^ [_1567207, _1567209, _1567211] : [c_Fun_Oinj__on(_1567207, _1567209, _1567211, c_Orderings_Otop__class_Otop(tc_fun(_1567207, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1567207), tc_List_Olist(_1567209), hAPP(c_List_Omap(_1567207, _1567209), _1567211), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1567207), tc_HOL_Obool))))], (40211 ^ _777081) ^ [_1567340, _1567342, _1567344, _1567346, _1567348] : [c_Fun_Oinj__on(_1567340, _1567342, _1567344, c_Orderings_Otop__class_Otop(tc_fun(_1567340, tc_HOL_Obool))), 40214 ^ _777081 : [(40215 ^ _777081) ^ [] : [hAPP(hAPP(c_List_Omap(_1567340, _1567342), _1567344), _1567346) = hAPP(hAPP(c_List_Omap(_1567340, _1567342), _1567344), _1567348), -(_1567346 = _1567348)], (40221 ^ _777081) ^ [] : [_1567346 = _1567348, -(hAPP(hAPP(c_List_Omap(_1567340, _1567342), _1567344), _1567346) = hAPP(hAPP(c_List_Omap(_1567340, _1567342), _1567344), _1567348))]]], (40227 ^ _777081) ^ [_1567633, _1567635, _1567637] : [c_Fun_Oinj__on(tc_List_Olist(_1567633), tc_List_Olist(_1567635), hAPP(c_List_Omap(_1567633, _1567635), _1567637), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1567633), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1567633, _1567635, _1567637, c_Orderings_Otop__class_Otop(tc_fun(_1567633, tc_HOL_Obool))))], (40233 ^ _777081) ^ [_1567764, _1567766, _1567768, _1567770, _1567772] : [hAPP(hAPP(c_List_Omap(_1567764, _1567766), _1567768), _1567770) = hAPP(hAPP(c_List_Omap(_1567764, _1567766), _1567768), _1567772), c_Fun_Oinj__on(_1567764, _1567766, _1567768, c_Orderings_Otop__class_Otop(tc_fun(_1567764, tc_HOL_Obool))), -(_1567770 = _1567772)], (40243 ^ _777081) ^ [_1567955, _1567957, _1567959, _1567961, _1567963, _1567965, _1567967] : [-(c_List_Ofoldr(_1567955, _1567957, _1567959, hAPP(hAPP(c_List_Omap(_1567961, _1567955), _1567963), _1567965), _1567967) = c_List_Ofoldr(_1567961, _1567957, hAPP(c_Fun_Ocomp(_1567955, tc_fun(_1567957, _1567957), _1567961, _1567959), _1567963), _1567965, _1567967))], (40245 ^ _777081) ^ [_1568022, _1568024, _1568026, _1568028, _1568030] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1568022), tc_List_Olist(_1568024), tc_List_Olist(_1568026), hAPP(c_List_Omap(_1568022, _1568024), _1568028)), hAPP(c_List_Omap(_1568026, _1568022), _1568030)) = hAPP(c_List_Omap(_1568026, _1568024), hAPP(c_Fun_Ocomp(_1568022, _1568024, _1568026, _1568028), _1568030)))], (40247 ^ _777081) ^ [_1568093, _1568095, _1568097, _1568099, _1568101] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1568093), tc_List_Olist(_1568095), tc_List_Olist(_1568097), hAPP(c_List_Omap(_1568093, _1568095), _1568099)), hAPP(c_List_Omap(_1568097, _1568093), _1568101)) = hAPP(c_List_Omap(_1568097, _1568095), hAPP(c_Fun_Ocomp(_1568093, _1568095, _1568097, _1568099), _1568101)))], (40249 ^ _777081) ^ [_1568164, _1568166, _1568168, _1568170, _1568172, _1568174] : [-(hAPP(hAPP(c_List_Omap(_1568164, _1568166), _1568168), hAPP(hAPP(c_List_Omap(_1568170, _1568164), _1568172), _1568174)) = hAPP(hAPP(c_List_Omap(_1568170, _1568166), hAPP(c_Fun_Ocomp(_1568164, _1568166, _1568170, _1568168), _1568172)), _1568174))], (40251 ^ _777081) ^ [_1568232, _1568234, _1568236, _1568238, _1568240, _1568242] : [-(hAPP(hAPP(c_List_Omap(_1568232, _1568234), _1568236), hAPP(hAPP(c_List_Omap(_1568238, _1568232), _1568240), _1568242)) = hAPP(hAPP(c_List_Omap(_1568238, _1568234), hAPP(c_Fun_Ocomp(_1568232, _1568234, _1568238, _1568236), _1568240)), _1568242))], (40253 ^ _777081) ^ [_1568300, _1568302] : [-(hAPP(hAPP(c_List_Omap(_1568300, _1568300), c_COMBI(_1568300)), _1568302) = _1568302)], (40255 ^ _777081) ^ [_1568336] : [-(hAPP(c_List_Omap(_1568336, _1568336), c_COMBI(_1568336)) = c_Fun_Oid(tc_List_Olist(_1568336)))], (40257 ^ _777081) ^ [_1568371] : [-(hAPP(c_List_Omap(_1568371, _1568371), c_Fun_Oid(_1568371)) = c_Fun_Oid(tc_List_Olist(_1568371)))], (40259 ^ _777081) ^ [_1568406, _1568408, _1568410, _1568412, _1568414] : [-(hAPP(c_Map_Omap__of(_1568406, _1568408), hAPP(hAPP(c_List_Omap(tc_prod(_1568406, _1568410), tc_prod(_1568406, _1568408)), hAPP(c_Product__Type_Oprod_Oprod__case(_1568406, _1568410, tc_prod(_1568406, _1568408)), hAPP(hAPP(c_COMBC(_1568406, tc_fun(_1568410, _1568408), tc_fun(_1568410, tc_prod(_1568406, _1568408))), hAPP(hAPP(c_COMBB(tc_fun(_1568408, tc_prod(_1568406, _1568408)), tc_fun(tc_fun(_1568410, _1568408), tc_fun(_1568410, tc_prod(_1568406, _1568408))), _1568406), c_COMBB(_1568408, tc_prod(_1568406, _1568408), _1568410)), c_Product__Type_OPair(_1568406, _1568408))), _1568412))), _1568414)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1568410), tc_Option_Ooption(_1568408), _1568406, hAPP(c_Option_Omap(_1568410, _1568408), _1568412)), hAPP(c_Map_Omap__of(_1568406, _1568410), _1568414)))], (40261 ^ _777081) ^ [_1568549, _1568551, _1568553, _1568555] : [-(hAPP(c_Map_Omap__of(_1568549, _1568551), hAPP(hAPP(c_List_Omap(_1568549, tc_prod(_1568549, _1568551)), hAPP(hAPP(c_COMBS(_1568549, _1568551, tc_prod(_1568549, _1568551)), c_Product__Type_OPair(_1568549, _1568551)), _1568553)), _1568555)) = c_Map_Orestrict__map(_1568549, _1568551, hAPP(c_Fun_Ocomp(_1568551, tc_Option_Ooption(_1568551), _1568549, c_Option_Ooption_OSome(_1568551)), _1568553), hAPP(c_List_Oset(_1568549), _1568555)))], (40263 ^ _777081) ^ [] : [-(c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))], (40265 ^ _777081) ^ [_1568652, _1568654] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1568652), hAPP(c_List_Oset(_1568652), _1568654))))], (40267 ^ _777081) ^ [_1568686, _1568688, _1568690, _1568692] : [-(hAPP(c_List_Oset(_1568686), hAPP(hAPP(c_List_Omap(_1568688, _1568686), _1568690), _1568692)) = hAPP(c_Set_Oimage(_1568688, _1568686, _1568690), hAPP(c_List_Oset(_1568688), _1568692)))], (40279 ^ _777081) ^ [_1569009, _1569011, _1569013, _1569015, _1569017] : [40281 ^ _777081 : [(40282 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1569009), 40280 ^ [_1569009, _1569011, _1569013, _1569015, _1569017]), hAPP(c_List_Oset(_1569009), _1569015))))], (40284 ^ _777081) ^ [] : [hAPP(_1569013, 40280 ^ [_1569009, _1569011, _1569013, _1569015, _1569017]) = hAPP(_1569017, 40280 ^ [_1569009, _1569011, _1569013, _1569015, _1569017])]], -(hAPP(hAPP(c_List_Omap(_1569009, _1569011), _1569013), _1569015) = hAPP(hAPP(c_List_Omap(_1569009, _1569011), _1569017), _1569015))], (40269 ^ _777081) ^ [_1568765, _1568767, _1568769, _1568771, _1568773] : [hAPP(hAPP(c_List_Omap(_1568765, _1568767), _1568769), _1568771) = hAPP(hAPP(c_List_Omap(_1568765, _1568767), _1568773), _1568771), 40272 ^ _777081 : [(40273 ^ _777081) ^ [_1568888] : [hBOOL(hAPP(hAPP(c_member(_1568765), _1568888), hAPP(c_List_Oset(_1568765), _1568771))), -(hAPP(_1568769, _1568888) = hAPP(_1568773, _1568888))]]], (40288 ^ _777081) ^ [_1569275] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1569275)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1569275), tc_HOL_Obool))))], (40300 ^ _777081) ^ [] : [40302 ^ _777081 : [(40303 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 40301 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))], (40305 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), 40301 ^ []))]], -(c_Com_OWT__bodies)], (40290 ^ _777081) ^ [] : [c_Com_OWT__bodies, 40293 ^ _777081 : [(40294 ^ _777081) ^ [_1569357] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1569357), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), _1569357)))]]], (40309 ^ _777081) ^ [_1569548, _1569550, _1569552, _1569554, _1569556] : [hAPP(hAPP(c_List_Omap(_1569548, _1569550), _1569552), _1569554) = hAPP(hAPP(c_List_Omap(_1569548, _1569550), _1569552), _1569556), c_Fun_Oinj__on(_1569548, _1569550, _1569552, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1569548, tc_HOL_Obool)), hAPP(c_List_Oset(_1569548), _1569554)), hAPP(c_List_Oset(_1569548), _1569556))), -(_1569554 = _1569556)], (40319 ^ _777081) ^ [_1569771, _1569773, _1569775, _1569777, _1569779] : [c_Fun_Oinj__on(_1569771, _1569773, _1569775, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1569771, tc_HOL_Obool)), hAPP(c_List_Oset(_1569771), _1569777)), hAPP(c_List_Oset(_1569771), _1569779))), 40322 ^ _777081 : [(40323 ^ _777081) ^ [] : [hAPP(hAPP(c_List_Omap(_1569771, _1569773), _1569775), _1569777) = hAPP(hAPP(c_List_Omap(_1569771, _1569773), _1569775), _1569779), -(_1569777 = _1569779)], (40329 ^ _777081) ^ [] : [_1569777 = _1569779, -(hAPP(hAPP(c_List_Omap(_1569771, _1569773), _1569775), _1569777) = hAPP(hAPP(c_List_Omap(_1569771, _1569773), _1569775), _1569779))]]], (40335 ^ _777081) ^ [_1570092, _1570094, _1570096, _1570098, _1570100, _1570102] : [-(hBOOL(hAPP(hAPP(c_member(_1570092), _1570094), hAPP(c_List_Oset(_1570092), _1570096)))), -(hAPP(hAPP(c_List_Omap(_1570092, _1570098), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1570092, _1570098), _1570100), _1570094), _1570102)), _1570096) = hAPP(hAPP(c_List_Omap(_1570092, _1570098), _1570100), _1570096))], (40341 ^ _777081) ^ [_1570178, _1570180, _1570182, _1570184] : [hAPP(c_Map_Omap__of(_1570178, _1570180), _1570182) = hAPP(c_Map_Omap__of(_1570178, _1570180), _1570184), -(hAPP(c_Set_Oimage(tc_prod(_1570178, _1570180), _1570178, c_Product__Type_Ofst(_1570178, _1570180)), hAPP(c_List_Oset(tc_prod(_1570178, _1570180)), _1570182)) = hAPP(c_Set_Oimage(tc_prod(_1570178, _1570180), _1570178, c_Product__Type_Ofst(_1570178, _1570180)), hAPP(c_List_Oset(tc_prod(_1570178, _1570180)), _1570184)))], (40347 ^ _777081) ^ [_1570367, _1570369, _1570371, _1570373, _1570375] : [hAPP(hAPP(c_Map_Omap__of(_1570367, _1570369), _1570371), _1570373) = hAPP(c_Option_Ooption_OSome(_1570369), _1570375), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570367, _1570369)), hAPP(hAPP(c_Product__Type_OPair(_1570367, _1570369), _1570373), _1570375)), hAPP(c_List_Oset(tc_prod(_1570367, _1570369)), _1570371))))], (40353 ^ _777081) ^ [_1570532, _1570534, _1570536, _1570538, _1570540] : [hAPP(hAPP(c_Map_Omap__of(_1570532, _1570534), _1570536), _1570538) = hAPP(c_Option_Ooption_OSome(_1570534), _1570540), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570532, _1570534)), hAPP(hAPP(c_Product__Type_OPair(_1570532, _1570534), _1570538), _1570540)), hAPP(c_List_Oset(tc_prod(_1570532, _1570534)), _1570536))))], (40359 ^ _777081) ^ [_1570697, _1570699, _1570701] : [-(c_Map_Odom(_1570697, _1570699, hAPP(c_Map_Omap__of(_1570697, _1570699), _1570701)) = hAPP(c_Set_Oimage(tc_prod(_1570697, _1570699), _1570697, c_Product__Type_Ofst(_1570697, _1570699)), hAPP(c_List_Oset(tc_prod(_1570697, _1570699)), _1570701)))], (40361 ^ _777081) ^ [_1570776, _1570778, _1570780, _1570782] : [hAPP(hAPP(c_Map_Omap__of(_1570776, _1570778), _1570780), _1570782) = c_Option_Ooption_ONone(_1570778), hBOOL(hAPP(hAPP(c_member(_1570776), _1570782), hAPP(c_Set_Oimage(tc_prod(_1570776, _1570778), _1570776, c_Product__Type_Ofst(_1570776, _1570778)), hAPP(c_List_Oset(tc_prod(_1570776, _1570778)), _1570780))))], (40367 ^ _777081) ^ [_1570930, _1570932, _1570934, _1570936] : [-(hBOOL(hAPP(hAPP(c_member(_1570930), _1570936), hAPP(c_Set_Oimage(tc_prod(_1570930, _1570932), _1570930, c_Product__Type_Ofst(_1570930, _1570932)), hAPP(c_List_Oset(tc_prod(_1570930, _1570932)), _1570934))))), -(hAPP(hAPP(c_Map_Omap__of(_1570930, _1570932), _1570934), _1570936) = c_Option_Ooption_ONone(_1570932))], (40373 ^ _777081) ^ [_1571011, _1571013, _1571015, _1571017] : [hAPP(c_List_Oset(_1571011), _1571013) = c_Map_Odom(_1571011, _1571015, _1571017), -(hAPP(c_Map_Omap__of(_1571011, _1571015), hAPP(hAPP(c_List_Omap(_1571011, tc_prod(_1571011, _1571015)), hAPP(hAPP(c_COMBS(_1571011, _1571015, tc_prod(_1571011, _1571015)), c_Product__Type_OPair(_1571011, _1571015)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1571015), _1571015, _1571011), c_Option_Othe(_1571015)), _1571017))), _1571013)) = _1571017)], (40379 ^ _777081) ^ [_1571206, _1571208, _1571210] : [hBOOL(hAPP(c_List_Odistinct(_1571206), hAPP(hAPP(c_List_Omap(tc_prod(_1571206, _1571208), _1571206), c_Product__Type_Ofst(_1571206, _1571208)), _1571210))), -(c_Map_Oran(_1571206, _1571208, hAPP(c_Map_Omap__of(_1571206, _1571208), _1571210)) = hAPP(c_Set_Oimage(tc_prod(_1571206, _1571208), _1571208, c_Product__Type_Osnd(_1571206, _1571208)), hAPP(c_List_Oset(tc_prod(_1571206, _1571208)), _1571210)))], (40385 ^ _777081) ^ [_1571385, _1571387, _1571389] : [hBOOL(hAPP(c_List_Odistinct(_1571385), hAPP(hAPP(c_List_Omap(tc_prod(_1571385, _1571387), _1571385), c_Product__Type_Ofst(_1571385, _1571387)), _1571389))), -(hAPP(c_List_Oset(tc_prod(_1571385, _1571387)), _1571389) = hAPP(c_Set_OCollect(tc_prod(_1571385, _1571387)), hAPP(c_Product__Type_Oprod_Oprod__case(_1571385, _1571387, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1571385, tc_fun(_1571387, tc_Option_Ooption(_1571387)), tc_fun(_1571387, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1571387), tc_HOL_Obool), tc_fun(tc_fun(_1571387, tc_Option_Ooption(_1571387)), tc_fun(_1571387, tc_HOL_Obool)), _1571385), c_COMBB(tc_Option_Ooption(_1571387), tc_HOL_Obool, _1571387)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1571387), tc_fun(tc_Option_Ooption(_1571387), tc_HOL_Obool), _1571385), c_fequal), hAPP(c_Map_Omap__of(_1571385, _1571387), _1571389)))), c_Option_Ooption_OSome(_1571387)))))], (40391 ^ _777081) ^ [_1571719, _1571721, _1571723, _1571725] : [hBOOL(hAPP(c_List_Odistinct(_1571719), hAPP(hAPP(c_List_Omap(_1571721, _1571719), _1571723), _1571725))), 40394 ^ _777081 : [(40395 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1571721), _1571725)))], (40397 ^ _777081) ^ [] : [-(c_Fun_Oinj__on(_1571721, _1571719, _1571723, hAPP(c_List_Oset(_1571721), _1571725)))]]], (40399 ^ _777081) ^ [_1571870, _1571872, _1571874, _1571876] : [-(hBOOL(hAPP(c_List_Odistinct(_1571870), hAPP(hAPP(c_List_Omap(_1571872, _1571870), _1571874), _1571876)))), hBOOL(hAPP(c_List_Odistinct(_1571872), _1571876)), c_Fun_Oinj__on(_1571872, _1571870, _1571874, hAPP(c_List_Oset(_1571872), _1571876))], (40409 ^ _777081) ^ [_1572057, _1572059, _1572061, _1572063] : [hBOOL(hAPP(c_List_Odistinct(_1572057), hAPP(hAPP(c_List_Omap(tc_prod(_1572057, _1572059), _1572057), c_Product__Type_Ofst(_1572057, _1572059)), _1572061))), hBOOL(hAPP(c_List_Odistinct(_1572057), hAPP(hAPP(c_List_Omap(tc_prod(_1572057, _1572059), _1572057), c_Product__Type_Ofst(_1572057, _1572059)), _1572063))), 40416 ^ _777081 : [(40417 ^ _777081) ^ [] : [hAPP(c_Map_Omap__of(_1572057, _1572059), _1572061) = hAPP(c_Map_Omap__of(_1572057, _1572059), _1572063), -(hAPP(c_List_Oset(tc_prod(_1572057, _1572059)), _1572061) = hAPP(c_List_Oset(tc_prod(_1572057, _1572059)), _1572063))], (40423 ^ _777081) ^ [] : [hAPP(c_List_Oset(tc_prod(_1572057, _1572059)), _1572061) = hAPP(c_List_Oset(tc_prod(_1572057, _1572059)), _1572063), -(hAPP(c_Map_Omap__of(_1572057, _1572059), _1572061) = hAPP(c_Map_Omap__of(_1572057, _1572059), _1572063))]]], (40429 ^ _777081) ^ [_1572492, _1572494, _1572496, _1572498, _1572500] : [hBOOL(hAPP(c_List_Odistinct(_1572492), hAPP(hAPP(c_List_Omap(tc_prod(_1572492, _1572494), _1572492), c_Product__Type_Ofst(_1572492, _1572494)), _1572496))), 40432 ^ _777081 : [(40433 ^ _777081) ^ [] : [hAPP(c_Option_Ooption_OSome(_1572494), _1572498) = hAPP(hAPP(c_Map_Omap__of(_1572492, _1572494), _1572496), _1572500), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572492, _1572494)), hAPP(hAPP(c_Product__Type_OPair(_1572492, _1572494), _1572500), _1572498)), hAPP(c_List_Oset(tc_prod(_1572492, _1572494)), _1572496))))], (40439 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572492, _1572494)), hAPP(hAPP(c_Product__Type_OPair(_1572492, _1572494), _1572500), _1572498)), hAPP(c_List_Oset(tc_prod(_1572492, _1572494)), _1572496))), -(hAPP(c_Option_Ooption_OSome(_1572494), _1572498) = hAPP(hAPP(c_Map_Omap__of(_1572492, _1572494), _1572496), _1572500))]]], (40445 ^ _777081) ^ [_1572878, _1572880, _1572882, _1572884, _1572886] : [hBOOL(hAPP(c_List_Odistinct(_1572878), hAPP(hAPP(c_List_Omap(tc_prod(_1572878, _1572880), _1572878), c_Product__Type_Ofst(_1572878, _1572880)), _1572882))), 40448 ^ _777081 : [(40449 ^ _777081) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1572878, _1572880), _1572882), _1572884) = hAPP(c_Option_Ooption_OSome(_1572880), _1572886), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572878, _1572880)), hAPP(hAPP(c_Product__Type_OPair(_1572878, _1572880), _1572884), _1572886)), hAPP(c_List_Oset(tc_prod(_1572878, _1572880)), _1572882))))], (40455 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572878, _1572880)), hAPP(hAPP(c_Product__Type_OPair(_1572878, _1572880), _1572884), _1572886)), hAPP(c_List_Oset(tc_prod(_1572878, _1572880)), _1572882))), -(hAPP(hAPP(c_Map_Omap__of(_1572878, _1572880), _1572882), _1572884) = hAPP(c_Option_Ooption_OSome(_1572880), _1572886))]]], (40461 ^ _777081) ^ [_1573264, _1573266, _1573268, _1573270, _1573272] : [hBOOL(hAPP(c_List_Odistinct(_1573264), hAPP(hAPP(c_List_Omap(tc_prod(_1573264, _1573266), _1573264), c_Product__Type_Ofst(_1573264, _1573266)), _1573268))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1573264, _1573266)), hAPP(hAPP(c_Product__Type_OPair(_1573264, _1573266), _1573270), _1573272)), hAPP(c_List_Oset(tc_prod(_1573264, _1573266)), _1573268))), -(hAPP(hAPP(c_Map_Omap__of(_1573264, _1573266), _1573268), _1573270) = hAPP(c_Option_Ooption_OSome(_1573266), _1573272))], (40471 ^ _777081) ^ [_1573525, _1573527] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1573525, _1573527) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1573525), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1573527), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (40473 ^ _777081) ^ [_1573572, _1573574, _1573576, _1573578, _1573580] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573572, _1573574)), hAPP(hAPP(c_Product__Type_OPair(_1573572, _1573574), _1573576), _1573578)), hAPP(c_List_Oset(tc_prod(_1573572, _1573574)), _1573580))), -(hAPP(hAPP(c_Map_Omap__of(_1573572, _1573574), _1573580), _1573576) = hAPP(c_Option_Ooption_OSome(_1573574), 40476 ^ [_1573572, _1573574, _1573576, _1573578, _1573580]))], (40480 ^ _777081) ^ [_1573755, _1573757] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1573755, _1573757)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1573755, _1573757))], (40482 ^ _777081) ^ [_1573790, _1573792] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1573790, _1573792) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1573790, _1573792)))], (40484 ^ _777081) ^ [_1573825, _1573827] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1573825, _1573827))))], (40486 ^ _777081) ^ [_1573855, _1573857] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1573855), _1573857) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1573855, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1573857), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (40488 ^ _777081) ^ [_1573898, _1573900] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1573898, _1573900) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1573898), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1573900)))], (40490 ^ _777081) ^ [_1573951] : [c_List_Onat__list(_1573951), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1573951)))], (40496 ^ _777081) ^ [_1574024] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1574024)), -(c_List_Onat__list(_1574024))], (40502 ^ _777081) ^ [_1574103, _1574105, _1574107] : [hBOOL(hAPP(c_List_Odistinct(_1574103), _1574105)), -(hAPP(c_List_Oset(_1574103), c_List_Oremove1(_1574103, _1574107, _1574105)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1574103, tc_HOL_Obool)), hAPP(c_List_Oset(_1574103), _1574105)), hAPP(hAPP(c_Set_Oinsert(_1574103), _1574107), c_Orderings_Obot__class_Obot(tc_fun(_1574103, tc_HOL_Obool)))))], (40508 ^ _777081) ^ [_1574266, _1574268, _1574270, _1574272] : [-(c_List_Oremove1(_1574266, _1574268, c_List_Oremove1(_1574266, _1574270, _1574272)) = c_List_Oremove1(_1574266, _1574270, c_List_Oremove1(_1574266, _1574268, _1574272)))], (40510 ^ _777081) ^ [_1574311, _1574313, _1574315] : [hBOOL(hAPP(c_List_Odistinct(_1574311), _1574313)), -(hBOOL(hAPP(c_List_Odistinct(_1574311), c_List_Oremove1(_1574311, _1574315, _1574313))))], (40516 ^ _777081) ^ [_1574413, _1574415, _1574417, _1574419] : [-(_1574413 = _1574415), 40519 ^ _777081 : [(40520 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1574417), _1574413), hAPP(c_List_Oset(_1574417), c_List_Oremove1(_1574417, _1574415, _1574419)))), -(hBOOL(hAPP(hAPP(c_member(_1574417), _1574413), hAPP(c_List_Oset(_1574417), _1574419))))], (40526 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1574417), _1574413), hAPP(c_List_Oset(_1574417), _1574419))), -(hBOOL(hAPP(hAPP(c_member(_1574417), _1574413), hAPP(c_List_Oset(_1574417), c_List_Oremove1(_1574417, _1574415, _1574419)))))]]], (40532 ^ _777081) ^ [_1574713, _1574715, _1574717, _1574719] : [-(hBOOL(hAPP(hAPP(c_member(_1574713), _1574715), hAPP(c_List_Oset(_1574713), _1574717)))), hBOOL(hAPP(hAPP(c_member(_1574713), _1574715), hAPP(c_List_Oset(_1574713), c_List_Oremove1(_1574713, _1574719, _1574717))))], (40538 ^ _777081) ^ [_1574833, _1574835, _1574837] : [-(hBOOL(hAPP(hAPP(c_member(_1574833), _1574835), hAPP(c_List_Oset(_1574833), _1574837)))), -(c_List_Oremove1(_1574833, _1574835, _1574837) = _1574837)], (40544 ^ _777081) ^ [_1574887, _1574889, _1574891] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1574887, tc_HOL_Obool)), hAPP(c_List_Oset(_1574887), c_List_Oremove1(_1574887, _1574889, _1574891))), hAPP(c_List_Oset(_1574887), _1574891))))], (40546 ^ _777081) ^ [_1574938, _1574940, _1574942] : [class_Orderings_Olinorder(_1574938), hBOOL(hAPP(c_Finite__Set_Ofinite(_1574938), _1574940)), -(c_List_Olinorder__class_Osorted__list__of__set(_1574938, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1574938, tc_HOL_Obool)), _1574940), hAPP(hAPP(c_Set_Oinsert(_1574938), _1574942), c_Orderings_Obot__class_Obot(tc_fun(_1574938, tc_HOL_Obool))))) = c_List_Oremove1(_1574938, _1574942, c_List_Olinorder__class_Osorted__list__of__set(_1574938, _1574940)))], (40556 ^ _777081) ^ [_1575163, _1575165, _1575167, _1575169, _1575171] : [hBOOL(hAPP(hAPP(c_member(_1575163), _1575165), hAPP(c_List_Oset(_1575163), _1575167))), -(hAPP(hAPP(c_Map_Omap__of(_1575163, _1575169), hAPP(hAPP(c_List_Ozip(_1575163, _1575169), _1575167), hAPP(hAPP(c_List_Omap(_1575163, _1575169), _1575171), _1575167))), _1575165) = hAPP(c_Option_Ooption_OSome(_1575169), hAPP(_1575171, _1575165)))], (40562 ^ _777081) ^ [_1575334, _1575336, _1575338, _1575340, _1575342] : [-(hBOOL(hAPP(hAPP(c_member(_1575334), _1575336), hAPP(c_List_Oset(_1575334), _1575338)))), -(hAPP(hAPP(c_Map_Omap__of(_1575334, _1575340), hAPP(hAPP(c_List_Ozip(_1575334, _1575340), _1575338), hAPP(hAPP(c_List_Omap(_1575334, _1575340), _1575342), _1575338))), _1575336) = c_Option_Ooption_ONone(_1575340))], (40568 ^ _777081) ^ [_1575419, _1575421, _1575423, _1575425] : [hBOOL(hAPP(c_List_Odistinct(_1575419), _1575421)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1575419, _1575423)), hAPP(hAPP(c_List_Ozip(_1575419, _1575423), _1575421), _1575425))))], (40574 ^ _777081) ^ [_1575540, _1575542, _1575544, _1575546] : [hBOOL(hAPP(c_List_Odistinct(_1575540), _1575542)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1575544, _1575540)), hAPP(hAPP(c_List_Ozip(_1575544, _1575540), _1575546), _1575542))))], (40580 ^ _777081) ^ [_1575661, _1575663] : [-(hAPP(hAPP(c_List_Ozip(_1575661, _1575661), _1575663), _1575663) = hAPP(hAPP(c_List_Omap(_1575661, tc_prod(_1575661, _1575661)), hAPP(hAPP(c_COMBS(_1575661, _1575661, tc_prod(_1575661, _1575661)), c_Product__Type_OPair(_1575661, _1575661)), c_COMBI(_1575661))), _1575663))], (40582 ^ _777081) ^ [_1575725, _1575727, _1575729] : [-(hAPP(hAPP(c_List_Ozip(_1575725, _1575727), hAPP(hAPP(c_List_Omap(tc_prod(_1575725, _1575727), _1575725), c_Product__Type_Ofst(_1575725, _1575727)), _1575729)), hAPP(hAPP(c_List_Omap(tc_prod(_1575725, _1575727), _1575727), c_Product__Type_Osnd(_1575725, _1575727)), _1575729)) = _1575729)], (40584 ^ _777081) ^ [_1575791, _1575793, _1575795, _1575797, _1575799, _1575801, _1575803, _1575805] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1575791, _1575793), _1575795), _1575797), hAPP(hAPP(c_List_Ozip(_1575791, _1575793), _1575799), hAPP(hAPP(c_List_Omap(_1575801, _1575793), _1575803), _1575805))) = hAPP(hAPP(c_List_Omap(tc_prod(_1575791, _1575801), _1575795), hAPP(c_Product__Type_Oprod_Oprod__case(_1575791, _1575801, _1575795), hAPP(hAPP(c_COMBB(tc_fun(_1575801, tc_prod(_1575791, _1575793)), tc_fun(_1575801, _1575795), _1575791), hAPP(c_COMBB(tc_prod(_1575791, _1575793), _1575795, _1575801), _1575797)), hAPP(hAPP(c_COMBC(_1575791, tc_fun(_1575801, _1575793), tc_fun(_1575801, tc_prod(_1575791, _1575793))), hAPP(hAPP(c_COMBB(tc_fun(_1575793, tc_prod(_1575791, _1575793)), tc_fun(tc_fun(_1575801, _1575793), tc_fun(_1575801, tc_prod(_1575791, _1575793))), _1575791), c_COMBB(_1575793, tc_prod(_1575791, _1575793), _1575801)), c_Product__Type_OPair(_1575791, _1575793))), _1575803)))), hAPP(hAPP(c_List_Ozip(_1575791, _1575801), _1575799), _1575805)))], (40586 ^ _777081) ^ [_1575972, _1575974, _1575976, _1575978, _1575980, _1575982, _1575984, _1575986] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1575972, _1575974), _1575976), _1575978), hAPP(hAPP(c_List_Ozip(_1575972, _1575974), hAPP(hAPP(c_List_Omap(_1575980, _1575972), _1575982), _1575984)), _1575986)) = hAPP(hAPP(c_List_Omap(tc_prod(_1575980, _1575974), _1575976), hAPP(c_Product__Type_Oprod_Oprod__case(_1575980, _1575974, _1575976), hAPP(hAPP(c_COMBB(tc_fun(_1575974, tc_prod(_1575972, _1575974)), tc_fun(_1575974, _1575976), _1575980), hAPP(c_COMBB(tc_prod(_1575972, _1575974), _1575976, _1575974), _1575978)), hAPP(hAPP(c_COMBB(_1575972, tc_fun(_1575974, tc_prod(_1575972, _1575974)), _1575980), c_Product__Type_OPair(_1575972, _1575974)), _1575982)))), hAPP(hAPP(c_List_Ozip(_1575980, _1575974), _1575984), _1575986)))], (40588 ^ _777081) ^ [_1576115, _1576117, _1576119, _1576121, _1576123, _1576125] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576115, _1576117)), hAPP(hAPP(c_Product__Type_OPair(_1576115, _1576117), _1576119), _1576121)), hAPP(c_List_Oset(tc_prod(_1576115, _1576117)), hAPP(hAPP(c_List_Ozip(_1576115, _1576117), _1576123), _1576125)))), 40591 ^ _777081 : [(40592 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576115), _1576119), hAPP(c_List_Oset(_1576115), _1576123))))], (40594 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576117), _1576121), hAPP(c_List_Oset(_1576117), _1576125))))]]], (40596 ^ _777081) ^ [_1576350, _1576352, _1576354, _1576356, _1576358, _1576360] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576350, _1576352)), hAPP(hAPP(c_Product__Type_OPair(_1576350, _1576352), _1576354), _1576356)), hAPP(c_List_Oset(tc_prod(_1576350, _1576352)), hAPP(hAPP(c_List_Ozip(_1576350, _1576352), _1576358), _1576360)))), -(hBOOL(hAPP(hAPP(c_member(_1576352), _1576356), hAPP(c_List_Oset(_1576352), _1576360))))], (40602 ^ _777081) ^ [_1576531, _1576533, _1576535, _1576537, _1576539, _1576541] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576531, _1576533)), hAPP(hAPP(c_Product__Type_OPair(_1576531, _1576533), _1576535), _1576537)), hAPP(c_List_Oset(tc_prod(_1576531, _1576533)), hAPP(hAPP(c_List_Ozip(_1576531, _1576533), _1576539), _1576541)))), -(hBOOL(hAPP(hAPP(c_member(_1576531), _1576535), hAPP(c_List_Oset(_1576531), _1576539))))], (40608 ^ _777081) ^ [_1576733, _1576735, _1576737, _1576739] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576733, _1576733)), hAPP(hAPP(c_Product__Type_OPair(_1576733, _1576733), _1576735), _1576737)), hAPP(c_List_Oset(tc_prod(_1576733, _1576733)), hAPP(hAPP(c_List_Ozip(_1576733, _1576733), _1576739), _1576739)))), 40611 ^ _777081 : [(40612 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1576733), _1576735), hAPP(c_List_Oset(_1576733), _1576739))))], (40614 ^ _777081) ^ [] : [-(_1576735 = _1576737)]]], (40616 ^ _777081) ^ [_1576932, _1576934, _1576936, _1576938] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576932, _1576932)), hAPP(hAPP(c_Product__Type_OPair(_1576932, _1576932), _1576934), _1576936)), hAPP(c_List_Oset(tc_prod(_1576932, _1576932)), hAPP(hAPP(c_List_Ozip(_1576932, _1576932), _1576938), _1576938))))), hBOOL(hAPP(hAPP(c_member(_1576932), _1576934), hAPP(c_List_Oset(_1576932), _1576938))), _1576934 = _1576936], (40626 ^ _777081) ^ [_1577167, _1577169, _1577171, _1577173, _1577175, _1577177] : [-(hAPP(hAPP(c_List_Ozip(_1577167, _1577169), _1577171), hAPP(hAPP(c_List_Omap(_1577173, _1577169), _1577175), _1577177)) = hAPP(hAPP(c_List_Omap(tc_prod(_1577167, _1577173), tc_prod(_1577167, _1577169)), hAPP(c_Product__Type_Oprod_Oprod__case(_1577167, _1577173, tc_prod(_1577167, _1577169)), hAPP(hAPP(c_COMBC(_1577167, tc_fun(_1577173, _1577169), tc_fun(_1577173, tc_prod(_1577167, _1577169))), hAPP(hAPP(c_COMBB(tc_fun(_1577169, tc_prod(_1577167, _1577169)), tc_fun(tc_fun(_1577173, _1577169), tc_fun(_1577173, tc_prod(_1577167, _1577169))), _1577167), c_COMBB(_1577169, tc_prod(_1577167, _1577169), _1577173)), c_Product__Type_OPair(_1577167, _1577169))), _1577175))), hAPP(hAPP(c_List_Ozip(_1577167, _1577173), _1577171), _1577177)))], (40628 ^ _777081) ^ [_1577309, _1577311, _1577313, _1577315, _1577317, _1577319] : [-(hAPP(hAPP(c_List_Ozip(_1577309, _1577311), hAPP(hAPP(c_List_Omap(_1577313, _1577309), _1577315), _1577317)), _1577319) = hAPP(hAPP(c_List_Omap(tc_prod(_1577313, _1577311), tc_prod(_1577309, _1577311)), hAPP(c_Product__Type_Oprod_Oprod__case(_1577313, _1577311, tc_prod(_1577309, _1577311)), hAPP(hAPP(c_COMBB(_1577309, tc_fun(_1577311, tc_prod(_1577309, _1577311)), _1577313), c_Product__Type_OPair(_1577309, _1577311)), _1577315))), hAPP(hAPP(c_List_Ozip(_1577313, _1577311), _1577317), _1577319)))], (40630 ^ _777081) ^ [_1577413, _1577415, _1577417, _1577419, _1577421, _1577423, _1577425, _1577427] : [-(hAPP(hAPP(c_List_Ozip(_1577413, _1577415), hAPP(hAPP(c_List_Omap(_1577417, _1577413), _1577419), _1577421)), hAPP(hAPP(c_List_Omap(_1577423, _1577415), _1577425), _1577427)) = hAPP(hAPP(c_List_Omap(tc_prod(_1577417, _1577423), tc_prod(_1577413, _1577415)), hAPP(c_Product__Type_Oprod_Oprod__case(_1577417, _1577423, tc_prod(_1577413, _1577415)), hAPP(hAPP(c_COMBC(_1577417, tc_fun(_1577423, _1577415), tc_fun(_1577423, tc_prod(_1577413, _1577415))), hAPP(hAPP(c_COMBB(tc_fun(_1577415, tc_prod(_1577413, _1577415)), tc_fun(tc_fun(_1577423, _1577415), tc_fun(_1577423, tc_prod(_1577413, _1577415))), _1577417), c_COMBB(_1577415, tc_prod(_1577413, _1577415), _1577423)), hAPP(hAPP(c_COMBB(_1577413, tc_fun(_1577415, tc_prod(_1577413, _1577415)), _1577417), c_Product__Type_OPair(_1577413, _1577415)), _1577419))), _1577425))), hAPP(hAPP(c_List_Ozip(_1577417, _1577423), _1577421), _1577427)))], (40632 ^ _777081) ^ [_1577584, _1577586, _1577588] : [class_Orderings_Olinorder(_1577584), hBOOL(hAPP(c_Finite__Set_Ofinite(_1577584), _1577586)), -(c_List_Olinorder__class_Osorted__list__of__set(_1577584, hAPP(hAPP(c_Set_Oinsert(_1577584), _1577588), _1577586)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1577584, _1577584, c_COMBI(_1577584)), _1577588), c_List_Olinorder__class_Osorted__list__of__set(_1577584, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1577584, tc_HOL_Obool)), _1577586), hAPP(hAPP(c_Set_Oinsert(_1577584), _1577588), c_Orderings_Obot__class_Obot(tc_fun(_1577584, tc_HOL_Obool)))))))], (40642 ^ _777081) ^ [_1577823, _1577825, _1577827, _1577829, _1577831, _1577833, _1577835, _1577837] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577823)), _1577825) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577827)), _1577829), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577823)), _1577831) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577827)), _1577829), -(hBOOL(hAPP(hAPP(c_member(_1577827), _1577833), hAPP(c_List_Oset(_1577827), _1577829)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1577827, tc_Option_Ooption(_1577823)), hAPP(c_Map_Omap__of(_1577827, _1577823), hAPP(hAPP(c_List_Ozip(_1577827, _1577823), _1577829), _1577825))), _1577833), hAPP(c_Option_Ooption_OSome(_1577823), _1577835)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1577827, tc_Option_Ooption(_1577823)), hAPP(c_Map_Omap__of(_1577827, _1577823), hAPP(hAPP(c_List_Ozip(_1577827, _1577823), _1577829), _1577831))), _1577833), hAPP(c_Option_Ooption_OSome(_1577823), _1577837)), -(hAPP(c_Map_Omap__of(_1577827, _1577823), hAPP(hAPP(c_List_Ozip(_1577827, _1577823), _1577829), _1577825)) = hAPP(c_Map_Omap__of(_1577827, _1577823), hAPP(hAPP(c_List_Ozip(_1577827, _1577823), _1577829), _1577831)))], (40660 ^ _777081) ^ [_1578383, _1578385, _1578387, _1578389] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1578383, _1578385))), hAPP(hAPP(c_List_Ozip(_1578383, _1578385), _1578387), _1578389)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578383)), _1578387)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578385)), _1578389)))], (40662 ^ _777081) ^ [_1578451, _1578453, _1578455, _1578457, _1578459] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1578451), tc_List_Olist(_1578451))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1578451), tc_List_Olist(_1578451)), _1578453), _1578455)), hAPP(c_List_Olexn(_1578451, _1578457), _1578459))), 40665 ^ _777081 : [(40666 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578451)), _1578453) = _1578459)], (40668 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578451)), _1578455) = _1578459)]]], (40670 ^ _777081) ^ [_1578654, _1578656, _1578658, _1578660, _1578662] : [class_Orderings_Olinorder(_1578654), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578656)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1578656, _1578654, _1578658), _1578660), _1578662)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578656)), _1578662)))], (40676 ^ _777081) ^ [_1578788, _1578790, _1578792] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578788)), _1578790) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1578788)), _1578792)), _1578790 = _1578792], (40682 ^ _777081) ^ [_1578880, _1578882, _1578884, _1578886] : [class_Orderings_Olinorder(_1578880), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1578880, _1578880, c_COMBI(_1578880)), _1578882), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1578880, _1578880, c_COMBI(_1578880)), _1578884), _1578886)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1578880, _1578880, c_COMBI(_1578880)), _1578884), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1578880, _1578880, c_COMBI(_1578880)), _1578882), _1578886)))], (40688 ^ _777081) ^ [_1579055, _1579057, _1579059, _1579061, _1579063, _1579065] : [class_Orderings_Olinorder(_1579055), -(hAPP(_1579057, _1579059) = hAPP(_1579057, _1579061)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1579063, _1579055, _1579057), _1579061), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1579063, _1579055, _1579057), _1579059), _1579065)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1579063, _1579055, _1579057), _1579059), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1579063, _1579055, _1579057), _1579061), _1579065)))], (40698 ^ _777081) ^ [_1579245, _1579247, _1579249, _1579251, _1579253, _1579255, _1579257] : [hAPP(hAPP(c_List_Omap(_1579245, _1579247), _1579249), _1579251) = hAPP(hAPP(c_List_Omap(_1579253, _1579247), _1579255), _1579257), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579245)), _1579251) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579253)), _1579257))], (40704 ^ _777081) ^ [_1579396, _1579398, _1579400, _1579402] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579396)), hAPP(hAPP(c_List_Omap(_1579398, _1579396), _1579400), _1579402)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579398)), _1579402))], (40706 ^ _777081) ^ [_1579448, _1579450, _1579452] : [class_Orderings_Olinorder(_1579448), -(c_List_Oremove1(_1579448, _1579450, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1579448, _1579448, c_COMBI(_1579448)), _1579450), _1579452)) = _1579452)], (40712 ^ _777081) ^ [_1579557, _1579559, _1579561, _1579563, _1579565] : [class_Orderings_Olinorder(_1579557), -(hAPP(c_List_Oset(_1579559), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1579559, _1579557, _1579561), _1579563), _1579565)) = hAPP(hAPP(c_Set_Oinsert(_1579559), _1579563), hAPP(c_List_Oset(_1579559), _1579565)))], (40718 ^ _777081) ^ [_1579694, _1579696] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1579694), hAPP(c_List_Oset(_1579694), _1579696))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579694)), _1579696))))], (40720 ^ _777081) ^ [_1579741, _1579743] : [hAPP(c_Finite__Set_Ocard(_1579741), hAPP(c_List_Oset(_1579741), _1579743)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579741)), _1579743), -(hBOOL(hAPP(c_List_Odistinct(_1579741), _1579743)))], (40726 ^ _777081) ^ [_1579860, _1579862] : [hBOOL(hAPP(c_List_Odistinct(_1579860), _1579862)), -(hAPP(c_Finite__Set_Ocard(_1579860), hAPP(c_List_Oset(_1579860), _1579862)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579860)), _1579862))], (40732 ^ _777081) ^ [_1579979, _1579981, _1579983, _1579985, _1579987] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579979)), _1579981) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579983)), _1579985), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579979)), _1579987) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1579983)), _1579985), hBOOL(hAPP(c_List_Odistinct(_1579983), _1579985)), hAPP(c_Map_Omap__of(_1579983, _1579979), hAPP(hAPP(c_List_Ozip(_1579983, _1579979), _1579985), _1579981)) = hAPP(c_Map_Omap__of(_1579983, _1579979), hAPP(hAPP(c_List_Ozip(_1579983, _1579979), _1579985), _1579987)), -(_1579981 = _1579987)], (40750 ^ _777081) ^ [_1580360, _1580362, _1580364, _1580366] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1580360)), _1580362) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1580364)), _1580366), -(hAPP(hAPP(c_List_Omap(tc_prod(_1580360, _1580364), _1580360), c_Product__Type_Ofst(_1580360, _1580364)), hAPP(hAPP(c_List_Ozip(_1580360, _1580364), _1580362), _1580366)) = _1580362)], (40756 ^ _777081) ^ [_1580517, _1580519, _1580521, _1580523] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1580517)), _1580519) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1580521)), _1580523), -(hAPP(hAPP(c_List_Omap(tc_prod(_1580517, _1580521), _1580521), c_Product__Type_Osnd(_1580517, _1580521)), hAPP(hAPP(c_List_Ozip(_1580517, _1580521), _1580519), _1580523)) = _1580523)], (40762 ^ _777081) ^ [_1580674, _1580676, _1580678, _1580680, _1580682] : [class_Orderings_Olinorder(_1580674), 40765 ^ _777081 : [(40766 ^ _777081) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1580676), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1580676, _1580674, _1580678), _1580680), _1580682))), 40769 ^ _777081 : [(40770 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1580676), _1580680), hAPP(c_List_Oset(_1580676), _1580682)))], (40772 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1580676), _1580682)))]]], (40774 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1580676), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1580676, _1580674, _1580678), _1580680), _1580682)))), -(hBOOL(hAPP(hAPP(c_member(_1580676), _1580680), hAPP(c_List_Oset(_1580676), _1580682)))), hBOOL(hAPP(c_List_Odistinct(_1580676), _1580682))]]], (40784 ^ _777081) ^ [_1581076, _1581078, _1581080] : [hBOOL(hAPP(hAPP(c_member(_1581076), _1581078), hAPP(c_List_Oset(_1581076), _1581080))), -(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(_1581076)), _1581080))))], (40790 ^ _777081) ^ [_1581197, _1581199, _1581201, _1581203, _1581205] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1581197)), _1581199) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1581201)), _1581203), 40793 ^ _777081 : [(40794 ^ _777081) ^ [] : [hAPP(hAPP(c_List_Ozip(_1581197, _1581201), _1581199), _1581203) = _1581205, 40797 ^ _777081 : [(40798 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1581197, _1581201), _1581197), c_Product__Type_Ofst(_1581197, _1581201)), _1581205) = _1581199)], (40800 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1581197, _1581201), _1581201), c_Product__Type_Osnd(_1581197, _1581201)), _1581205) = _1581203)]]], (40802 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1581197, _1581201), _1581199), _1581203) = _1581205), hAPP(hAPP(c_List_Omap(tc_prod(_1581197, _1581201), _1581197), c_Product__Type_Ofst(_1581197, _1581201)), _1581205) = _1581199, hAPP(hAPP(c_List_Omap(tc_prod(_1581197, _1581201), _1581201), c_Product__Type_Osnd(_1581197, _1581201)), _1581205) = _1581203]]], (40812 ^ _777081) ^ [_1581645, _1581647] : [-(c_List_Olenlex(_1581645, _1581647) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1581645), tc_List_Olist(_1581645))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1581645), tc_List_Olist(_1581645), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1581645), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1581645), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool)), tc_List_Olist(_1581645)), c_COMBS(tc_List_Olist(_1581645), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool), tc_fun(tc_List_Olist(_1581645), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1581645)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1581645)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1581645), tc_fun(tc_List_Olist(_1581645), tc_Nat_Onat), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1581645), tc_Nat_Onat), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool)), tc_List_Olist(_1581645)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1581645))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1581645)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1581645))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1581645)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1581645), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1581645), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool)), tc_List_Olist(_1581645)), c_COMBS(tc_List_Olist(_1581645), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool), tc_fun(tc_List_Olist(_1581645), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1581645)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1581645)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1581645), tc_fun(tc_List_Olist(_1581645), tc_Nat_Onat), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1581645), tc_Nat_Onat), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool)), tc_List_Olist(_1581645)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1581645))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1581645)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1581645))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1581645)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1581645), tc_fun(tc_prod(tc_List_Olist(_1581645), tc_List_Olist(_1581645)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1581645), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1581645), tc_List_Olist(_1581645)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1581645), tc_List_Olist(_1581645)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1581645), tc_HOL_Obool)), tc_List_Olist(_1581645)), c_COMBC(tc_List_Olist(_1581645), tc_fun(tc_prod(tc_List_Olist(_1581645), tc_List_Olist(_1581645)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1581645), tc_prod(tc_List_Olist(_1581645), tc_List_Olist(_1581645))), tc_fun(tc_List_Olist(_1581645), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1581645), tc_List_Olist(_1581645)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1581645)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1581645), tc_List_Olist(_1581645)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1581645), tc_List_Olist(_1581645)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1581645)), c_member(tc_prod(tc_List_Olist(_1581645), tc_List_Olist(_1581645))))), c_Product__Type_OPair(tc_List_Olist(_1581645), tc_List_Olist(_1581645))))), c_List_Olex(_1581645, _1581647)))))))], (40814 ^ _777081) ^ [_1582201, _1582203] : [-(c_List_Olenlex(_1582201, _1582203) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1582201)), tc_List_Olist(_1582201)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1582201), c_Wellfounded_Oless__than, c_List_Olex(_1582201, _1582203))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1582201), tc_List_Olist(_1582201), tc_prod(tc_Nat_Onat, tc_List_Olist(_1582201))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1582201), tc_prod(tc_Nat_Onat, tc_List_Olist(_1582201))), tc_List_Olist(_1582201)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1582201))), c_Nat_Osize__class_Osize(tc_List_Olist(_1582201)))), c_COMBI(tc_List_Olist(_1582201)))))], (40816 ^ _777081) ^ [_1582309, _1582311, _1582313] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1582309), _1582311)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1582309)), hAPP(c_Set_OCollect(tc_List_Olist(_1582309)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1582309), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1582309)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1582309), tc_fun(_1582309, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1582309, tc_HOL_Obool), tc_fun(tc_fun(_1582309, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1582309)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1582309, tc_HOL_Obool))), c_List_Oset(_1582309))), _1582311))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1582309), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1582309)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1582309)))), _1582313))))))], (40822 ^ _777081) ^ [_1582630, _1582632, _1582634] : [_1582630 = _1582632, 40825 ^ _777081 : [(40826 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1582634)), _1582630) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1582634)), _1582632))], (40828 ^ _777081) ^ [_1582786] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582634, _1582634)), _1582786), hAPP(c_List_Oset(tc_prod(_1582634, _1582634)), hAPP(hAPP(c_List_Ozip(_1582634, _1582634), _1582630), _1582632)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1582634, _1582634, tc_HOL_Obool), c_fequal), _1582786)))]]], (40834 ^ _777081) ^ [_1582941, _1582943, _1582945] : [-(_1582941 = _1582943), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1582945)), _1582941) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1582945)), _1582943), 40840 ^ _777081 : [(40841 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582945, _1582945)), 40839 ^ [_1582941, _1582943, _1582945]), hAPP(c_List_Oset(tc_prod(_1582945, _1582945)), hAPP(hAPP(c_List_Ozip(_1582945, _1582945), _1582941), _1582943)))))], (40843 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1582945, _1582945, tc_HOL_Obool), c_fequal), 40839 ^ [_1582941, _1582943, _1582945]))]]], (40847 ^ _777081) ^ [_1583255, _1583257, _1583259, _1583261, _1583263] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583255)), _1583257) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583259)), _1583261), 40850 ^ _777081 : [(40851 ^ _777081) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1583255, _1583259), hAPP(hAPP(c_List_Ozip(_1583255, _1583259), _1583257), _1583261)), _1583263) = c_Option_Ooption_ONone(_1583259), hBOOL(hAPP(hAPP(c_member(_1583255), _1583263), hAPP(c_List_Oset(_1583255), _1583257)))], (40857 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1583255), _1583263), hAPP(c_List_Oset(_1583255), _1583257)))), -(hAPP(hAPP(c_Map_Omap__of(_1583255, _1583259), hAPP(hAPP(c_List_Ozip(_1583255, _1583259), _1583257), _1583261)), _1583263) = c_Option_Ooption_ONone(_1583259))]]], (40863 ^ _777081) ^ [_1583560, _1583562, _1583564, _1583566, _1583568] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583560)), _1583562) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583564)), _1583566), 40866 ^ _777081 : [(40867 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1583560), _1583568), hAPP(c_List_Oset(_1583560), _1583562))), -(hAPP(hAPP(c_Map_Omap__of(_1583560, _1583564), hAPP(hAPP(c_List_Ozip(_1583560, _1583564), _1583562), _1583566)), _1583568) = hAPP(c_Option_Ooption_OSome(_1583564), 40870 ^ [_1583560, _1583562, _1583564, _1583566, _1583568]))], (40874 ^ _777081) ^ [] : [40875 ^ _777081 : [(40876 ^ _777081) ^ [_1583852] : [hAPP(hAPP(c_Map_Omap__of(_1583560, _1583564), hAPP(hAPP(c_List_Ozip(_1583560, _1583564), _1583562), _1583566)), _1583568) = hAPP(c_Option_Ooption_OSome(_1583564), _1583852)]], -(hBOOL(hAPP(hAPP(c_member(_1583560), _1583568), hAPP(c_List_Oset(_1583560), _1583562))))]]], (40880 ^ _777081) ^ [_1583956, _1583958, _1583960] : [hBOOL(hAPP(hAPP(c_member(_1583956), _1583958), hAPP(c_List_Oset(_1583956), _1583960))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583956)), c_List_Oremove1(_1583956, _1583958, _1583960)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1583956)), _1583960)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (40886 ^ _777081) ^ [_1584101, _1584103, _1584105] : [-(hBOOL(hAPP(hAPP(c_member(_1584101), _1584103), hAPP(c_List_Oset(_1584101), _1584105)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1584101)), c_List_Oremove1(_1584101, _1584103, _1584105)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1584101)), _1584105))], (40892 ^ _777081) ^ [_1584171, _1584173, _1584175, _1584177] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1584171)), _1584173) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1584175)), _1584177), hBOOL(hAPP(c_List_Odistinct(_1584171), _1584173)), -(c_Map_Odom(_1584171, _1584175, hAPP(c_Map_Omap__of(_1584171, _1584175), hAPP(hAPP(c_List_Ozip(_1584171, _1584175), _1584173), _1584177))) = hAPP(c_List_Oset(_1584171), _1584173))], (40902 ^ _777081) ^ [_1584392, _1584394, _1584396] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1584392), _1584394)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1584392)), hAPP(c_Set_OCollect(tc_List_Olist(_1584392)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1584392), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1584392)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1584392), tc_fun(_1584392, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1584392, tc_HOL_Obool), tc_fun(tc_fun(_1584392, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1584392)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1584392, tc_HOL_Obool))), c_List_Oset(_1584392))), _1584394))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1584392), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1584392)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1584392)))), _1584396))))))], (40908 ^ _777081) ^ [_1584716, _1584718, _1584720, _1584722] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1584716), tc_List_Olist(_1584716))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1584716), tc_List_Olist(_1584716)), _1584718), _1584720)), c_List_Olistrel(_1584716, _1584722))), 40911 ^ _777081 : [(40912 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1584716)), _1584718) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1584716)), _1584720))], (40914 ^ _777081) ^ [_1585052] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584716, _1584716)), _1585052), hAPP(c_List_Oset(tc_prod(_1584716, _1584716)), hAPP(hAPP(c_List_Ozip(_1584716, _1584716), _1584718), _1584720)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1584716, _1584716, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1584716, tc_fun(tc_prod(_1584716, _1584716), tc_HOL_Obool), tc_fun(_1584716, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584716, tc_fun(tc_fun(tc_prod(_1584716, _1584716), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1584716, _1584716), tc_HOL_Obool), tc_fun(_1584716, tc_HOL_Obool)), _1584716), c_COMBC(_1584716, tc_fun(tc_prod(_1584716, _1584716), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584716, tc_prod(_1584716, _1584716)), tc_fun(_1584716, tc_fun(tc_fun(tc_prod(_1584716, _1584716), tc_HOL_Obool), tc_HOL_Obool)), _1584716), hAPP(c_COMBB(tc_prod(_1584716, _1584716), tc_fun(tc_fun(tc_prod(_1584716, _1584716), tc_HOL_Obool), tc_HOL_Obool), _1584716), c_member(tc_prod(_1584716, _1584716)))), c_Product__Type_OPair(_1584716, _1584716)))), _1584722)), _1585052)))]]], (40920 ^ _777081) ^ [_1585445, _1585447, _1585449, _1585451] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1585445), tc_List_Olist(_1585445))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1585445), tc_List_Olist(_1585445)), _1585447), _1585449)), c_List_Olistrel(_1585445, _1585451)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1585445)), _1585447) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1585445)), _1585449), 40926 ^ _777081 : [(40927 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585445, _1585445)), 40925 ^ [_1585445, _1585447, _1585449, _1585451]), hAPP(c_List_Oset(tc_prod(_1585445, _1585445)), hAPP(hAPP(c_List_Ozip(_1585445, _1585445), _1585447), _1585449)))))], (40929 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1585445, _1585445, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1585445, tc_fun(tc_prod(_1585445, _1585445), tc_HOL_Obool), tc_fun(_1585445, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585445, tc_fun(tc_fun(tc_prod(_1585445, _1585445), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585445, _1585445), tc_HOL_Obool), tc_fun(_1585445, tc_HOL_Obool)), _1585445), c_COMBC(_1585445, tc_fun(tc_prod(_1585445, _1585445), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585445, tc_prod(_1585445, _1585445)), tc_fun(_1585445, tc_fun(tc_fun(tc_prod(_1585445, _1585445), tc_HOL_Obool), tc_HOL_Obool)), _1585445), hAPP(c_COMBB(tc_prod(_1585445, _1585445), tc_fun(tc_fun(tc_prod(_1585445, _1585445), tc_HOL_Obool), tc_HOL_Obool), _1585445), c_member(tc_prod(_1585445, _1585445)))), c_Product__Type_OPair(_1585445, _1585445)))), _1585451)), 40925 ^ [_1585445, _1585447, _1585449, _1585451]))]]], (40933 ^ _777081) ^ [_1586183, _1586185, _1586187] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1586183)), c_List_Osublist(_1586183, _1586185, _1586187)) = 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(_1586183)), _1586185)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1586187)))))], (40935 ^ _777081) ^ [_1586249, _1586251, _1586253, _1586255] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1586249), tc_List_Olist(_1586249))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1586249), tc_List_Olist(_1586249)), _1586251), _1586253)), c_List_Olistrel(_1586249, _1586255))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1586249)), _1586251) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1586249)), _1586253))], (40941 ^ _777081) ^ [_1586418, _1586420, _1586422] : [hBOOL(hAPP(c_List_Odistinct(_1586418), _1586420)), -(hBOOL(hAPP(c_List_Odistinct(_1586418), c_List_Osublist(_1586418, _1586420, _1586422))))], (40947 ^ _777081) ^ [_1586521, _1586523, _1586525] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1586521, _1586521), tc_HOL_Obool)), _1586523), _1586525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1586521), tc_List_Olist(_1586521)), tc_HOL_Obool)), c_List_Olistrel(_1586521, _1586523)), c_List_Olistrel(_1586521, _1586525))))], (40953 ^ _777081) ^ [_1586672, _1586674, _1586676, _1586678] : [hBOOL(hAPP(hAPP(c_member(_1586672), _1586674), hAPP(c_List_Oset(_1586672), c_List_Osublist(_1586672, _1586676, _1586678)))), -(hBOOL(hAPP(hAPP(c_member(_1586672), _1586674), hAPP(c_List_Oset(_1586672), _1586676))))], (40959 ^ _777081) ^ [_1586808, _1586810, _1586812, _1586814] : [-(hBOOL(hAPP(hAPP(c_member(_1586808), _1586810), hAPP(c_List_Oset(_1586808), _1586812)))), hBOOL(hAPP(hAPP(c_member(_1586808), _1586810), hAPP(c_List_Oset(_1586808), c_List_Osublist(_1586808, _1586812, _1586814))))], (40965 ^ _777081) ^ [_1586932, _1586934, _1586936] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1586932, tc_HOL_Obool)), hAPP(c_List_Oset(_1586932), c_List_Osublist(_1586932, _1586934, _1586936))), hAPP(c_List_Oset(_1586932), _1586934))))], (40967 ^ _777081) ^ [_1587004, _1587006, _1587008, _1587010] : [c_List_Olistrelp(_1587004, hAPP(hAPP(c_COMBC(_1587004, tc_fun(tc_prod(_1587004, _1587004), tc_HOL_Obool), tc_fun(_1587004, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1587004, tc_fun(tc_fun(tc_prod(_1587004, _1587004), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1587004, _1587004), tc_HOL_Obool), tc_fun(_1587004, tc_HOL_Obool)), _1587004), c_COMBC(_1587004, tc_fun(tc_prod(_1587004, _1587004), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1587004, tc_prod(_1587004, _1587004)), tc_fun(_1587004, tc_fun(tc_fun(tc_prod(_1587004, _1587004), tc_HOL_Obool), tc_HOL_Obool)), _1587004), hAPP(c_COMBB(tc_prod(_1587004, _1587004), tc_fun(tc_fun(tc_prod(_1587004, _1587004), tc_HOL_Obool), tc_HOL_Obool), _1587004), c_member(tc_prod(_1587004, _1587004)))), c_Product__Type_OPair(_1587004, _1587004)))), _1587006), _1587008, _1587010), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1587004), tc_List_Olist(_1587004))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1587004), tc_List_Olist(_1587004)), _1587008), _1587010)), c_List_Olistrel(_1587004, _1587006))))], (40973 ^ _777081) ^ [_1587381, _1587383, _1587385, _1587387] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1587381), tc_List_Olist(_1587381))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1587381), tc_List_Olist(_1587381)), _1587385), _1587387)), c_List_Olistrel(_1587381, _1587383))), -(c_List_Olistrelp(_1587381, hAPP(hAPP(c_COMBC(_1587381, tc_fun(tc_prod(_1587381, _1587381), tc_HOL_Obool), tc_fun(_1587381, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1587381, tc_fun(tc_fun(tc_prod(_1587381, _1587381), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1587381, _1587381), tc_HOL_Obool), tc_fun(_1587381, tc_HOL_Obool)), _1587381), c_COMBC(_1587381, tc_fun(tc_prod(_1587381, _1587381), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1587381, tc_prod(_1587381, _1587381)), tc_fun(_1587381, tc_fun(tc_fun(tc_prod(_1587381, _1587381), tc_HOL_Obool), tc_HOL_Obool)), _1587381), hAPP(c_COMBB(tc_prod(_1587381, _1587381), tc_fun(tc_fun(tc_prod(_1587381, _1587381), tc_HOL_Obool), tc_HOL_Obool), _1587381), c_member(tc_prod(_1587381, _1587381)))), c_Product__Type_OPair(_1587381, _1587381)))), _1587383), _1587385, _1587387))], (40979 ^ _777081) ^ [_1587764, _1587766, _1587768] : [-(hAPP(c_List_Olexn(_1587764, _1587766), hAPP(c_Nat_OSuc, _1587768)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1587764), tc_List_Olist(_1587764)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1587764, tc_List_Olist(_1587764)), tc_prod(_1587764, tc_List_Olist(_1587764))), tc_prod(tc_List_Olist(_1587764), tc_List_Olist(_1587764)), c_Product__Type_Omap__pair(tc_prod(_1587764, tc_List_Olist(_1587764)), tc_List_Olist(_1587764), tc_prod(_1587764, tc_List_Olist(_1587764)), tc_List_Olist(_1587764), hAPP(c_Product__Type_Oprod_Oprod__case(_1587764, tc_List_Olist(_1587764), tc_List_Olist(_1587764)), c_List_Olist_OCons(_1587764)), hAPP(c_Product__Type_Oprod_Oprod__case(_1587764, tc_List_Olist(_1587764), tc_List_Olist(_1587764)), c_List_Olist_OCons(_1587764)))), c_Wellfounded_Olex__prod(_1587764, tc_List_Olist(_1587764), _1587766, hAPP(c_List_Olexn(_1587764, _1587766), _1587768)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1587764), tc_List_Olist(_1587764))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1587764), tc_List_Olist(_1587764), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1587764), tc_fun(tc_List_Olist(_1587764), tc_HOL_Obool), tc_fun(tc_List_Olist(_1587764), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1587764), tc_HOL_Obool), tc_fun(tc_List_Olist(_1587764), tc_HOL_Obool)), tc_List_Olist(_1587764)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1587764))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1587764)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1587764), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1587764)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1587764)))), hAPP(c_Nat_OSuc, _1587768))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1587764), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1587764)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1587764)))), hAPP(c_Nat_OSuc, _1587768)))))))], (40981 ^ _777081) ^ [_1588055, _1588057, _1588059, _1588061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588055)), _1588057)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588055)), _1588059))), _1588057 = hAPP(hAPP(c_List_Olist_OCons(_1588055), _1588061), _1588059)], (40987 ^ _777081) ^ [_1588191, _1588193, _1588195, _1588197] : [hBOOL(hAPP(hAPP(c_member(_1588191), _1588193), hAPP(c_List_Oset(_1588191), hAPP(hAPP(c_List_Olist_OCons(_1588191), _1588195), _1588197)))), -(_1588193 = _1588195), -(hBOOL(hAPP(hAPP(c_member(_1588191), _1588193), hAPP(c_List_Oset(_1588191), _1588197))))], (40997 ^ _777081) ^ [_1588349, _1588351, _1588353, _1588355, _1588357, _1588359] : [-(hAPP(hAPP(c_List_Ozip(_1588349, _1588351), hAPP(hAPP(c_List_Olist_OCons(_1588349), _1588353), _1588355)), hAPP(hAPP(c_List_Olist_OCons(_1588351), _1588357), _1588359)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1588349, _1588351)), hAPP(hAPP(c_Product__Type_OPair(_1588349, _1588351), _1588353), _1588357)), hAPP(hAPP(c_List_Ozip(_1588349, _1588351), _1588355), _1588359)))], (40999 ^ _777081) ^ [_1588436, _1588438, _1588440] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1588436, tc_HOL_Obool)), hAPP(c_List_Oset(_1588436), _1588438)), hAPP(c_List_Oset(_1588436), hAPP(hAPP(c_List_Olist_OCons(_1588436), _1588440), _1588438)))))], (41001 ^ _777081) ^ [_1588491, _1588493, _1588495] : [-(hAPP(c_List_Oset(_1588491), hAPP(hAPP(c_List_Olist_OCons(_1588491), _1588493), _1588495)) = hAPP(hAPP(c_Set_Oinsert(_1588491), _1588493), hAPP(c_List_Oset(_1588491), _1588495)))], (41003 ^ _777081) ^ [_1588544, _1588546, _1588548, _1588550, _1588552, _1588554] : [-(c_List_Ofoldr(_1588544, _1588546, _1588548, hAPP(hAPP(c_List_Olist_OCons(_1588544), _1588550), _1588552), _1588554) = hAPP(hAPP(_1588548, _1588550), c_List_Ofoldr(_1588544, _1588546, _1588548, _1588552, _1588554)))], (41005 ^ _777081) ^ [_1588603, _1588605, _1588607, _1588609, _1588611, _1588613] : [hBOOL(hAPP(hAPP(_1588603, _1588605), _1588607)), c_List_Olistrelp(_1588609, _1588603, _1588611, _1588613), -(c_List_Olistrelp(_1588609, _1588603, hAPP(hAPP(c_List_Olist_OCons(_1588609), _1588605), _1588611), hAPP(hAPP(c_List_Olist_OCons(_1588609), _1588607), _1588613)))], (41015 ^ _777081) ^ [_1588825, _1588827, _1588829, _1588831, _1588833, _1588835] : [c_List_Olistrelp(_1588825, _1588827, hAPP(hAPP(c_List_Olist_OCons(_1588825), _1588829), _1588831), hAPP(hAPP(c_List_Olist_OCons(_1588825), _1588833), _1588835)), 41018 ^ _777081 : [(41019 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1588827, _1588829), _1588833)))], (41021 ^ _777081) ^ [] : [-(c_List_Olistrelp(_1588825, _1588827, _1588831, _1588835))]]], (41023 ^ _777081) ^ [_1588982, _1588984, _1588986, _1588988, _1588990, _1588992] : [-(c_List_Olistrelp(_1588982, _1588984, hAPP(hAPP(c_List_Olist_OCons(_1588982), _1588986), _1588988), hAPP(hAPP(c_List_Olist_OCons(_1588982), _1588990), _1588992))), hBOOL(hAPP(hAPP(_1588984, _1588986), _1588990)), c_List_Olistrelp(_1588982, _1588984, _1588988, _1588992)], (41033 ^ _777081) ^ [_1589203, _1589205, _1589207, _1589209, _1589211] : [hAPP(hAPP(c_List_Olist_OCons(_1589203), _1589205), _1589207) = hAPP(hAPP(c_List_Olist_OCons(_1589203), _1589209), _1589211), 41036 ^ _777081 : [(41037 ^ _777081) ^ [] : [-(_1589205 = _1589209)], (41039 ^ _777081) ^ [] : [-(_1589207 = _1589211)]]], (41041 ^ _777081) ^ [_1589340, _1589342, _1589344, _1589346, _1589348] : [-(hAPP(hAPP(c_List_Olist_OCons(_1589340), _1589342), _1589344) = hAPP(hAPP(c_List_Olist_OCons(_1589340), _1589346), _1589348)), _1589342 = _1589346, _1589344 = _1589348], (41051 ^ _777081) ^ [_1589530, _1589532, _1589534] : [hAPP(hAPP(c_List_Olist_OCons(_1589530), _1589532), _1589534) = _1589534], (41053 ^ _777081) ^ [_1589580, _1589582, _1589584] : [_1589580 = hAPP(hAPP(c_List_Olist_OCons(_1589582), _1589584), _1589580)], (41055 ^ _777081) ^ [_1589615, _1589617, _1589619, _1589621, _1589623] : [-(hAPP(hAPP(c_List_Omap(_1589615, _1589617), _1589619), hAPP(hAPP(c_List_Olist_OCons(_1589615), _1589621), _1589623)) = hAPP(hAPP(c_List_Olist_OCons(_1589617), hAPP(_1589619, _1589621)), hAPP(hAPP(c_List_Omap(_1589615, _1589617), _1589619), _1589623)))], (41057 ^ _777081) ^ [_1589698, _1589700, _1589702, _1589704] : [_1589698 = _1589700, -(c_List_Oremove1(_1589702, _1589698, hAPP(hAPP(c_List_Olist_OCons(_1589702), _1589700), _1589704)) = _1589704)], (41063 ^ _777081) ^ [_1589797, _1589799, _1589801, _1589803] : [-(_1589797 = _1589799), -(c_List_Oremove1(_1589801, _1589797, hAPP(hAPP(c_List_Olist_OCons(_1589801), _1589799), _1589803)) = hAPP(hAPP(c_List_Olist_OCons(_1589801), _1589799), c_List_Oremove1(_1589801, _1589797, _1589803)))], (41069 ^ _777081) ^ [_1589863, _1589865, _1589867, _1589869, _1589871, _1589873] : [class_Orderings_Olinorder(_1589863), 41072 ^ _777081 : [(41073 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1589863), hAPP(_1589865, _1589867)), hAPP(_1589865, _1589869))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1589871, _1589863, _1589865), _1589867), hAPP(hAPP(c_List_Olist_OCons(_1589871), _1589869), _1589873)) = hAPP(hAPP(c_List_Olist_OCons(_1589871), _1589867), hAPP(hAPP(c_List_Olist_OCons(_1589871), _1589869), _1589873)))], (41079 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1589863), hAPP(_1589865, _1589867)), hAPP(_1589865, _1589869)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1589871, _1589863, _1589865), _1589867), hAPP(hAPP(c_List_Olist_OCons(_1589871), _1589869), _1589873)) = hAPP(hAPP(c_List_Olist_OCons(_1589871), _1589869), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1589871, _1589863, _1589865), _1589867), _1589873)))]]], (41085 ^ _777081) ^ [_1590263, _1590265, _1590267] : [hBOOL(hAPP(c_List_Odistinct(_1590263), hAPP(hAPP(c_List_Olist_OCons(_1590263), _1590265), _1590267))), 41088 ^ _777081 : [(41089 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1590263), _1590265), hAPP(c_List_Oset(_1590263), _1590267)))], (41091 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1590263), _1590267)))]]], (41093 ^ _777081) ^ [_1590430, _1590432, _1590434] : [-(hBOOL(hAPP(c_List_Odistinct(_1590430), hAPP(hAPP(c_List_Olist_OCons(_1590430), _1590432), _1590434)))), -(hBOOL(hAPP(hAPP(c_member(_1590430), _1590432), hAPP(c_List_Oset(_1590430), _1590434)))), hBOOL(hAPP(c_List_Odistinct(_1590430), _1590434))], (41103 ^ _777081) ^ [_1590645, _1590647, _1590649, _1590651, _1590653, _1590655] : [_1590645 = _1590647, -(hAPP(hAPP(c_Map_Omap__of(_1590649, _1590651), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1590649, _1590651)), hAPP(hAPP(c_Product__Type_OPair(_1590649, _1590651), _1590645), _1590653)), _1590655)), _1590647) = hAPP(c_Option_Ooption_OSome(_1590651), _1590653))], (41109 ^ _777081) ^ [_1590792, _1590794, _1590796, _1590798, _1590800, _1590802] : [-(_1590792 = _1590794), -(hAPP(hAPP(c_Map_Omap__of(_1590796, _1590798), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1590796, _1590798)), hAPP(hAPP(c_Product__Type_OPair(_1590796, _1590798), _1590792), _1590800)), _1590802)), _1590794) = hAPP(hAPP(c_Map_Omap__of(_1590796, _1590798), _1590802), _1590794))], (41115 ^ _777081) ^ [_1590876, _1590878, _1590880] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1590876)), hAPP(hAPP(c_List_Olist_OCons(_1590876), _1590878), _1590880)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1590876)), _1590880)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41117 ^ _777081) ^ [_1590931, _1590933, _1590935, _1590937, _1590939, _1590941] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590931, _1590931)), hAPP(hAPP(c_Product__Type_OPair(_1590931, _1590931), _1590933), _1590935)), _1590937)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1590931), tc_List_Olist(_1590931))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1590931), tc_List_Olist(_1590931)), _1590939), _1590941)), c_List_Olistrel(_1590931, _1590937))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1590931), tc_List_Olist(_1590931))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1590931), tc_List_Olist(_1590931)), hAPP(hAPP(c_List_Olist_OCons(_1590931), _1590933), _1590939)), hAPP(hAPP(c_List_Olist_OCons(_1590931), _1590935), _1590941))), c_List_Olistrel(_1590931, _1590937))))], (41127 ^ _777081) ^ [_1591266, _1591268, _1591270, _1591272] : [-(hAPP(c_Map_Omap__of(_1591266, _1591268), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1591266, _1591268)), _1591270), _1591272)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1591266, tc_Option_Ooption(_1591268)), hAPP(c_Map_Omap__of(_1591266, _1591268), _1591272)), hAPP(c_Product__Type_Ofst(_1591266, _1591268), _1591270)), hAPP(c_Option_Ooption_OSome(_1591268), hAPP(c_Product__Type_Osnd(_1591266, _1591268), _1591270))))], (41129 ^ _777081) ^ [_1591376, _1591378, _1591380, _1591382, _1591384, _1591386] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1591376), tc_List_Olist(_1591376))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1591376), tc_List_Olist(_1591376)), hAPP(hAPP(c_List_Olist_OCons(_1591376), _1591378), _1591380)), hAPP(hAPP(c_List_Olist_OCons(_1591376), _1591382), _1591384))), c_List_Olex(_1591376, _1591386))), 41134 ^ _777081 : [(41135 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591376, _1591376)), hAPP(hAPP(c_Product__Type_OPair(_1591376, _1591376), _1591378), _1591382)), _1591386)))], (41137 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1591376)), _1591380) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1591376)), _1591384))]], 41138 ^ _777081 : [(41139 ^ _777081) ^ [] : [-(_1591378 = _1591382)], (41141 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1591376), tc_List_Olist(_1591376))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1591376), tc_List_Olist(_1591376)), _1591380), _1591384)), c_List_Olex(_1591376, _1591386))))]]], (41143 ^ _777081) ^ [_1591774, _1591776, _1591778, _1591780, _1591782, _1591784] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1591774), tc_List_Olist(_1591774))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1591774), tc_List_Olist(_1591774)), hAPP(hAPP(c_List_Olist_OCons(_1591774), _1591776), _1591778)), hAPP(hAPP(c_List_Olist_OCons(_1591774), _1591780), _1591782))), c_List_Olex(_1591774, _1591784)))), 41144 ^ _777081 : [(41145 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591774, _1591774)), hAPP(hAPP(c_Product__Type_OPair(_1591774, _1591774), _1591776), _1591780)), _1591784)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1591774)), _1591778) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1591774)), _1591782)], (41151 ^ _777081) ^ [] : [_1591776 = _1591780, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1591774), tc_List_Olist(_1591774))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1591774), tc_List_Olist(_1591774)), _1591778), _1591782)), c_List_Olex(_1591774, _1591784)))]]], (41159 ^ _777081) ^ [_1592230, _1592232, _1592234, _1592236] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1592230), tc_List_Olist(_1592230), c_List_Olistrel(_1592230, _1592232)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1592230)), hAPP(hAPP(c_List_Olist_OCons(_1592230), _1592234), _1592236)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1592230), tc_HOL_Obool)))) = c_List_Oset__Cons(_1592230, hAPP(c_Relation_OImage(_1592230, _1592230, _1592232), hAPP(hAPP(c_Set_Oinsert(_1592230), _1592234), c_Orderings_Obot__class_Obot(tc_fun(_1592230, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1592230), tc_List_Olist(_1592230), c_List_Olistrel(_1592230, _1592232)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1592230)), _1592236), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1592230), tc_HOL_Obool))))))], (41161 ^ _777081) ^ [_1592353, _1592355, _1592357] : [-(c_List_Oset__Cons(_1592353, _1592355, _1592357) = hAPP(c_Set_OCollect(tc_List_Olist(_1592353)), hAPP(hAPP(c_COMBB(tc_fun(_1592353, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1592353)), c_HOL_OEx(_1592353)), hAPP(hAPP(c_COMBB(tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool)), tc_fun(_1592353, tc_HOL_Obool), tc_List_Olist(_1592353)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool), tc_HOL_Obool, _1592353), c_HOL_OEx(tc_List_Olist(_1592353)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592353), tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool)), tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1592353, tc_fun(tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool))), tc_fun(tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool)), tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool))), tc_List_Olist(_1592353)), c_COMBS(_1592353, tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1592353, tc_fun(tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool))), tc_List_Olist(_1592353)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592353), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool)), _1592353), c_COMBS(tc_List_Olist(_1592353), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool)), tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1592353)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592353), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1592353), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1592353)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592353), tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_List_Olist(_1592353))), tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1592353), tc_List_Olist(_1592353)), tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool)), tc_fun(tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_List_Olist(_1592353))), tc_fun(_1592353, tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool))), tc_List_Olist(_1592353)), c_COMBB(tc_fun(tc_List_Olist(_1592353), tc_List_Olist(_1592353)), tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool), _1592353)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1592353), tc_List_Olist(_1592353)), tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool)), tc_List_Olist(_1592353)), c_COMBB(tc_List_Olist(_1592353), tc_HOL_Obool, tc_List_Olist(_1592353))), c_fequal))), c_List_Olist_OCons(_1592353)))))), hAPP(hAPP(c_COMBC(_1592353, tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool), tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool)), _1592353), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1592353))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1592353), c_fconj), hAPP(hAPP(c_COMBC(_1592353, tc_fun(_1592353, tc_HOL_Obool), tc_HOL_Obool), c_member(_1592353)), _1592355)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1592353), tc_fun(tc_List_Olist(_1592353), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1592353))), _1592357)))))))], (41163 ^ _777081) ^ [_1592888, _1592890, _1592892, _1592894, _1592896] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1592888), tc_List_Olist(_1592888))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1592888), tc_List_Olist(_1592888)), hAPP(hAPP(c_List_Olist_OCons(_1592888), _1592890), _1592892)), _1592894)), c_List_Olistrel(_1592888, _1592896))), 41168 ^ _777081 : [(41169 ^ _777081) ^ [] : [-(_1592894 = hAPP(hAPP(c_List_Olist_OCons(_1592888), 41166 ^ [_1592888, _1592890, _1592892, _1592894, _1592896]), 41167 ^ [_1592888, _1592890, _1592892, _1592894, _1592896]))], (41171 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592888, _1592888)), hAPP(hAPP(c_Product__Type_OPair(_1592888, _1592888), _1592890), 41166 ^ [_1592888, _1592890, _1592892, _1592894, _1592896])), _1592896)))], (41173 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1592888), tc_List_Olist(_1592888))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1592888), tc_List_Olist(_1592888)), _1592892), 41167 ^ [_1592888, _1592890, _1592892, _1592894, _1592896])), c_List_Olistrel(_1592888, _1592896))))]]], (41175 ^ _777081) ^ [_1593277, _1593279, _1593281, _1593283, _1593285] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1593277), tc_List_Olist(_1593277))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1593277), tc_List_Olist(_1593277)), _1593279), hAPP(hAPP(c_List_Olist_OCons(_1593277), _1593281), _1593283))), c_List_Olistrel(_1593277, _1593285))), 41180 ^ _777081 : [(41181 ^ _777081) ^ [] : [-(_1593279 = hAPP(hAPP(c_List_Olist_OCons(_1593277), 41178 ^ [_1593277, _1593279, _1593281, _1593283, _1593285]), 41179 ^ [_1593277, _1593279, _1593281, _1593283, _1593285]))], (41183 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593277, _1593277)), hAPP(hAPP(c_Product__Type_OPair(_1593277, _1593277), 41178 ^ [_1593277, _1593279, _1593281, _1593283, _1593285]), _1593281)), _1593285)))], (41185 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1593277), tc_List_Olist(_1593277))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1593277), tc_List_Olist(_1593277)), 41179 ^ [_1593277, _1593279, _1593281, _1593283, _1593285]), _1593283)), c_List_Olistrel(_1593277, _1593285))))]]], (41187 ^ _777081) ^ [_1593666, _1593668, _1593670, _1593672, _1593674] : [class_Orderings_Olinorder(_1593666), -(hBOOL(hAPP(hAPP(c_member(_1593666), hAPP(_1593668, _1593670)), hAPP(c_Set_Oimage(_1593672, _1593666, _1593668), hAPP(c_List_Oset(_1593672), _1593674))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1593672, _1593666, _1593668, _1593670, _1593674) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1593672, _1593666, _1593668), _1593670), _1593674))], (41197 ^ _777081) ^ [_1593865, _1593867, _1593869, _1593871, _1593873, _1593875] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1593865), tc_List_Olist(_1593865))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1593865), tc_List_Olist(_1593865)), hAPP(hAPP(c_List_Olist_OCons(_1593865), _1593867), _1593869)), hAPP(hAPP(c_List_Olist_OCons(_1593865), _1593871), _1593873))), c_List_Olexord(_1593865, _1593875))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593865, _1593865)), hAPP(hAPP(c_Product__Type_OPair(_1593865, _1593865), _1593867), _1593871)), _1593875))), 41204 ^ _777081 : [(41205 ^ _777081) ^ [] : [-(_1593867 = _1593871)], (41207 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1593865), tc_List_Olist(_1593865))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1593865), tc_List_Olist(_1593865)), _1593869), _1593873)), c_List_Olexord(_1593865, _1593875))))]]], (41209 ^ _777081) ^ [_1594192, _1594194, _1594196, _1594198, _1594200, _1594202] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594192), tc_List_Olist(_1594192))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594192), tc_List_Olist(_1594192)), hAPP(hAPP(c_List_Olist_OCons(_1594192), _1594194), _1594196)), hAPP(hAPP(c_List_Olist_OCons(_1594192), _1594198), _1594200))), c_List_Olexord(_1594192, _1594202)))), 41210 ^ _777081 : [(41211 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594192, _1594192)), hAPP(hAPP(c_Product__Type_OPair(_1594192, _1594192), _1594194), _1594198)), _1594202))], (41213 ^ _777081) ^ [] : [_1594194 = _1594198, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594192), tc_List_Olist(_1594192))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594192), tc_List_Olist(_1594192)), _1594196), _1594200)), c_List_Olexord(_1594192, _1594202)))]]], (41221 ^ _777081) ^ [_1594565, _1594567, _1594569, _1594571, _1594573] : [class_Orderings_Olinorder(_1594565), hBOOL(hAPP(c_List_Odistinct(_1594567), _1594569)), -(hBOOL(hAPP(c_List_Odistinct(_1594567), c_List_Olinorder__class_Oinsort__insert__key(_1594567, _1594565, _1594571, _1594573, _1594569))))], (41231 ^ _777081) ^ [_1594732, _1594734, _1594736] : [class_Orderings_Olinorder(_1594732), hBOOL(hAPP(hAPP(c_member(_1594732), _1594734), hAPP(c_List_Oset(_1594732), _1594736))), -(c_List_Olinorder__class_Oinsort__insert__key(_1594732, _1594732, c_COMBI(_1594732), _1594734, _1594736) = _1594736)], (41241 ^ _777081) ^ [_1594903, _1594905, _1594907] : [class_Orderings_Olinorder(_1594903), -(hAPP(c_List_Oset(_1594903), c_List_Olinorder__class_Oinsort__insert__key(_1594903, _1594903, c_COMBI(_1594903), _1594905, _1594907)) = hAPP(hAPP(c_Set_Oinsert(_1594903), _1594905), hAPP(c_List_Oset(_1594903), _1594907)))], (41247 ^ _777081) ^ [_1595032, _1595034, _1595036, _1595038, _1595040] : [class_Orderings_Olinorder(_1595032), hBOOL(hAPP(hAPP(c_member(_1595032), hAPP(_1595034, _1595036)), hAPP(c_Set_Oimage(_1595038, _1595032, _1595034), hAPP(c_List_Oset(_1595038), _1595040)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1595038, _1595032, _1595034, _1595036, _1595040) = _1595040)], (41257 ^ _777081) ^ [_1595248, _1595250, _1595252, _1595254] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595248), tc_List_Olist(_1595248))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595248), tc_List_Olist(_1595248)), _1595250), _1595252)), c_List_Olex(_1595248, _1595254))), 41260 ^ _777081 : [(41261 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595248), tc_List_Olist(_1595248))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595248), tc_List_Olist(_1595248)), _1595250), _1595252)), c_List_Olexord(_1595248, _1595254))))], (41263 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595248)), _1595250) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595248)), _1595252))]]], (41265 ^ _777081) ^ [_1595499, _1595501, _1595503, _1595505] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595499), tc_List_Olist(_1595499))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595499), tc_List_Olist(_1595499)), _1595501), _1595503)), c_List_Olex(_1595499, _1595505)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595499), tc_List_Olist(_1595499))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595499), tc_List_Olist(_1595499)), _1595501), _1595503)), c_List_Olexord(_1595499, _1595505))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595499)), _1595501) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595499)), _1595503)], (41275 ^ _777081) ^ [_1595786, _1595788, _1595790] : [class_Orderings_Olinorder(_1595786), -(hBOOL(hAPP(hAPP(c_member(_1595786), _1595788), hAPP(c_List_Oset(_1595786), _1595790)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1595786, _1595786, c_COMBI(_1595786), _1595788, _1595790) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1595786, _1595786, c_COMBI(_1595786)), _1595788), _1595790))], (41285 ^ _777081) ^ [_1595942, _1595944, _1595946, _1595948] : [-(hAPP(c_List_Oset(tc_prod(_1595942, _1595944)), hAPP(hAPP(c_List_Ozip(_1595942, _1595944), _1595946), _1595948)) = hAPP(c_Set_OCollect(tc_prod(_1595942, _1595944)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1595942, _1595944)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1595942, _1595944), 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(_1595942, _1595944)), 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(_1595942, _1595944)), 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(_1595942, _1595944), tc_fun(tc_Nat_Onat, tc_prod(_1595942, _1595944)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1595942, _1595944), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1595942, _1595944)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1595942, _1595944)), c_COMBB(tc_prod(_1595942, _1595944), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1595944, tc_prod(_1595942, _1595944)), hAPP(hAPP(c_COMBB(_1595942, tc_fun(_1595944, tc_prod(_1595942, _1595944)), tc_Nat_Onat), c_Product__Type_OPair(_1595942, _1595944)), hAPP(c_List_Onth(_1595942), _1595946))), hAPP(c_List_Onth(_1595944), _1595948)))))), 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(_1595942)), _1595946)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595944)), _1595948)))))))], (41287 ^ _777081) ^ [_1596167, _1596169, _1596171, _1596173] : [-(c_List_Olist_Olist__size(_1596167, _1596169, hAPP(hAPP(c_List_Olist_OCons(_1596167), _1596171), _1596173)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1596169, _1596171)), c_List_Olist_Olist__size(_1596167, _1596169, _1596173))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41289 ^ _777081) ^ [_1596227, _1596229, _1596231, _1596233] : [-(hAPP(hAPP(c_List_Onth(_1596227), hAPP(hAPP(c_List_Olist_OCons(_1596227), _1596229), _1596231)), hAPP(c_Nat_OSuc, _1596233)) = hAPP(hAPP(c_List_Onth(_1596227), _1596231), _1596233))], (41291 ^ _777081) ^ [_1596283, _1596285, _1596287] : [-(hAPP(hAPP(c_List_Onth(_1596283), hAPP(hAPP(c_List_Olist_OCons(_1596283), _1596285), _1596287)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1596285)], (41293 ^ _777081) ^ [_1596326, _1596328, _1596330, _1596332, _1596334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1596326), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596328)), _1596330))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1596326), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596332)), _1596334))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1596328, _1596332)), hAPP(hAPP(c_List_Ozip(_1596328, _1596332), _1596330), _1596334)), _1596326) = hAPP(hAPP(c_Product__Type_OPair(_1596328, _1596332), hAPP(hAPP(c_List_Onth(_1596328), _1596330), _1596326)), hAPP(hAPP(c_List_Onth(_1596332), _1596334), _1596326)))], (41303 ^ _777081) ^ [_1596623, _1596625, _1596627] : [_1596623 = _1596625, 41306 ^ _777081 : [(41307 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596627)), _1596623) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596627)), _1596625))], (41309 ^ _777081) ^ [_1596771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1596771), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596627)), _1596623))), -(hAPP(hAPP(c_List_Onth(_1596627), _1596623), _1596771) = hAPP(hAPP(c_List_Onth(_1596627), _1596625), _1596771))]]], (41315 ^ _777081) ^ [_1596910, _1596912, _1596914] : [-(_1596910 = _1596912), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596914)), _1596910) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596914)), _1596912), 41321 ^ _777081 : [(41322 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41320 ^ [_1596910, _1596912, _1596914]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1596914)), _1596910))))], (41324 ^ _777081) ^ [] : [hAPP(hAPP(c_List_Onth(_1596914), _1596910), 41320 ^ [_1596910, _1596912, _1596914]) = hAPP(hAPP(c_List_Onth(_1596914), _1596912), 41320 ^ [_1596910, _1596912, _1596914])]]], (41328 ^ _777081) ^ [_1597225, _1597227, _1597229, _1597231, _1597233] : [-(c_List_Olist_Olist__size(_1597225, _1597227, hAPP(hAPP(c_List_Omap(_1597229, _1597225), _1597231), _1597233)) = c_List_Olist_Olist__size(_1597229, hAPP(c_Fun_Ocomp(_1597225, tc_Nat_Onat, _1597229, _1597227), _1597231), _1597233))], (41330 ^ _777081) ^ [_1597281, _1597283, _1597285, _1597287] : [-(hAPP(hAPP(c_List_Onth(_1597281), hAPP(hAPP(c_List_Olist_OCons(_1597281), _1597283), _1597285)), _1597287) = c_Nat_Onat_Onat__case(_1597281, _1597283, hAPP(c_List_Onth(_1597281), _1597285), _1597287))], (41332 ^ _777081) ^ [_1597354, _1597356, _1597358] : [41334 ^ _777081 : [(41335 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1597354), 41333 ^ [_1597354, _1597356, _1597358]), hAPP(c_List_Oset(_1597354), _1597356))))], (41337 ^ _777081) ^ [] : [hBOOL(hAPP(_1597358, 41333 ^ [_1597354, _1597356, _1597358]))]], 41338 ^ _777081 : [(41339 ^ _777081) ^ [_1597538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1597538), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597354)), _1597356))), -(hBOOL(hAPP(_1597358, hAPP(hAPP(c_List_Onth(_1597354), _1597356), _1597538))))]]], (41345 ^ _777081) ^ [_1597665, _1597667, _1597669] : [41347 ^ _777081 : [(41348 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41346 ^ [_1597665, _1597667, _1597669]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597665)), _1597667))))], (41350 ^ _777081) ^ [] : [hBOOL(hAPP(_1597669, hAPP(hAPP(c_List_Onth(_1597665), _1597667), 41346 ^ [_1597665, _1597667, _1597669])))]], 41351 ^ _777081 : [(41352 ^ _777081) ^ [_1597867] : [hBOOL(hAPP(hAPP(c_member(_1597665), _1597867), hAPP(c_List_Oset(_1597665), _1597667))), -(hBOOL(hAPP(_1597669, _1597867)))]]], (41358 ^ _777081) ^ [_1597984, _1597986, _1597988, _1597990, _1597992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1597984), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597986)), _1597988))), -(hAPP(hAPP(c_List_Onth(_1597990), hAPP(hAPP(c_List_Omap(_1597986, _1597990), _1597992), _1597988)), _1597984) = hAPP(_1597992, hAPP(hAPP(c_List_Onth(_1597986), _1597988), _1597984)))], (41382 ^ _777081) ^ [_1598622, _1598624] : [41384 ^ _777081 : [(41385 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41383 ^ [_1598622, _1598624]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598622)), _1598624))))], (41388 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41386 ^ [_1598622, _1598624]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598622)), _1598624))))], (41390 ^ _777081) ^ [] : [41383 ^ [_1598622, _1598624] = 41386 ^ [_1598622, _1598624]], (41392 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1598622), _1598624), 41383 ^ [_1598622, _1598624]) = hAPP(hAPP(c_List_Onth(_1598622), _1598624), 41386 ^ [_1598622, _1598624]))]], -(hBOOL(hAPP(c_List_Odistinct(_1598622), _1598624)))], (41364 ^ _777081) ^ [_1598162, _1598164] : [hBOOL(hAPP(c_List_Odistinct(_1598162), _1598164)), 41367 ^ _777081 : [(41368 ^ _777081) ^ [_1598294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1598294), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598162)), _1598164))), 41371 ^ _777081 : [(41372 ^ _777081) ^ [_1598421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1598421), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1598162)), _1598164))), -(_1598294 = _1598421), hAPP(hAPP(c_List_Onth(_1598162), _1598164), _1598294) = hAPP(hAPP(c_List_Onth(_1598162), _1598164), _1598421)]]]]], (41396 ^ _777081) ^ [_1599054, _1599056, _1599058, _1599060] : [hBOOL(hAPP(c_List_Odistinct(_1599054), _1599056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1599058), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599054)), _1599056))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1599060), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599054)), _1599056))), 41407 ^ _777081 : [(41408 ^ _777081) ^ [] : [hAPP(hAPP(c_List_Onth(_1599054), _1599056), _1599058) = hAPP(hAPP(c_List_Onth(_1599054), _1599056), _1599060), -(_1599058 = _1599060)], (41414 ^ _777081) ^ [] : [_1599058 = _1599060, -(hAPP(hAPP(c_List_Onth(_1599054), _1599056), _1599058) = hAPP(hAPP(c_List_Onth(_1599054), _1599056), _1599060))]]], (41420 ^ _777081) ^ [_1599507, _1599509, _1599511] : [hBOOL(hAPP(hAPP(c_member(_1599507), _1599509), hAPP(c_List_Oset(_1599507), _1599511))), 41424 ^ _777081 : [(41425 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41423 ^ [_1599507, _1599509, _1599511]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599507)), _1599511))))], (41427 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1599507), _1599511), 41423 ^ [_1599507, _1599509, _1599511]) = _1599509)]]], (41429 ^ _777081) ^ [_1599695, _1599697, _1599699] : [-(hBOOL(hAPP(hAPP(c_member(_1599695), _1599697), hAPP(c_List_Oset(_1599695), _1599699)))), 41430 ^ _777081 : [(41431 ^ _777081) ^ [_1599769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1599769), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599695)), _1599699))), hAPP(hAPP(c_List_Onth(_1599695), _1599699), _1599769) = _1599697]]], (41439 ^ _777081) ^ [_1599931, _1599933, _1599935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1599931), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599933)), _1599935))), -(hBOOL(hAPP(hAPP(c_member(_1599933), hAPP(hAPP(c_List_Onth(_1599933), _1599935), _1599931)), hAPP(c_List_Oset(_1599933), _1599935))))], (41445 ^ _777081) ^ [_1600089, _1600091, _1600093, _1600095] : [_1600089 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1600091), hAPP(hAPP(c_List_Olist_OCons(_1600091), _1600093), _1600095)), _1600089) = _1600093)], (41451 ^ _777081) ^ [_1600196, _1600198, _1600200, _1600202] : [-(_1600196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1600198), hAPP(hAPP(c_List_Olist_OCons(_1600198), _1600200), _1600202)), _1600196) = hAPP(hAPP(c_List_Onth(_1600198), _1600202), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1600196), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41457 ^ _777081) ^ [_1600268, _1600270] : [-(hAPP(c_List_Oset(_1600268), _1600270) = hAPP(c_Set_OCollect(_1600268), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1600268), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1600268, 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)), _1600268), 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)), _1600268), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1600268, tc_fun(tc_Nat_Onat, _1600268), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1600268, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1600268), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1600268), c_COMBB(_1600268, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1600268), _1600270))))), 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(_1600268)), _1600270))))))], (41459 ^ _777081) ^ [_1600409, _1600411, _1600413, _1600415] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1600409) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1600411), hAPP(hAPP(c_List_Olist_OCons(_1600411), _1600413), _1600415)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1600409)) = _1600413)], (41465 ^ _777081) ^ [_1600528, _1600530, _1600532, _1600534] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1600528) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1600530), hAPP(hAPP(c_List_Olist_OCons(_1600530), _1600532), _1600534)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1600528)) = hAPP(hAPP(c_List_Onth(_1600530), _1600534), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1600528)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (41471 ^ _777081) ^ [_1600609, _1600611, _1600613, _1600615, _1600617] : [hBOOL(hAPP(hAPP(c_member(_1600609), _1600611), hAPP(c_List_Oset(_1600609), _1600613))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1600615), hAPP(_1600617, _1600611))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1600615), c_List_Olist_Olist__size(_1600609, _1600617, _1600613))))], (41481 ^ _777081) ^ [_1600808, _1600810, _1600812, _1600814, _1600816] : [hBOOL(hAPP(hAPP(c_member(_1600808), _1600810), hAPP(c_List_Oset(_1600808), _1600812))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1600814), hAPP(_1600816, _1600810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1600814), c_List_Olist_Olist__size(_1600808, _1600816, _1600812))))], (41491 ^ _777081) ^ [_1601007, _1601009, _1601011] : [-(hAPP(c_List_Oset(_1601007), c_List_Osublist(_1601007, _1601009, _1601011)) = hAPP(c_Set_OCollect(_1601007), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1601007), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1601007, 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)), _1601007), 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)), _1601007), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1601007, tc_fun(tc_Nat_Onat, _1601007), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1601007, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1601007), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1601007), c_COMBB(_1601007, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1601007), _1601009))))), 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(_1601007)), _1601009)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1601011))))))], (41493 ^ _777081) ^ [_1601172, _1601174, _1601176, _1601178] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601172), tc_List_Olist(_1601172))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601172), tc_List_Olist(_1601172)), _1601174), _1601176)), c_List_Olistrel(_1601172, _1601178))), 41496 ^ _777081 : [(41497 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601172)), _1601174) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601172)), _1601176))], (41499 ^ _777081) ^ [_1601401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1601401), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601172)), _1601174))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601172, _1601172)), hAPP(hAPP(c_Product__Type_OPair(_1601172, _1601172), hAPP(hAPP(c_List_Onth(_1601172), _1601174), _1601401)), hAPP(hAPP(c_List_Onth(_1601172), _1601176), _1601401))), _1601178)))]]], (41505 ^ _777081) ^ [_1601580, _1601582, _1601584, _1601586] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601580), tc_List_Olist(_1601580))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601580), tc_List_Olist(_1601580)), _1601582), _1601584)), c_List_Olistrel(_1601580, _1601586)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601580)), _1601582) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601580)), _1601584), 41511 ^ _777081 : [(41512 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41510 ^ [_1601580, _1601582, _1601584, _1601586]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1601580)), _1601582))))], (41514 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601580, _1601580)), hAPP(hAPP(c_Product__Type_OPair(_1601580, _1601580), hAPP(hAPP(c_List_Onth(_1601580), _1601582), 41510 ^ [_1601580, _1601582, _1601584, _1601586])), hAPP(hAPP(c_List_Onth(_1601580), _1601584), 41510 ^ [_1601580, _1601582, _1601584, _1601586]))), _1601586))]]], (41518 ^ _777081) ^ [_1602045, _1602047, _1602049, _1602051] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602045), tc_List_Olist(_1602045))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602045), tc_List_Olist(_1602045)), _1602047), _1602049)), c_List_Olexord(_1602045, _1602051))), 41523 ^ _777081 : [(41524 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602045)), _1602047)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602045)), _1602049))))], (41526 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1602045), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602045)), _1602047)), _1602049) = _1602047)]], 41528 ^ _777081 : [(41529 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41527 ^ [_1602045, _1602047, _1602049, _1602051]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602045)), _1602047)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602045)), _1602049)))))], (41531 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1602045), 41527 ^ [_1602045, _1602047, _1602049, _1602051]), _1602047) = hAPP(hAPP(c_List_Otake(_1602045), 41527 ^ [_1602045, _1602047, _1602049, _1602051]), _1602049))], (41533 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602045, _1602045)), hAPP(hAPP(c_Product__Type_OPair(_1602045, _1602045), hAPP(hAPP(c_List_Onth(_1602045), _1602047), 41527 ^ [_1602045, _1602047, _1602049, _1602051])), hAPP(hAPP(c_List_Onth(_1602045), _1602049), 41527 ^ [_1602045, _1602047, _1602049, _1602051]))), _1602051)))]]], (41535 ^ _777081) ^ [_1602585, _1602587, _1602589, _1602591] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602585), tc_List_Olist(_1602585))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602585), tc_List_Olist(_1602585)), _1602587), _1602589)), c_List_Olexord(_1602585, _1602591)))), 41536 ^ _777081 : [(41537 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602585)), _1602587)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602585)), _1602589))), hAPP(hAPP(c_List_Otake(_1602585), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602585)), _1602587)), _1602589) = _1602587], (41543 ^ _777081) ^ [_1602892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1602892), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602585)), _1602587)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602585)), _1602589)))), hAPP(hAPP(c_List_Otake(_1602585), _1602892), _1602587) = hAPP(hAPP(c_List_Otake(_1602585), _1602892), _1602589), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602585, _1602585)), hAPP(hAPP(c_Product__Type_OPair(_1602585, _1602585), hAPP(hAPP(c_List_Onth(_1602585), _1602587), _1602892)), hAPP(hAPP(c_List_Onth(_1602585), _1602589), _1602892))), _1602591))]]], (41555 ^ _777081) ^ [_1603246, _1603248, _1603250, _1603252] : [hBOOL(hAPP(c_List_Odistinct(_1603246), _1603248)), -(hBOOL(hAPP(hAPP(c_member(_1603246), _1603250), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1603246, tc_HOL_Obool)), hAPP(c_List_Oset(_1603246), _1603248)), hAPP(hAPP(c_Set_Oinsert(_1603246), hAPP(hAPP(c_List_Onth(_1603246), _1603248), _1603252)), c_Orderings_Obot__class_Obot(tc_fun(_1603246, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1603246), hAPP(hAPP(c_List_Olist__update(_1603246, _1603248), _1603252), _1603250))))], (41565 ^ _777081) ^ [_1603460, _1603462, _1603464, _1603466, _1603468] : [-(_1603460 = _1603462), -(hAPP(hAPP(c_List_Onth(_1603464), hAPP(hAPP(c_List_Olist__update(_1603464, _1603466), _1603460), _1603468)), _1603462) = hAPP(hAPP(c_List_Onth(_1603464), _1603466), _1603462))], (41571 ^ _777081) ^ [_1603527, _1603529, _1603531] : [-(hAPP(hAPP(c_List_Olist__update(_1603527, _1603529), _1603531), hAPP(hAPP(c_List_Onth(_1603527), _1603529), _1603531)) = _1603529)], (41573 ^ _777081) ^ [_1603571, _1603573, _1603575, _1603577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1603571), _1603573)), -(hAPP(hAPP(c_List_Onth(_1603575), hAPP(hAPP(c_List_Otake(_1603575), _1603573), _1603577)), _1603571) = hAPP(hAPP(c_List_Onth(_1603575), _1603577), _1603571))], (41579 ^ _777081) ^ [_1603710, _1603712, _1603714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603710)), _1603712)), _1603714)), -(hAPP(hAPP(c_List_Otake(_1603710), _1603714), _1603712) = _1603712)], (41585 ^ _777081) ^ [_1603829, _1603831, _1603833, _1603835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603829)), _1603831)), _1603833)), -(hAPP(hAPP(c_List_Olist__update(_1603829, _1603831), _1603833), _1603835) = _1603831)], (41591 ^ _777081) ^ [_1603952, _1603954, _1603956] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1603952, tc_HOL_Obool)), hAPP(c_List_Oset(_1603952), hAPP(hAPP(c_List_Otake(_1603952), _1603954), _1603956))), hAPP(c_List_Oset(_1603952), _1603956))))], (41593 ^ _777081) ^ [_1604007, _1604009, _1604011] : [hBOOL(hAPP(c_List_Odistinct(_1604007), _1604009)), -(hBOOL(hAPP(c_List_Odistinct(_1604007), hAPP(hAPP(c_List_Otake(_1604007), _1604011), _1604009))))], (41599 ^ _777081) ^ [_1604118, _1604120, _1604122, _1604124, _1604126, _1604128] : [-(hAPP(hAPP(c_List_Omap(_1604118, _1604120), _1604122), hAPP(hAPP(c_List_Olist__update(_1604118, _1604124), _1604126), _1604128)) = hAPP(hAPP(c_List_Olist__update(_1604120, hAPP(hAPP(c_List_Omap(_1604118, _1604120), _1604122), _1604124)), _1604126), hAPP(_1604122, _1604128)))], (41601 ^ _777081) ^ [_1604190, _1604192, _1604194, _1604196, _1604198] : [-(hAPP(hAPP(c_List_Otake(_1604190), _1604192), hAPP(hAPP(c_List_Omap(_1604194, _1604190), _1604196), _1604198)) = hAPP(hAPP(c_List_Omap(_1604194, _1604190), _1604196), hAPP(hAPP(c_List_Otake(_1604194), _1604192), _1604198)))], (41603 ^ _777081) ^ [_1604255, _1604257, _1604259, _1604261, _1604263] : [-(hAPP(hAPP(c_List_Olist__update(_1604255, hAPP(hAPP(c_List_Olist__update(_1604255, _1604257), _1604259), _1604261)), _1604259), _1604263) = hAPP(hAPP(c_List_Olist__update(_1604255, _1604257), _1604259), _1604263))], (41605 ^ _777081) ^ [_1604309, _1604311, _1604313, _1604315, _1604317, _1604319] : [-(_1604309 = _1604311), -(hAPP(hAPP(c_List_Olist__update(_1604313, hAPP(hAPP(c_List_Olist__update(_1604313, _1604315), _1604309), _1604317)), _1604311), _1604319) = hAPP(hAPP(c_List_Olist__update(_1604313, hAPP(hAPP(c_List_Olist__update(_1604313, _1604315), _1604311), _1604319)), _1604309), _1604317))], (41611 ^ _777081) ^ [_1604389, _1604391, _1604393, _1604395] : [-(hAPP(hAPP(c_List_Otake(_1604389), _1604391), hAPP(hAPP(c_List_Otake(_1604389), _1604393), _1604395)) = hAPP(hAPP(c_List_Otake(_1604389), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1604391), _1604393)), _1604395))], (41613 ^ _777081) ^ [_1604448, _1604450, _1604452, _1604454, _1604456, _1604458] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1604448, _1604450), hAPP(hAPP(c_List_Ozip(_1604448, _1604450), _1604452), _1604454)), _1604456), _1604458) = hAPP(hAPP(c_List_Ozip(_1604448, _1604450), hAPP(hAPP(c_List_Olist__update(_1604448, _1604452), _1604456), hAPP(c_Product__Type_Ofst(_1604448, _1604450), _1604458))), hAPP(hAPP(c_List_Olist__update(_1604450, _1604454), _1604456), hAPP(c_Product__Type_Osnd(_1604448, _1604450), _1604458))))], (41615 ^ _777081) ^ [_1604541, _1604543, _1604545, _1604547, _1604549] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1604541, _1604543)), _1604545), hAPP(hAPP(c_List_Ozip(_1604541, _1604543), _1604547), _1604549)) = hAPP(hAPP(c_List_Ozip(_1604541, _1604543), hAPP(hAPP(c_List_Otake(_1604541), _1604545), _1604547)), hAPP(hAPP(c_List_Otake(_1604543), _1604545), _1604549)))], (41617 ^ _777081) ^ [_1604617, _1604619, _1604621, _1604623, _1604625, _1604627, _1604629] : [-(hAPP(hAPP(c_List_Ozip(_1604617, _1604619), hAPP(hAPP(c_List_Olist__update(_1604617, _1604621), _1604623), _1604625)), hAPP(hAPP(c_List_Olist__update(_1604619, _1604627), _1604623), _1604629)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1604617, _1604619), hAPP(hAPP(c_List_Ozip(_1604617, _1604619), _1604621), _1604627)), _1604623), hAPP(hAPP(c_Product__Type_OPair(_1604617, _1604619), _1604625), _1604629)))], (41619 ^ _777081) ^ [_1604709, _1604711, _1604713] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604709)), hAPP(hAPP(c_List_Otake(_1604709), _1604711), _1604713)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604709)), _1604713)), _1604711))], (41621 ^ _777081) ^ [_1604764, _1604766, _1604768, _1604770] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604764)), hAPP(hAPP(c_List_Olist__update(_1604764, _1604766), _1604768), _1604770)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604764)), _1604766))], (41623 ^ _777081) ^ [_1604816, _1604818, _1604820, _1604822] : [hBOOL(hAPP(hAPP(c_member(_1604816), _1604818), hAPP(c_List_Oset(_1604816), hAPP(hAPP(c_List_Otake(_1604816), _1604820), _1604822)))), -(hBOOL(hAPP(hAPP(c_member(_1604816), _1604818), hAPP(c_List_Oset(_1604816), _1604822))))], (41629 ^ _777081) ^ [_1604961, _1604963, _1604965, _1604967] : [-(hAPP(hAPP(c_List_Olist__update(_1604961, hAPP(hAPP(c_List_Olist_OCons(_1604961), _1604963), _1604965)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604967) = hAPP(hAPP(c_List_Olist_OCons(_1604961), _1604967), _1604965))], (41631 ^ _777081) ^ [_1605015, _1605017, _1605019, _1605021, _1605023] : [-(hAPP(hAPP(c_List_Olist__update(_1605015, hAPP(hAPP(c_List_Olist_OCons(_1605015), _1605017), _1605019)), _1605021), _1605023) = c_Nat_Onat_Onat__case(tc_List_Olist(_1605015), hAPP(hAPP(c_List_Olist_OCons(_1605015), _1605023), _1605019), hAPP(hAPP(c_COMBB(tc_List_Olist(_1605015), tc_List_Olist(_1605015), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1605015), _1605017)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1605015, tc_List_Olist(_1605015)), c_List_Olist__update(_1605015, _1605019)), _1605023)), _1605021))], (41633 ^ _777081) ^ [_1605112, _1605114, _1605116, _1605118, _1605120] : [-(hAPP(hAPP(c_List_Olist__update(_1605112, hAPP(hAPP(c_List_Olist_OCons(_1605112), _1605114), _1605116)), hAPP(c_Nat_OSuc, _1605118)), _1605120) = hAPP(hAPP(c_List_Olist_OCons(_1605112), _1605114), hAPP(hAPP(c_List_Olist__update(_1605112, _1605116), _1605118), _1605120)))], (41635 ^ _777081) ^ [_1605180, _1605182, _1605184, _1605186] : [-(hAPP(hAPP(c_List_Otake(_1605180), hAPP(c_Nat_OSuc, _1605182)), hAPP(hAPP(c_List_Olist_OCons(_1605180), _1605184), _1605186)) = hAPP(hAPP(c_List_Olist_OCons(_1605180), _1605184), hAPP(hAPP(c_List_Otake(_1605180), _1605182), _1605186)))], (41637 ^ _777081) ^ [_1605244, _1605246, _1605248] : [-(c_List_Osublist(_1605244, _1605246, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1605248)) = hAPP(hAPP(c_List_Otake(_1605244), _1605248), _1605246))], (41639 ^ _777081) ^ [_1605286, _1605288, _1605290, _1605292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1605286), _1605288)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605290, tc_HOL_Obool)), hAPP(c_List_Oset(_1605290), hAPP(hAPP(c_List_Otake(_1605290), _1605286), _1605292))), hAPP(c_List_Oset(_1605290), hAPP(hAPP(c_List_Otake(_1605290), _1605288), _1605292)))))], (41645 ^ _777081) ^ [_1605449, _1605451, _1605453, _1605455, _1605457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605449, tc_HOL_Obool)), hAPP(c_List_Oset(_1605449), _1605451)), _1605453)), hBOOL(hAPP(hAPP(c_member(_1605449), _1605455), _1605453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605449, tc_HOL_Obool)), hAPP(c_List_Oset(_1605449), hAPP(hAPP(c_List_Olist__update(_1605449, _1605451), _1605457), _1605455))), _1605453)))], (41655 ^ _777081) ^ [_1605682, _1605684, _1605686, _1605688] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1605682, tc_HOL_Obool)), hAPP(c_List_Oset(_1605682), hAPP(hAPP(c_List_Olist__update(_1605682, _1605684), _1605686), _1605688))), hAPP(hAPP(c_Set_Oinsert(_1605682), _1605688), hAPP(c_List_Oset(_1605682), _1605684)))))], (41657 ^ _777081) ^ [_1605748, _1605750, _1605752, _1605754, _1605756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1605748), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605750)), _1605752))), 41660 ^ _777081 : [(41661 ^ _777081) ^ [] : [_1605748 = _1605754, -(hAPP(hAPP(c_List_Onth(_1605750), hAPP(hAPP(c_List_Olist__update(_1605750, _1605752), _1605748), _1605756)), _1605754) = _1605756)], (41667 ^ _777081) ^ [] : [-(_1605748 = _1605754), -(hAPP(hAPP(c_List_Onth(_1605750), hAPP(hAPP(c_List_Olist__update(_1605750, _1605752), _1605748), _1605756)), _1605754) = hAPP(hAPP(c_List_Onth(_1605750), _1605752), _1605754))]]], (41673 ^ _777081) ^ [_1606044, _1606046, _1606048, _1606050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1606044), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606046)), _1606048))), 41676 ^ _777081 : [(41677 ^ _777081) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1606046, _1606048), _1606044), _1606050) = _1606048, -(hAPP(hAPP(c_List_Onth(_1606046), _1606048), _1606044) = _1606050)], (41683 ^ _777081) ^ [] : [hAPP(hAPP(c_List_Onth(_1606046), _1606048), _1606044) = _1606050, -(hAPP(hAPP(c_List_Olist__update(_1606046, _1606048), _1606044), _1606050) = _1606048)]]], (41689 ^ _777081) ^ [_1606338, _1606340, _1606342, _1606344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1606338), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606340)), _1606342))), -(hAPP(hAPP(c_List_Onth(_1606340), hAPP(hAPP(c_List_Olist__update(_1606340, _1606342), _1606338), _1606344)), _1606338) = _1606344)], (41695 ^ _777081) ^ [_1606477, _1606479, _1606481, _1606483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1606477), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606479)), _1606481))), -(hBOOL(hAPP(hAPP(c_member(_1606479), _1606483), hAPP(c_List_Oset(_1606479), hAPP(hAPP(c_List_Olist__update(_1606479, _1606481), _1606477), _1606483)))))], (41701 ^ _777081) ^ [_1606648, _1606650, _1606652, _1606654, _1606656, _1606658, _1606660] : [hBOOL(hAPP(hAPP(c_member(_1606648), _1606650), hAPP(c_List_Oset(_1606648), hAPP(hAPP(c_List_Otake(_1606648), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606652)), _1606654)), _1606656)))), -(c_Map_Omap__upds(_1606648, _1606652, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1606648, tc_Option_Ooption(_1606652)), _1606658), _1606650), hAPP(c_Option_Ooption_OSome(_1606652), _1606660)), _1606656, _1606654) = c_Map_Omap__upds(_1606648, _1606652, _1606658, _1606656, _1606654))], (41707 ^ _777081) ^ [_1606845, _1606847, _1606849, _1606851, _1606853, _1606855, _1606857] : [-(hBOOL(hAPP(hAPP(c_member(_1606845), _1606847), hAPP(c_List_Oset(_1606845), hAPP(hAPP(c_List_Otake(_1606845), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606849)), _1606851)), _1606853))))), -(c_Map_Omap__upds(_1606845, _1606849, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1606845, tc_Option_Ooption(_1606849)), _1606855), _1606847), hAPP(c_Option_Ooption_OSome(_1606849), _1606857)), _1606853, _1606851) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1606845, tc_Option_Ooption(_1606849)), c_Map_Omap__upds(_1606845, _1606849, _1606855, _1606853, _1606851)), _1606847), hAPP(c_Option_Ooption_OSome(_1606849), _1606857)))], (41713 ^ _777081) ^ [_1606970, _1606972, _1606974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1606970, _1606970), tc_HOL_Obool)), _1606972), hAPP(hAPP(c_Product__Type_OSigma(_1606970, _1606970), _1606974), hAPP(c_COMBK(tc_fun(_1606970, tc_HOL_Obool), _1606970), _1606974)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1606970), tc_List_Olist(_1606970)), tc_HOL_Obool)), c_List_Olistrel(_1606970, _1606972)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1606970), tc_List_Olist(_1606970)), c_List_Olists(_1606970, _1606974)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1606970), tc_HOL_Obool), tc_List_Olist(_1606970)), c_List_Olists(_1606970, _1606974))))))], (41719 ^ _777081) ^ [_1607215, _1607217, _1607219, _1607221, _1607223, _1607225] : [-(c_Map_Omap__add(_1607215, _1607217, _1607219, c_Map_Omap__upds(_1607215, _1607217, _1607221, _1607223, _1607225)) = c_Map_Omap__upds(_1607215, _1607217, c_Map_Omap__add(_1607215, _1607217, _1607219, _1607221), _1607223, _1607225))], (41721 ^ _777081) ^ [_1607270, _1607272, _1607274, _1607276, _1607278, _1607280] : [c_Map_Omap__le(_1607270, _1607272, _1607274, _1607276), -(c_Map_Omap__le(_1607270, _1607272, c_Map_Omap__upds(_1607270, _1607272, _1607274, _1607278, _1607280), c_Map_Omap__upds(_1607270, _1607272, _1607276, _1607278, _1607280)))], (41727 ^ _777081) ^ [_1607387, _1607389, _1607391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1607387, tc_HOL_Obool)), _1607389), _1607391)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1607387), tc_HOL_Obool)), c_List_Olists(_1607387, _1607389)), c_List_Olists(_1607387, _1607391))))], (41733 ^ _777081) ^ [_1607518, _1607520, _1607522, _1607524, _1607526, _1607528] : [-(hBOOL(hAPP(hAPP(c_member(_1607518), _1607520), hAPP(c_List_Oset(_1607518), _1607522)))), -(hAPP(c_Map_Omap__upds(_1607518, _1607524, _1607526, _1607522, _1607528), _1607520) = hAPP(_1607526, _1607520))], (41739 ^ _777081) ^ [_1607586] : [-(c_List_Olists(_1607586, c_Orderings_Otop__class_Otop(tc_fun(_1607586, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1607586), tc_HOL_Obool)))], (41741 ^ _777081) ^ [_1607624, _1607626, _1607628] : [c_Equiv__Relations_Oequiv(_1607624, _1607626, _1607628), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1607624), c_List_Olists(_1607624, _1607626), c_List_Olistrel(_1607624, _1607628)))], (41747 ^ _777081) ^ [_1607723, _1607725, _1607727] : [c_Relation_Orefl__on(_1607723, _1607725, _1607727), -(c_Relation_Orefl__on(tc_List_Olist(_1607723), c_List_Olists(_1607723, _1607725), c_List_Olistrel(_1607723, _1607727)))], (41753 ^ _777081) ^ [_1607822, _1607824, _1607826, _1607828, _1607830, _1607832, _1607834] : [-(c_Map_Omap__upds(_1607822, _1607824, _1607826, hAPP(hAPP(c_List_Olist_OCons(_1607822), _1607828), _1607830), hAPP(hAPP(c_List_Olist_OCons(_1607824), _1607832), _1607834)) = c_Map_Omap__upds(_1607822, _1607824, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1607822, tc_Option_Ooption(_1607824)), _1607826), _1607828), hAPP(c_Option_Ooption_OSome(_1607824), _1607832)), _1607830, _1607834))], (41755 ^ _777081) ^ [_1607925, _1607927, _1607929, _1607931] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607925)), hAPP(hAPP(c_List_Olist_OCons(_1607925), _1607927), _1607929)), c_List_Olists(_1607925, _1607931))), 41758 ^ _777081 : [(41759 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1607925), _1607927), _1607931)))], (41761 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607925)), _1607929), c_List_Olists(_1607925, _1607931))))]]], (41763 ^ _777081) ^ [_1608106, _1608108, _1608110, _1608112] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1608106)), hAPP(hAPP(c_List_Olist_OCons(_1608106), _1608108), _1608110)), c_List_Olists(_1608106, _1608112)))), hBOOL(hAPP(hAPP(c_member(_1608106), _1608108), _1608112)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1608106)), _1608110), c_List_Olists(_1608106, _1608112)))], (41783 ^ _777081) ^ [_1608568, _1608570, _1608572] : [41785 ^ _777081 : [(41786 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1608568), 41784 ^ [_1608568, _1608570, _1608572]), hAPP(c_List_Oset(_1608568), _1608570))))], (41788 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1608568), 41784 ^ [_1608568, _1608570, _1608572]), _1608572))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1608568)), _1608570), c_List_Olists(_1608568, _1608572))))], (41773 ^ _777081) ^ [_1608341, _1608343, _1608345] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1608341)), _1608343), c_List_Olists(_1608341, _1608345))), 41776 ^ _777081 : [(41777 ^ _777081) ^ [_1608449] : [hBOOL(hAPP(hAPP(c_member(_1608341), _1608449), hAPP(c_List_Oset(_1608341), _1608343))), -(hBOOL(hAPP(hAPP(c_member(_1608341), _1608449), _1608345)))]]], (41792 ^ _777081) ^ [_1608788, _1608790, _1608792, _1608794, _1608796, _1608798, _1608800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608788)), _1608790)), _1608792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1608792), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608794)), _1608796))), -(c_Map_Omap__upds(_1608788, _1608794, _1608798, _1608790, hAPP(hAPP(c_List_Olist__update(_1608794, _1608796), _1608792), _1608800)) = c_Map_Omap__upds(_1608788, _1608794, _1608798, _1608790, _1608796))], (41802 ^ _777081) ^ [_1609023, _1609025, _1609027, _1609029, _1609031, _1609033, _1609035] : [-(hBOOL(hAPP(hAPP(c_member(_1609023), _1609025), hAPP(c_List_Oset(_1609023), _1609027)))), -(c_Map_Omap__upds(_1609023, _1609029, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1609023, tc_Option_Ooption(_1609029)), _1609031), _1609025), hAPP(c_Option_Ooption_OSome(_1609029), _1609033)), _1609027, _1609035) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1609023, tc_Option_Ooption(_1609029)), c_Map_Omap__upds(_1609023, _1609029, _1609031, _1609027, _1609035)), _1609025), hAPP(c_Option_Ooption_OSome(_1609029), _1609033)))], (41808 ^ _777081) ^ [_1609131, _1609133] : [-(c_List_Olists(_1609131, _1609133) = hAPP(c_Set_OCollect(tc_List_Olist(_1609131)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1609131), tc_fun(_1609131, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1609131, tc_HOL_Obool), tc_fun(tc_fun(_1609131, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1609131)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1609131, tc_HOL_Obool))), c_List_Oset(_1609131))), _1609133)))], (41810 ^ _777081) ^ [_1609209, _1609211, _1609213, _1609215, _1609217, _1609219] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609209)), _1609211) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609213)), _1609215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1609209, tc_HOL_Obool)), hAPP(c_List_Oset(_1609209), _1609211)), _1609217)), -(c_Map_Orestrict__map(_1609209, _1609213, c_Map_Omap__upds(_1609209, _1609213, _1609219, _1609211, _1609215), _1609217) = c_Map_Omap__upds(_1609209, _1609213, c_Map_Orestrict__map(_1609209, _1609213, _1609219, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1609209, tc_HOL_Obool)), _1609217), hAPP(c_List_Oset(_1609209), _1609211))), _1609211, _1609215))], (41820 ^ _777081) ^ [_1609488, _1609490, _1609492, _1609494, _1609496] : [-(c_Map_Odom(_1609488, _1609490, c_Map_Omap__upds(_1609488, _1609490, _1609492, _1609494, _1609496)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609488, tc_HOL_Obool)), hAPP(c_List_Oset(_1609488), hAPP(hAPP(c_List_Otake(_1609488), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609490)), _1609496)), _1609494))), c_Map_Odom(_1609488, _1609490, _1609492)))], (41822 ^ _777081) ^ [_1609564, _1609566, _1609568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1609564, _1609564), tc_HOL_Obool)), _1609566), _1609568)), c_Relation_Orefl__on(_1609564, c_Orderings_Otop__class_Otop(tc_fun(_1609564, tc_HOL_Obool)), _1609568), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1609564), tc_List_Olist(_1609564)), tc_HOL_Obool)), c_List_Olistrel1(_1609564, _1609566)), c_List_Olistrel(_1609564, _1609568))))], (41832 ^ _777081) ^ [_1609781, _1609783, _1609785, _1609787] : [41835 ^ _777081 : [(41836 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609781, _1609781)), hAPP(hAPP(c_Product__Type_OPair(_1609781, _1609781), 41833 ^ [_1609781, _1609783, _1609785, _1609787]), 41834 ^ [_1609781, _1609783, _1609785, _1609787])), _1609783))], (41838 ^ _777081) ^ [] : [41833 ^ [_1609781, _1609783, _1609785, _1609787] = 41834 ^ [_1609781, _1609783, _1609785, _1609787]], (41840 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609781, _1609781)), hAPP(hAPP(c_Product__Type_OPair(_1609781, _1609781), 41834 ^ [_1609781, _1609783, _1609785, _1609787]), 41833 ^ [_1609781, _1609783, _1609785, _1609787])), _1609783))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609781), tc_List_Olist(_1609781))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609781), tc_List_Olist(_1609781)), _1609785), _1609787)), c_List_Olexord(_1609781, _1609783)))), -(_1609785 = _1609787), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609781), tc_List_Olist(_1609781))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609781), tc_List_Olist(_1609781)), _1609787), _1609785)), c_List_Olexord(_1609781, _1609783))))], (41852 ^ _777081) ^ [_1610328, _1610330, _1610332, _1610334] : [hBOOL(hAPP(hAPP(c_member(_1610328), _1610330), c_Wellfounded_Oacc(_1610328, _1610332))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1610328)), _1610334), c_Wellfounded_Oacc(tc_List_Olist(_1610328), c_List_Olistrel1(_1610328, _1610332)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1610328)), hAPP(hAPP(c_List_Olist_OCons(_1610328), _1610330), _1610334)), c_Wellfounded_Oacc(tc_List_Olist(_1610328), c_List_Olistrel1(_1610328, _1610332)))))], (41862 ^ _777081) ^ [_1610569, _1610571, _1610573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1610569, _1610569), tc_HOL_Obool)), _1610571), _1610573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1610569), tc_List_Olist(_1610569)), tc_HOL_Obool)), c_List_Olistrel1(_1610569, _1610571)), c_List_Olistrel1(_1610569, _1610573))))], (41868 ^ _777081) ^ [_1610720, _1610722, _1610724, _1610726, _1610728] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610720), tc_List_Olist(_1610720))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610720), tc_List_Olist(_1610720)), _1610722), _1610724)), c_List_Olistrel1(_1610720, _1610726))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610720), tc_List_Olist(_1610720))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610720), tc_List_Olist(_1610720)), hAPP(hAPP(c_List_Olist_OCons(_1610720), _1610728), _1610722)), hAPP(hAPP(c_List_Olist_OCons(_1610720), _1610728), _1610724))), c_List_Olistrel1(_1610720, _1610726))))], (41874 ^ _777081) ^ [_1610955, _1610957, _1610959, _1610961] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610955), tc_List_Olist(_1610955))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610955), tc_List_Olist(_1610955)), _1610957), _1610959)), c_List_Olistrel1(_1610955, _1610961))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610955)), _1610957) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610955)), _1610959))], (41880 ^ _777081) ^ [_1611124, _1611126, _1611128] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611124)), _1611126), c_Wellfounded_Oacc(tc_List_Olist(_1611124), c_List_Olistrel1(_1611124, _1611128)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611124)), _1611126), c_List_Olists(_1611124, c_Wellfounded_Oacc(_1611124, _1611128)))))], (41886 ^ _777081) ^ [_1611267, _1611269, _1611271] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611267)), _1611269), c_List_Olists(_1611267, c_Wellfounded_Oacc(_1611267, _1611271)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1611267)), _1611269), c_Wellfounded_Oacc(tc_List_Olist(_1611267), c_List_Olistrel1(_1611267, _1611271)))))], (41892 ^ _777081) ^ [_1611437, _1611439, _1611441, _1611443, _1611445, _1611447] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611437), tc_List_Olist(_1611437))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611437), tc_List_Olist(_1611437)), hAPP(hAPP(c_List_Olist_OCons(_1611437), _1611439), _1611441)), hAPP(hAPP(c_List_Olist_OCons(_1611437), _1611443), _1611445))), c_List_Olistrel1(_1611437, _1611447))), 41897 ^ _777081 : [(41898 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1611437, _1611437)), hAPP(hAPP(c_Product__Type_OPair(_1611437, _1611437), _1611439), _1611443)), _1611447)))], (41900 ^ _777081) ^ [] : [-(_1611441 = _1611445)]], 41901 ^ _777081 : [(41902 ^ _777081) ^ [] : [-(_1611439 = _1611443)], (41904 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611437), tc_List_Olist(_1611437))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611437), tc_List_Olist(_1611437)), _1611441), _1611445)), c_List_Olistrel1(_1611437, _1611447))))]]], (41906 ^ _777081) ^ [_1611807, _1611809, _1611811, _1611813, _1611815, _1611817] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611807), tc_List_Olist(_1611807))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611807), tc_List_Olist(_1611807)), hAPP(hAPP(c_List_Olist_OCons(_1611807), _1611809), _1611811)), hAPP(hAPP(c_List_Olist_OCons(_1611807), _1611813), _1611815))), c_List_Olistrel1(_1611807, _1611817)))), 41907 ^ _777081 : [(41908 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1611807, _1611807)), hAPP(hAPP(c_Product__Type_OPair(_1611807, _1611807), _1611809), _1611813)), _1611817)), _1611811 = _1611815], (41914 ^ _777081) ^ [] : [_1611809 = _1611813, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611807), tc_List_Olist(_1611807))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611807), tc_List_Olist(_1611807)), _1611811), _1611815)), c_List_Olistrel1(_1611807, _1611817)))]]], (41922 ^ _777081) ^ [_1612235, _1612237, _1612239, _1612241, _1612243] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612235, _1612235)), hAPP(hAPP(c_Product__Type_OPair(_1612235, _1612235), _1612237), _1612239)), _1612241)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612235), tc_List_Olist(_1612235))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612235), tc_List_Olist(_1612235)), hAPP(hAPP(c_List_Olist_OCons(_1612235), _1612237), _1612243)), hAPP(hAPP(c_List_Olist_OCons(_1612235), _1612239), _1612243))), c_List_Olistrel1(_1612235, _1612241))))], (41928 ^ _777081) ^ [_1612469, _1612471, _1612473, _1612475] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612469), tc_List_Olist(_1612469))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612469), tc_List_Olist(_1612469)), _1612471), _1612473)), c_List_Olistrel1(_1612469, _1612475))), 41933 ^ _777081 : [(41934 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612469, _1612469)), hAPP(hAPP(c_Product__Type_OPair(_1612469, _1612469), hAPP(hAPP(c_List_Onth(_1612469), _1612471), 41932 ^ [_1612469, _1612471, _1612473, _1612475])), 41931 ^ [_1612469, _1612471, _1612473, _1612475])), _1612475)))], (41936 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41932 ^ [_1612469, _1612471, _1612473, _1612475]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612469)), _1612471))))], (41938 ^ _777081) ^ [] : [-(_1612473 = hAPP(hAPP(c_List_Olist__update(_1612469, _1612471), 41932 ^ [_1612469, _1612471, _1612473, _1612475]), 41931 ^ [_1612469, _1612471, _1612473, _1612475]))]]], (41940 ^ _777081) ^ [_1612817, _1612819, _1612821, _1612823] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612817), tc_List_Olist(_1612817))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612817), tc_List_Olist(_1612817)), _1612819), _1612821)), c_List_Olistrel1(_1612817, _1612823)))), 41941 ^ _777081 : [(41942 ^ _777081) ^ [_1612950, _1612952] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612817, _1612817)), hAPP(hAPP(c_Product__Type_OPair(_1612817, _1612817), hAPP(hAPP(c_List_Onth(_1612817), _1612819), _1612950)), _1612952)), _1612823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612950), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612817)), _1612819))), _1612821 = hAPP(hAPP(c_List_Olist__update(_1612817, _1612819), _1612950), _1612952)]]], (41954 ^ _777081) ^ [_1613249, _1613251, _1613253] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613249, _1613249)), hAPP(hAPP(c_Product__Type_OPair(_1613249, _1613249), 41955 ^ [_1613249, _1613251, _1613253]), 41955 ^ [_1613249, _1613251, _1613253])), _1613251))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613249), tc_List_Olist(_1613249))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613249), tc_List_Olist(_1613249)), _1613253), _1613253)), c_List_Olexord(_1613249, _1613251)))], (41961 ^ _777081) ^ [_1613424, _1613426] : [class_Groups_Ocomm__monoid__add(_1613424), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1613424), _1613426) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1613424), hAPP(c_List_Onth(_1613424), _1613426)), 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(_1613424)), _1613426))))], (41967 ^ _777081) ^ [_1613557, _1613559, _1613561, _1613563] : [41969 ^ _777081 : [(41970 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613557), 41968 ^ [_1613557, _1613559, _1613561, _1613563]), hAPP(c_List_Oset(_1613557), _1613559))))], (41972 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1613561, 41968 ^ [_1613557, _1613559, _1613561, _1613563])), hAPP(_1613563, 41968 ^ [_1613557, _1613559, _1613561, _1613563])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1613557, _1613561, _1613559)), c_List_Olist_Olist__size(_1613557, _1613563, _1613559))))], (41986 ^ _777081) ^ [_1613987] : [41988 ^ _777081 : [(41989 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 41987 ^ [_1613987]), hAPP(c_List_Oset(tc_Nat_Onat), _1613987))))], (41991 ^ _777081) ^ [] : [41987 ^ [_1613987] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1613987) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41976 ^ _777081) ^ [_1613819] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1613819) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 41979 ^ _777081 : [(41980 ^ _777081) ^ [_1613894] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1613894), hAPP(c_List_Oset(tc_Nat_Onat), _1613819))), -(_1613894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (41995 ^ _777081) ^ [_1614143, _1614145, _1614147] : [class_Groups_Omonoid__add(_1614143), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1614143), hAPP(hAPP(c_List_Olist_OCons(_1614143), _1614145), _1614147)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1614143), _1614145), hAPP(c_List_Omonoid__add__class_Olistsum(_1614143), _1614147)))], (42001 ^ _777081) ^ [_1614272, _1614274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1614272), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1614274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1614274), _1614272)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1614274))))], (42007 ^ _777081) ^ [_1614393, _1614395, _1614397] : [class_Groups_Omonoid__add(_1614393), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1614393), hAPP(hAPP(c_List_Omap(_1614395, _1614393), hAPP(c_COMBK(_1614393, _1614395), c_Groups_Ozero__class_Ozero(_1614393))), _1614397)) = c_Groups_Ozero__class_Ozero(_1614393))], (42013 ^ _777081) ^ [_1614518, _1614520, _1614522, _1614524, _1614526] : [class_Groups_Ocomm__monoid__add(_1614518), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1614518), hAPP(hAPP(c_List_Omap(_1614520, _1614518), hAPP(hAPP(c_COMBS(_1614520, _1614518, _1614518), hAPP(hAPP(c_COMBB(_1614518, tc_fun(_1614518, _1614518), _1614520), c_Groups_Oplus__class_Oplus(_1614518)), _1614522)), _1614524)), _1614526)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1614518), hAPP(c_List_Omonoid__add__class_Olistsum(_1614518), hAPP(hAPP(c_List_Omap(_1614520, _1614518), _1614522), _1614526))), hAPP(c_List_Omonoid__add__class_Olistsum(_1614518), hAPP(hAPP(c_List_Omap(_1614520, _1614518), _1614524), _1614526))))], (42019 ^ _777081) ^ [_1614749, _1614751, _1614753, _1614755, _1614757] : [class_Rings_Osemiring__0(_1614749), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1614749), hAPP(hAPP(c_List_Omap(_1614751, _1614749), hAPP(hAPP(c_COMBB(_1614749, _1614749, _1614751), hAPP(c_Groups_Otimes__class_Otimes(_1614749), _1614753)), _1614755)), _1614757)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1614749), _1614753), hAPP(c_List_Omonoid__add__class_Olistsum(_1614749), hAPP(hAPP(c_List_Omap(_1614751, _1614749), _1614755), _1614757))))], (42025 ^ _777081) ^ [_1614932, _1614934, _1614936, _1614938, _1614940] : [class_Rings_Osemiring__0(_1614932), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1614932), hAPP(hAPP(c_List_Omap(_1614934, _1614932), hAPP(hAPP(c_COMBC(_1614934, _1614932, _1614932), hAPP(hAPP(c_COMBB(_1614932, tc_fun(_1614932, _1614932), _1614934), c_Groups_Otimes__class_Otimes(_1614932)), _1614936)), _1614938)), _1614940)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1614932), hAPP(c_List_Omonoid__add__class_Olistsum(_1614932), hAPP(hAPP(c_List_Omap(_1614934, _1614932), _1614936), _1614940))), _1614938))], (42031 ^ _777081) ^ [_1615135, _1615137, _1615139, _1615141, _1615143] : [class_Groups_Oab__group__add(_1615135), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1615135), hAPP(hAPP(c_List_Omap(_1615137, _1615135), hAPP(hAPP(c_COMBS(_1615137, _1615135, _1615135), hAPP(hAPP(c_COMBB(_1615135, tc_fun(_1615135, _1615135), _1615137), c_Groups_Ominus__class_Ominus(_1615135)), _1615139)), _1615141)), _1615143)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1615135), hAPP(c_List_Omonoid__add__class_Olistsum(_1615135), hAPP(hAPP(c_List_Omap(_1615137, _1615135), _1615139), _1615143))), hAPP(c_List_Omonoid__add__class_Olistsum(_1615135), hAPP(hAPP(c_List_Omap(_1615137, _1615135), _1615141), _1615143))))], (42037 ^ _777081) ^ [_1615366, _1615368, _1615370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1615366), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1615368))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1615368), _1615366), _1615370)) = 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), _1615368)), _1615370)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1615368), _1615366)))], (42043 ^ _777081) ^ [_1615527, _1615529] : [class_Groups_Oordered__ab__group__add__abs(_1615527), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1615527), hAPP(c_Groups_Oabs__class_Oabs(_1615527), hAPP(c_List_Omonoid__add__class_Olistsum(_1615527), _1615529))), hAPP(c_List_Omonoid__add__class_Olistsum(_1615527), hAPP(hAPP(c_List_Omap(_1615527, _1615527), c_Groups_Oabs__class_Oabs(_1615527)), _1615529)))))], (42049 ^ _777081) ^ [_1615668, _1615670, _1615672, _1615674] : [class_Groups_Oab__group__add(_1615668), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1615668), hAPP(c_List_Omonoid__add__class_Olistsum(_1615668), hAPP(hAPP(c_List_Omap(_1615670, _1615668), _1615672), _1615674))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1615668), hAPP(hAPP(c_List_Omap(_1615670, _1615668), hAPP(c_Fun_Ocomp(_1615668, _1615668, _1615670, c_Groups_Ouminus__class_Ouminus(_1615668)), _1615672)), _1615674)))], (42055 ^ _777081) ^ [_1615833, _1615835, _1615837] : [-(c_List_Olist_Olist__size(_1615833, _1615835, _1615837) = 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(_1615833, tc_Nat_Onat), _1615835), _1615837))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615833)), _1615837)))], (42057 ^ _777081) ^ [_1615889, _1615891] : [class_Groups_Ocomm__monoid__add(_1615889), hBOOL(hAPP(c_List_Odistinct(_1615889), _1615891)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1615889), _1615891) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1615889, _1615889), c_COMBI(_1615889)), hAPP(c_List_Oset(_1615889), _1615891)))], (42067 ^ _777081) ^ [_1616066, _1616068, _1616070, _1616072] : [class_Groups_Ocomm__monoid__add(_1616066), hBOOL(hAPP(c_List_Odistinct(_1616068), _1616070)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1616066), hAPP(hAPP(c_List_Omap(_1616068, _1616066), _1616072), _1616070)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1616068, _1616066), _1616072), hAPP(c_List_Oset(_1616068), _1616070)))], (42077 ^ _777081) ^ [_1616265, _1616267, _1616269, _1616271] : [class_Groups_Ocomm__monoid__add(_1616265), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1616265), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1616265), _1616267), c_List_Oupto(_1616269, _1616271))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1616265), _1616267), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1616269, _1616271))))], (42083 ^ _777081) ^ [_1616408, _1616410, _1616412, _1616414] : [class_Groups_Ocomm__monoid__add(_1616408), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1616408), _1616410), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1616412, _1616414))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1616408), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1616408), _1616410), c_List_Oupto(_1616412, _1616414))))], (42089 ^ _777081) ^ [_1616551, _1616553, _1616555, _1616557] : [class_Rings_Osemiring__1(_1616551), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1616551), hAPP(hAPP(c_List_Omap(_1616553, _1616551), hAPP(c_COMBK(_1616551, _1616553), _1616555)), _1616557)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1616551), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1616551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616553)), _1616557))), _1616555))], (42095 ^ _777081) ^ [_1616710, _1616712, _1616714, _1616716, _1616718] : [class_Groups_Ocomm__monoid__add(_1616710), hBOOL(hAPP(hAPP(c_member(_1616712), _1616714), hAPP(c_List_Oset(_1616712), _1616716))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1616710), hAPP(hAPP(c_List_Omap(_1616712, _1616710), _1616718), _1616716)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1616710), hAPP(_1616718, _1616714)), hAPP(c_List_Omonoid__add__class_Olistsum(_1616710), hAPP(hAPP(c_List_Omap(_1616712, _1616710), _1616718), c_List_Oremove1(_1616712, _1616714, _1616716)))))], (42105 ^ _777081) ^ [_1616959, _1616961, _1616963, _1616965] : [class_Groups_Ocomm__monoid__add(_1616959), 42108 ^ _777081 : [(42109 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1616961), _1616963)), -(c_Nitpick_Osetsum_H(_1616961, _1616959, _1616965, _1616963) = hAPP(c_List_Omonoid__add__class_Olistsum(_1616959), hAPP(hAPP(c_List_Omap(_1616961, _1616959), _1616965), c_Hilbert__Choice_OEps(tc_List_Olist(_1616961), hAPP(hAPP(c_COMBS(tc_List_Olist(_1616961), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1616961)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1616961), tc_fun(_1616961, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1616961, tc_HOL_Obool), tc_fun(tc_fun(_1616961, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1616961)), c_fequal), c_List_Oset(_1616961))), _1616963))), c_List_Odistinct(_1616961))))))], (42115 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1616961), _1616963))), -(c_Nitpick_Osetsum_H(_1616961, _1616959, _1616965, _1616963) = c_Groups_Ozero__class_Ozero(_1616959))]]], (42121 ^ _777081) ^ [_1617347, _1617349, _1617351, _1617353, _1617355] : [class_Groups_Omonoid__add(_1617347), class_Groups_Oordered__ab__semigroup__add(_1617347), 42131 ^ _777081 : [(42132 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617349), 42130 ^ [_1617347, _1617349, _1617351, _1617353, _1617355]), hAPP(c_List_Oset(_1617349), _1617351))))], (42134 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1617347), hAPP(_1617353, 42130 ^ [_1617347, _1617349, _1617351, _1617353, _1617355])), hAPP(_1617355, 42130 ^ [_1617347, _1617349, _1617351, _1617353, _1617355])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1617347), hAPP(c_List_Omonoid__add__class_Olistsum(_1617347), hAPP(hAPP(c_List_Omap(_1617349, _1617347), _1617353), _1617351))), hAPP(c_List_Omonoid__add__class_Olistsum(_1617347), hAPP(hAPP(c_List_Omap(_1617349, _1617347), _1617355), _1617351)))))], (42138 ^ _777081) ^ [_1617771, _1617773, _1617775] : [hBOOL(hAPP(_1617771, _1617773)), -(hBOOL(hAPP(_1617771, c_Hilbert__Choice_OEps(_1617775, _1617771))))], (42144 ^ _777081) ^ [_1617864, _1617866] : [42145 ^ _777081 : [(42146 ^ _777081) ^ [_1617910] : [hBOOL(hAPP(_1617864, _1617910))]], -(hBOOL(hAPP(_1617864, c_Hilbert__Choice_OEps(_1617866, _1617864))))], (42150 ^ _777081) ^ [_1617968, _1617970] : [42151 ^ _777081 : [(42152 ^ _777081) ^ [_1618014] : [hBOOL(hAPP(_1617968, _1618014))]], -(hBOOL(hAPP(_1617968, c_Hilbert__Choice_OEps(_1617970, _1617968))))], (42156 ^ _777081) ^ [_1618087, _1618089] : [hBOOL(hAPP(_1618087, c_Hilbert__Choice_OEps(_1618089, _1618087))), -(hBOOL(hAPP(_1618087, 42159 ^ [_1618087, _1618089])))], (42163 ^ _777081) ^ [_1618186, _1618188] : [42164 ^ _777081 : [(42165 ^ _777081) ^ [_1618232] : [hBOOL(hAPP(_1618186, _1618232))]], -(hBOOL(hAPP(_1618186, c_Hilbert__Choice_OEps(_1618188, _1618186))))], (42169 ^ _777081) ^ [_1618292, _1618294] : [-(c_Hilbert__Choice_OEps(_1618292, hAPP(hAPP(c_COMBC(_1618292, _1618292, tc_HOL_Obool), c_fequal), _1618294)) = _1618294)], (42171 ^ _777081) ^ [_1618330, _1618332] : [-(c_Hilbert__Choice_OEps(_1618330, hAPP(c_fequal, _1618332)) = _1618332)], (42173 ^ _777081) ^ [_1618361, _1618363, _1618365] : [42174 ^ _777081 : [(42175 ^ _777081) ^ [_1618415] : [hBOOL(hAPP(_1618361, _1618415))]], _1618363 = c_Hilbert__Choice_OEps(_1618365, _1618361), -(hBOOL(hAPP(_1618361, _1618363)))], (42183 ^ _777081) ^ [_1618530, _1618532] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1618530), _1618532)), -(c_Nitpick_Ocard_H(_1618530, _1618532) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618530)), c_Hilbert__Choice_OEps(tc_List_Olist(_1618530), hAPP(hAPP(c_COMBS(tc_List_Olist(_1618530), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1618530)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1618530), tc_fun(_1618530, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1618530, tc_HOL_Obool), tc_fun(tc_fun(_1618530, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1618530)), c_fequal), c_List_Oset(_1618530))), _1618532))), c_List_Odistinct(_1618530)))))], (42189 ^ _777081) ^ [_1618767, _1618769] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1618767), _1618769))), -(c_Nitpick_Ocard_H(_1618767, _1618769) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42195 ^ _777081) ^ [_1618812, _1618814, _1618816, _1618818] : [class_Orderings_Oord(_1618812), -(c_Hilbert__Choice_OLeastM(_1618814, _1618812, _1618816, _1618818) = c_Hilbert__Choice_OEps(_1618814, hAPP(hAPP(c_COMBS(_1618814, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1618814), c_fconj), _1618818)), hAPP(hAPP(c_COMBB(tc_fun(_1618814, tc_HOL_Obool), tc_HOL_Obool, _1618814), c_HOL_OAll(_1618814)), hAPP(hAPP(c_COMBB(tc_fun(_1618814, tc_HOL_Obool), tc_fun(_1618814, tc_HOL_Obool), _1618814), hAPP(c_COMBS(_1618814, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1618814), c_fimplies), _1618818))), hAPP(hAPP(c_COMBC(_1618814, tc_fun(_1618814, _1618812), tc_fun(_1618814, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1618812, tc_HOL_Obool), tc_fun(tc_fun(_1618814, _1618812), tc_fun(_1618814, tc_HOL_Obool)), _1618814), c_COMBB(_1618812, tc_HOL_Obool, _1618814)), hAPP(hAPP(c_COMBB(_1618812, tc_fun(_1618812, tc_HOL_Obool), _1618814), c_Orderings_Oord__class_Oless__eq(_1618812)), _1618816))), _1618816))))))], (42201 ^ _777081) ^ [_1619157, _1619159, _1619161, _1619163] : [hBOOL(hAPP(_1619157, _1619159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1619161, c_Hilbert__Choice_OLeastM(_1619163, tc_Nat_Onat, _1619161, _1619157))), hAPP(_1619161, _1619159))))], (42207 ^ _777081) ^ [_1619274, _1619276, _1619278, _1619280] : [hBOOL(hAPP(_1619274, _1619276)), 42210 ^ _777081 : [(42211 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1619274, c_Hilbert__Choice_OLeastM(_1619278, tc_Nat_Onat, _1619280, _1619274))))], (42213 ^ _777081) ^ [_1619404] : [hBOOL(hAPP(_1619274, _1619404)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1619280, c_Hilbert__Choice_OLeastM(_1619278, tc_Nat_Onat, _1619280, _1619274))), hAPP(_1619280, _1619404))))]]], (42219 ^ _777081) ^ [_1619529, _1619531, _1619533] : [-(c_Hilbert__Choice_OEps(tc_prod(_1619529, _1619531), _1619533) = c_Hilbert__Choice_OEps(tc_prod(_1619529, _1619531), hAPP(c_Product__Type_Oprod_Oprod__case(_1619529, _1619531, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1619531, tc_prod(_1619529, _1619531)), tc_fun(_1619531, tc_HOL_Obool), _1619529), hAPP(c_COMBB(tc_prod(_1619529, _1619531), tc_HOL_Obool, _1619531), _1619533)), c_Product__Type_OPair(_1619529, _1619531)))))], (42221 ^ _777081) ^ [_1619607, _1619609, _1619611, _1619613] : [-(c_Hilbert__Choice_OEps(tc_prod(_1619607, _1619609), hAPP(c_Product__Type_Oprod_Oprod__case(_1619607, _1619609, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1619607, tc_fun(_1619609, tc_HOL_Obool), tc_fun(_1619609, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1619609, tc_HOL_Obool), tc_fun(_1619609, tc_HOL_Obool)), _1619607), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1619609)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1619607), c_fconj), hAPP(c_fequal, _1619611)))), hAPP(c_fequal, _1619613)))) = hAPP(hAPP(c_Product__Type_OPair(_1619607, _1619609), _1619611), _1619613))], (42223 ^ _777081) ^ [_1619713, _1619715, _1619717] : [-(c_Hilbert__Choice_OEps(tc_prod(_1619713, _1619715), hAPP(c_Product__Type_Oprod_Oprod__case(_1619713, _1619715, tc_HOL_Obool), _1619717)) = c_Hilbert__Choice_OEps(tc_prod(_1619713, _1619715), hAPP(hAPP(c_COMBS(tc_prod(_1619713, _1619715), _1619715, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1619713, tc_fun(_1619715, tc_HOL_Obool), tc_prod(_1619713, _1619715)), _1619717), c_Product__Type_Ofst(_1619713, _1619715))), c_Product__Type_Osnd(_1619713, _1619715))))], (42225 ^ _777081) ^ [_1619794, _1619796, _1619798, _1619800] : [class_Orderings_Oord(_1619794), -(hAPP(c_Hilbert__Choice_OGreatestM(_1619796, _1619794, _1619798), _1619800) = c_Hilbert__Choice_OEps(_1619796, hAPP(hAPP(c_COMBS(_1619796, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1619796), c_fconj), _1619800)), hAPP(hAPP(c_COMBB(tc_fun(_1619796, tc_HOL_Obool), tc_HOL_Obool, _1619796), c_HOL_OAll(_1619796)), hAPP(hAPP(c_COMBB(tc_fun(_1619796, tc_HOL_Obool), tc_fun(_1619796, tc_HOL_Obool), _1619796), hAPP(c_COMBS(_1619796, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1619796), c_fimplies), _1619800))), hAPP(hAPP(c_COMBB(_1619794, tc_fun(_1619796, tc_HOL_Obool), _1619796), hAPP(c_COMBC(_1619796, _1619794, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1619794, tc_fun(_1619794, tc_HOL_Obool), _1619796), c_Orderings_Oord__class_Oless__eq(_1619794)), _1619798))), _1619798))))))], (42231 ^ _777081) ^ [_1620099, _1620101, _1620103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1620099), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620101)), _1620103))), -(c_List_Obutlast(_1620101, hAPP(hAPP(c_List_Otake(_1620101), _1620099), _1620103)) = hAPP(hAPP(c_List_Otake(_1620101), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1620099), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1620103))], (42237 ^ _777081) ^ [_1620252, _1620254, _1620256, _1620258] : [hBOOL(hAPP(_1620252, _1620254)), -(hBOOL(hAPP(_1620252, c_Hilbert__Choice_OLeastM(_1620256, tc_Nat_Onat, _1620258, _1620252))))], (42243 ^ _777081) ^ [_1620351, _1620353, _1620355, _1620357] : [-(hAPP(hAPP(c_List_Omap(_1620351, _1620353), _1620355), c_List_Obutlast(_1620351, _1620357)) = c_List_Obutlast(_1620353, hAPP(hAPP(c_List_Omap(_1620351, _1620353), _1620355), _1620357)))], (42245 ^ _777081) ^ [_1620404, _1620406, _1620408] : [hBOOL(hAPP(hAPP(c_member(_1620404), _1620406), hAPP(c_List_Oset(_1620404), c_List_Obutlast(_1620404, _1620408)))), -(hBOOL(hAPP(hAPP(c_member(_1620404), _1620406), hAPP(c_List_Oset(_1620404), _1620408))))], (42251 ^ _777081) ^ [_1620537, _1620539, _1620541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1620537), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620539)), _1620541))), -(hAPP(hAPP(c_List_Otake(_1620539), _1620537), c_List_Obutlast(_1620539, _1620541)) = hAPP(hAPP(c_List_Otake(_1620539), _1620537), _1620541))], (42257 ^ _777081) ^ [_1620678, _1620680] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620678)), c_List_Obutlast(_1620678, _1620680)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620678)), _1620680)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42259 ^ _777081) ^ [_1620726, _1620728] : [-(c_List_Obutlast(_1620726, _1620728) = hAPP(hAPP(c_List_Otake(_1620726), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620726)), _1620728)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1620728))], (42261 ^ _777081) ^ [_1620790, _1620792, _1620794, _1620796] : [_1620790 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620792)), _1620794)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1620792, hAPP(hAPP(c_List_Olist__update(_1620792, _1620794), _1620790), _1620796)) = c_List_Obutlast(_1620792, _1620794))], (42267 ^ _777081) ^ [_1620921, _1620923, _1620925, _1620927] : [-(_1620921 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620923)), _1620925)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1620923, hAPP(hAPP(c_List_Olist__update(_1620923, _1620925), _1620921), _1620927)) = hAPP(hAPP(c_List_Olist__update(_1620923, c_List_Obutlast(_1620923, _1620925)), _1620921), _1620927))], (42273 ^ _777081) ^ [_1621000] : [class_Orderings_Oord(_1621000), -(c_Hilbert__Choice_OGreatest(_1621000) = c_Hilbert__Choice_OGreatestM(_1621000, _1621000, c_COMBI(_1621000)))], (42279 ^ _777081) ^ [_1621089, _1621091, _1621093, _1621095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1621089), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621091)), _1621093))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1621089), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621091)), _1621095))), 42289 ^ _777081 : [(42290 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42288 ^ [_1621089, _1621091, _1621093, _1621095]), _1621089)))], (42292 ^ _777081) ^ [] : [hAPP(hAPP(c_List_Onth(_1621091), _1621093), 42288 ^ [_1621089, _1621091, _1621093, _1621095]) = hAPP(hAPP(c_List_Onth(_1621091), _1621095), 42288 ^ [_1621089, _1621091, _1621093, _1621095])]], -(hAPP(hAPP(c_List_Otake(_1621091), _1621089), _1621093) = hAPP(hAPP(c_List_Otake(_1621091), _1621089), _1621095))], (42296 ^ _777081) ^ [_1621521, _1621523, _1621525, _1621527] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1621521) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1621523), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1621521)), hAPP(hAPP(c_List_Olist_OCons(_1621523), _1621525), _1621527)) = c_List_Olist_ONil(_1621523))], (42302 ^ _777081) ^ [_1621644, _1621646, _1621648, _1621650] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1621644) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1621646), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1621644)), hAPP(hAPP(c_List_Olist_OCons(_1621646), _1621648), _1621650)) = hAPP(hAPP(c_List_Olist_OCons(_1621646), _1621648), hAPP(hAPP(c_List_Otake(_1621646), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1621644)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1621650)))], (42308 ^ _777081) ^ [_1621733, _1621735, _1621737, _1621739, _1621741] : [c_List_Opartition(_1621733, _1621735, _1621737) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621733), tc_List_Olist(_1621733)), _1621739), _1621741), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1621733, tc_HOL_Obool)), hAPP(c_List_Oset(_1621733), _1621739)), hAPP(c_List_Oset(_1621733), _1621741)) = hAPP(c_List_Oset(_1621733), _1621737))], (42314 ^ _777081) ^ [_1621902, _1621904] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1621902)), c_List_Olist_ONil(_1621902)), c_List_Olists(_1621902, _1621904))))], (42316 ^ _777081) ^ [_1621941, _1621943, _1621945] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1621941), tc_List_Olist(_1621941))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1621941), tc_List_Olist(_1621941)), c_List_Olist_ONil(_1621941)), _1621943)), c_List_Olistrel(_1621941, _1621945))), -(_1621943 = c_List_Olist_ONil(_1621941))], (42322 ^ _777081) ^ [_1622088, _1622090, _1622092] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1622088), tc_List_Olist(_1622088))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622088), tc_List_Olist(_1622088)), _1622090), c_List_Olist_ONil(_1622088))), c_List_Olistrel(_1622088, _1622092))), -(_1622090 = c_List_Olist_ONil(_1622088))], (42328 ^ _777081) ^ [_1622250, _1622252, _1622254] : [hAPP(hAPP(c_List_Olist_OCons(_1622250), _1622252), _1622254) = c_List_Olist_ONil(_1622250)], (42330 ^ _777081) ^ [_1622302, _1622304, _1622306] : [c_List_Olist_ONil(_1622302) = hAPP(hAPP(c_List_Olist_OCons(_1622302), _1622304), _1622306)], (42332 ^ _777081) ^ [_1622339, _1622341, _1622343, _1622345] : [class_Orderings_Olinorder(_1622339), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1622341, _1622339, _1622343), _1622345), c_List_Olist_ONil(_1622341)) = hAPP(hAPP(c_List_Olist_OCons(_1622341), _1622345), c_List_Olist_ONil(_1622341)))], (42338 ^ _777081) ^ [_1622462, _1622464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1622462), _1622464)), -(c_List_Oupto(_1622464, _1622462) = c_List_Olist_ONil(tc_Int_Oint))], (42344 ^ _777081) ^ [_1622555, _1622557] : [-(c_List_Osublist(_1622555, c_List_Olist_ONil(_1622555), _1622557) = c_List_Olist_ONil(_1622555))], (42346 ^ _777081) ^ [_1622588, _1622590] : [-(c_List_Opartition(_1622588, _1622590, c_List_Olist_ONil(_1622588)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1622588), tc_List_Olist(_1622588)), c_List_Olist_ONil(_1622588)), c_List_Olist_ONil(_1622588)))], (42348 ^ _777081) ^ [_1622636, _1622638, _1622640] : [-(hAPP(hAPP(c_List_Ozip(_1622636, _1622638), c_List_Olist_ONil(_1622636)), _1622640) = c_List_Olist_ONil(tc_prod(_1622636, _1622638)))], (42350 ^ _777081) ^ [_1622679, _1622681, _1622683] : [-(hAPP(hAPP(c_List_Ozip(_1622679, _1622681), _1622683), c_List_Olist_ONil(_1622681)) = c_List_Olist_ONil(tc_prod(_1622679, _1622681)))], (42352 ^ _777081) ^ [_1622722, _1622724, _1622726, _1622728] : [-(c_List_Ofoldr(_1622722, _1622724, _1622726, c_List_Olist_ONil(_1622722), _1622728) = _1622728)], (42354 ^ _777081) ^ [_1622759, _1622761, _1622763] : [-(hAPP(hAPP(c_Map_Omap__of(_1622759, _1622761), c_List_Olist_ONil(tc_prod(_1622759, _1622761))), _1622763) = c_Option_Ooption_ONone(_1622761))], (42356 ^ _777081) ^ [_1622802, _1622804] : [-(c_List_Oremove1(_1622802, _1622804, c_List_Olist_ONil(_1622802)) = c_List_Olist_ONil(_1622802))], (42358 ^ _777081) ^ [_1622835] : [-(hBOOL(hAPP(c_List_Odistinct(_1622835), c_List_Olist_ONil(_1622835))))], (42360 ^ _777081) ^ [_1622864, _1622866, _1622868, _1622870, _1622872] : [class_Orderings_Olinorder(_1622864), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1622866, _1622864, _1622868), _1622870), _1622872) = c_List_Olist_ONil(_1622866)], (42366 ^ _777081) ^ [_1622970, _1622972] : [-(c_List_Olistrelp(_1622970, _1622972, c_List_Olist_ONil(_1622970), c_List_Olist_ONil(_1622970)))], (42368 ^ _777081) ^ [_1623001, _1623003] : [-(c_List_Olistrelp(_1623001, _1623003, c_List_Olist_ONil(_1623001), c_List_Olist_ONil(_1623001)))], (42370 ^ _777081) ^ [_1623032, _1623034] : [-(c_List_Olist_Olist__size(_1623032, _1623034, c_List_Olist_ONil(_1623032)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42372 ^ _777081) ^ [_1623063, _1623065, _1623067, _1623069] : [-(c_Map_Omap__upds(_1623063, _1623065, _1623067, c_List_Olist_ONil(_1623063), _1623069) = _1623067)], (42374 ^ _777081) ^ [_1623100, _1623102, _1623104, _1623106] : [-(c_Map_Omap__upds(_1623100, _1623102, _1623104, _1623106, c_List_Olist_ONil(_1623102)) = _1623104)], (42376 ^ _777081) ^ [_1623137, _1623139] : [-(hAPP(hAPP(c_List_Otake(_1623137), _1623139), c_List_Olist_ONil(_1623137)) = c_List_Olist_ONil(_1623137))], (42388 ^ _777081) ^ [_1623304, _1623306, _1623308] : [42389 ^ _777081 : [(42390 ^ _777081) ^ [] : [_1623306 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42392 ^ _777081) ^ [] : [_1623308 = c_List_Olist_ONil(_1623304)]], -(hAPP(hAPP(c_List_Otake(_1623304), _1623306), _1623308) = c_List_Olist_ONil(_1623304))], (42378 ^ _777081) ^ [_1623192, _1623194, _1623196] : [hAPP(hAPP(c_List_Otake(_1623192), _1623194), _1623196) = c_List_Olist_ONil(_1623192), -(_1623194 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1623196 = c_List_Olist_ONil(_1623192))], (42396 ^ _777081) ^ [_1623447, _1623449] : [-(hAPP(hAPP(c_List_Otake(_1623447), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1623449) = c_List_Olist_ONil(_1623447))], (42398 ^ _777081) ^ [_1623482] : [class_Orderings_Olinorder(_1623482), -(c_List_Olinorder__class_Osorted__list__of__set(_1623482, c_Orderings_Obot__class_Obot(tc_fun(_1623482, tc_HOL_Obool))) = c_List_Olist_ONil(_1623482))], (42404 ^ _777081) ^ [_1623596, _1623598, _1623600, _1623602] : [hAPP(hAPP(c_List_Olist__update(_1623596, _1623598), _1623600), _1623602) = c_List_Olist_ONil(_1623596), -(_1623598 = c_List_Olist_ONil(_1623596))], (42410 ^ _777081) ^ [_1623699, _1623701, _1623703, _1623705] : [_1623701 = c_List_Olist_ONil(_1623699), -(hAPP(hAPP(c_List_Olist__update(_1623699, _1623701), _1623703), _1623705) = c_List_Olist_ONil(_1623699))], (42416 ^ _777081) ^ [_1623808, _1623810, _1623812] : [-(hAPP(hAPP(c_List_Olist__update(_1623808, c_List_Olist_ONil(_1623808)), _1623810), _1623812) = c_List_Olist_ONil(_1623808))], (42418 ^ _777081) ^ [_1623848, _1623850, _1623852] : [-(hAPP(hAPP(c_List_Olist__update(_1623848, c_List_Olist_ONil(_1623848)), _1623850), _1623852) = c_List_Olist_ONil(_1623848))], (42420 ^ _777081) ^ [_1623909, _1623911, _1623913, _1623915] : [hAPP(hAPP(c_List_Omap(_1623909, _1623911), _1623913), _1623915) = c_List_Olist_ONil(_1623911), -(_1623915 = c_List_Olist_ONil(_1623909))], (42426 ^ _777081) ^ [_1624012, _1624014, _1624016, _1624018] : [_1624018 = c_List_Olist_ONil(_1624012), -(hAPP(hAPP(c_List_Omap(_1624012, _1624014), _1624016), _1624018) = c_List_Olist_ONil(_1624014))], (42432 ^ _777081) ^ [_1624121, _1624123, _1624125] : [-(hAPP(hAPP(c_List_Omap(_1624121, _1624123), _1624125), c_List_Olist_ONil(_1624121)) = c_List_Olist_ONil(_1624123))], (42434 ^ _777081) ^ [_1624182, _1624184, _1624186, _1624188] : [c_List_Olist_ONil(_1624182) = hAPP(hAPP(c_List_Omap(_1624184, _1624182), _1624186), _1624188), -(_1624188 = c_List_Olist_ONil(_1624184))], (42440 ^ _777081) ^ [_1624285, _1624287, _1624289, _1624291] : [_1624291 = c_List_Olist_ONil(_1624287), -(c_List_Olist_ONil(_1624285) = hAPP(hAPP(c_List_Omap(_1624287, _1624285), _1624289), _1624291))], (42446 ^ _777081) ^ [_1624394] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624394)), c_List_Olist_ONil(_1624394)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42448 ^ _777081) ^ [_1624441, _1624443] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624441)), _1624443) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1624443 = c_List_Olist_ONil(_1624441))], (42454 ^ _777081) ^ [_1624532, _1624534] : [_1624534 = c_List_Olist_ONil(_1624532), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624532)), _1624534) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42460 ^ _777081) ^ [_1624644, _1624646] : [hAPP(c_List_Oset(_1624644), _1624646) = c_Orderings_Obot__class_Obot(tc_fun(_1624644, tc_HOL_Obool)), -(_1624646 = c_List_Olist_ONil(_1624644))], (42466 ^ _777081) ^ [_1624741, _1624743] : [_1624743 = c_List_Olist_ONil(_1624741), -(hAPP(c_List_Oset(_1624741), _1624743) = c_Orderings_Obot__class_Obot(tc_fun(_1624741, tc_HOL_Obool)))], (42472 ^ _777081) ^ [_1624859, _1624861] : [c_Orderings_Obot__class_Obot(tc_fun(_1624859, tc_HOL_Obool)) = hAPP(c_List_Oset(_1624859), _1624861), -(_1624861 = c_List_Olist_ONil(_1624859))], (42478 ^ _777081) ^ [_1624956, _1624958] : [_1624958 = c_List_Olist_ONil(_1624956), -(c_Orderings_Obot__class_Obot(tc_fun(_1624956, tc_HOL_Obool)) = hAPP(c_List_Oset(_1624956), _1624958))], (42484 ^ _777081) ^ [_1625059] : [-(hAPP(c_List_Oset(_1625059), c_List_Olist_ONil(_1625059)) = c_Orderings_Obot__class_Obot(tc_fun(_1625059, tc_HOL_Obool)))], (42486 ^ _777081) ^ [_1625094] : [class_Groups_Omonoid__add(_1625094), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1625094), c_List_Olist_ONil(_1625094)) = c_Groups_Ozero__class_Ozero(_1625094))], (42492 ^ _777081) ^ [_1625184, _1625186] : [-(_1625184 = c_List_Olist_ONil(_1625186)), hBOOL(hAPP(c_List_Odistinct(_1625186), _1625184)), -(hBOOL(hAPP(c_List_Odistinct(_1625186), c_List_Obutlast(_1625186, _1625184))))], (42502 ^ _777081) ^ [_1625335] : [-(c_List_Obutlast(_1625335, c_List_Olist_ONil(_1625335)) = c_List_Olist_ONil(_1625335))], (42504 ^ _777081) ^ [_1625377, _1625379, _1625381] : [_1625377 = c_List_Olist_ONil(_1625379), -(c_List_Obutlast(_1625379, hAPP(hAPP(c_List_Olist_OCons(_1625379), _1625381), _1625377)) = c_List_Olist_ONil(_1625379))], (42510 ^ _777081) ^ [_1625480, _1625482, _1625484] : [-(_1625480 = c_List_Olist_ONil(_1625482)), -(c_List_Obutlast(_1625482, hAPP(hAPP(c_List_Olist_OCons(_1625482), _1625484), _1625480)) = hAPP(hAPP(c_List_Olist_OCons(_1625482), _1625484), c_List_Obutlast(_1625482, _1625480)))], (42516 ^ _777081) ^ [_1625544, _1625546] : [-(c_List_Osublist(_1625544, _1625546, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1625544))], (42518 ^ _777081) ^ [_1625575, _1625577, _1625579] : [-(hAPP(hAPP(c_Map_Omap__of(_1625575, _1625577), c_List_Olist_ONil(tc_prod(_1625575, _1625577))), _1625579) = c_Option_Ooption_ONone(_1625577))], (42520 ^ _777081) ^ [_1625633, _1625635] : [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(_1625633)), _1625635))), _1625635 = c_List_Olist_ONil(_1625633)], (42526 ^ _777081) ^ [_1625727, _1625729] : [-(_1625729 = c_List_Olist_ONil(_1625727)), -(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(_1625727)), _1625729))))], (42532 ^ _777081) ^ [_1625776, _1625778, _1625780] : [-(hAPP(hAPP(c_List_Otake(_1625776), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1625776), _1625778), _1625780)) = hAPP(hAPP(c_List_Olist_OCons(_1625776), _1625778), c_List_Olist_ONil(_1625776)))], (42534 ^ _777081) ^ [_1625844, _1625846, _1625848] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625844), tc_List_Olist(_1625844))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625844), tc_List_Olist(_1625844)), c_List_Olist_ONil(_1625844)), _1625846)), c_List_Olistrel1(_1625844, _1625848)))], (42536 ^ _777081) ^ [_1625918, _1625920, _1625922] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625918), tc_List_Olist(_1625918))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625918), tc_List_Olist(_1625918)), _1625920), c_List_Olist_ONil(_1625918))), c_List_Olistrel1(_1625918, _1625922)))], (42538 ^ _777081) ^ [_1625977, _1625979] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625977), tc_List_Olist(_1625977))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625977), tc_List_Olist(_1625977)), c_List_Olist_ONil(_1625977)), c_List_Olist_ONil(_1625977))), c_List_Olistrel(_1625977, _1625979))))], (42540 ^ _777081) ^ [_1626051, _1626053, _1626055] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1626051), tc_List_Olist(_1626051))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1626051), tc_List_Olist(_1626051)), _1626053), c_List_Olist_ONil(_1626051))), c_List_Olexord(_1626051, _1626055)))], (42542 ^ _777081) ^ [_1626125, _1626127, _1626129] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1626125), tc_List_Olist(_1626125))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1626125), tc_List_Olist(_1626125)), _1626127), c_List_Olist_ONil(_1626125))), c_List_Olex(_1626125, _1626129)))], (42544 ^ _777081) ^ [_1626199, _1626201, _1626203] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1626199), tc_List_Olist(_1626199))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1626199), tc_List_Olist(_1626199)), c_List_Olist_ONil(_1626199)), _1626201)), c_List_Olex(_1626199, _1626203)))], (42546 ^ _777081) ^ [_1626258, _1626260, _1626262, _1626264, _1626266] : [c_List_Opartition(_1626258, _1626260, _1626262) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1626258), tc_List_Olist(_1626258)), _1626264), _1626266), 42549 ^ _777081 : [(42550 ^ _777081) ^ [_1626411] : [hBOOL(hAPP(hAPP(c_member(_1626258), _1626411), hAPP(c_List_Oset(_1626258), _1626264))), -(hBOOL(hAPP(_1626260, _1626411)))], (42556 ^ _777081) ^ [_1626520] : [hBOOL(hAPP(hAPP(c_member(_1626258), _1626520), hAPP(c_List_Oset(_1626258), _1626266))), hBOOL(hAPP(_1626260, _1626520))]]], (42562 ^ _777081) ^ [_1626640, _1626642, _1626644, _1626646] : [-(hAPP(hAPP(c_List_Otake(_1626640), _1626642), hAPP(hAPP(c_List_Olist_OCons(_1626640), _1626644), _1626646)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1626640), c_List_Olist_ONil(_1626640), hAPP(hAPP(c_COMBB(tc_List_Olist(_1626640), tc_List_Olist(_1626640), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1626640), _1626644)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1626640), tc_List_Olist(_1626640)), c_List_Otake(_1626640)), _1626646)), _1626642))], (42564 ^ _777081) ^ [_1626738, _1626740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1626738), _1626740)), -(c_List_Oupto(_1626738, _1626740) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1626738), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1626738), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1626740)))], (42570 ^ _777081) ^ [_1626855, _1626857] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1626855), _1626857))), -(c_List_Oupto(_1626855, _1626857) = c_List_Olist_ONil(tc_Int_Oint))], (42576 ^ _777081) ^ [_1626913, _1626915, _1626917] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1626913)), -(c_List_Osublist(_1626915, hAPP(hAPP(c_List_Olist_OCons(_1626915), _1626917), c_List_Olist_ONil(_1626915)), _1626913) = hAPP(hAPP(c_List_Olist_OCons(_1626915), _1626917), c_List_Olist_ONil(_1626915)))], (42582 ^ _777081) ^ [_1627038, _1627040, _1627042] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1627038))), -(c_List_Osublist(_1627040, hAPP(hAPP(c_List_Olist_OCons(_1627040), _1627042), c_List_Olist_ONil(_1627040)), _1627038) = c_List_Olist_ONil(_1627040))], (42588 ^ _777081) ^ [_1627096, _1627098, _1627100, _1627102] : [-(c_List_Opartition(_1627096, _1627098, hAPP(hAPP(c_List_Olist_OCons(_1627096), _1627100), _1627102)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1627096), tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627096), tc_fun(tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096))), tc_fun(tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627096), tc_fun(tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)))), tc_fun(tc_fun(tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096))), tc_fun(tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)))), tc_List_Olist(_1627096)), c_COMBS(tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096))), tc_fun(tc_List_Olist(_1627096), tc_fun(tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)))), tc_List_Olist(_1627096)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)), tc_fun(tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096))), tc_List_Olist(_1627096)), hAPP(c_If(tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096))), hAPP(_1627098, _1627100)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1627096), tc_fun(tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096))), tc_List_Olist(_1627096)), c_Product__Type_OPair(tc_List_Olist(_1627096), tc_List_Olist(_1627096))), hAPP(c_List_Olist_OCons(_1627096), _1627100))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627096), tc_fun(tc_List_Olist(_1627096), tc_List_Olist(_1627096)), tc_fun(tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096))), tc_fun(tc_fun(tc_List_Olist(_1627096), tc_List_Olist(_1627096)), tc_fun(tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)))), tc_List_Olist(_1627096)), c_COMBB(tc_List_Olist(_1627096), tc_prod(tc_List_Olist(_1627096), tc_List_Olist(_1627096)), tc_List_Olist(_1627096))), c_Product__Type_OPair(tc_List_Olist(_1627096), tc_List_Olist(_1627096)))), hAPP(c_List_Olist_OCons(_1627096), _1627100)))), c_List_Opartition(_1627096, _1627098, _1627102)))], (42590 ^ _777081) ^ [_1627515] : [-(c_List_Olists(_1627515, c_Orderings_Obot__class_Obot(tc_fun(_1627515, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1627515)), c_List_Olist_ONil(_1627515)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1627515), tc_HOL_Obool))))], (42592 ^ _777081) ^ [_1627580, _1627582, _1627584, _1627586] : [_1627580 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1627582), _1627580), hAPP(hAPP(c_List_Olist_OCons(_1627582), _1627584), _1627586)) = c_List_Olist_ONil(_1627582))], (42598 ^ _777081) ^ [_1627691, _1627693, _1627695, _1627697] : [-(_1627691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1627693), _1627691), hAPP(hAPP(c_List_Olist_OCons(_1627693), _1627695), _1627697)) = hAPP(hAPP(c_List_Olist_OCons(_1627693), _1627695), hAPP(hAPP(c_List_Otake(_1627693), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1627691), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1627697)))], (42604 ^ _777081) ^ [_1627780, _1627782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1627780)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1627782))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1627780), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1627782)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1627780)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1627780)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1627782))))], (42610 ^ _777081) ^ [_1627939, _1627941] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1627939)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1627941)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1627939), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1627941)) = c_List_Olist_ONil(tc_Int_Oint))], (42616 ^ _777081) ^ [_1627997, _1627999] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1627997), tc_List_Olist(_1627997), c_List_Olistrel(_1627997, _1627999)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1627997)), c_List_Olist_ONil(_1627997)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1627997), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1627997)), c_List_Olist_ONil(_1627997)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1627997), tc_HOL_Obool))))], (42618 ^ _777081) ^ [_1628074, _1628076] : [-(c_List_Oset__Cons(_1628074, _1628076, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1628074)), c_List_Olist_ONil(_1628074)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1628074), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1628074, tc_List_Olist(_1628074), hAPP(hAPP(c_COMBC(_1628074, tc_List_Olist(_1628074), tc_List_Olist(_1628074)), c_List_Olist_OCons(_1628074)), c_List_Olist_ONil(_1628074))), _1628076))], (42620 ^ _777081) ^ [_1628149, _1628151] : [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), _1628149), _1628151))), 42623 ^ _777081 : [(42624 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1628149), _1628151)), -(c_List_Oupto(_1628149, _1628151) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1628149), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1628149), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1628151)))], (42630 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1628149), _1628151))), -(c_List_Oupto(_1628149, _1628151) = c_List_Olist_ONil(tc_Int_Oint))]]], (42636 ^ _777081) ^ [_1628421, _1628423, _1628425, _1628427, _1628429] : [_1628421 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Lazy__Sequence_Oanamorph(_1628423, _1628425, _1628427, _1628421), _1628429) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628425), _1628423), c_List_Olist_ONil(_1628425)), _1628429))], (42642 ^ _777081) ^ [_1628540, _1628542, _1628544, _1628546, _1628548] : [-(_1628540 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Lazy__Sequence_Oanamorph(_1628542, _1628544, _1628546, _1628540), _1628548) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1628544), _1628542), tc_prod(_1628544, _1628542), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628544), _1628542), c_List_Olist_ONil(_1628544)), _1628548), hAPP(c_Product__Type_Oprod_Oprod__case(_1628544, _1628542, tc_prod(tc_List_Olist(_1628544), _1628542)), hAPP(hAPP(c_COMBC(_1628544, tc_fun(_1628542, tc_prod(tc_List_Olist(_1628544), _1628542)), tc_fun(_1628542, tc_prod(tc_List_Olist(_1628544), _1628542))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1628544), _1628542), tc_prod(tc_List_Olist(_1628544), _1628542)), tc_fun(tc_fun(_1628542, tc_prod(tc_List_Olist(_1628544), _1628542)), tc_fun(_1628542, tc_prod(tc_List_Olist(_1628544), _1628542))), _1628544), c_COMBB(tc_prod(tc_List_Olist(_1628544), _1628542), tc_prod(tc_List_Olist(_1628544), _1628542), _1628542)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1628544), tc_fun(_1628542, tc_prod(tc_List_Olist(_1628544), _1628542))), tc_fun(tc_prod(tc_List_Olist(_1628544), _1628542), tc_prod(tc_List_Olist(_1628544), _1628542)), _1628544), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1628544), _1628542, tc_prod(tc_List_Olist(_1628544), _1628542))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1628544), tc_List_Olist(_1628544)), tc_fun(tc_List_Olist(_1628544), tc_fun(_1628542, tc_prod(tc_List_Olist(_1628544), _1628542))), _1628544), hAPP(c_COMBB(tc_List_Olist(_1628544), tc_fun(_1628542, tc_prod(tc_List_Olist(_1628544), _1628542)), tc_List_Olist(_1628544)), c_Product__Type_OPair(tc_List_Olist(_1628544), _1628542))), c_List_Olist_OCons(_1628544))))), c_Lazy__Sequence_Oanamorph(_1628542, _1628544, _1628546, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1628540), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1628546, _1628548)))], (42648 ^ _777081) ^ [_1628832] : [-(c_List_Olistset(_1628832, c_List_Olist_ONil(tc_fun(_1628832, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1628832)), c_List_Olist_ONil(_1628832)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1628832), tc_HOL_Obool))))], (42650 ^ _777081) ^ [_1628882, _1628884, _1628886, _1628888, _1628890] : [-(hAPP(hAPP(c_List_Ozip(_1628882, _1628884), _1628886), hAPP(hAPP(c_List_Olist_OCons(_1628884), _1628888), _1628890)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1628882, _1628884)), _1628882, c_List_Olist_ONil(tc_prod(_1628882, _1628884)), hAPP(hAPP(c_COMBC(_1628882, tc_fun(tc_List_Olist(_1628882), tc_List_Olist(tc_prod(_1628882, _1628884))), tc_fun(tc_List_Olist(_1628882), tc_List_Olist(tc_prod(_1628882, _1628884)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1628882, _1628884)), tc_List_Olist(tc_prod(_1628882, _1628884))), tc_fun(tc_fun(tc_List_Olist(_1628882), tc_List_Olist(tc_prod(_1628882, _1628884))), tc_fun(tc_List_Olist(_1628882), tc_List_Olist(tc_prod(_1628882, _1628884)))), _1628882), c_COMBB(tc_List_Olist(tc_prod(_1628882, _1628884)), tc_List_Olist(tc_prod(_1628882, _1628884)), tc_List_Olist(_1628882))), hAPP(hAPP(c_COMBB(tc_prod(_1628882, _1628884), tc_fun(tc_List_Olist(tc_prod(_1628882, _1628884)), tc_List_Olist(tc_prod(_1628882, _1628884))), _1628882), c_List_Olist_OCons(tc_prod(_1628882, _1628884))), hAPP(hAPP(c_COMBC(_1628882, _1628884, tc_prod(_1628882, _1628884)), c_Product__Type_OPair(_1628882, _1628884)), _1628888)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1628882), tc_List_Olist(_1628884), tc_List_Olist(tc_prod(_1628882, _1628884))), c_List_Ozip(_1628882, _1628884)), _1628890))), _1628886))], (42652 ^ _777081) ^ [_1629109, _1629111, _1629113, _1629115, _1629117, _1629119] : [-(hAPP(c_List_Olist_Olist__case(_1629109, _1629111, _1629113, _1629115), hAPP(hAPP(c_List_Olist_OCons(_1629111), _1629117), _1629119)) = hAPP(hAPP(_1629115, _1629117), _1629119))], (42654 ^ _777081) ^ [_1629164, _1629166, _1629168, _1629170] : [-(hAPP(c_List_Olist_Olist__case(_1629164, _1629166, _1629168, _1629170), c_List_Olist_ONil(_1629166)) = _1629168)], (42656 ^ _777081) ^ [_1629203, _1629205, _1629207] : [-(c_List_Olistset(_1629203, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1629203, tc_HOL_Obool)), _1629205), _1629207)) = c_List_Oset__Cons(_1629203, _1629205, c_List_Olistset(_1629203, _1629207)))], (42658 ^ _777081) ^ [_1629251, _1629253, _1629255, _1629257, _1629259] : [-(hAPP(hAPP(c_List_Ozip(_1629251, _1629253), hAPP(hAPP(c_List_Olist_OCons(_1629251), _1629255), _1629257)), _1629259) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1629251, _1629253)), _1629253, c_List_Olist_ONil(tc_prod(_1629251, _1629253)), hAPP(hAPP(c_COMBC(_1629253, tc_fun(tc_List_Olist(_1629253), tc_List_Olist(tc_prod(_1629251, _1629253))), tc_fun(tc_List_Olist(_1629253), tc_List_Olist(tc_prod(_1629251, _1629253)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1629251, _1629253)), tc_List_Olist(tc_prod(_1629251, _1629253))), tc_fun(tc_fun(tc_List_Olist(_1629253), tc_List_Olist(tc_prod(_1629251, _1629253))), tc_fun(tc_List_Olist(_1629253), tc_List_Olist(tc_prod(_1629251, _1629253)))), _1629253), c_COMBB(tc_List_Olist(tc_prod(_1629251, _1629253)), tc_List_Olist(tc_prod(_1629251, _1629253)), tc_List_Olist(_1629253))), hAPP(hAPP(c_COMBB(tc_prod(_1629251, _1629253), tc_fun(tc_List_Olist(tc_prod(_1629251, _1629253)), tc_List_Olist(tc_prod(_1629251, _1629253))), _1629253), c_List_Olist_OCons(tc_prod(_1629251, _1629253))), hAPP(c_Product__Type_OPair(_1629251, _1629253), _1629255)))), hAPP(c_List_Ozip(_1629251, _1629253), _1629257))), _1629259))], (42660 ^ _777081) ^ [_1629452, _1629454, _1629456] : [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), _1629452), _1629454))), -(hBOOL(hAPP(hAPP(_1629456, _1629452), _1629454))), 42667 ^ _777081 : [(42668 ^ _777081) ^ [] : [-(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), 42665 ^ [_1629452, _1629454, _1629456]), 42666 ^ [_1629452, _1629454, _1629456]))))], (42676 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1629456, 42665 ^ [_1629452, _1629454, _1629456]), 42666 ^ [_1629452, _1629454, _1629456]))], (42670 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 42665 ^ [_1629452, _1629454, _1629456]), 42666 ^ [_1629452, _1629454, _1629456])), -(hBOOL(hAPP(hAPP(_1629456, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 42665 ^ [_1629452, _1629454, _1629456]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 42666 ^ [_1629452, _1629454, _1629456])))]]], (42680 ^ _777081) ^ [_1629943, _1629945, _1629947, _1629949, _1629951, _1629953] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629943)), _1629945)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629947)), _1629949))), -(c_Map_Omap__upds(_1629943, _1629947, _1629951, hAPP(hAPP(c_List_Oappend(_1629943), _1629945), hAPP(hAPP(c_List_Olist_OCons(_1629943), _1629953), c_List_Olist_ONil(_1629943))), _1629949) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1629943, tc_Option_Ooption(_1629947)), c_Map_Omap__upds(_1629943, _1629947, _1629951, _1629945, _1629949)), _1629953), hAPP(c_Option_Ooption_OSome(_1629947), hAPP(hAPP(c_List_Onth(_1629947), _1629949), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629943)), _1629945)))))], (42686 ^ _777081) ^ [_1630218, _1630220, _1630222, _1630224, _1630226] : [hAPP(hAPP(c_List_Oappend(_1630218), _1630220), hAPP(hAPP(c_List_Olist_OCons(_1630218), _1630222), c_List_Olist_ONil(_1630218))) = hAPP(hAPP(c_List_Oappend(_1630218), _1630224), hAPP(hAPP(c_List_Olist_OCons(_1630218), _1630226), c_List_Olist_ONil(_1630218))), 42689 ^ _777081 : [(42690 ^ _777081) ^ [] : [-(_1630220 = _1630224)], (42692 ^ _777081) ^ [] : [-(_1630222 = _1630226)]]], (42694 ^ _777081) ^ [_1630395, _1630397, _1630399, _1630401, _1630403] : [-(hAPP(hAPP(c_List_Oappend(_1630395), _1630397), hAPP(hAPP(c_List_Olist_OCons(_1630395), _1630399), c_List_Olist_ONil(_1630395))) = hAPP(hAPP(c_List_Oappend(_1630395), _1630401), hAPP(hAPP(c_List_Olist_OCons(_1630395), _1630403), c_List_Olist_ONil(_1630395)))), _1630397 = _1630401, _1630399 = _1630403], (42704 ^ _777081) ^ [_1630634, _1630636, _1630638, _1630640, _1630642] : [hAPP(hAPP(c_List_Olist_OCons(_1630634), _1630636), _1630638) = hAPP(hAPP(c_List_Oappend(_1630634), _1630640), _1630642), 42709 ^ _777081 : [(42710 ^ _777081) ^ [] : [-(_1630640 = c_List_Olist_ONil(_1630634))], (42712 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1630634), _1630636), _1630638) = _1630642)]], 42714 ^ _777081 : [(42715 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1630634), _1630636), 42713 ^ [_1630634, _1630636, _1630638, _1630640, _1630642]) = _1630640)], (42717 ^ _777081) ^ [] : [-(_1630638 = hAPP(hAPP(c_List_Oappend(_1630634), 42713 ^ [_1630634, _1630636, _1630638, _1630640, _1630642]), _1630642))]]], (42719 ^ _777081) ^ [_1630927, _1630929, _1630931, _1630933, _1630935] : [-(hAPP(hAPP(c_List_Olist_OCons(_1630927), _1630929), _1630931) = hAPP(hAPP(c_List_Oappend(_1630927), _1630933), _1630935)), 42720 ^ _777081 : [(42721 ^ _777081) ^ [] : [_1630933 = c_List_Olist_ONil(_1630927), hAPP(hAPP(c_List_Olist_OCons(_1630927), _1630929), _1630931) = _1630935], (42727 ^ _777081) ^ [_1631110] : [hAPP(hAPP(c_List_Olist_OCons(_1630927), _1630929), _1631110) = _1630933, _1630931 = hAPP(hAPP(c_List_Oappend(_1630927), _1631110), _1630935)]]], (42735 ^ _777081) ^ [_1631298, _1631300, _1631302, _1631304, _1631306] : [hAPP(hAPP(c_List_Oappend(_1631298), _1631300), _1631302) = hAPP(hAPP(c_List_Olist_OCons(_1631298), _1631304), _1631306), 42740 ^ _777081 : [(42741 ^ _777081) ^ [] : [-(_1631300 = c_List_Olist_ONil(_1631298))], (42743 ^ _777081) ^ [] : [-(_1631302 = hAPP(hAPP(c_List_Olist_OCons(_1631298), _1631304), _1631306))]], 42745 ^ _777081 : [(42746 ^ _777081) ^ [] : [-(_1631300 = hAPP(hAPP(c_List_Olist_OCons(_1631298), _1631304), 42744 ^ [_1631298, _1631300, _1631302, _1631304, _1631306]))], (42748 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1631298), 42744 ^ [_1631298, _1631300, _1631302, _1631304, _1631306]), _1631302) = _1631306)]]], (42750 ^ _777081) ^ [_1631591, _1631593, _1631595, _1631597, _1631599] : [-(hAPP(hAPP(c_List_Oappend(_1631591), _1631593), _1631595) = hAPP(hAPP(c_List_Olist_OCons(_1631591), _1631597), _1631599)), 42751 ^ _777081 : [(42752 ^ _777081) ^ [] : [_1631593 = c_List_Olist_ONil(_1631591), _1631595 = hAPP(hAPP(c_List_Olist_OCons(_1631591), _1631597), _1631599)], (42758 ^ _777081) ^ [_1631774] : [_1631593 = hAPP(hAPP(c_List_Olist_OCons(_1631591), _1631597), _1631774), hAPP(hAPP(c_List_Oappend(_1631591), _1631774), _1631595) = _1631599]]], (42766 ^ _777081) ^ [_1631938, _1631940, _1631942] : [_1631938 = _1631940, -(_1631938 = hAPP(hAPP(c_List_Oappend(_1631942), c_List_Olist_ONil(_1631942)), _1631940))], (42772 ^ _777081) ^ [_1632055, _1632057, _1632059] : [hAPP(hAPP(c_List_Oappend(_1632055), _1632057), _1632059) = _1632059, -(_1632057 = c_List_Olist_ONil(_1632055))], (42778 ^ _777081) ^ [_1632150, _1632152, _1632154] : [_1632152 = c_List_Olist_ONil(_1632150), -(hAPP(hAPP(c_List_Oappend(_1632150), _1632152), _1632154) = _1632154)], (42784 ^ _777081) ^ [_1632269, _1632271, _1632273] : [hAPP(hAPP(c_List_Oappend(_1632269), _1632271), _1632273) = _1632271, -(_1632273 = c_List_Olist_ONil(_1632269))], (42790 ^ _777081) ^ [_1632364, _1632366, _1632368] : [_1632368 = c_List_Olist_ONil(_1632364), -(hAPP(hAPP(c_List_Oappend(_1632364), _1632366), _1632368) = _1632366)], (42796 ^ _777081) ^ [_1632483, _1632485, _1632487] : [hAPP(hAPP(c_List_Oappend(_1632483), _1632485), _1632487) = c_List_Olist_ONil(_1632483), 42799 ^ _777081 : [(42800 ^ _777081) ^ [] : [-(_1632485 = c_List_Olist_ONil(_1632483))], (42802 ^ _777081) ^ [] : [-(_1632487 = c_List_Olist_ONil(_1632483))]]], (42804 ^ _777081) ^ [_1632612, _1632614, _1632616] : [-(hAPP(hAPP(c_List_Oappend(_1632612), _1632614), _1632616) = c_List_Olist_ONil(_1632612)), _1632614 = c_List_Olist_ONil(_1632612), _1632616 = c_List_Olist_ONil(_1632612)], (42814 ^ _777081) ^ [_1632793, _1632795, _1632797] : [_1632793 = hAPP(hAPP(c_List_Oappend(_1632795), _1632797), _1632793), -(_1632797 = c_List_Olist_ONil(_1632795))], (42820 ^ _777081) ^ [_1632888, _1632890, _1632892] : [_1632892 = c_List_Olist_ONil(_1632890), -(_1632888 = hAPP(hAPP(c_List_Oappend(_1632890), _1632892), _1632888))], (42826 ^ _777081) ^ [_1633007, _1633009, _1633011] : [_1633007 = hAPP(hAPP(c_List_Oappend(_1633009), _1633007), _1633011), -(_1633011 = c_List_Olist_ONil(_1633009))], (42832 ^ _777081) ^ [_1633102, _1633104, _1633106] : [_1633106 = c_List_Olist_ONil(_1633104), -(_1633102 = hAPP(hAPP(c_List_Oappend(_1633104), _1633102), _1633106))], (42838 ^ _777081) ^ [_1633203, _1633205] : [-(hAPP(hAPP(c_List_Oappend(_1633203), _1633205), c_List_Olist_ONil(_1633203)) = _1633205)], (42840 ^ _777081) ^ [_1633256, _1633258, _1633260] : [c_List_Olist_ONil(_1633256) = hAPP(hAPP(c_List_Oappend(_1633256), _1633258), _1633260), 42843 ^ _777081 : [(42844 ^ _777081) ^ [] : [-(_1633258 = c_List_Olist_ONil(_1633256))], (42846 ^ _777081) ^ [] : [-(_1633260 = c_List_Olist_ONil(_1633256))]]], (42848 ^ _777081) ^ [_1633385, _1633387, _1633389] : [-(c_List_Olist_ONil(_1633385) = hAPP(hAPP(c_List_Oappend(_1633385), _1633387), _1633389)), _1633387 = c_List_Olist_ONil(_1633385), _1633389 = c_List_Olist_ONil(_1633385)], (42858 ^ _777081) ^ [_1633548, _1633550] : [-(hAPP(hAPP(c_List_Oappend(_1633548), c_List_Olist_ONil(_1633548)), _1633550) = _1633550)], (42860 ^ _777081) ^ [_1633595, _1633597, _1633599] : [_1633595 = c_List_Olist_ONil(_1633597), -(c_List_Obutlast(_1633597, hAPP(hAPP(c_List_Oappend(_1633597), _1633599), _1633595)) = c_List_Obutlast(_1633597, _1633599))], (42866 ^ _777081) ^ [_1633700, _1633702, _1633704] : [-(_1633700 = c_List_Olist_ONil(_1633702)), -(c_List_Obutlast(_1633702, hAPP(hAPP(c_List_Oappend(_1633702), _1633704), _1633700)) = hAPP(hAPP(c_List_Oappend(_1633702), _1633704), c_List_Obutlast(_1633702, _1633700)))], (42872 ^ _777081) ^ [_1633764, _1633766, _1633768] : [class_Groups_Omonoid__add(_1633764), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1633764), hAPP(hAPP(c_List_Oappend(_1633764), _1633766), _1633768)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1633764), hAPP(c_List_Omonoid__add__class_Olistsum(_1633764), _1633766)), hAPP(c_List_Omonoid__add__class_Olistsum(_1633764), _1633768)))], (42878 ^ _777081) ^ [_1633903, _1633905, _1633907, _1633909, _1633911, _1633913] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633903)), _1633905) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633907)), _1633909), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633903)), _1633911) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633907)), _1633913), -(hAPP(hAPP(c_List_Ozip(_1633903, _1633907), hAPP(hAPP(c_List_Oappend(_1633903), _1633905), _1633911)), hAPP(hAPP(c_List_Oappend(_1633907), _1633909), _1633913)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1633903, _1633907)), hAPP(hAPP(c_List_Ozip(_1633903, _1633907), _1633905), _1633909)), hAPP(hAPP(c_List_Ozip(_1633903, _1633907), _1633911), _1633913)))], (42888 ^ _777081) ^ [_1634212, _1634214, _1634216] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634212)), hAPP(hAPP(c_List_Oappend(_1634212), _1634214), _1634216)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634212)), _1634214)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634212)), _1634216)))], (42890 ^ _777081) ^ [_1634274, _1634276, _1634278] : [-(hAPP(c_List_Oset(_1634274), hAPP(hAPP(c_List_Oappend(_1634274), _1634276), _1634278)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1634274, tc_HOL_Obool)), hAPP(c_List_Oset(_1634274), _1634276)), hAPP(c_List_Oset(_1634274), _1634278)))], (42892 ^ _777081) ^ [_1634335, _1634337, _1634339, _1634341, _1634343] : [-(hAPP(hAPP(c_List_Omap(_1634335, _1634337), _1634339), hAPP(hAPP(c_List_Oappend(_1634335), _1634341), _1634343)) = hAPP(hAPP(c_List_Oappend(_1634337), hAPP(hAPP(c_List_Omap(_1634335, _1634337), _1634339), _1634341)), hAPP(hAPP(c_List_Omap(_1634335, _1634337), _1634339), _1634343)))], (42894 ^ _777081) ^ [_1634409, _1634411, _1634413, _1634415, _1634417, _1634419] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634409)), _1634411) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634413)), _1634415), -(c_Map_Omap__upds(_1634409, _1634413, _1634417, hAPP(hAPP(c_List_Oappend(_1634409), _1634411), _1634419), _1634415) = c_Map_Omap__upds(_1634409, _1634413, _1634417, _1634411, _1634415))], (42900 ^ _777081) ^ [_1634562, _1634564, _1634566, _1634568, _1634570, _1634572] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634562)), _1634564) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634566)), _1634568), -(c_Map_Omap__upds(_1634562, _1634566, _1634570, _1634564, hAPP(hAPP(c_List_Oappend(_1634566), _1634568), _1634572)) = c_Map_Omap__upds(_1634562, _1634566, _1634570, _1634564, _1634568))], (42906 ^ _777081) ^ [_1634736, _1634738, _1634740, _1634742] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1634736)), hAPP(hAPP(c_List_Oappend(_1634736), _1634738), _1634740)), c_List_Olists(_1634736, _1634742))), 42909 ^ _777081 : [(42910 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1634736)), _1634738), c_List_Olists(_1634736, _1634742))))], (42912 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1634736)), _1634740), c_List_Olists(_1634736, _1634742))))]]], (42914 ^ _777081) ^ [_1634927, _1634929, _1634931, _1634933] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1634927)), hAPP(hAPP(c_List_Oappend(_1634927), _1634929), _1634931)), c_List_Olists(_1634927, _1634933)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1634927)), _1634929), c_List_Olists(_1634927, _1634933))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1634927)), _1634931), c_List_Olists(_1634927, _1634933)))], (42924 ^ _777081) ^ [_1635154, _1635156, _1635158, _1635160] : [-(hAPP(hAPP(c_List_Oappend(_1635154), hAPP(hAPP(c_List_Oappend(_1635154), _1635156), _1635158)), _1635160) = hAPP(hAPP(c_List_Oappend(_1635154), _1635156), hAPP(hAPP(c_List_Oappend(_1635154), _1635158), _1635160)))], (42926 ^ _777081) ^ [_1635239, _1635241, _1635243, _1635245, _1635247] : [hAPP(hAPP(c_List_Oappend(_1635239), _1635241), _1635243) = hAPP(hAPP(c_List_Oappend(_1635239), _1635245), _1635247), 42932 ^ _777081 : [(42933 ^ _777081) ^ [] : [-(_1635241 = hAPP(hAPP(c_List_Oappend(_1635239), _1635245), 42929 ^ [_1635239, _1635241, _1635243, _1635245, _1635247]))], (42935 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1635239), 42929 ^ [_1635239, _1635241, _1635243, _1635245, _1635247]), _1635243) = _1635247)]], 42936 ^ _777081 : [(42937 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1635239), _1635241), 42929 ^ [_1635239, _1635241, _1635243, _1635245, _1635247]) = _1635245)], (42939 ^ _777081) ^ [] : [-(_1635243 = hAPP(hAPP(c_List_Oappend(_1635239), 42929 ^ [_1635239, _1635241, _1635243, _1635245, _1635247]), _1635247))]]], (42941 ^ _777081) ^ [_1635570, _1635572, _1635574, _1635576, _1635578] : [-(hAPP(hAPP(c_List_Oappend(_1635570), _1635572), _1635574) = hAPP(hAPP(c_List_Oappend(_1635570), _1635576), _1635578)), 42942 ^ _777081 : [(42943 ^ _777081) ^ [_1635682] : [_1635572 = hAPP(hAPP(c_List_Oappend(_1635570), _1635576), _1635682), hAPP(hAPP(c_List_Oappend(_1635570), _1635682), _1635574) = _1635578], (42949 ^ _777081) ^ [_1635794] : [hAPP(hAPP(c_List_Oappend(_1635570), _1635572), _1635794) = _1635576, _1635574 = hAPP(hAPP(c_List_Oappend(_1635570), _1635794), _1635578)]]], (42957 ^ _777081) ^ [_1635979, _1635981, _1635983, _1635985] : [hAPP(hAPP(c_List_Oappend(_1635979), _1635981), _1635983) = hAPP(hAPP(c_List_Oappend(_1635979), _1635981), _1635985), -(_1635983 = _1635985)], (42963 ^ _777081) ^ [_1636088, _1636090, _1636092, _1636094] : [_1636092 = _1636094, -(hAPP(hAPP(c_List_Oappend(_1636088), _1636090), _1636092) = hAPP(hAPP(c_List_Oappend(_1636088), _1636090), _1636094))], (42969 ^ _777081) ^ [_1636224, _1636226, _1636228, _1636230] : [hAPP(hAPP(c_List_Oappend(_1636224), _1636226), _1636228) = hAPP(hAPP(c_List_Oappend(_1636224), _1636230), _1636228), -(_1636226 = _1636230)], (42975 ^ _777081) ^ [_1636333, _1636335, _1636337, _1636339] : [_1636335 = _1636339, -(hAPP(hAPP(c_List_Oappend(_1636333), _1636335), _1636337) = hAPP(hAPP(c_List_Oappend(_1636333), _1636339), _1636337))], (42981 ^ _777081) ^ [_1636448, _1636450, _1636452, _1636454, _1636456, _1636458] : [hAPP(hAPP(c_List_Oappend(_1636448), _1636450), _1636452) = _1636454, _1636456 = hAPP(hAPP(c_List_Oappend(_1636448), _1636452), _1636458), -(hAPP(hAPP(c_List_Oappend(_1636448), _1636450), _1636456) = hAPP(hAPP(c_List_Oappend(_1636448), _1636454), _1636458))], (42991 ^ _777081) ^ [_1636657, _1636659, _1636661, _1636663] : [-(hAPP(c_Map_Omap__of(_1636657, _1636659), hAPP(hAPP(c_List_Oappend(tc_prod(_1636657, _1636659)), _1636661), _1636663)) = c_Map_Omap__add(_1636657, _1636659, hAPP(c_Map_Omap__of(_1636657, _1636659), _1636663), hAPP(c_Map_Omap__of(_1636657, _1636659), _1636661)))], (42993 ^ _777081) ^ [_1636720, _1636722, _1636724, _1636726, _1636728, _1636730] : [-(c_List_Ofoldr(_1636720, _1636722, _1636724, hAPP(hAPP(c_List_Oappend(_1636720), _1636726), _1636728), _1636730) = c_List_Ofoldr(_1636720, _1636722, _1636724, _1636726, c_List_Ofoldr(_1636720, _1636722, _1636724, _1636728, _1636730)))], (42995 ^ _777081) ^ [_1636779, _1636781, _1636783, _1636785, _1636787, _1636789] : [hAPP(hAPP(c_List_Olist_OCons(_1636779), _1636781), _1636783) = _1636785, _1636787 = hAPP(hAPP(c_List_Oappend(_1636779), _1636783), _1636789), -(hAPP(hAPP(c_List_Olist_OCons(_1636779), _1636781), _1636787) = hAPP(hAPP(c_List_Oappend(_1636779), _1636785), _1636789))], (43005 ^ _777081) ^ [_1636988, _1636990, _1636992, _1636994] : [-(hAPP(hAPP(c_List_Oappend(_1636988), hAPP(hAPP(c_List_Olist_OCons(_1636988), _1636990), _1636992)), _1636994) = hAPP(hAPP(c_List_Olist_OCons(_1636988), _1636990), hAPP(hAPP(c_List_Oappend(_1636988), _1636992), _1636994)))], (43007 ^ _777081) ^ [_1637049, _1637051, _1637053, _1637055] : [-(hAPP(hAPP(c_List_Onth(_1637049), hAPP(hAPP(c_List_Oappend(_1637049), _1637051), hAPP(hAPP(c_List_Olist_OCons(_1637049), _1637053), _1637055))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637049)), _1637051)) = _1637053)], (43009 ^ _777081) ^ [_1637109, _1637111, _1637113, _1637115] : [-(hAPP(hAPP(c_List_Onth(_1637109), hAPP(hAPP(c_List_Oappend(_1637109), _1637111), _1637113)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637109)), _1637111)), _1637115)) = hAPP(hAPP(c_List_Onth(_1637109), _1637113), _1637115))], (43011 ^ _777081) ^ [_1637175, _1637177, _1637179, _1637181] : [-(hAPP(hAPP(c_List_Otake(_1637175), _1637177), hAPP(hAPP(c_List_Oappend(_1637175), _1637179), _1637181)) = hAPP(hAPP(c_List_Oappend(_1637175), hAPP(hAPP(c_List_Otake(_1637175), _1637177), _1637179)), hAPP(hAPP(c_List_Otake(_1637175), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1637177), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637175)), _1637179))), _1637181)))], (43013 ^ _777081) ^ [_1637257, _1637259, _1637261, _1637263, _1637265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1637257), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637259)), _1637261))), -(hAPP(hAPP(c_List_Olist__update(_1637259, hAPP(hAPP(c_List_Oappend(_1637259), _1637261), _1637263)), _1637257), _1637265) = hAPP(hAPP(c_List_Oappend(_1637259), hAPP(hAPP(c_List_Olist__update(_1637259, _1637261), _1637257), _1637265)), _1637263))], (43019 ^ _777081) ^ [_1637432, _1637434, _1637436, _1637438, _1637440] : [-(hAPP(hAPP(c_List_Olist__update(_1637432, hAPP(hAPP(c_List_Oappend(_1637432), _1637434), hAPP(hAPP(c_List_Olist_OCons(_1637432), _1637436), _1637438))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637432)), _1637434)), _1637440) = hAPP(hAPP(c_List_Oappend(_1637432), _1637434), hAPP(hAPP(c_List_Olist_OCons(_1637432), _1637440), _1637438)))], (43021 ^ _777081) ^ [_1637526, _1637528, _1637530, _1637532] : [hBOOL(hAPP(hAPP(c_member(_1637526), _1637528), hAPP(c_List_Oset(_1637526), _1637530))), -(c_List_Oremove1(_1637526, _1637528, hAPP(hAPP(c_List_Oappend(_1637526), _1637530), _1637532)) = hAPP(hAPP(c_List_Oappend(_1637526), c_List_Oremove1(_1637526, _1637528, _1637530)), _1637532))], (43027 ^ _777081) ^ [_1637673, _1637675, _1637677, _1637679] : [-(hBOOL(hAPP(hAPP(c_member(_1637673), _1637675), hAPP(c_List_Oset(_1637673), _1637677)))), -(c_List_Oremove1(_1637673, _1637675, hAPP(hAPP(c_List_Oappend(_1637673), _1637677), _1637679)) = hAPP(hAPP(c_List_Oappend(_1637673), _1637677), c_List_Oremove1(_1637673, _1637675, _1637679)))], (43033 ^ _777081) ^ [_1637751, _1637753, _1637755, _1637757] : [43034 ^ _777081 : [(43035 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1637751), _1637753), hAPP(c_List_Oset(_1637751), c_List_Obutlast(_1637751, _1637755))))], (43037 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1637751), _1637753), hAPP(c_List_Oset(_1637751), c_List_Obutlast(_1637751, _1637757))))]], -(hBOOL(hAPP(hAPP(c_member(_1637751), _1637753), hAPP(c_List_Oset(_1637751), c_List_Obutlast(_1637751, hAPP(hAPP(c_List_Oappend(_1637751), _1637755), _1637757))))))], (43041 ^ _777081) ^ [_1637976, _1637978, _1637980] : [-(c_List_Obutlast(_1637976, hAPP(hAPP(c_List_Oappend(_1637976), _1637978), hAPP(hAPP(c_List_Olist_OCons(_1637976), _1637980), c_List_Olist_ONil(_1637976)))) = _1637978)], (43043 ^ _777081) ^ [_1638024, _1638026, _1638028, _1638030, _1638032, _1638034] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638024), tc_List_Olist(_1638024))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638024), tc_List_Olist(_1638024)), hAPP(hAPP(c_List_Oappend(_1638024), _1638026), _1638032)), hAPP(hAPP(c_List_Oappend(_1638024), _1638028), _1638034))), c_List_Olistrel1(_1638024, _1638030)))), 43044 ^ _777081 : [(43045 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638024), tc_List_Olist(_1638024))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638024), tc_List_Olist(_1638024)), _1638026), _1638028)), c_List_Olistrel1(_1638024, _1638030))), _1638032 = _1638034], (43051 ^ _777081) ^ [] : [_1638026 = _1638028, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638024), tc_List_Olist(_1638024))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638024), tc_List_Olist(_1638024)), _1638032), _1638034)), c_List_Olistrel1(_1638024, _1638030)))]]], (43059 ^ _777081) ^ [_1638472, _1638474, _1638476, _1638478, _1638480] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638472), tc_List_Olist(_1638472))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638472), tc_List_Olist(_1638472)), _1638474), _1638476)), c_List_Olexord(_1638472, _1638478))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638472), tc_List_Olist(_1638472))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638472), tc_List_Olist(_1638472)), hAPP(hAPP(c_List_Oappend(_1638472), _1638480), _1638474)), hAPP(hAPP(c_List_Oappend(_1638472), _1638480), _1638476))), c_List_Olexord(_1638472, _1638478))))], (43065 ^ _777081) ^ [_1638725, _1638727, _1638729] : [hBOOL(hAPP(c_List_Odistinct(_1638725), hAPP(hAPP(c_List_Oappend(_1638725), _1638727), _1638729))), 43068 ^ _777081 : [(43069 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1638725), _1638727)))], (43071 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1638725), _1638729)))], (43073 ^ _777081) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638725, tc_HOL_Obool)), hAPP(c_List_Oset(_1638725), _1638727)), hAPP(c_List_Oset(_1638725), _1638729)) = c_Orderings_Obot__class_Obot(tc_fun(_1638725, tc_HOL_Obool)))]]], (43075 ^ _777081) ^ [_1638942, _1638944, _1638946] : [-(hBOOL(hAPP(c_List_Odistinct(_1638942), hAPP(hAPP(c_List_Oappend(_1638942), _1638944), _1638946)))), hBOOL(hAPP(c_List_Odistinct(_1638942), _1638944)), hBOOL(hAPP(c_List_Odistinct(_1638942), _1638946)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1638942, tc_HOL_Obool)), hAPP(c_List_Oset(_1638942), _1638944)), hAPP(c_List_Oset(_1638942), _1638946)) = c_Orderings_Obot__class_Obot(tc_fun(_1638942, tc_HOL_Obool))], (43089 ^ _777081) ^ [_1639238, _1639240, _1639242, _1639244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639238), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639240)), _1639242))), -(hAPP(hAPP(c_List_Onth(_1639240), hAPP(hAPP(c_List_Oappend(_1639240), _1639242), _1639244)), _1639238) = hAPP(hAPP(c_List_Onth(_1639240), _1639242), _1639238))], (43095 ^ _777081) ^ [_1639385, _1639387, _1639389, _1639391] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639385), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639387)), _1639389)))), -(hAPP(hAPP(c_List_Onth(_1639387), hAPP(hAPP(c_List_Oappend(_1639387), _1639389), _1639391)), _1639385) = hAPP(hAPP(c_List_Onth(_1639387), _1639391), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1639385), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639387)), _1639389))))], (43101 ^ _777081) ^ [_1639494, _1639496, _1639498, _1639500, _1639502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639494), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639496)), _1639498))), -(hAPP(hAPP(c_List_Olist__update(_1639496, hAPP(hAPP(c_List_Oappend(_1639496), _1639498), _1639500)), _1639494), _1639502) = hAPP(hAPP(c_List_Oappend(_1639496), hAPP(hAPP(c_List_Olist__update(_1639496, _1639498), _1639494), _1639502)), _1639500))], (43107 ^ _777081) ^ [_1639663, _1639665, _1639667, _1639669, _1639671] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1639663), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639665)), _1639667)))), -(hAPP(hAPP(c_List_Olist__update(_1639665, hAPP(hAPP(c_List_Oappend(_1639665), _1639667), _1639669)), _1639663), _1639671) = hAPP(hAPP(c_List_Oappend(_1639665), _1639667), hAPP(hAPP(c_List_Olist__update(_1639665, _1639669), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1639663), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639665)), _1639667))), _1639671)))], (43113 ^ _777081) ^ [_1639766, _1639768, _1639770, _1639772] : [-(c_List_Osublist(_1639766, hAPP(hAPP(c_List_Oappend(_1639766), _1639768), _1639770), _1639772) = hAPP(hAPP(c_List_Oappend(_1639766), c_List_Osublist(_1639766, _1639768, _1639772)), c_List_Osublist(_1639766, _1639770, 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(_1639766)), _1639768)))), _1639772)))))], (43115 ^ _777081) ^ [_1639845, _1639847, _1639849, _1639851, _1639853, _1639855, _1639857, _1639859] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1639845, _1639845)), hAPP(hAPP(c_Product__Type_OPair(_1639845, _1639845), _1639847), _1639849)), _1639851)), _1639853 = hAPP(hAPP(c_List_Oappend(_1639845), _1639855), hAPP(hAPP(c_List_Olist_OCons(_1639845), _1639847), _1639857)), _1639859 = hAPP(hAPP(c_List_Oappend(_1639845), _1639855), hAPP(hAPP(c_List_Olist_OCons(_1639845), _1639849), _1639857)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639845), tc_List_Olist(_1639845))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639845), tc_List_Olist(_1639845)), _1639853), _1639859)), c_List_Olistrel1(_1639845, _1639851))))], (43129 ^ _777081) ^ [_1640224, _1640226, _1640228, _1640230, _1640232, _1640234, _1640236] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1640224, _1640224)), hAPP(hAPP(c_Product__Type_OPair(_1640224, _1640224), _1640226), _1640228)), _1640230)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640224), tc_List_Olist(_1640224))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640224), tc_List_Olist(_1640224)), hAPP(hAPP(c_List_Oappend(_1640224), _1640232), hAPP(hAPP(c_List_Olist_OCons(_1640224), _1640226), _1640234))), hAPP(hAPP(c_List_Oappend(_1640224), _1640232), hAPP(hAPP(c_List_Olist_OCons(_1640224), _1640228), _1640236)))), c_List_Olexord(_1640224, _1640230))))], (43135 ^ _777081) ^ [_1640473, _1640475, _1640477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1640473), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640475)), _1640477))), -(hAPP(hAPP(c_List_Otake(_1640475), hAPP(c_Nat_OSuc, _1640473)), _1640477) = hAPP(hAPP(c_List_Oappend(_1640475), hAPP(hAPP(c_List_Otake(_1640475), _1640473), _1640477)), hAPP(hAPP(c_List_Olist_OCons(_1640475), hAPP(hAPP(c_List_Onth(_1640475), _1640477), _1640473)), c_List_Olist_ONil(_1640475))))], (43141 ^ _777081) ^ [_1640693, _1640695, _1640697, _1640699, _1640701, _1640703] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640693), tc_List_Olist(_1640693))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640693), tc_List_Olist(_1640693)), hAPP(hAPP(c_List_Oappend(_1640693), _1640695), hAPP(hAPP(c_List_Olist_OCons(_1640693), _1640697), c_List_Olist_ONil(_1640693)))), hAPP(hAPP(c_List_Oappend(_1640693), _1640699), hAPP(hAPP(c_List_Olist_OCons(_1640693), _1640701), c_List_Olist_ONil(_1640693))))), c_List_Olistrel1(_1640693, _1640703))), 43146 ^ _777081 : [(43147 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1640693), tc_List_Olist(_1640693))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1640693), tc_List_Olist(_1640693)), _1640695), _1640699)), c_List_Olistrel1(_1640693, _1640703))))], (43149 ^ _777081) ^ [] : [-(_1640697 = _1640701)]], 43150 ^ _777081 : [(43151 ^ _777081) ^ [] : [-(_1640695 = _1640699)], (43153 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1640693, _1640693)), hAPP(hAPP(c_Product__Type_OPair(_1640693, _1640693), _1640697), _1640701)), _1640703)))]]], (43155 ^ _777081) ^ [_1641103, _1641105, _1641107, _1641109, _1641111, _1641113] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641103), tc_List_Olist(_1641103))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641103), tc_List_Olist(_1641103)), hAPP(hAPP(c_List_Oappend(_1641103), _1641105), hAPP(hAPP(c_List_Olist_OCons(_1641103), _1641107), c_List_Olist_ONil(_1641103)))), hAPP(hAPP(c_List_Oappend(_1641103), _1641109), hAPP(hAPP(c_List_Olist_OCons(_1641103), _1641111), c_List_Olist_ONil(_1641103))))), c_List_Olistrel1(_1641103, _1641113)))), 43156 ^ _777081 : [(43157 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641103), tc_List_Olist(_1641103))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641103), tc_List_Olist(_1641103)), _1641105), _1641109)), c_List_Olistrel1(_1641103, _1641113))), _1641107 = _1641111], (43163 ^ _777081) ^ [] : [_1641105 = _1641109, hBOOL(hAPP(hAPP(c_member(tc_prod(_1641103, _1641103)), hAPP(hAPP(c_Product__Type_OPair(_1641103, _1641103), _1641107), _1641111)), _1641113))]]], (43171 ^ _777081) ^ [_1641571, _1641573, _1641575, _1641577] : [-(c_List_Osublist(_1641571, hAPP(hAPP(c_List_Olist_OCons(_1641571), _1641573), _1641575), _1641577) = hAPP(hAPP(c_List_Oappend(_1641571), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1641571)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1641577)), hAPP(hAPP(c_List_Olist_OCons(_1641571), _1641573), c_List_Olist_ONil(_1641571))), c_List_Olist_ONil(_1641571))), c_List_Osublist(_1641571, _1641575, 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)), _1641577)))))], (43173 ^ _777081) ^ [_1641658, _1641660, _1641662, _1641664] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641658), tc_List_Olist(_1641658))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641658), tc_List_Olist(_1641658)), _1641660), _1641662)), c_List_Olistrel1(_1641658, _1641664))), 43178 ^ _777081 : [(43179 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641658, _1641658)), hAPP(hAPP(c_Product__Type_OPair(_1641658, _1641658), 43176 ^ [_1641658, _1641660, _1641662, _1641664]), 43177 ^ [_1641658, _1641660, _1641662, _1641664])), _1641664)))], (43183 ^ _777081) ^ [] : [-(_1641660 = hAPP(hAPP(c_List_Oappend(_1641658), 43180 ^ [_1641658, _1641660, _1641662, _1641664]), hAPP(hAPP(c_List_Olist_OCons(_1641658), 43176 ^ [_1641658, _1641660, _1641662, _1641664]), 43181 ^ [_1641658, _1641660, _1641662, _1641664])))], (43185 ^ _777081) ^ [] : [-(_1641662 = hAPP(hAPP(c_List_Oappend(_1641658), 43180 ^ [_1641658, _1641660, _1641662, _1641664]), hAPP(hAPP(c_List_Olist_OCons(_1641658), 43177 ^ [_1641658, _1641660, _1641662, _1641664]), 43181 ^ [_1641658, _1641660, _1641662, _1641664])))]]], (43187 ^ _777081) ^ [_1642063, _1642065, _1642067, _1642069, _1642071] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642063), tc_List_Olist(_1642063))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642063), tc_List_Olist(_1642063)), hAPP(hAPP(c_List_Oappend(_1642063), _1642065), _1642067)), hAPP(hAPP(c_List_Oappend(_1642063), _1642065), _1642069))), c_List_Olexord(_1642063, _1642071))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1642063, _1642063)), hAPP(hAPP(c_Product__Type_OPair(_1642063, _1642063), 43192 ^ [_1642063, _1642065, _1642067, _1642069, _1642071]), 43192 ^ [_1642063, _1642065, _1642067, _1642069, _1642071])), _1642071))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1642063), tc_List_Olist(_1642063))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1642063), tc_List_Olist(_1642063)), _1642067), _1642069)), c_List_Olexord(_1642063, _1642071))))], (43198 ^ _777081) ^ [_1642382, _1642384] : [-(hAPP(c_List_Orotate1(_1642382), _1642384) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1642382), _1642382, c_List_Olist_ONil(_1642382), hAPP(hAPP(c_COMBB(tc_List_Olist(_1642382), tc_fun(tc_List_Olist(_1642382), tc_List_Olist(_1642382)), _1642382), hAPP(c_COMBC(tc_List_Olist(_1642382), tc_List_Olist(_1642382), tc_List_Olist(_1642382)), c_List_Oappend(_1642382))), hAPP(hAPP(c_COMBC(_1642382, tc_List_Olist(_1642382), tc_List_Olist(_1642382)), c_List_Olist_OCons(_1642382)), c_List_Olist_ONil(_1642382)))), _1642384))], (43200 ^ _777081) ^ [_1642476, _1642478, _1642480, _1642482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642476), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642478)), _1642480))), -(hAPP(hAPP(c_List_Olist__update(_1642478, _1642480), _1642476), _1642482) = hAPP(hAPP(c_List_Oappend(_1642478), hAPP(hAPP(c_List_Otake(_1642478), _1642476), _1642480)), hAPP(hAPP(c_List_Olist_OCons(_1642478), _1642482), hAPP(hAPP(c_List_Odrop(_1642478), hAPP(c_Nat_OSuc, _1642476)), _1642480))))], (43206 ^ _777081) ^ [_1642669, _1642671, _1642673] : [-(hAPP(hAPP(c_List_Oappend(_1642669), hAPP(hAPP(c_List_Otake(_1642669), _1642671), _1642673)), hAPP(hAPP(c_List_Odrop(_1642669), _1642671), _1642673)) = _1642673)], (43208 ^ _777081) ^ [_1642735, _1642737] : [hAPP(c_List_Orotate1(_1642735), _1642737) = c_List_Olist_ONil(_1642735), -(_1642737 = c_List_Olist_ONil(_1642735))], (43214 ^ _777081) ^ [_1642826, _1642828] : [_1642828 = c_List_Olist_ONil(_1642826), -(hAPP(c_List_Orotate1(_1642826), _1642828) = c_List_Olist_ONil(_1642826))], (43220 ^ _777081) ^ [_1642923, _1642925] : [-(hAPP(hAPP(c_List_Odrop(_1642923), _1642925), c_List_Olist_ONil(_1642923)) = c_List_Olist_ONil(_1642923))], (43222 ^ _777081) ^ [_1642960, _1642962, _1642964] : [-(hAPP(hAPP(c_List_Odrop(_1642960), _1642962), c_List_Obutlast(_1642960, _1642964)) = c_List_Obutlast(_1642960, hAPP(hAPP(c_List_Odrop(_1642960), _1642962), _1642964)))], (43224 ^ _777081) ^ [_1643009, _1643011, _1643013] : [-(c_List_Obutlast(_1643009, hAPP(hAPP(c_List_Odrop(_1643009), _1643011), _1643013)) = hAPP(hAPP(c_List_Odrop(_1643009), _1643011), c_List_Obutlast(_1643009, _1643013)))], (43226 ^ _777081) ^ [_1643058, _1643060, _1643062] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1643058, tc_HOL_Obool)), hAPP(c_List_Oset(_1643058), hAPP(hAPP(c_List_Odrop(_1643058), _1643060), _1643062))), hAPP(c_List_Oset(_1643058), _1643062))))], (43228 ^ _777081) ^ [_1643113, _1643115, _1643117, _1643119] : [hBOOL(hAPP(hAPP(c_member(_1643113), _1643115), hAPP(c_List_Oset(_1643113), hAPP(hAPP(c_List_Odrop(_1643113), _1643117), _1643119)))), -(hBOOL(hAPP(hAPP(c_member(_1643113), _1643115), hAPP(c_List_Oset(_1643113), _1643119))))], (43234 ^ _777081) ^ [_1643258, _1643260, _1643262] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643258)), hAPP(hAPP(c_List_Odrop(_1643258), _1643260), _1643262)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643258)), _1643262)), _1643260))], (43236 ^ _777081) ^ [_1643313, _1643315] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643313)), hAPP(c_List_Orotate1(_1643313), _1643315)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643313)), _1643315))], (43238 ^ _777081) ^ [_1643357, _1643359] : [-(hAPP(c_List_Oset(_1643357), hAPP(c_List_Orotate1(_1643357), _1643359)) = hAPP(c_List_Oset(_1643357), _1643359))], (43240 ^ _777081) ^ [_1643397, _1643399, _1643401, _1643403, _1643405] : [-(hAPP(hAPP(c_List_Odrop(_1643397), _1643399), hAPP(hAPP(c_List_Omap(_1643401, _1643397), _1643403), _1643405)) = hAPP(hAPP(c_List_Omap(_1643401, _1643397), _1643403), hAPP(hAPP(c_List_Odrop(_1643401), _1643399), _1643405)))], (43242 ^ _777081) ^ [_1643462, _1643464, _1643466, _1643468] : [-(hAPP(hAPP(c_List_Otake(_1643462), _1643464), hAPP(hAPP(c_List_Odrop(_1643462), _1643466), _1643468)) = hAPP(hAPP(c_List_Odrop(_1643462), _1643466), hAPP(hAPP(c_List_Otake(_1643462), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1643464), _1643466)), _1643468)))], (43244 ^ _777081) ^ [_1643529, _1643531, _1643533, _1643535] : [-(hAPP(hAPP(c_List_Odrop(_1643529), _1643531), hAPP(hAPP(c_List_Otake(_1643529), _1643533), _1643535)) = hAPP(hAPP(c_List_Otake(_1643529), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1643533), _1643531)), hAPP(hAPP(c_List_Odrop(_1643529), _1643531), _1643535)))], (43246 ^ _777081) ^ [_1643596, _1643598, _1643600] : [hBOOL(hAPP(c_List_Odistinct(_1643596), _1643598)), -(hBOOL(hAPP(c_List_Odistinct(_1643596), hAPP(hAPP(c_List_Odrop(_1643596), _1643600), _1643598))))], (43252 ^ _777081) ^ [_1643722, _1643724] : [hBOOL(hAPP(c_List_Odistinct(_1643722), hAPP(c_List_Orotate1(_1643722), _1643724))), -(hBOOL(hAPP(c_List_Odistinct(_1643722), _1643724)))], (43258 ^ _777081) ^ [_1643821, _1643823] : [hBOOL(hAPP(c_List_Odistinct(_1643821), _1643823)), -(hBOOL(hAPP(c_List_Odistinct(_1643821), hAPP(c_List_Orotate1(_1643821), _1643823))))], (43264 ^ _777081) ^ [_1643926, _1643928] : [-(hAPP(hAPP(c_List_Odrop(_1643926), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1643928) = _1643928)], (43266 ^ _777081) ^ [_1643959, _1643961, _1643963, _1643965] : [-(hAPP(hAPP(c_List_Odrop(_1643959), _1643961), hAPP(hAPP(c_List_Odrop(_1643959), _1643963), _1643965)) = hAPP(hAPP(c_List_Odrop(_1643959), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1643961), _1643963)), _1643965))], (43268 ^ _777081) ^ [_1644018, _1644020, _1644022, _1644024, _1644026] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1644018, _1644020)), _1644022), hAPP(hAPP(c_List_Ozip(_1644018, _1644020), _1644024), _1644026)) = hAPP(hAPP(c_List_Ozip(_1644018, _1644020), hAPP(hAPP(c_List_Odrop(_1644018), _1644022), _1644024)), hAPP(hAPP(c_List_Odrop(_1644020), _1644022), _1644026)))], (43270 ^ _777081) ^ [_1644094, _1644096, _1644098, _1644100, _1644102] : [hAPP(hAPP(c_List_Odrop(_1644094), _1644096), _1644098) = hAPP(hAPP(c_List_Olist_OCons(_1644094), _1644100), _1644102), -(hAPP(hAPP(c_List_Onth(_1644094), _1644098), _1644096) = _1644100)], (43276 ^ _777081) ^ [_1644225, _1644227, _1644229] : [-(hAPP(hAPP(c_List_Odrop(_1644225), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1644225), _1644227), _1644229)) = _1644229)], (43278 ^ _777081) ^ [_1644268, _1644270, _1644272, _1644274] : [-(hAPP(hAPP(c_List_Odrop(_1644268), hAPP(c_Nat_OSuc, _1644270)), hAPP(hAPP(c_List_Olist_OCons(_1644268), _1644272), _1644274)) = hAPP(hAPP(c_List_Odrop(_1644268), _1644270), _1644274))], (43280 ^ _777081) ^ [_1644324, _1644326, _1644328, _1644330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1644324), _1644326)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1644328, tc_HOL_Obool)), hAPP(c_List_Oset(_1644328), hAPP(hAPP(c_List_Odrop(_1644328), _1644326), _1644330))), hAPP(c_List_Oset(_1644328), hAPP(hAPP(c_List_Odrop(_1644328), _1644324), _1644330)))))], (43286 ^ _777081) ^ [_1644505, _1644507, _1644509] : [hAPP(hAPP(c_List_Odrop(_1644505), _1644507), _1644509) = c_List_Olist_ONil(_1644505), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644505)), _1644509)), _1644507)))], (43292 ^ _777081) ^ [_1644624, _1644626, _1644628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644624)), _1644628)), _1644626)), -(hAPP(hAPP(c_List_Odrop(_1644624), _1644626), _1644628) = c_List_Olist_ONil(_1644624))], (43298 ^ _777081) ^ [_1644749, _1644751, _1644753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644749)), _1644751)), _1644753)), -(hAPP(hAPP(c_List_Odrop(_1644749), _1644753), _1644751) = c_List_Olist_ONil(_1644749))], (43304 ^ _777081) ^ [_1644872, _1644874, _1644876, _1644878] : [-(hAPP(hAPP(c_List_Odrop(_1644872), _1644874), hAPP(hAPP(c_List_Oappend(_1644872), _1644876), _1644878)) = hAPP(hAPP(c_List_Oappend(_1644872), hAPP(hAPP(c_List_Odrop(_1644872), _1644874), _1644876)), hAPP(hAPP(c_List_Odrop(_1644872), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644874), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644872)), _1644876))), _1644878)))], (43306 ^ _777081) ^ [_1644975, _1644977, _1644979, _1644981] : [hAPP(hAPP(c_List_Oappend(_1644975), _1644977), _1644979) = _1644981, 43309 ^ _777081 : [(43310 ^ _777081) ^ [] : [-(_1644977 = hAPP(hAPP(c_List_Otake(_1644975), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644975)), _1644977)), _1644981))], (43312 ^ _777081) ^ [] : [-(_1644979 = hAPP(hAPP(c_List_Odrop(_1644975), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644975)), _1644977)), _1644981))]]], (43314 ^ _777081) ^ [_1645154, _1645156, _1645158, _1645160] : [-(hAPP(hAPP(c_List_Oappend(_1645154), _1645156), _1645158) = _1645160), _1645156 = hAPP(hAPP(c_List_Otake(_1645154), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645154)), _1645156)), _1645160), _1645158 = hAPP(hAPP(c_List_Odrop(_1645154), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645154)), _1645156)), _1645160)], (43324 ^ _777081) ^ [_1645369, _1645371, _1645373, _1645375] : [-(hAPP(hAPP(c_List_Odrop(_1645369), _1645371), hAPP(hAPP(c_List_Olist_OCons(_1645369), _1645373), _1645375)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1645369), hAPP(hAPP(c_List_Olist_OCons(_1645369), _1645373), _1645375), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1645369), tc_List_Olist(_1645369)), c_List_Odrop(_1645369)), _1645375), _1645371))], (43326 ^ _777081) ^ [_1645460, _1645462, _1645464, _1645466] : [_1645460 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1645462), _1645460), hAPP(hAPP(c_List_Olist_OCons(_1645462), _1645464), _1645466)) = hAPP(hAPP(c_List_Olist_OCons(_1645462), _1645464), _1645466))], (43332 ^ _777081) ^ [_1645583, _1645585, _1645587, _1645589] : [-(_1645583 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1645585), _1645583), hAPP(hAPP(c_List_Olist_OCons(_1645585), _1645587), _1645589)) = hAPP(hAPP(c_List_Odrop(_1645585), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1645583), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1645589))], (43338 ^ _777081) ^ [_1645655, _1645657, _1645659, _1645661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1645655), _1645657)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645659)), _1645661))), -(hAPP(hAPP(c_List_Onth(_1645659), hAPP(hAPP(c_List_Odrop(_1645659), _1645655), _1645661)), _1645657) = hAPP(hAPP(c_List_Onth(_1645659), _1645661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1645655), _1645657)))], (43344 ^ _777081) ^ [_1645856, _1645858, _1645860, _1645862, _1645864] : [hAPP(hAPP(c_List_Oappend(_1645856), _1645858), _1645860) = hAPP(hAPP(c_List_Oappend(_1645856), _1645862), _1645864), 43347 ^ _777081 : [(43348 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645856)), _1645858)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645856)), _1645862))), 43351 ^ _777081 : [(43352 ^ _777081) ^ [] : [-(_1645858 = hAPP(hAPP(c_List_Otake(_1645856), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645856)), _1645858)), _1645862))], (43354 ^ _777081) ^ [] : [-(_1645860 = hAPP(hAPP(c_List_Oappend(_1645856), hAPP(hAPP(c_List_Odrop(_1645856), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645856)), _1645858)), _1645862)), _1645864))]]], (43356 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645856)), _1645858)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645856)), _1645862)))), 43359 ^ _777081 : [(43360 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1645856), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645856)), _1645862)), _1645858) = _1645862)], (43362 ^ _777081) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1645856), hAPP(hAPP(c_List_Odrop(_1645856), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645856)), _1645862)), _1645858)), _1645860) = _1645864)]]]]], (43364 ^ _777081) ^ [_1646369, _1646371, _1646373, _1646375, _1646377] : [-(hAPP(hAPP(c_List_Oappend(_1646369), _1646371), _1646373) = hAPP(hAPP(c_List_Oappend(_1646369), _1646375), _1646377)), 43367 ^ _777081 : [(43368 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646369)), _1646371)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646369)), _1646375))))], (43370 ^ _777081) ^ [] : [_1646371 = hAPP(hAPP(c_List_Otake(_1646369), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646369)), _1646371)), _1646375), _1646373 = hAPP(hAPP(c_List_Oappend(_1646369), hAPP(hAPP(c_List_Odrop(_1646369), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646369)), _1646371)), _1646375)), _1646377)]], 43375 ^ _777081 : [(43376 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646369)), _1646371)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646369)), _1646375)))], (43378 ^ _777081) ^ [] : [hAPP(hAPP(c_List_Otake(_1646369), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646369)), _1646375)), _1646371) = _1646375, hAPP(hAPP(c_List_Oappend(_1646369), hAPP(hAPP(c_List_Odrop(_1646369), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646369)), _1646375)), _1646371)), _1646373) = _1646377]]], (43386 ^ _777081) ^ [_1646957, _1646959, _1646961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1646957), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646959)), _1646961))), -(hAPP(hAPP(c_List_Olist_OCons(_1646959), hAPP(hAPP(c_List_Onth(_1646959), _1646961), _1646957)), hAPP(hAPP(c_List_Odrop(_1646959), hAPP(c_Nat_OSuc, _1646957)), _1646961)) = hAPP(hAPP(c_List_Odrop(_1646959), _1646957), _1646961))], (43392 ^ _777081) ^ [_1647128, _1647130, _1647132, _1647134] : [-(hAPP(c_List_Orotate1(_1647128), c_List_Olist_ONil(_1647128)) = c_List_Olist_ONil(_1647128))], (43394 ^ _777081) ^ [_1647163, _1647165, _1647167, _1647169] : [-(hAPP(c_List_Orotate1(_1647165), hAPP(hAPP(c_List_Olist_OCons(_1647165), _1647167), _1647169)) = hAPP(hAPP(c_List_Oappend(_1647165), _1647169), hAPP(hAPP(c_List_Olist_OCons(_1647165), _1647167), c_List_Olist_ONil(_1647165))))], (43396 ^ _777081) ^ [_1647240, _1647242, _1647244, _1647246] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647240) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1647242), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647240)), hAPP(hAPP(c_List_Olist_OCons(_1647242), _1647244), _1647246)) = hAPP(hAPP(c_List_Olist_OCons(_1647242), _1647244), _1647246))], (43402 ^ _777081) ^ [_1647375, _1647377, _1647379, _1647381] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647375) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1647377), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647375)), hAPP(hAPP(c_List_Olist_OCons(_1647377), _1647379), _1647381)) = hAPP(hAPP(c_List_Odrop(_1647377), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1647375)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1647381))], (43408 ^ _777081) ^ [_1647456, _1647458, _1647460, _1647462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1647456), _1647458)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647460)), _1647462))), -(hAPP(hAPP(c_List_Otake(_1647460), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1647456), _1647458)), _1647462) = hAPP(hAPP(c_List_Oappend(_1647460), hAPP(hAPP(c_List_Otake(_1647460), _1647456), _1647462)), hAPP(hAPP(c_List_Otake(_1647460), _1647458), hAPP(hAPP(c_List_Odrop(_1647460), _1647456), _1647462))))], (43414 ^ _777081) ^ [_1647665, _1647667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647665)), _1647667)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1647665), _1647667) = _1647667)], (43420 ^ _777081) ^ [_1647776, _1647778, _1647780, _1647782, _1647784] : [-(hAPP(hAPP(c_List_Ozip(_1647776, _1647778), hAPP(hAPP(c_List_Oappend(_1647776), _1647780), _1647782)), _1647784) = hAPP(hAPP(c_List_Oappend(tc_prod(_1647776, _1647778)), hAPP(hAPP(c_List_Ozip(_1647776, _1647778), _1647780), hAPP(hAPP(c_List_Otake(_1647778), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647776)), _1647780)), _1647784))), hAPP(hAPP(c_List_Ozip(_1647776, _1647778), _1647782), hAPP(hAPP(c_List_Odrop(_1647778), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647776)), _1647780)), _1647784))))], (43422 ^ _777081) ^ [_1647883, _1647885, _1647887, _1647889, _1647891] : [-(hAPP(hAPP(c_List_Ozip(_1647883, _1647885), _1647887), hAPP(hAPP(c_List_Oappend(_1647885), _1647889), _1647891)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1647883, _1647885)), hAPP(hAPP(c_List_Ozip(_1647883, _1647885), hAPP(hAPP(c_List_Otake(_1647883), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647885)), _1647889)), _1647887)), _1647889)), hAPP(hAPP(c_List_Ozip(_1647883, _1647885), hAPP(hAPP(c_List_Odrop(_1647883), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647885)), _1647889)), _1647887)), _1647891)))], (43424 ^ _777081) ^ [_1647990, _1647992, _1647994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647990), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647992)), _1647994))), -(_1647994 = hAPP(hAPP(c_List_Oappend(_1647992), hAPP(hAPP(c_List_Otake(_1647992), _1647990), _1647994)), hAPP(hAPP(c_List_Olist_OCons(_1647992), hAPP(hAPP(c_List_Onth(_1647992), _1647994), _1647990)), hAPP(hAPP(c_List_Odrop(_1647992), hAPP(c_Nat_OSuc, _1647990)), _1647994))))], (43430 ^ _777081) ^ [_1648179, _1648181, _1648183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1648179), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648181)), _1648183))), -(hAPP(hAPP(c_List_Oappend(_1648181), hAPP(hAPP(c_List_Otake(_1648181), _1648179), _1648183)), hAPP(hAPP(c_List_Olist_OCons(_1648181), hAPP(c_List_Ohd(_1648181), hAPP(hAPP(c_List_Odrop(_1648181), _1648179), _1648183))), c_List_Olist_ONil(_1648181))) = hAPP(hAPP(c_List_Otake(_1648181), hAPP(c_Nat_OSuc, _1648179)), _1648183))], (43436 ^ _777081) ^ [_1648381, _1648383, _1648385] : [-(_1648381 = c_List_Olist_ONil(_1648383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1648385), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648383)), _1648381))), -(hAPP(c_List_Ohd(_1648383), hAPP(hAPP(c_List_Odrop(_1648383), _1648385), _1648381)) = hAPP(hAPP(c_List_Onth(_1648383), _1648381), _1648385))], (43446 ^ _777081) ^ [_1648580, _1648582, _1648584] : [-(hAPP(c_List_Ohd(_1648580), hAPP(hAPP(c_List_Olist_OCons(_1648580), _1648582), _1648584)) = _1648582)], (43448 ^ _777081) ^ [_1648616, _1648618, _1648620, _1648622] : [-(_1648616 = c_List_Olist_ONil(_1648618)), -(hAPP(c_List_Ohd(_1648620), hAPP(hAPP(c_List_Omap(_1648618, _1648620), _1648622), _1648616)) = hAPP(_1648622, hAPP(c_List_Ohd(_1648618), _1648616)))], (43454 ^ _777081) ^ [_1648692, _1648694, _1648696] : [_1648692 = c_List_Olist_ONil(_1648694), -(hAPP(c_List_Ohd(_1648694), hAPP(hAPP(c_List_Oappend(_1648694), _1648692), _1648696)) = hAPP(c_List_Ohd(_1648694), _1648696))], (43460 ^ _777081) ^ [_1648805, _1648807, _1648809] : [-(_1648805 = c_List_Olist_ONil(_1648807)), -(hAPP(c_List_Ohd(_1648807), hAPP(hAPP(c_List_Oappend(_1648807), _1648805), _1648809)) = hAPP(c_List_Ohd(_1648807), _1648805))], (43466 ^ _777081) ^ [_1648861, _1648863, _1648865] : [-(_1648861 = c_List_Olist_ONil(_1648863)), -(hAPP(c_List_Ohd(_1648863), hAPP(hAPP(c_List_Oappend(_1648863), _1648861), _1648865)) = hAPP(c_List_Ohd(_1648863), _1648861))], (43472 ^ _777081) ^ [_1648915, _1648917] : [-(_1648915 = c_List_Olist_ONil(_1648917)), -(hBOOL(hAPP(hAPP(c_member(_1648917), hAPP(c_List_Ohd(_1648917), _1648915)), hAPP(c_List_Oset(_1648917), _1648915))))], (43478 ^ _777081) ^ [_1648966, _1648968] : [-(_1648966 = c_List_Olist_ONil(_1648968)), -(hAPP(c_List_Ohd(_1648968), _1648966) = hAPP(hAPP(c_List_Onth(_1648968), _1648966), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (43484 ^ _777081) ^ [_1649013, _1649015] : [-(_1649013 = c_List_Olist_ONil(_1649015)), -(hAPP(c_List_Orotate1(_1649015), _1649013) = hAPP(hAPP(c_List_Oappend(_1649015), hAPP(c_List_Otl(_1649015), _1649013)), hAPP(hAPP(c_List_Olist_OCons(_1649015), hAPP(c_List_Ohd(_1649015), _1649013)), c_List_Olist_ONil(_1649015))))], (43490 ^ _777081) ^ [_1649080, _1649082, _1649084] : [-(_1649080 = c_List_Olist_ONil(_1649082)), -(hAPP(c_List_Ohd(_1649082), hAPP(c_List_Orotate(_1649082, _1649084), _1649080)) = hAPP(hAPP(c_List_Onth(_1649082), _1649080), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1649084, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649082)), _1649080))))], (43496 ^ _777081) ^ [_1649150, _1649152, _1649154] : [-(hAPP(c_List_Otl(_1649150), hAPP(hAPP(c_List_Odrop(_1649150), _1649152), _1649154)) = hAPP(hAPP(c_List_Odrop(_1649150), _1649152), hAPP(c_List_Otl(_1649150), _1649154)))], (43498 ^ _777081) ^ [_1649203, _1649205, _1649207] : [-(hAPP(hAPP(c_List_Odrop(_1649203), _1649205), hAPP(c_List_Otl(_1649203), _1649207)) = hAPP(c_List_Otl(_1649203), hAPP(hAPP(c_List_Odrop(_1649203), _1649205), _1649207)))], (43500 ^ _777081) ^ [_1649274, _1649276, _1649278] : [hAPP(c_List_Orotate(_1649274, _1649276), _1649278) = c_List_Olist_ONil(_1649274), -(_1649278 = c_List_Olist_ONil(_1649274))], (43506 ^ _777081) ^ [_1649369, _1649371, _1649373] : [_1649373 = c_List_Olist_ONil(_1649369), -(hAPP(c_List_Orotate(_1649369, _1649371), _1649373) = c_List_Olist_ONil(_1649369))], (43512 ^ _777081) ^ [_1649470] : [-(hAPP(c_List_Otl(_1649470), c_List_Olist_ONil(_1649470)) = c_List_Olist_ONil(_1649470))], (43514 ^ _777081) ^ [_1649502, _1649504, _1649506] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649502)), hAPP(c_List_Orotate(_1649502, _1649504), _1649506)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649502)), _1649506))], (43516 ^ _777081) ^ [_1649549, _1649551, _1649553] : [-(hAPP(c_List_Oset(_1649549), hAPP(c_List_Orotate(_1649549, _1649551), _1649553)) = hAPP(c_List_Oset(_1649549), _1649553))], (43518 ^ _777081) ^ [_1649592, _1649594, _1649596, _1649598] : [-(hAPP(hAPP(c_List_Omap(_1649592, _1649594), _1649596), hAPP(c_List_Otl(_1649592), _1649598)) = hAPP(c_List_Otl(_1649594), hAPP(hAPP(c_List_Omap(_1649592, _1649594), _1649596), _1649598)))], (43520 ^ _777081) ^ [_1649649, _1649651, _1649653, _1649655, _1649657] : [-(hAPP(c_List_Orotate(_1649649, _1649651), hAPP(hAPP(c_List_Omap(_1649653, _1649649), _1649655), _1649657)) = hAPP(hAPP(c_List_Omap(_1649653, _1649649), _1649655), hAPP(c_List_Orotate(_1649653, _1649651), _1649657)))], (43522 ^ _777081) ^ [_1649710, _1649712] : [hBOOL(hAPP(c_List_Odistinct(_1649710), _1649712)), -(hBOOL(hAPP(c_List_Odistinct(_1649710), hAPP(c_List_Otl(_1649710), _1649712))))], (43528 ^ _777081) ^ [_1649831, _1649833, _1649835] : [hBOOL(hAPP(c_List_Odistinct(_1649831), hAPP(c_List_Orotate(_1649831, _1649833), _1649835))), -(hBOOL(hAPP(c_List_Odistinct(_1649831), _1649835)))], (43534 ^ _777081) ^ [_1649934, _1649936, _1649938] : [hBOOL(hAPP(c_List_Odistinct(_1649934), _1649938)), -(hBOOL(hAPP(c_List_Odistinct(_1649934), hAPP(c_List_Orotate(_1649934, _1649936), _1649938))))], (43540 ^ _777081) ^ [_1650043, _1650045, _1650047, _1650049] : [-(hAPP(c_List_Orotate(_1650043, _1650045), hAPP(c_List_Orotate(_1650043, _1650047), _1650049)) = hAPP(c_List_Orotate(_1650043, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650045), _1650047)), _1650049))], (43542 ^ _777081) ^ [_1650096, _1650098, _1650100] : [-(hAPP(c_List_Otl(_1650096), hAPP(hAPP(c_List_Olist_OCons(_1650096), _1650098), _1650100)) = _1650100)], (43544 ^ _777081) ^ [_1650136, _1650138, _1650140] : [-(hAPP(c_List_Orotate1(_1650136), hAPP(c_List_Orotate(_1650136, _1650138), _1650140)) = hAPP(c_List_Orotate(_1650136, _1650138), hAPP(c_List_Orotate1(_1650136), _1650140)))], (43546 ^ _777081) ^ [_1650181, _1650183, _1650185] : [-(_1650181 = c_List_Olist_ONil(_1650183)), -(hAPP(c_List_Otl(_1650183), hAPP(hAPP(c_List_Oappend(_1650183), _1650181), _1650185)) = hAPP(hAPP(c_List_Oappend(_1650183), hAPP(c_List_Otl(_1650183), _1650181)), _1650185))], (43552 ^ _777081) ^ [_1650247, _1650249, _1650251] : [-(hAPP(hAPP(c_List_Otake(_1650247), _1650249), hAPP(c_List_Otl(_1650247), _1650251)) = hAPP(c_List_Otl(_1650247), hAPP(hAPP(c_List_Otake(_1650247), hAPP(c_Nat_OSuc, _1650249)), _1650251)))], (43554 ^ _777081) ^ [_1650303, _1650305, _1650307] : [-(hAPP(c_List_Orotate(_1650303, _1650305), _1650307) = hAPP(c_List_Orotate(_1650303, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1650305, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650303)), _1650307))), _1650307))], (43556 ^ _777081) ^ [_1650353, _1650355, _1650357] : [-(hAPP(hAPP(c_List_Odrop(_1650353), hAPP(c_Nat_OSuc, _1650355)), _1650357) = hAPP(hAPP(c_List_Odrop(_1650353), _1650355), hAPP(c_List_Otl(_1650353), _1650357)))], (43558 ^ _777081) ^ [_1650404, _1650406, _1650408] : [-(hAPP(c_List_Orotate(_1650404, hAPP(c_Nat_OSuc, _1650406)), _1650408) = hAPP(c_List_Orotate1(_1650404), hAPP(c_List_Orotate(_1650404, _1650406), _1650408)))], (43560 ^ _777081) ^ [_1650451, _1650453, _1650455] : [-(hAPP(c_List_Otl(_1650451), hAPP(hAPP(c_List_Oappend(_1650451), _1650453), _1650455)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1650451), _1650451, hAPP(c_List_Otl(_1650451), _1650455), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1650451), tc_List_Olist(_1650451)), _1650451), hAPP(hAPP(c_COMBC(tc_List_Olist(_1650451), tc_List_Olist(_1650451), tc_List_Olist(_1650451)), c_List_Oappend(_1650451)), _1650455))), _1650453))], (43562 ^ _777081) ^ [_1650537] : [-(c_List_Orotate(_1650537, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1650537)))], (43564 ^ _777081) ^ [_1650567, _1650569, _1650571] : [-(c_List_Orotate(_1650567, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650569), _1650571)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1650567), tc_List_Olist(_1650567), tc_List_Olist(_1650567), c_List_Orotate(_1650567, _1650569)), c_List_Orotate(_1650567, _1650571)))], (43566 ^ _777081) ^ [_1650623, _1650625, _1650627] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1650623, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650625)), _1650627)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1650625, _1650623), _1650627) = _1650627)], (43572 ^ _777081) ^ [_1650736, _1650738, _1650740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650736)), _1650738)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1650736, _1650740), _1650738) = _1650738)], (43578 ^ _777081) ^ [_1650851, _1650853] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650851)), hAPP(c_List_Otl(_1650851), _1650853)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650851)), _1650853)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43580 ^ _777081) ^ [_1650901, _1650903, _1650905] : [-(hAPP(c_List_Otl(_1650901), hAPP(hAPP(c_List_Otake(_1650901), _1650903), _1650905)) = hAPP(hAPP(c_List_Otake(_1650901), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1650903), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1650901), _1650905)))], (43582 ^ _777081) ^ [_1650956, _1650958, _1650960] : [-(_1650956 = c_List_Olist_ONil(_1650958)), -(hAPP(hAPP(c_List_Otake(_1650958), hAPP(c_Nat_OSuc, _1650960)), _1650956) = hAPP(hAPP(c_List_Olist_OCons(_1650958), hAPP(c_List_Ohd(_1650958), _1650956)), hAPP(hAPP(c_List_Otake(_1650958), _1650960), hAPP(c_List_Otl(_1650958), _1650956))))], (43588 ^ _777081) ^ [_1651033, _1651035, _1651037] : [-(hAPP(c_List_Orotate(_1651033, _1651035), _1651037) = hAPP(hAPP(c_List_Oappend(_1651033), hAPP(hAPP(c_List_Odrop(_1651033), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1651035, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651033)), _1651037))), _1651037)), hAPP(hAPP(c_List_Otake(_1651033), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1651035, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651033)), _1651037))), _1651037)))], (43590 ^ _777081) ^ [_1651112, _1651114] : [class_Lattices_Oab__semigroup__idem__mult(_1651112), -(_1651114 = c_List_Olist_ONil(_1651112)), -(hAPP(c_Finite__Set_Ofold1(_1651112, c_Groups_Otimes__class_Otimes(_1651112)), hAPP(c_List_Oset(_1651112), _1651114)) = hAPP(c_List_Ofoldl(_1651112, _1651112, c_Groups_Otimes__class_Otimes(_1651112), hAPP(c_List_Ohd(_1651112), _1651114)), hAPP(c_List_Otl(_1651112), _1651114)))], (43600 ^ _777081) ^ [_1651272, _1651274, _1651276, _1651278] : [43601 ^ _777081 : [(43602 ^ _777081) ^ [_1651369, _1651371] : [_1651272 = hAPP(hAPP(c_List_Olist_OCons(_1651274), _1651371), _1651369)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1651274), tc_List_Olist(_1651274))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1651274), tc_List_Olist(_1651274)), _1651276), hAPP(hAPP(c_List_Oappend(_1651274), _1651276), _1651272))), c_List_Olexord(_1651274, _1651278))))], (43606 ^ _777081) ^ [_1651468, _1651470, _1651472, _1651474, _1651476, _1651478] : [-(hAPP(c_List_Ofoldl(_1651468, _1651470, _1651472, _1651474), hAPP(hAPP(c_List_Olist_OCons(_1651470), _1651476), _1651478)) = hAPP(c_List_Ofoldl(_1651468, _1651470, _1651472, hAPP(hAPP(_1651472, _1651474), _1651476)), _1651478))], (43608 ^ _777081) ^ [_1651531, _1651533, _1651535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651531), _1651533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1651531), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1651533), _1651535))))], (43614 ^ _777081) ^ [_1651646, _1651648, _1651650] : [class_Groups_Oab__semigroup__add(_1651646), -(c_List_Ofoldr(_1651646, _1651646, c_Groups_Oplus__class_Oplus(_1651646), _1651648, _1651650) = hAPP(c_List_Ofoldl(_1651646, _1651646, c_Groups_Oplus__class_Oplus(_1651646), _1651650), _1651648))], (43620 ^ _777081) ^ [_1651759, _1651761, _1651763, _1651765] : [class_Groups_Osemigroup__add(_1651759), -(hAPP(c_List_Ofoldl(_1651759, _1651759, c_Groups_Oplus__class_Oplus(_1651759), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1651759), _1651761), _1651763)), _1651765) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1651759), _1651761), hAPP(c_List_Ofoldl(_1651759, _1651759, c_Groups_Oplus__class_Oplus(_1651759), _1651763), _1651765)))], (43626 ^ _777081) ^ [_1651910, _1651912, _1651914] : [class_Groups_Omonoid__add(_1651910), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1651910), _1651912), hAPP(c_List_Ofoldl(_1651910, _1651910, c_Groups_Oplus__class_Oplus(_1651910), c_Groups_Ozero__class_Ozero(_1651910)), _1651914)) = hAPP(c_List_Ofoldl(_1651910, _1651910, c_Groups_Oplus__class_Oplus(_1651910), _1651912), _1651914))], (43632 ^ _777081) ^ [_1652047, _1652049, _1652051, _1652053, _1652055, _1652057, _1652059] : [-(hAPP(c_List_Ofoldl(_1652047, _1652049, _1652051, _1652053), hAPP(hAPP(c_List_Omap(_1652055, _1652049), _1652057), _1652059)) = hAPP(c_List_Ofoldl(_1652047, _1652055, hAPP(hAPP(c_COMBC(_1652047, tc_fun(_1652055, _1652049), tc_fun(_1652055, _1652047)), hAPP(hAPP(c_COMBB(tc_fun(_1652049, _1652047), tc_fun(tc_fun(_1652055, _1652049), tc_fun(_1652055, _1652047)), _1652047), c_COMBB(_1652049, _1652047, _1652055)), _1652051)), _1652057), _1652053), _1652059))], (43634 ^ _777081) ^ [_1652149, _1652151, _1652153, _1652155] : [-(hAPP(c_List_Ofoldl(_1652149, _1652151, _1652153, _1652155), c_List_Olist_ONil(_1652151)) = _1652155)], (43636 ^ _777081) ^ [_1652188, _1652190, _1652192, _1652194, _1652196, _1652198] : [-(hAPP(c_List_Ofoldl(_1652188, _1652190, _1652192, _1652194), hAPP(hAPP(c_List_Oappend(_1652190), _1652196), _1652198)) = hAPP(c_List_Ofoldl(_1652188, _1652190, _1652192, hAPP(c_List_Ofoldl(_1652188, _1652190, _1652192, _1652194), _1652196)), _1652198))], (43638 ^ _777081) ^ [_1652253] : [class_Groups_Omonoid__add(_1652253), -(c_List_Omonoid__add__class_Olistsum(_1652253) = c_List_Ofoldl(_1652253, _1652253, c_Groups_Oplus__class_Oplus(_1652253), c_Groups_Ozero__class_Ozero(_1652253)))], (43644 ^ _777081) ^ [_1652348, _1652350] : [class_Groups_Omonoid__add(_1652348), -(hAPP(c_List_Ofoldl(_1652348, _1652348, c_Groups_Oplus__class_Oplus(_1652348), c_Groups_Ozero__class_Ozero(_1652348)), _1652350) = c_List_Ofoldr(_1652348, _1652348, c_Groups_Oplus__class_Oplus(_1652348), _1652350, c_Groups_Ozero__class_Ozero(_1652348)))], (43650 ^ _777081) ^ [_1652467, _1652469, _1652471] : [class_Groups_Omonoid__add(_1652467), -(hAPP(c_List_Ofoldl(_1652467, _1652467, c_Groups_Oplus__class_Oplus(_1652467), _1652469), _1652471) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1652467), _1652469), c_List_Ofoldr(_1652467, _1652467, c_Groups_Oplus__class_Oplus(_1652467), _1652471, c_Groups_Ozero__class_Ozero(_1652467))))], (43656 ^ _777081) ^ [_1652615, _1652617] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1652615), _1652617) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43659 ^ _777081 : [(43660 ^ _777081) ^ [] : [-(_1652615 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43662 ^ _777081) ^ [_1652729] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1652729), hAPP(c_List_Oset(tc_Nat_Onat), _1652617))), -(_1652729 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43668 ^ _777081) ^ [_1652826, _1652828] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1652826), _1652828) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1652826 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43674 ^ _777081 : [(43675 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43673 ^ [_1652826, _1652828]), hAPP(c_List_Oset(tc_Nat_Onat), _1652828))))], (43677 ^ _777081) ^ [] : [43673 ^ [_1652826, _1652828] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (43681 ^ _777081) ^ [_1653052, _1653054, _1653056] : [class_Lattices_Olattice(_1653052), -(c_Big__Operators_Olattice__class_OSup__fin(_1653052, hAPP(c_List_Oset(_1653052), hAPP(hAPP(c_List_Olist_OCons(_1653052), _1653054), _1653056))) = hAPP(c_List_Ofoldl(_1653052, _1653052, c_Lattices_Osemilattice__sup__class_Osup(_1653052), _1653054), _1653056))], (43687 ^ _777081) ^ [_1653181, _1653183, _1653185] : [class_Lattices_Olattice(_1653181), -(c_Big__Operators_Olattice__class_OInf__fin(_1653181, hAPP(c_List_Oset(_1653181), hAPP(hAPP(c_List_Olist_OCons(_1653181), _1653183), _1653185))) = hAPP(c_List_Ofoldl(_1653181, _1653181, c_Lattices_Osemilattice__inf__class_Oinf(_1653181), _1653183), _1653185))], (43693 ^ _777081) ^ [_1653310, _1653312, _1653314] : [class_Orderings_Olinorder(_1653310), -(c_Big__Operators_Olinorder__class_OMin(_1653310, hAPP(c_List_Oset(_1653310), hAPP(hAPP(c_List_Olist_OCons(_1653310), _1653312), _1653314))) = hAPP(c_List_Ofoldl(_1653310, _1653310, c_Orderings_Oord__class_Omin(_1653310), _1653312), _1653314))], (43699 ^ _777081) ^ [_1653439, _1653441, _1653443] : [class_Orderings_Olinorder(_1653439), -(c_Big__Operators_Olinorder__class_OMax(_1653439, hAPP(c_List_Oset(_1653439), hAPP(hAPP(c_List_Olist_OCons(_1653439), _1653441), _1653443))) = hAPP(c_List_Ofoldl(_1653439, _1653439, c_Orderings_Oord__class_Omax(_1653439), _1653441), _1653443))], (43705 ^ _777081) ^ [_1653568, _1653570, _1653572] : [class_Orderings_Olinorder(_1653568), -(c_Big__Operators_Olattice_OInf__fin(_1653568, c_Orderings_Oord__class_Omin(_1653568), hAPP(c_List_Oset(_1653568), hAPP(hAPP(c_List_Olist_OCons(_1653568), _1653570), _1653572))) = hAPP(c_List_Ofoldl(_1653568, _1653568, c_Orderings_Oord__class_Omin(_1653568), _1653570), _1653572))], (43711 ^ _777081) ^ [_1653703, _1653705, _1653707] : [class_Orderings_Olinorder(_1653703), -(c_Big__Operators_Olattice_OSup__fin(_1653703, c_Orderings_Oord__class_Omax(_1653703), hAPP(c_List_Oset(_1653703), hAPP(hAPP(c_List_Olist_OCons(_1653703), _1653705), _1653707))) = hAPP(c_List_Ofoldl(_1653703, _1653703, c_Orderings_Oord__class_Omax(_1653703), _1653705), _1653707))], (43717 ^ _777081) ^ [_1653838, _1653840, _1653842, _1653844] : [class_Complete__Lattice_Ocomplete__lattice(_1653838), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1653840, _1653838), hAPP(c_List_Oset(_1653840), _1653842)), _1653844) = hAPP(c_List_Ofoldl(_1653838, _1653840, hAPP(c_COMBC(_1653840, _1653838, _1653838), hAPP(hAPP(c_COMBB(_1653838, tc_fun(_1653838, _1653838), _1653840), c_Lattices_Osemilattice__sup__class_Osup(_1653838)), _1653844)), c_Orderings_Obot__class_Obot(_1653838)), _1653842))], (43723 ^ _777081) ^ [_1654009, _1654011, _1654013, _1654015, _1654017] : [-(c_Map_Omap__upds(_1654009, _1654011, _1654013, _1654015, _1654017) = hAPP(c_List_Ofoldl(tc_fun(_1654009, tc_Option_Ooption(_1654011)), tc_prod(_1654009, _1654011), hAPP(hAPP(c_COMBB(tc_fun(_1654009, tc_fun(_1654011, tc_fun(_1654009, tc_Option_Ooption(_1654011)))), tc_fun(tc_prod(_1654009, _1654011), tc_fun(_1654009, tc_Option_Ooption(_1654011))), tc_fun(_1654009, tc_Option_Ooption(_1654011))), c_Product__Type_Oprod_Oprod__case(_1654009, _1654011, tc_fun(_1654009, tc_Option_Ooption(_1654011)))), hAPP(hAPP(c_COMBC(tc_fun(_1654009, tc_Option_Ooption(_1654011)), tc_fun(_1654011, tc_Option_Ooption(_1654011)), tc_fun(_1654009, tc_fun(_1654011, tc_fun(_1654009, tc_Option_Ooption(_1654011))))), hAPP(hAPP(c_COMBB(tc_fun(_1654009, tc_fun(tc_fun(_1654011, tc_Option_Ooption(_1654011)), tc_fun(_1654011, tc_fun(_1654009, tc_Option_Ooption(_1654011))))), tc_fun(tc_fun(_1654011, tc_Option_Ooption(_1654011)), tc_fun(_1654009, tc_fun(_1654011, tc_fun(_1654009, tc_Option_Ooption(_1654011))))), tc_fun(_1654009, tc_Option_Ooption(_1654011))), c_COMBC(_1654009, tc_fun(_1654011, tc_Option_Ooption(_1654011)), tc_fun(_1654011, tc_fun(_1654009, tc_Option_Ooption(_1654011))))), hAPP(hAPP(c_COMBB(tc_fun(_1654009, tc_fun(tc_Option_Ooption(_1654011), tc_fun(_1654009, tc_Option_Ooption(_1654011)))), tc_fun(_1654009, tc_fun(tc_fun(_1654011, tc_Option_Ooption(_1654011)), tc_fun(_1654011, tc_fun(_1654009, tc_Option_Ooption(_1654011))))), tc_fun(_1654009, tc_Option_Ooption(_1654011))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1654011), tc_fun(_1654009, tc_Option_Ooption(_1654011))), tc_fun(tc_fun(_1654011, tc_Option_Ooption(_1654011)), tc_fun(_1654011, tc_fun(_1654009, tc_Option_Ooption(_1654011)))), _1654009), c_COMBB(tc_Option_Ooption(_1654011), tc_fun(_1654009, tc_Option_Ooption(_1654011)), _1654011))), c_Fun_Ofun__upd(_1654009, tc_Option_Ooption(_1654011))))), c_Option_Ooption_OSome(_1654011))), _1654013), hAPP(hAPP(c_List_Ozip(_1654009, _1654011), _1654015), _1654017)))], (43725 ^ _777081) ^ [_1654316, _1654318] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1654316), hAPP(c_List_Oset(tc_Nat_Onat), _1654318))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1654316), 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)), _1654318))))], (43731 ^ _777081) ^ [_1654443, _1654445, _1654447] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654443), tc_List_Olist(_1654443))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654443), tc_List_Olist(_1654443)), c_List_Olist_ONil(_1654443)), _1654445)), c_List_Olexord(_1654443, _1654447))), -(_1654445 = hAPP(hAPP(c_List_Olist_OCons(_1654443), 43734 ^ [_1654443, _1654445, _1654447]), 43735 ^ [_1654443, _1654445, _1654447]))], (43739 ^ _777081) ^ [_1654626, _1654628, _1654630] : [43740 ^ _777081 : [(43741 ^ _777081) ^ [_1654715, _1654717] : [_1654628 = hAPP(hAPP(c_List_Olist_OCons(_1654626), _1654717), _1654715)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654626), tc_List_Olist(_1654626))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654626), tc_List_Olist(_1654626)), c_List_Olist_ONil(_1654626)), _1654628)), c_List_Olexord(_1654626, _1654630))))], (43745 ^ _777081) ^ [_1654809, _1654811, _1654813, _1654815] : [-(_1654809 = c_List_Olist_ONil(_1654811)), 43748 ^ _777081 : [(43749 ^ _777081) ^ [] : [_1654813 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654811)), _1654809)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1654811, hAPP(hAPP(c_List_Olist__update(_1654811, _1654809), _1654813), _1654815)) = _1654815)], (43755 ^ _777081) ^ [] : [-(_1654813 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654811)), _1654809)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1654811, hAPP(hAPP(c_List_Olist__update(_1654811, _1654809), _1654813), _1654815)) = c_List_Olast(_1654811, _1654809))]]], (43761 ^ _777081) ^ [_1655111, _1655113, _1655115] : [_1655111 = c_List_Olist_ONil(_1655113), -(c_List_Olast(_1655113, hAPP(hAPP(c_List_Olist_OCons(_1655113), _1655115), _1655111)) = _1655115)], (43767 ^ _777081) ^ [_1655210, _1655212, _1655214] : [-(_1655210 = c_List_Olist_ONil(_1655212)), -(c_List_Olast(_1655212, hAPP(hAPP(c_List_Olist_OCons(_1655212), _1655214), _1655210)) = c_List_Olast(_1655212, _1655210))], (43773 ^ _777081) ^ [_1655262, _1655264, _1655266] : [-(_1655262 = c_List_Olist_ONil(_1655264)), -(c_List_Olast(_1655264, hAPP(hAPP(c_List_Olist_OCons(_1655264), _1655266), _1655262)) = c_List_Olast(_1655264, _1655262))], (43779 ^ _777081) ^ [_1655316, _1655318, _1655320] : [_1655316 = c_List_Olist_ONil(_1655318), -(c_List_Olast(_1655318, hAPP(hAPP(c_List_Olist_OCons(_1655318), _1655320), _1655316)) = _1655320)], (43785 ^ _777081) ^ [_1655417, _1655419, _1655421, _1655423] : [-(_1655417 = c_List_Olist_ONil(_1655419)), -(c_List_Olast(_1655421, hAPP(hAPP(c_List_Omap(_1655419, _1655421), _1655423), _1655417)) = hAPP(_1655423, c_List_Olast(_1655419, _1655417)))], (43791 ^ _777081) ^ [_1655477, _1655479, _1655481] : [_1655477 = c_List_Olist_ONil(_1655479), -(c_List_Olast(_1655479, hAPP(hAPP(c_List_Oappend(_1655479), _1655481), _1655477)) = c_List_Olast(_1655479, _1655481))], (43797 ^ _777081) ^ [_1655584, _1655586, _1655588] : [-(_1655584 = c_List_Olist_ONil(_1655586)), -(c_List_Olast(_1655586, hAPP(hAPP(c_List_Oappend(_1655586), _1655588), _1655584)) = c_List_Olast(_1655586, _1655584))], (43803 ^ _777081) ^ [_1655650, _1655652, _1655654] : [_1655650 = c_List_Olist_ONil(_1655652), -(c_List_Olast(_1655652, hAPP(hAPP(c_List_Oappend(_1655652), _1655654), _1655650)) = c_List_Olast(_1655652, _1655654))], (43809 ^ _777081) ^ [_1655755, _1655757, _1655759] : [-(_1655755 = c_List_Olist_ONil(_1655757)), -(c_List_Olast(_1655757, hAPP(hAPP(c_List_Oappend(_1655757), _1655759), _1655755)) = c_List_Olast(_1655757, _1655755))], (43815 ^ _777081) ^ [_1655807, _1655809] : [-(_1655807 = c_List_Olist_ONil(_1655809)), -(hBOOL(hAPP(hAPP(c_member(_1655809), c_List_Olast(_1655809, _1655807)), hAPP(c_List_Oset(_1655809), _1655807))))], (43821 ^ _777081) ^ [_1655860, _1655862, _1655864] : [-(c_List_Olast(_1655860, hAPP(hAPP(c_List_Oappend(_1655860), _1655862), hAPP(hAPP(c_List_Olist_OCons(_1655860), _1655864), c_List_Olist_ONil(_1655860)))) = _1655864)], (43823 ^ _777081) ^ [_1655908, _1655910, _1655912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655908), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655910)), _1655912))), -(c_List_Olast(_1655910, hAPP(hAPP(c_List_Odrop(_1655910), _1655908), _1655912)) = c_List_Olast(_1655910, _1655912))], (43829 ^ _777081) ^ [_1656060, _1656062, _1656064, _1656066] : [hAPP(hAPP(c_List_Oappend(_1656060), _1656062), hAPP(hAPP(c_List_Olist_OCons(_1656060), _1656064), c_List_Olist_ONil(_1656060))) = _1656066, 43832 ^ _777081 : [(43833 ^ _777081) ^ [] : [_1656066 = c_List_Olist_ONil(_1656060)], (43835 ^ _777081) ^ [] : [-(c_List_Obutlast(_1656060, _1656066) = _1656062)], (43837 ^ _777081) ^ [] : [-(c_List_Olast(_1656060, _1656066) = _1656064)]]], (43839 ^ _777081) ^ [_1656249, _1656251, _1656253, _1656255] : [-(hAPP(hAPP(c_List_Oappend(_1656249), _1656251), hAPP(hAPP(c_List_Olist_OCons(_1656249), _1656253), c_List_Olist_ONil(_1656249))) = _1656255), -(_1656255 = c_List_Olist_ONil(_1656249)), c_List_Obutlast(_1656249, _1656255) = _1656251, c_List_Olast(_1656249, _1656255) = _1656253], (43853 ^ _777081) ^ [_1656495, _1656497] : [-(_1656495 = c_List_Olist_ONil(_1656497)), -(hAPP(hAPP(c_List_Oappend(_1656497), c_List_Obutlast(_1656497, _1656495)), hAPP(hAPP(c_List_Olist_OCons(_1656497), c_List_Olast(_1656497, _1656495)), c_List_Olist_ONil(_1656497))) = _1656495)], (43859 ^ _777081) ^ [_1656553, _1656555] : [-(_1656553 = c_List_Olist_ONil(_1656555)), -(c_List_Olast(_1656555, _1656553) = hAPP(hAPP(c_List_Onth(_1656555), _1656553), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656555)), _1656553)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (43865 ^ _777081) ^ [_1656633, _1656635, _1656637] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1656633)), _1656635), c_List_Olists(_1656633, _1656637))), -(_1656635 = c_List_Olist_ONil(_1656633)), 43874 ^ _777081 : [(43875 ^ _777081) ^ [] : [-(_1656635 = hAPP(hAPP(c_List_Olist_OCons(_1656633), 43872 ^ [_1656633, _1656635, _1656637]), 43873 ^ [_1656633, _1656635, _1656637]))], (43877 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1656633), 43872 ^ [_1656633, _1656635, _1656637]), _1656637)))], (43879 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1656633)), 43873 ^ [_1656633, _1656635, _1656637]), c_List_Olists(_1656633, _1656637))))]]], (43881 ^ _777081) ^ [_1656916, _1656918, _1656920] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1656916)), _1656918), c_List_Olists(_1656916, _1656920)))), 43882 ^ _777081 : [(43883 ^ _777081) ^ [] : [_1656918 = c_List_Olist_ONil(_1656916)], (43885 ^ _777081) ^ [_1657044, _1657046] : [_1656918 = hAPP(hAPP(c_List_Olist_OCons(_1656916), _1657046), _1657044), hBOOL(hAPP(hAPP(c_member(_1656916), _1657046), _1656920)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1656916)), _1657044), c_List_Olists(_1656916, _1656920)))]]], (43897 ^ _777081) ^ [_1657282, _1657284, _1657286, _1657288] : [class_Complete__Lattice_Ocomplete__lattice(_1657282), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657284, _1657282), hAPP(c_List_Oset(_1657284), _1657286)), _1657288) = hAPP(c_List_Ofoldl(_1657282, _1657284, hAPP(c_COMBC(_1657284, _1657282, _1657282), hAPP(hAPP(c_COMBB(_1657282, tc_fun(_1657282, _1657282), _1657284), c_Lattices_Osemilattice__inf__class_Oinf(_1657282)), _1657288)), c_Orderings_Otop__class_Otop(_1657282)), _1657286))], (43903 ^ _777081) ^ [_1657453, _1657455, _1657457, _1657459, _1657461, _1657463, _1657465, _1657467] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657453, tc_fun(_1657455, tc_fun(_1657457, tc_HOL_Obool))), _1657459), _1657461), _1657463), _1657465)), -(hBOOL(hAPP(hAPP(hAPP(_1657461, _1657467), _1657463), _1657465))), hBOOL(hAPP(hAPP(c_member(_1657453), _1657467), _1657459))], (43913 ^ _777081) ^ [_1657680, _1657682, _1657684, _1657686, _1657688, _1657690, _1657692, _1657694] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657680, tc_fun(_1657682, tc_fun(_1657684, tc_HOL_Obool))), _1657686), _1657688), _1657690), _1657692)), hBOOL(hAPP(hAPP(c_member(_1657680), _1657694), _1657686)), -(hBOOL(hAPP(hAPP(hAPP(_1657688, _1657694), _1657690), _1657692)))], (43923 ^ _777081) ^ [_1657903, _1657905, _1657907, _1657909, _1657911, _1657913] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1657903, tc_fun(_1657905, tc_HOL_Obool)), _1657907), _1657909), _1657911)), -(hBOOL(hAPP(hAPP(_1657909, _1657913), _1657911))), hBOOL(hAPP(hAPP(c_member(_1657903), _1657913), _1657907))], (43933 ^ _777081) ^ [_1658104, _1658106, _1658108, _1658110, _1658112, _1658114] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658104, tc_fun(_1658106, tc_HOL_Obool)), _1658108), _1658110), _1658112)), hBOOL(hAPP(hAPP(c_member(_1658104), _1658114), _1658108)), -(hBOOL(hAPP(hAPP(_1658110, _1658114), _1658112)))], (43943 ^ _777081) ^ [_1658301, _1658303, _1658305, _1658307, _1658309, _1658311] : [hBOOL(hAPP(hAPP(c_member(_1658301), _1658303), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658305, tc_fun(_1658301, tc_HOL_Obool)), _1658307), _1658309))), -(hBOOL(hAPP(hAPP(c_member(_1658301), _1658303), hAPP(_1658309, _1658311)))), hBOOL(hAPP(hAPP(c_member(_1658305), _1658311), _1658307))], (43953 ^ _777081) ^ [_1658522, _1658524, _1658526, _1658528, _1658530, _1658532] : [hBOOL(hAPP(hAPP(c_member(_1658522), _1658524), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658526, tc_fun(_1658522, tc_HOL_Obool)), _1658528), _1658530))), hBOOL(hAPP(hAPP(c_member(_1658526), _1658532), _1658528)), -(hBOOL(hAPP(hAPP(c_member(_1658522), _1658524), hAPP(_1658530, _1658532))))], (43963 ^ _777081) ^ [_1658739, _1658741, _1658743, _1658745] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1658743), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658739, tc_fun(_1658743, tc_HOL_Obool)), _1658741), _1658745)))), 43964 ^ _777081 : [(43965 ^ _777081) ^ [_1658813] : [hBOOL(hAPP(hAPP(c_member(_1658739), _1658813), _1658741)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1658743), hAPP(_1658745, _1658813)))]]], (43973 ^ _777081) ^ [_1658967, _1658969, _1658971, _1658973, _1658975, _1658977] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658967, tc_fun(_1658969, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1658971, _1658967, _1658973), _1658975)), _1658977) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658971, tc_fun(_1658969, tc_HOL_Obool)), _1658975), hAPP(hAPP(c_COMBB(_1658967, tc_fun(_1658969, tc_HOL_Obool), _1658971), _1658977), _1658973)))], (43975 ^ _777081) ^ [_1659044, _1659046, _1659048, _1659050, _1659052, _1659054] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659044, tc_fun(_1659046, tc_HOL_Obool)), _1659048), hAPP(hAPP(c_COMBB(_1659050, tc_fun(_1659046, tc_HOL_Obool), _1659044), _1659052), _1659054)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659050, tc_fun(_1659046, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1659044, _1659050, _1659054), _1659048)), _1659052))], (43977 ^ _777081) ^ [_1659148, _1659150, _1659152, _1659154, _1659156, _1659158] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659148, tc_fun(_1659150, tc_fun(_1659152, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1659148, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1659150, _1659152), tc_HOL_Obool), tc_fun(_1659150, tc_fun(_1659152, tc_HOL_Obool)), _1659148), hAPP(c_COMBC(_1659150, tc_fun(tc_prod(_1659150, _1659152), tc_HOL_Obool), tc_fun(_1659152, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1659152, tc_fun(tc_fun(tc_prod(_1659150, _1659152), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1659150, _1659152), tc_HOL_Obool), tc_fun(_1659152, tc_HOL_Obool)), _1659150), c_COMBC(_1659152, tc_fun(tc_prod(_1659150, _1659152), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1659152, tc_prod(_1659150, _1659152)), tc_fun(_1659152, tc_fun(tc_fun(tc_prod(_1659150, _1659152), tc_HOL_Obool), tc_HOL_Obool)), _1659150), hAPP(c_COMBB(tc_prod(_1659150, _1659152), tc_fun(tc_fun(tc_prod(_1659150, _1659152), tc_HOL_Obool), tc_HOL_Obool), _1659152), c_member(tc_prod(_1659150, _1659152)))), c_Product__Type_OPair(_1659150, _1659152))))), _1659154)), _1659156), _1659158)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1659150, _1659152)), hAPP(hAPP(c_Product__Type_OPair(_1659150, _1659152), _1659156), _1659158)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659148, tc_fun(tc_prod(_1659150, _1659152), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1659148, tc_HOL_Obool))), _1659154))))], (43983 ^ _777081) ^ [_1659631, _1659633, _1659635, _1659637, _1659639, _1659641] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1659633, _1659635)), hAPP(hAPP(c_Product__Type_OPair(_1659633, _1659635), _1659639), _1659641)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659631, tc_fun(tc_prod(_1659633, _1659635), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1659631, tc_HOL_Obool))), _1659637))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1659631, tc_fun(_1659633, tc_fun(_1659635, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1659631, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1659633, _1659635), tc_HOL_Obool), tc_fun(_1659633, tc_fun(_1659635, tc_HOL_Obool)), _1659631), hAPP(c_COMBC(_1659633, tc_fun(tc_prod(_1659633, _1659635), tc_HOL_Obool), tc_fun(_1659635, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1659635, tc_fun(tc_fun(tc_prod(_1659633, _1659635), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1659633, _1659635), tc_HOL_Obool), tc_fun(_1659635, tc_HOL_Obool)), _1659633), c_COMBC(_1659635, tc_fun(tc_prod(_1659633, _1659635), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1659635, tc_prod(_1659633, _1659635)), tc_fun(_1659635, tc_fun(tc_fun(tc_prod(_1659633, _1659635), tc_HOL_Obool), tc_HOL_Obool)), _1659633), hAPP(c_COMBB(tc_prod(_1659633, _1659635), tc_fun(tc_fun(tc_prod(_1659633, _1659635), tc_HOL_Obool), tc_HOL_Obool), _1659635), c_member(tc_prod(_1659633, _1659635)))), c_Product__Type_OPair(_1659633, _1659635))))), _1659637)), _1659639), _1659641)))], (43999 ^ _777081) ^ [_1660402, _1660404, _1660406, _1660408, _1660410] : [44001 ^ _777081 : [(44002 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1660406), 44000 ^ [_1660402, _1660404, _1660406, _1660408, _1660410]), _1660408)))], (44004 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660402, tc_HOL_Obool)), _1660404), hAPP(_1660410, 44000 ^ [_1660402, _1660404, _1660406, _1660408, _1660410])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660402, tc_HOL_Obool)), _1660404), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660406, tc_fun(_1660402, tc_HOL_Obool)), _1660408), _1660410))))], (43989 ^ _777081) ^ [_1660144, _1660146, _1660148, _1660150, _1660152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660144, tc_HOL_Obool)), _1660146), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660148, tc_fun(_1660144, tc_HOL_Obool)), _1660150), _1660152))), 43992 ^ _777081 : [(43993 ^ _777081) ^ [_1660277] : [hBOOL(hAPP(hAPP(c_member(_1660148), _1660277), _1660150)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1660144, tc_HOL_Obool)), _1660146), hAPP(_1660152, _1660277))))]]], (44008 ^ _777081) ^ [_1660665, _1660667, _1660669, _1660671, _1660673] : [class_Complete__Lattice_Ocomplete__lattice(_1660665), 44011 ^ _777081 : [(44022 ^ _777081) ^ [] : [44024 ^ _777081 : [(44025 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1660669), 44023 ^ [_1660665, _1660667, _1660669, _1660671, _1660673]), _1660671)))], (44027 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1660665), _1660667), hAPP(_1660673, 44023 ^ [_1660665, _1660667, _1660669, _1660671, _1660673])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1660665), _1660667), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660669, _1660665), _1660671), _1660673))))], (44012 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1660665), _1660667), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1660669, _1660665), _1660671), _1660673))), 44015 ^ _777081 : [(44016 ^ _777081) ^ [_1660846] : [hBOOL(hAPP(hAPP(c_member(_1660669), _1660846), _1660671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1660665), _1660667), hAPP(_1660673, _1660846))))]]]]], (44031 ^ _777081) ^ [_1661159, _1661161, _1661163, _1661165, _1661167, _1661169] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1661159, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1661161, _1661159, _1661163), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661165, tc_fun(_1661161, tc_HOL_Obool)), _1661167), _1661169))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661165, tc_fun(_1661159, tc_HOL_Obool)), _1661167), hAPP(hAPP(c_COMBB(tc_fun(_1661161, tc_HOL_Obool), tc_fun(_1661159, tc_HOL_Obool), _1661165), c_Relation_OImage(_1661161, _1661159, _1661163)), _1661169)))))], (44033 ^ _777081) ^ [_1661253, _1661255, _1661257, _1661259, _1661261] : [hBOOL(hAPP(hAPP(c_member(_1661253), _1661255), _1661257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1661259, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661253, tc_fun(_1661259, tc_HOL_Obool)), _1661257), _1661261)), hAPP(_1661261, _1661255))))], (44039 ^ _777081) ^ [_1661400, _1661402, _1661404, _1661406, _1661408] : [hBOOL(hAPP(hAPP(c_member(_1661400), _1661402), _1661404)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1661406, tc_HOL_Obool)), hAPP(_1661408, _1661402)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661400, tc_fun(_1661406, tc_HOL_Obool)), _1661404), _1661408)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661400, tc_fun(_1661406, tc_HOL_Obool)), _1661404), _1661408))], (44045 ^ _777081) ^ [_1661573, _1661575, _1661577, _1661579, _1661581] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661573, tc_fun(_1661575, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1661573), _1661577), _1661579)), _1661581) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1661575, tc_HOL_Obool)), hAPP(_1661581, _1661577)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661573, tc_fun(_1661575, tc_HOL_Obool)), _1661579), _1661581)))], (44047 ^ _777081) ^ [_1661668, _1661670, _1661672, _1661674, _1661676] : [_1661668 = c_Orderings_Obot__class_Obot(tc_fun(_1661670, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1661672, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661670, tc_fun(_1661672, tc_HOL_Obool)), _1661668), _1661674)), _1661676) = _1661676)], (44053 ^ _777081) ^ [_1661801, _1661803, _1661805, _1661807, _1661809] : [-(_1661801 = c_Orderings_Obot__class_Obot(tc_fun(_1661803, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1661805, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661803, tc_fun(_1661805, tc_HOL_Obool)), _1661801), _1661807)), _1661809) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661803, tc_fun(_1661805, tc_HOL_Obool)), _1661801), hAPP(hAPP(c_COMBC(_1661803, tc_fun(_1661805, tc_HOL_Obool), tc_fun(_1661805, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1661805, tc_HOL_Obool), tc_fun(tc_fun(_1661805, tc_HOL_Obool), tc_fun(_1661805, tc_HOL_Obool)), _1661803), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1661805, tc_HOL_Obool))), _1661807)), _1661809)))], (44059 ^ _777081) ^ [_1661946, _1661948, _1661950, _1661952, _1661954] : [_1661946 = c_Orderings_Obot__class_Obot(tc_fun(_1661948, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1661950, tc_HOL_Obool)), _1661952), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1661948, tc_fun(_1661950, tc_HOL_Obool)), _1661946), _1661954)) = _1661952)], (44065 ^ _777081) ^ [_1662079, _1662081, _1662083, _1662085, _1662087] : [-(_1662079 = c_Orderings_Obot__class_Obot(tc_fun(_1662081, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1662083, tc_HOL_Obool)), _1662085), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662081, tc_fun(_1662083, tc_HOL_Obool)), _1662079), _1662087)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662081, tc_fun(_1662083, tc_HOL_Obool)), _1662079), hAPP(hAPP(c_COMBB(tc_fun(_1662083, tc_HOL_Obool), tc_fun(_1662083, tc_HOL_Obool), _1662081), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1662083, tc_HOL_Obool)), _1662085)), _1662087)))], (44071 ^ _777081) ^ [_1662187, _1662189, _1662191, _1662193] : [class_Complete__Lattice_Ocomplete__lattice(_1662187), -(_1662189 = c_Orderings_Obot__class_Obot(tc_fun(_1662191, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662191, _1662187), _1662189), hAPP(c_COMBK(_1662187, _1662191), _1662193)) = _1662193)], (44081 ^ _777081) ^ [_1662321, _1662323, _1662325, _1662327, _1662329] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662321, tc_fun(_1662323, tc_HOL_Obool)), _1662325), hAPP(hAPP(c_COMBB(tc_fun(_1662323, tc_HOL_Obool), tc_fun(_1662323, tc_HOL_Obool), _1662321), hAPP(c_Set_Oinsert(_1662323), _1662327)), _1662329)) = hAPP(hAPP(c_Set_Oinsert(_1662323), _1662327), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662321, tc_fun(_1662323, tc_HOL_Obool)), _1662325), _1662329)))], (44083 ^ _777081) ^ [_1662405, _1662407, _1662409, _1662411, _1662413] : [-(hAPP(hAPP(c_Set_Oinsert(_1662405), _1662407), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662409, tc_fun(_1662405, tc_HOL_Obool)), _1662411), _1662413)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662409, tc_fun(_1662405, tc_HOL_Obool)), _1662411), hAPP(hAPP(c_COMBB(tc_fun(_1662405, tc_HOL_Obool), tc_fun(_1662405, tc_HOL_Obool), _1662409), hAPP(c_Set_Oinsert(_1662405), _1662407)), _1662413)))], (44085 ^ _777081) ^ [_1662489, _1662491, _1662493] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662489, tc_fun(_1662491, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1662489, tc_HOL_Obool))), _1662493) = c_Orderings_Otop__class_Otop(tc_fun(_1662491, tc_HOL_Obool)))], (44087 ^ _777081) ^ [_1662553, _1662555, _1662557, _1662559] : [_1662553 = c_Orderings_Obot__class_Obot(tc_fun(_1662555, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662555, tc_fun(_1662557, tc_HOL_Obool)), _1662553), hAPP(c_COMBK(tc_fun(_1662557, tc_HOL_Obool), _1662555), _1662559)) = c_Orderings_Otop__class_Otop(tc_fun(_1662557, tc_HOL_Obool)))], (44093 ^ _777081) ^ [_1662690, _1662692, _1662694, _1662696] : [-(_1662690 = c_Orderings_Obot__class_Obot(tc_fun(_1662692, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662692, tc_fun(_1662694, tc_HOL_Obool)), _1662690), hAPP(c_COMBK(tc_fun(_1662694, tc_HOL_Obool), _1662692), _1662696)) = _1662696)], (44099 ^ _777081) ^ [_1662779, _1662781, _1662783, _1662785] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662779, tc_fun(_1662781, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1662779, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1662781, tc_HOL_Obool), tc_fun(_1662781, tc_HOL_Obool), _1662779), hAPP(c_COMBC(_1662781, tc_fun(_1662781, tc_HOL_Obool), tc_HOL_Obool), c_member(_1662781))), _1662783)), _1662785)), -(hBOOL(hAPP(hAPP(c_member(_1662781), _1662785), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662779, tc_fun(_1662781, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1662779, tc_HOL_Obool))), _1662783))))], (44105 ^ _777081) ^ [_1662998, _1663000, _1663002, _1663004] : [hBOOL(hAPP(hAPP(c_member(_1663000), _1663004), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662998, tc_fun(_1663000, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1662998, tc_HOL_Obool))), _1663002))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1662998, tc_fun(_1663000, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1662998, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1663000, tc_HOL_Obool), tc_fun(_1663000, tc_HOL_Obool), _1662998), hAPP(c_COMBC(_1663000, tc_fun(_1663000, tc_HOL_Obool), tc_HOL_Obool), c_member(_1663000))), _1663002)), _1663004)))], (44111 ^ _777081) ^ [_1663223, _1663225, _1663227, _1663229, _1663231, _1663233] : [hBOOL(hAPP(hAPP(c_member(_1663223), _1663225), _1663227)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1663223, tc_fun(_1663229, tc_HOL_Obool)), _1663227), hAPP(hAPP(c_COMBB(tc_fun(_1663229, tc_HOL_Obool), tc_fun(_1663229, tc_HOL_Obool), _1663223), hAPP(c_Set_Oinsert(_1663229), _1663231)), _1663233)) = hAPP(hAPP(c_Set_Oinsert(_1663229), _1663231), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1663223, tc_fun(_1663229, tc_HOL_Obool)), _1663227), _1663233)))], (44127 ^ _777081) ^ [_1663695, _1663697, _1663699, _1663701, _1663703] : [44129 ^ _777081 : [(44130 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1663699), 44128 ^ [_1663695, _1663697, _1663699, _1663701, _1663703]), _1663701)))], (44132 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1663695), _1663697), hAPP(_1663703, 44128 ^ [_1663695, _1663697, _1663699, _1663701, _1663703])))]], -(hBOOL(hAPP(hAPP(c_member(_1663695), _1663697), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1663699, tc_fun(_1663695, tc_HOL_Obool)), _1663701), _1663703))))], (44117 ^ _777081) ^ [_1663452, _1663454, _1663456, _1663458, _1663460] : [hBOOL(hAPP(hAPP(c_member(_1663452), _1663454), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1663456, tc_fun(_1663452, tc_HOL_Obool)), _1663458), _1663460))), 44120 ^ _777081 : [(44121 ^ _777081) ^ [_1663576] : [hBOOL(hAPP(hAPP(c_member(_1663456), _1663576), _1663458)), -(hBOOL(hAPP(hAPP(c_member(_1663452), _1663454), hAPP(_1663460, _1663576))))]]], (44136 ^ _777081) ^ [_1663943, _1663945, _1663947, _1663949] : [-(hAPP(c_Set_OCollect(_1663943), hAPP(hAPP(c_COMBB(tc_fun(_1663945, tc_HOL_Obool), tc_HOL_Obool, _1663943), c_HOL_OAll(_1663945)), hAPP(hAPP(c_COMBB(tc_fun(_1663945, tc_HOL_Obool), tc_fun(_1663945, tc_HOL_Obool), _1663943), hAPP(c_COMBS(_1663945, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1663945), c_fimplies), hAPP(hAPP(c_COMBC(_1663945, tc_fun(_1663945, tc_HOL_Obool), tc_HOL_Obool), c_member(_1663945)), _1663947)))), _1663949))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1663945, tc_fun(_1663943, tc_HOL_Obool)), _1663947), hAPP(hAPP(c_COMBB(tc_fun(_1663943, tc_HOL_Obool), tc_fun(_1663943, tc_HOL_Obool), _1663945), c_Set_OCollect(_1663943)), hAPP(c_COMBC(_1663943, _1663945, tc_HOL_Obool), _1663949))))], (44148 ^ _777081) ^ [_1664327, _1664329, _1664331, _1664333] : [44150 ^ _777081 : [(44151 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1664327), 44149 ^ [_1664327, _1664329, _1664331, _1664333]), _1664331)))], (44153 ^ _777081) ^ [] : [hAPP(_1664333, 44149 ^ [_1664327, _1664329, _1664331, _1664333]) = c_Orderings_Otop__class_Otop(tc_fun(_1664329, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664327, tc_fun(_1664329, tc_HOL_Obool)), _1664331), _1664333) = c_Orderings_Otop__class_Otop(tc_fun(_1664329, tc_HOL_Obool)))], (44138 ^ _777081) ^ [_1664098, _1664100, _1664102, _1664104] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664098, tc_fun(_1664100, tc_HOL_Obool)), _1664102), _1664104) = c_Orderings_Otop__class_Otop(tc_fun(_1664100, tc_HOL_Obool)), 44141 ^ _777081 : [(44142 ^ _777081) ^ [_1664214] : [hBOOL(hAPP(hAPP(c_member(_1664098), _1664214), _1664102)), -(hAPP(_1664104, _1664214) = c_Orderings_Otop__class_Otop(tc_fun(_1664100, tc_HOL_Obool)))]]], (44167 ^ _777081) ^ [_1664807, _1664809, _1664811, _1664813] : [44169 ^ _777081 : [(44170 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1664809), 44168 ^ [_1664807, _1664809, _1664811, _1664813]), _1664811)))], (44172 ^ _777081) ^ [] : [hAPP(_1664813, 44168 ^ [_1664807, _1664809, _1664811, _1664813]) = c_Orderings_Otop__class_Otop(tc_fun(_1664807, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1664807, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664809, tc_fun(_1664807, tc_HOL_Obool)), _1664811), _1664813))], (44157 ^ _777081) ^ [_1664578, _1664580, _1664582, _1664584] : [c_Orderings_Otop__class_Otop(tc_fun(_1664578, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1664580, tc_fun(_1664578, tc_HOL_Obool)), _1664582), _1664584), 44160 ^ _777081 : [(44161 ^ _777081) ^ [_1664694] : [hBOOL(hAPP(hAPP(c_member(_1664580), _1664694), _1664582)), -(hAPP(_1664584, _1664694) = c_Orderings_Otop__class_Otop(tc_fun(_1664578, tc_HOL_Obool)))]]], (44176 ^ _777081) ^ [_1665037, _1665039, _1665041, _1665043, _1665045] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665037, tc_fun(_1665039, tc_HOL_Obool)), _1665041), hAPP(hAPP(c_COMBB(tc_fun(_1665039, tc_HOL_Obool), tc_fun(_1665039, tc_HOL_Obool), _1665037), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665039, tc_HOL_Obool)), _1665043)), _1665045)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665039, tc_HOL_Obool)), _1665043), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665037, tc_fun(_1665039, tc_HOL_Obool)), _1665041), _1665045)))], (44178 ^ _777081) ^ [_1665127, _1665129, _1665131, _1665133, _1665135] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665127, tc_fun(_1665129, tc_HOL_Obool)), _1665131), hAPP(hAPP(c_COMBC(_1665127, tc_fun(_1665129, tc_HOL_Obool), tc_fun(_1665129, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1665129, tc_HOL_Obool), tc_fun(tc_fun(_1665129, tc_HOL_Obool), tc_fun(_1665129, tc_HOL_Obool)), _1665127), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665129, tc_HOL_Obool))), _1665133)), _1665135)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665129, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665127, tc_fun(_1665129, tc_HOL_Obool)), _1665131), _1665133)), _1665135))], (44180 ^ _777081) ^ [_1665236, _1665238, _1665240, _1665242, _1665244] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665236, tc_HOL_Obool)), _1665238), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665240, tc_fun(_1665236, tc_HOL_Obool)), _1665242), _1665244)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665240, tc_fun(_1665236, tc_HOL_Obool)), _1665242), hAPP(hAPP(c_COMBB(tc_fun(_1665236, tc_HOL_Obool), tc_fun(_1665236, tc_HOL_Obool), _1665240), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665236, tc_HOL_Obool)), _1665238)), _1665244)))], (44182 ^ _777081) ^ [_1665326, _1665328, _1665330, _1665332, _1665334] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665326, tc_HOL_Obool)), _1665328), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665330, tc_fun(_1665326, tc_HOL_Obool)), _1665332), _1665334)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665330, tc_fun(_1665326, tc_HOL_Obool)), _1665332), hAPP(hAPP(c_COMBB(tc_fun(_1665326, tc_HOL_Obool), tc_fun(_1665326, tc_HOL_Obool), _1665330), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665326, tc_HOL_Obool)), _1665328)), _1665334)))], (44184 ^ _777081) ^ [_1665416, _1665418, _1665420, _1665422, _1665424] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665416, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665418, tc_fun(_1665416, tc_HOL_Obool)), _1665420), _1665422)), _1665424) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665418, tc_fun(_1665416, tc_HOL_Obool)), _1665420), hAPP(hAPP(c_COMBC(_1665418, tc_fun(_1665416, tc_HOL_Obool), tc_fun(_1665416, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1665416, tc_HOL_Obool), tc_fun(tc_fun(_1665416, tc_HOL_Obool), tc_fun(_1665416, tc_HOL_Obool)), _1665418), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665416, tc_HOL_Obool))), _1665422)), _1665424)))], (44186 ^ _777081) ^ [_1665525, _1665527, _1665529, _1665531, _1665533, _1665535, _1665537] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665525, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665527, tc_fun(_1665525, tc_HOL_Obool)), _1665529), _1665531)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665533, tc_fun(_1665525, tc_HOL_Obool)), _1665535), _1665537)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665527, tc_fun(_1665525, tc_HOL_Obool)), _1665529), hAPP(hAPP(c_COMBB(tc_fun(_1665533, tc_fun(_1665525, tc_HOL_Obool)), tc_fun(_1665525, tc_HOL_Obool), _1665527), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665533, tc_fun(_1665525, tc_HOL_Obool)), _1665535)), hAPP(hAPP(c_COMBC(_1665527, tc_fun(_1665533, tc_fun(_1665525, tc_HOL_Obool)), tc_fun(_1665533, tc_fun(_1665525, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1665525, tc_HOL_Obool), tc_fun(_1665525, tc_HOL_Obool)), tc_fun(tc_fun(_1665533, tc_fun(_1665525, tc_HOL_Obool)), tc_fun(_1665533, tc_fun(_1665525, tc_HOL_Obool))), _1665527), c_COMBB(tc_fun(_1665525, tc_HOL_Obool), tc_fun(_1665525, tc_HOL_Obool), _1665533)), hAPP(hAPP(c_COMBB(tc_fun(_1665525, tc_HOL_Obool), tc_fun(tc_fun(_1665525, tc_HOL_Obool), tc_fun(_1665525, tc_HOL_Obool)), _1665527), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1665525, tc_HOL_Obool))), _1665531))), _1665537))))], (44188 ^ _777081) ^ [_1665728, _1665730, _1665732, _1665734, _1665736] : [class_Complete__Lattice_Ocomplete__lattice(_1665728), class_Orderings_Olinorder(_1665728), 44195 ^ _777081 : [(44196 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665728), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665730, _1665728), _1665732), _1665734)), _1665736)), 44200 ^ _777081 : [(44201 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1665730), 44199 ^ [_1665728, _1665730, _1665732, _1665734, _1665736]), _1665732)))], (44203 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665728), hAPP(_1665734, 44199 ^ [_1665728, _1665730, _1665732, _1665734, _1665736])), _1665736)))]]], (44205 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665728), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1665730, _1665728), _1665732), _1665734)), _1665736))), 44206 ^ _777081 : [(44207 ^ _777081) ^ [_1666076] : [hBOOL(hAPP(hAPP(c_member(_1665730), _1666076), _1665732)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1665728), hAPP(_1665734, _1666076)), _1665736))]]]]], (44215 ^ _777081) ^ [_1666246, _1666248, _1666250, _1666252, _1666254, _1666256] : [-(hAPP(c_Set_Ovimage(_1666246, _1666248, _1666250), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666252, tc_fun(_1666248, tc_HOL_Obool)), _1666254), _1666256)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666252, tc_fun(_1666246, tc_HOL_Obool)), _1666254), hAPP(hAPP(c_COMBB(tc_fun(_1666248, tc_HOL_Obool), tc_fun(_1666246, tc_HOL_Obool), _1666252), c_Set_Ovimage(_1666246, _1666248, _1666250)), _1666256)))], (44217 ^ _777081) ^ [_1666330, _1666332, _1666334, _1666336] : [-(hAPP(c_Set_OPow(_1666330), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666332, tc_fun(_1666330, tc_HOL_Obool)), _1666334), _1666336)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666332, tc_fun(tc_fun(_1666330, tc_HOL_Obool), tc_HOL_Obool)), _1666334), hAPP(hAPP(c_COMBB(tc_fun(_1666330, tc_HOL_Obool), tc_fun(tc_fun(_1666330, tc_HOL_Obool), tc_HOL_Obool), _1666332), c_Set_OPow(_1666330)), _1666336)))], (44219 ^ _777081) ^ [_1666412, _1666414, _1666416, _1666418, _1666420, _1666422] : [class_Complete__Lattice_Ocomplete__lattice(_1666412), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666414, tc_fun(_1666416, _1666412)), _1666418), _1666420), _1666422) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666414, _1666412), _1666418), hAPP(hAPP(c_COMBC(_1666414, _1666416, _1666412), _1666420), _1666422)))], (44225 ^ _777081) ^ [_1666563, _1666565, _1666567, _1666569, _1666571, _1666573] : [class_Complete__Lattice_Ocomplete__lattice(_1666563), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666565, _1666563), _1666567), hAPP(hAPP(c_COMBB(tc_fun(_1666569, _1666563), _1666563, _1666565), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666569, _1666563), _1666571)), _1666573)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666569, _1666563), _1666571), hAPP(hAPP(c_COMBB(tc_fun(_1666565, _1666563), _1666563, _1666569), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666565, _1666563), _1666567)), hAPP(c_COMBC(_1666565, _1666569, _1666563), _1666573))))], (44231 ^ _777081) ^ [_1666772, _1666774, _1666776, _1666778, _1666780, _1666782] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666772, tc_fun(_1666774, tc_HOL_Obool)), _1666776), hAPP(hAPP(c_COMBC(_1666772, tc_fun(_1666778, tc_fun(_1666774, tc_HOL_Obool)), tc_fun(_1666774, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1666778, tc_HOL_Obool), tc_fun(tc_fun(_1666778, tc_fun(_1666774, tc_HOL_Obool)), tc_fun(_1666774, tc_HOL_Obool)), _1666772), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666778, tc_fun(_1666774, tc_HOL_Obool))), _1666780)), _1666782)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666778, tc_fun(_1666774, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1666772, tc_fun(_1666778, tc_HOL_Obool)), _1666776), _1666780)), _1666782))], (44233 ^ _777081) ^ [_1666891, _1666893, _1666895, _1666897, _1666899, _1666901] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666891, tc_fun(_1666893, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1666895, tc_fun(_1666891, tc_HOL_Obool)), _1666897), _1666899)), _1666901) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666895, tc_fun(_1666893, tc_HOL_Obool)), _1666897), hAPP(hAPP(c_COMBC(_1666895, tc_fun(_1666891, tc_fun(_1666893, tc_HOL_Obool)), tc_fun(_1666893, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1666891, tc_HOL_Obool), tc_fun(tc_fun(_1666891, tc_fun(_1666893, tc_HOL_Obool)), tc_fun(_1666893, tc_HOL_Obool)), _1666895), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1666891, tc_fun(_1666893, tc_HOL_Obool))), _1666899)), _1666901)))], (44235 ^ _777081) ^ [_1667010, _1667012, _1667014, _1667016, _1667018] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1667010, tc_HOL_Obool)), _1667012), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667014, tc_fun(_1667010, tc_HOL_Obool)), _1667016), _1667018)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667014, tc_fun(_1667010, tc_HOL_Obool)), _1667016), hAPP(hAPP(c_COMBB(tc_fun(_1667010, tc_HOL_Obool), tc_fun(_1667010, tc_HOL_Obool), _1667014), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1667010, tc_HOL_Obool)), _1667012)), _1667018)))], (44237 ^ _777081) ^ [_1667100, _1667102, _1667104, _1667106, _1667108] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667100, tc_fun(_1667102, tc_HOL_Obool)), _1667104), hAPP(hAPP(c_COMBB(tc_fun(_1667102, tc_HOL_Obool), tc_fun(_1667102, tc_HOL_Obool), _1667100), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1667102, tc_HOL_Obool)), _1667106)), _1667108)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1667102, tc_HOL_Obool)), _1667106), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667100, tc_fun(_1667102, tc_HOL_Obool)), _1667104), _1667108)))], (44239 ^ _777081) ^ [_1667190, _1667192, _1667194, _1667196] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1667190, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667192, tc_fun(_1667190, tc_HOL_Obool)), _1667194), _1667196)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667192, tc_fun(_1667190, tc_HOL_Obool)), _1667194), hAPP(hAPP(c_COMBB(tc_fun(_1667190, tc_HOL_Obool), tc_fun(_1667190, tc_HOL_Obool), _1667192), c_Groups_Ouminus__class_Ouminus(tc_fun(_1667190, tc_HOL_Obool))), _1667196)))], (44241 ^ _777081) ^ [_1667272, _1667274, _1667276, _1667278] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1667272, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667274, tc_fun(_1667272, tc_HOL_Obool)), _1667276), _1667278)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667274, tc_fun(_1667272, tc_HOL_Obool)), _1667276), hAPP(hAPP(c_COMBB(tc_fun(_1667272, tc_HOL_Obool), tc_fun(_1667272, tc_HOL_Obool), _1667274), c_Groups_Ouminus__class_Ouminus(tc_fun(_1667272, tc_HOL_Obool))), _1667278)))], (44243 ^ _777081) ^ [_1667354] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667354, tc_HOL_Obool) = c_Set_OBall(_1667354))], (44245 ^ _777081) ^ [_1667382, _1667384, _1667386, _1667388, _1667390] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667382, tc_fun(_1667384, tc_HOL_Obool)), _1667386), hAPP(hAPP(c_COMBS(_1667382, tc_fun(_1667384, tc_HOL_Obool), tc_fun(_1667384, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1667384, tc_HOL_Obool), tc_fun(tc_fun(_1667384, tc_HOL_Obool), tc_fun(_1667384, tc_HOL_Obool)), _1667382), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667384, tc_HOL_Obool))), _1667388)), _1667390)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667384, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667382, tc_fun(_1667384, tc_HOL_Obool)), _1667386), _1667388)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667382, tc_fun(_1667384, tc_HOL_Obool)), _1667386), _1667390)))], (44247 ^ _777081) ^ [_1667503, _1667505, _1667507, _1667509, _1667511] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667503, tc_fun(_1667505, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1667503, tc_HOL_Obool)), _1667507), _1667509)), _1667511) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667505, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667503, tc_fun(_1667505, tc_HOL_Obool)), _1667507), _1667511)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667503, tc_fun(_1667505, tc_HOL_Obool)), _1667509), _1667511)))], (44249 ^ _777081) ^ [_1667592, _1667594, _1667596, _1667598, _1667600] : [class_Complete__Lattice_Ocomplete__lattice(_1667592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1667594, tc_HOL_Obool)), _1667596), _1667598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1667592), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667594, _1667592), _1667598), _1667600)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667594, _1667592), _1667596), _1667600))))], (44259 ^ _777081) ^ [_1667801, _1667803, _1667805, _1667807] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667801, tc_fun(_1667803, tc_HOL_Obool)), _1667805), _1667807) = hAPP(c_Set_OCollect(_1667803), hAPP(hAPP(c_COMBB(tc_fun(_1667801, tc_HOL_Obool), tc_HOL_Obool, _1667803), c_HOL_OAll(_1667801)), hAPP(hAPP(c_COMBB(tc_fun(_1667801, tc_HOL_Obool), tc_fun(_1667801, tc_HOL_Obool), _1667803), hAPP(c_COMBS(_1667801, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1667801), c_fimplies), hAPP(hAPP(c_COMBC(_1667801, tc_fun(_1667801, tc_HOL_Obool), tc_HOL_Obool), c_member(_1667801)), _1667805)))), hAPP(hAPP(c_COMBC(_1667803, tc_fun(_1667801, tc_fun(_1667803, tc_HOL_Obool)), tc_fun(_1667801, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1667803, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1667801, tc_fun(_1667803, tc_HOL_Obool)), tc_fun(_1667801, tc_HOL_Obool)), _1667803), c_COMBB(tc_fun(_1667803, tc_HOL_Obool), tc_HOL_Obool, _1667801)), c_member(_1667803))), _1667807)))))], (44261 ^ _777081) ^ [_1667984, _1667986, _1667988, _1667990, _1667992] : [_1667984 = c_Orderings_Obot__class_Obot(tc_fun(_1667986, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1667986, tc_fun(_1667988, tc_HOL_Obool)), _1667984), hAPP(hAPP(c_COMBB(tc_fun(_1667988, tc_HOL_Obool), tc_fun(_1667988, tc_HOL_Obool), _1667986), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1667988, tc_HOL_Obool)), _1667990)), _1667992)) = c_Orderings_Otop__class_Otop(tc_fun(_1667988, tc_HOL_Obool)))], (44267 ^ _777081) ^ [_1668153, _1668155, _1668157, _1668159, _1668161] : [-(_1668153 = c_Orderings_Obot__class_Obot(tc_fun(_1668155, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668155, tc_fun(_1668157, tc_HOL_Obool)), _1668153), hAPP(hAPP(c_COMBB(tc_fun(_1668157, tc_HOL_Obool), tc_fun(_1668157, tc_HOL_Obool), _1668155), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668157, tc_HOL_Obool)), _1668159)), _1668161)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668157, tc_HOL_Obool)), _1668159), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668155, tc_fun(_1668157, tc_HOL_Obool)), _1668153), _1668161)))], (44273 ^ _777081) ^ [_1668279, _1668281, _1668283, _1668285, _1668287] : [_1668279 = c_Orderings_Obot__class_Obot(tc_fun(_1668281, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668281, tc_fun(_1668283, tc_HOL_Obool)), _1668279), hAPP(hAPP(c_COMBC(_1668281, tc_fun(_1668283, tc_HOL_Obool), tc_fun(_1668283, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1668283, tc_HOL_Obool), tc_fun(tc_fun(_1668283, tc_HOL_Obool), tc_fun(_1668283, tc_HOL_Obool)), _1668281), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668283, tc_HOL_Obool))), _1668285)), _1668287)) = c_Orderings_Otop__class_Otop(tc_fun(_1668283, tc_HOL_Obool)))], (44279 ^ _777081) ^ [_1668486, _1668488, _1668490, _1668492, _1668494] : [-(_1668486 = c_Orderings_Obot__class_Obot(tc_fun(_1668488, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668488, tc_fun(_1668490, tc_HOL_Obool)), _1668486), hAPP(hAPP(c_COMBC(_1668488, tc_fun(_1668490, tc_HOL_Obool), tc_fun(_1668490, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1668490, tc_HOL_Obool), tc_fun(tc_fun(_1668490, tc_HOL_Obool), tc_fun(_1668490, tc_HOL_Obool)), _1668488), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668490, tc_HOL_Obool))), _1668492)), _1668494)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1668490, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668488, tc_fun(_1668490, tc_HOL_Obool)), _1668486), _1668492)), _1668494))], (44285 ^ _777081) ^ [_1668613, _1668615, _1668617] : [-(hAPP(c_Set_OCollect(_1668613), hAPP(hAPP(c_COMBB(tc_fun(_1668615, tc_HOL_Obool), tc_HOL_Obool, _1668613), c_HOL_OAll(_1668615)), _1668617)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668615, tc_fun(_1668613, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1668615, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1668613, tc_HOL_Obool), tc_fun(_1668613, tc_HOL_Obool), _1668615), c_Set_OCollect(_1668613)), hAPP(c_COMBC(_1668613, _1668615, tc_HOL_Obool), _1668617))))], (44287 ^ _777081) ^ [_1668720, _1668722, _1668724, _1668726, _1668728] : [_1668720 = c_Orderings_Obot__class_Obot(tc_fun(_1668722, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668722, tc_fun(_1668724, tc_HOL_Obool)), _1668720), hAPP(hAPP(c_COMBC(_1668722, tc_fun(_1668724, tc_HOL_Obool), tc_fun(_1668724, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1668724, tc_HOL_Obool), tc_fun(tc_fun(_1668724, tc_HOL_Obool), tc_fun(_1668724, tc_HOL_Obool)), _1668722), c_Groups_Ominus__class_Ominus(tc_fun(_1668724, tc_HOL_Obool))), _1668726)), _1668728)) = c_Orderings_Otop__class_Otop(tc_fun(_1668724, tc_HOL_Obool)))], (44293 ^ _777081) ^ [_1668927, _1668929, _1668931, _1668933, _1668935] : [-(_1668927 = c_Orderings_Obot__class_Obot(tc_fun(_1668929, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668929, tc_fun(_1668931, tc_HOL_Obool)), _1668927), hAPP(hAPP(c_COMBC(_1668929, tc_fun(_1668931, tc_HOL_Obool), tc_fun(_1668931, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1668931, tc_HOL_Obool), tc_fun(tc_fun(_1668931, tc_HOL_Obool), tc_fun(_1668931, tc_HOL_Obool)), _1668929), c_Groups_Ominus__class_Ominus(tc_fun(_1668931, tc_HOL_Obool))), _1668933)), _1668935)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1668931, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668929, tc_fun(_1668931, tc_HOL_Obool)), _1668927), _1668933)), _1668935))], (44299 ^ _777081) ^ [_1669072, _1669074, _1669076, _1669078, _1669080] : [_1669072 = c_Orderings_Obot__class_Obot(tc_fun(_1669074, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1669076, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1669074, tc_fun(_1669076, tc_HOL_Obool)), _1669072), _1669078)), _1669080) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1669076, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1669076, tc_HOL_Obool))), _1669080))], (44305 ^ _777081) ^ [_1669237, _1669239, _1669241, _1669243, _1669245] : [-(_1669237 = c_Orderings_Obot__class_Obot(tc_fun(_1669239, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1669241, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1669239, tc_fun(_1669241, tc_HOL_Obool)), _1669237), _1669243)), _1669245) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1669239, tc_fun(_1669241, tc_HOL_Obool)), _1669237), hAPP(hAPP(c_COMBC(_1669239, tc_fun(_1669241, tc_HOL_Obool), tc_fun(_1669241, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1669241, tc_HOL_Obool), tc_fun(tc_fun(_1669241, tc_HOL_Obool), tc_fun(_1669241, tc_HOL_Obool)), _1669239), c_Groups_Ominus__class_Ominus(tc_fun(_1669241, tc_HOL_Obool))), _1669243)), _1669245)))], (44311 ^ _777081) ^ [_1669382, _1669384, _1669386, _1669388, _1669390] : [_1669382 = c_Orderings_Obot__class_Obot(tc_fun(_1669384, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1669386, tc_HOL_Obool)), _1669388), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1669384, tc_fun(_1669386, tc_HOL_Obool)), _1669382), _1669390)) = _1669388)], (44317 ^ _777081) ^ [_1669515, _1669517, _1669519, _1669521, _1669523] : [-(_1669515 = c_Orderings_Obot__class_Obot(tc_fun(_1669517, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1669519, tc_HOL_Obool)), _1669521), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1669517, tc_fun(_1669519, tc_HOL_Obool)), _1669515), _1669523)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1669517, tc_fun(_1669519, tc_HOL_Obool)), _1669515), hAPP(hAPP(c_COMBB(tc_fun(_1669519, tc_HOL_Obool), tc_fun(_1669519, tc_HOL_Obool), _1669517), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1669519, tc_HOL_Obool)), _1669521)), _1669523)))], (44323 ^ _777081) ^ [_1669623, _1669625, _1669627, _1669629, _1669631] : [class_Complete__Lattice_Ocomplete__lattice(_1669623), hBOOL(hAPP(hAPP(c_member(_1669625), _1669627), _1669629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1669623), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1669625, _1669623), _1669629), _1669631)), hAPP(_1669631, _1669627))))], (44333 ^ _777081) ^ [] : [-(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)))], (44335 ^ _777081) ^ [_1669850, _1669852, _1669854, _1669856, _1669858] : [_1669850 = c_Orderings_Obot__class_Obot(tc_fun(_1669852, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1669852, tc_fun(_1669854, tc_HOL_Obool)), _1669850), hAPP(hAPP(c_COMBB(tc_fun(_1669854, tc_HOL_Obool), tc_fun(_1669854, tc_HOL_Obool), _1669852), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1669854, tc_HOL_Obool)), _1669856)), _1669858)) = c_Orderings_Otop__class_Otop(tc_fun(_1669854, tc_HOL_Obool)))], (44341 ^ _777081) ^ [_1670019, _1670021, _1670023, _1670025, _1670027] : [-(_1670019 = c_Orderings_Obot__class_Obot(tc_fun(_1670021, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1670021, tc_fun(_1670023, tc_HOL_Obool)), _1670019), hAPP(hAPP(c_COMBB(tc_fun(_1670023, tc_HOL_Obool), tc_fun(_1670023, tc_HOL_Obool), _1670021), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1670023, tc_HOL_Obool)), _1670025)), _1670027)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1670023, tc_HOL_Obool)), _1670025), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1670021, tc_fun(_1670023, tc_HOL_Obool)), _1670019), _1670027)))], (44347 ^ _777081) ^ [_1670127, _1670129, _1670131, _1670133] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670127)), _1670129))), c_List_Ofoldr(tc_List_Olist(_1670131), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1670131)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1670131))), _1670133, 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(_1670127)), _1670129)), c_List_Ofoldr(tc_List_Olist(_1670131), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1670131)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1670131), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1670131)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1670131)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1670131), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1670131)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1670131), tc_List_Olist(_1670131), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1670131)))), _1670133), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (44349 ^ _777081) ^ [_1670296, _1670298, _1670300] : [-(c_List_Olistsp(_1670296, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1670296, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1670296, tc_fun(_1670296, tc_HOL_Obool), tc_HOL_Obool), c_member(_1670296)), _1670298)), hAPP(hAPP(c_COMBC(_1670296, tc_fun(_1670296, tc_HOL_Obool), tc_HOL_Obool), c_member(_1670296)), _1670300))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1670296), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1670296), tc_fun(tc_List_Olist(_1670296), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1670296))), c_List_Olists(_1670296, _1670298))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1670296), tc_fun(tc_List_Olist(_1670296), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1670296))), c_List_Olists(_1670296, _1670300))))], (44351 ^ _777081) ^ [_1670428, _1670430] : [-(hBOOL(hAPP(c_List_Olistsp(_1670428, _1670430), c_List_Olist_ONil(_1670428))))], (44363 ^ _777081) ^ [_1670702, _1670704, _1670706, _1670708, _1670710] : [44365 ^ _777081 : [(44366 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1670702), 44364 ^ [_1670702, _1670704, _1670706, _1670708, _1670710]), _1670706)))], (44368 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1670708, 44364 ^ [_1670702, _1670704, _1670706, _1670708, _1670710]), _1670710))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1670702, tc_fun(_1670704, tc_HOL_Obool)), _1670706), _1670708), _1670710)))], (44353 ^ _777081) ^ [_1670484, _1670486, _1670488, _1670490, _1670492] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1670484, tc_fun(_1670486, tc_HOL_Obool)), _1670488), _1670490), _1670492)), 44356 ^ _777081 : [(44357 ^ _777081) ^ [_1670593] : [hBOOL(hAPP(hAPP(c_member(_1670484), _1670593), _1670488)), -(hBOOL(hAPP(hAPP(_1670490, _1670593), _1670492)))]]], (44382 ^ _777081) ^ [_1671202, _1671204, _1671206, _1671208, _1671210, _1671212, _1671214] : [44384 ^ _777081 : [(44385 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1671202), 44383 ^ [_1671202, _1671204, _1671206, _1671208, _1671210, _1671212, _1671214]), _1671208)))], (44387 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1671210, 44383 ^ [_1671202, _1671204, _1671206, _1671208, _1671210, _1671212, _1671214]), _1671212), _1671214))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1671202, tc_fun(_1671204, tc_fun(_1671206, tc_HOL_Obool))), _1671208), _1671210), _1671212), _1671214)))], (44372 ^ _777081) ^ [_1670955, _1670957, _1670959, _1670961, _1670963, _1670965, _1670967] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1670955, tc_fun(_1670957, tc_fun(_1670959, tc_HOL_Obool))), _1670961), _1670963), _1670965), _1670967)), 44375 ^ _777081 : [(44376 ^ _777081) ^ [_1671083] : [hBOOL(hAPP(hAPP(c_member(_1670955), _1671083), _1670961)), -(hBOOL(hAPP(hAPP(hAPP(_1670963, _1671083), _1670965), _1670967)))]]], (44391 ^ _777081) ^ [_1671462, _1671464, _1671466, _1671468] : [-(hAPP(c_List_Ofilter(_1671462, _1671464), hAPP(hAPP(c_List_Oappend(_1671462), _1671466), _1671468)) = hAPP(hAPP(c_List_Oappend(_1671462), hAPP(c_List_Ofilter(_1671462, _1671464), _1671466)), hAPP(c_List_Ofilter(_1671462, _1671464), _1671468)))], (44393 ^ _777081) ^ [_1671546, _1671548, _1671550, _1671552] : [hBOOL(hAPP(c_List_Olistsp(_1671546, _1671548), hAPP(hAPP(c_List_Oappend(_1671546), _1671550), _1671552))), 44396 ^ _777081 : [(44397 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1671546, _1671548), _1671550)))], (44399 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1671546, _1671548), _1671552)))]]], (44401 ^ _777081) ^ [_1671695, _1671697, _1671699, _1671701] : [-(hBOOL(hAPP(c_List_Olistsp(_1671695, _1671697), hAPP(hAPP(c_List_Oappend(_1671695), _1671699), _1671701)))), hBOOL(hAPP(c_List_Olistsp(_1671695, _1671697), _1671699)), hBOOL(hAPP(c_List_Olistsp(_1671695, _1671697), _1671701))], (44411 ^ _777081) ^ [_1671880, _1671882] : [-(hBOOL(hAPP(c_List_Olistsp(_1671880, _1671882), c_List_Olist_ONil(_1671880))))], (44413 ^ _777081) ^ [_1671912, _1671914] : [-(hAPP(c_List_Ofilter(_1671912, _1671914), c_List_Olist_ONil(_1671912)) = c_List_Olist_ONil(_1671912))], (44425 ^ _777081) ^ [_1672170, _1672172, _1672174] : [44427 ^ _777081 : [(44428 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1672170), 44426 ^ [_1672170, _1672172, _1672174]), hAPP(c_List_Oset(_1672170), _1672174))))], (44430 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1672172, 44426 ^ [_1672170, _1672172, _1672174])))]], -(hAPP(c_List_Ofilter(_1672170, _1672172), _1672174) = c_List_Olist_ONil(_1672170))], (44415 ^ _777081) ^ [_1671965, _1671967, _1671969] : [hAPP(c_List_Ofilter(_1671965, _1671967), _1671969) = c_List_Olist_ONil(_1671965), 44418 ^ _777081 : [(44419 ^ _777081) ^ [_1672062] : [hBOOL(hAPP(hAPP(c_member(_1671965), _1672062), hAPP(c_List_Oset(_1671965), _1671969))), hBOOL(hAPP(_1671967, _1672062))]]], (44434 ^ _777081) ^ [_1672287, _1672289, _1672291] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1672287), tc_List_Olist(_1672287)), c_List_Opartition(_1672287, _1672289, _1672291)) = hAPP(c_List_Ofilter(_1672287, _1672289), _1672291))], (44436 ^ _777081) ^ [_1672334, _1672336, _1672338] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672334)), hAPP(c_List_Ofilter(_1672334, _1672336), _1672338))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672334)), _1672338))))], (44438 ^ _777081) ^ [_1672386, _1672388, _1672390] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1672386, tc_HOL_Obool)), hAPP(c_List_Oset(_1672386), hAPP(c_List_Ofilter(_1672386, _1672388), _1672390))), hAPP(c_List_Oset(_1672386), _1672390))))], (44440 ^ _777081) ^ [_1672439, _1672441, _1672443, _1672445, _1672447] : [-(hAPP(c_List_Ofilter(_1672439, _1672441), hAPP(hAPP(c_List_Omap(_1672443, _1672439), _1672445), _1672447)) = hAPP(hAPP(c_List_Omap(_1672443, _1672439), _1672445), hAPP(c_List_Ofilter(_1672443, hAPP(c_Fun_Ocomp(_1672439, tc_HOL_Obool, _1672443, _1672441), _1672445)), _1672447)))], (44452 ^ _777081) ^ [_1672724, _1672726, _1672728] : [44454 ^ _777081 : [(44455 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1672724), 44453 ^ [_1672724, _1672726, _1672728]), hAPP(c_List_Oset(_1672724), _1672728))))], (44457 ^ _777081) ^ [] : [hBOOL(hAPP(_1672726, 44453 ^ [_1672724, _1672726, _1672728]))]], -(hBOOL(hAPP(c_List_Olistsp(_1672724, _1672726), _1672728)))], (44442 ^ _777081) ^ [_1672526, _1672528, _1672530] : [hBOOL(hAPP(c_List_Olistsp(_1672526, _1672528), _1672530)), 44445 ^ _777081 : [(44446 ^ _777081) ^ [_1672615] : [hBOOL(hAPP(hAPP(c_member(_1672526), _1672615), hAPP(c_List_Oset(_1672526), _1672530))), -(hBOOL(hAPP(_1672528, _1672615)))]]], (44471 ^ _777081) ^ [_1673132, _1673134, _1673136] : [44473 ^ _777081 : [(44474 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1673132), 44472 ^ [_1673132, _1673134, _1673136]), hAPP(c_List_Oset(_1673132), _1673136))))], (44476 ^ _777081) ^ [] : [hBOOL(hAPP(_1673134, 44472 ^ [_1673132, _1673134, _1673136]))]], -(hAPP(c_List_Ofilter(_1673132, _1673134), _1673136) = _1673136)], (44461 ^ _777081) ^ [_1672932, _1672934, _1672936] : [hAPP(c_List_Ofilter(_1672932, _1672934), _1672936) = _1672936, 44464 ^ _777081 : [(44465 ^ _777081) ^ [_1673023] : [hBOOL(hAPP(hAPP(c_member(_1672932), _1673023), hAPP(c_List_Oset(_1672932), _1672936))), -(hBOOL(hAPP(_1672934, _1673023)))]]], (44480 ^ _777081) ^ [_1673324, _1673326, _1673328] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673324)), hAPP(c_List_Ofilter(_1673324, _1673326), _1673328))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673324)), hAPP(c_List_Ofilter(_1673324, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1673324), c_fNot), _1673326)), _1673328))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673324)), _1673328))], (44482 ^ _777081) ^ [_1673400, _1673402, _1673404] : [-(c_List_Olistsp(_1673400, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1673400, tc_HOL_Obool)), _1673402), _1673404)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1673400), tc_HOL_Obool)), c_List_Olistsp(_1673400, _1673402)), c_List_Olistsp(_1673400, _1673404)))], (44484 ^ _777081) ^ [_1673460, _1673462, _1673464, _1673466] : [hBOOL(hAPP(c_List_Olistsp(_1673460, _1673462), _1673464)), hBOOL(hAPP(c_List_Olistsp(_1673460, _1673466), _1673464)), -(hBOOL(hAPP(c_List_Olistsp(_1673460, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1673460, tc_HOL_Obool)), _1673462), _1673466)), _1673464)))], (44494 ^ _777081) ^ [_1673649, _1673651, _1673653, _1673655, _1673657, _1673659] : [class_Orderings_Olinorder(_1673649), -(hBOOL(hAPP(_1673651, _1673653))), -(hAPP(c_List_Ofilter(_1673655, _1673651), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1673655, _1673649, _1673657), _1673653), _1673659)) = hAPP(c_List_Ofilter(_1673655, _1673651), _1673659))], (44504 ^ _777081) ^ [_1673795, _1673797, _1673799] : [hBOOL(hAPP(c_List_Odistinct(_1673795), _1673797)), -(hBOOL(hAPP(c_List_Odistinct(_1673795), hAPP(c_List_Ofilter(_1673795, _1673799), _1673797))))], (44510 ^ _777081) ^ [_1673898, _1673900, _1673902, _1673904] : [-(hBOOL(hAPP(_1673898, _1673900))), -(c_List_Oremove1(_1673902, _1673900, hAPP(c_List_Ofilter(_1673902, _1673898), _1673904)) = hAPP(c_List_Ofilter(_1673902, _1673898), _1673904))], (44516 ^ _777081) ^ [_1673956, _1673958, _1673960, _1673962] : [-(hAPP(c_List_Ofilter(_1673956, _1673958), c_List_Oremove1(_1673956, _1673960, _1673962)) = c_List_Oremove1(_1673956, _1673960, hAPP(c_List_Ofilter(_1673956, _1673958), _1673962)))], (44518 ^ _777081) ^ [_1674026, _1674028, _1674030, _1674032] : [hBOOL(hAPP(c_List_Olistsp(_1674026, hAPP(hAPP(c_COMBS(_1674026, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1674026), c_fconj), _1674028)), _1674030)), _1674032)), 44521 ^ _777081 : [(44522 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1674026, _1674028), _1674032)))], (44524 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1674026, _1674030), _1674032)))]]], (44526 ^ _777081) ^ [_1674199, _1674201, _1674203, _1674205] : [-(hBOOL(hAPP(c_List_Olistsp(_1674199, hAPP(hAPP(c_COMBS(_1674199, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1674199), c_fconj), _1674201)), _1674203)), _1674205))), hBOOL(hAPP(c_List_Olistsp(_1674199, _1674201), _1674205)), hBOOL(hAPP(c_List_Olistsp(_1674199, _1674203), _1674205))], (44536 ^ _777081) ^ [_1674408, _1674410, _1674412, _1674414] : [-(hAPP(c_List_Ofilter(_1674408, _1674410), hAPP(c_List_Ofilter(_1674408, _1674412), _1674414)) = hAPP(c_List_Ofilter(_1674408, hAPP(hAPP(c_COMBS(_1674408, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1674408), c_fconj), _1674412)), _1674410)), _1674414))], (44538 ^ _777081) ^ [_1674496, _1674498, _1674500, _1674502] : [hBOOL(hAPP(c_List_Olistsp(_1674496, _1674498), hAPP(hAPP(c_List_Olist_OCons(_1674496), _1674500), _1674502))), 44541 ^ _777081 : [(44542 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1674498, _1674500)))], (44544 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1674496, _1674498), _1674502)))]]], (44546 ^ _777081) ^ [_1674639, _1674641, _1674643, _1674645] : [-(hBOOL(hAPP(c_List_Olistsp(_1674639, _1674641), hAPP(hAPP(c_List_Olist_OCons(_1674639), _1674643), _1674645)))), hBOOL(hAPP(_1674641, _1674643)), hBOOL(hAPP(c_List_Olistsp(_1674639, _1674641), _1674645))], (44556 ^ _777081) ^ [_1674833, _1674835, _1674837, _1674839] : [hBOOL(hAPP(_1674833, _1674835)), -(hAPP(c_List_Ofilter(_1674837, _1674833), hAPP(hAPP(c_List_Olist_OCons(_1674837), _1674835), _1674839)) = hAPP(hAPP(c_List_Olist_OCons(_1674837), _1674835), hAPP(c_List_Ofilter(_1674837, _1674833), _1674839)))], (44562 ^ _777081) ^ [_1674968, _1674970, _1674972, _1674974] : [-(hBOOL(hAPP(_1674968, _1674970))), -(hAPP(c_List_Ofilter(_1674972, _1674968), hAPP(hAPP(c_List_Olist_OCons(_1674972), _1674970), _1674974)) = hAPP(c_List_Ofilter(_1674972, _1674968), _1674974))], (44568 ^ _777081) ^ [_1675032, _1675034, _1675036] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1675032), tc_List_Olist(_1675032)), c_List_Opartition(_1675032, _1675034, _1675036)) = hAPP(c_List_Ofilter(_1675032, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1675032, c_fNot), _1675034)), _1675036))], (44570 ^ _777081) ^ [_1675087, _1675089, _1675091] : [-(hAPP(c_List_Oset(_1675087), hAPP(c_List_Ofilter(_1675087, _1675089), _1675091)) = hAPP(c_Set_OCollect(_1675087), hAPP(hAPP(c_COMBS(_1675087, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1675087), c_fconj), hAPP(hAPP(c_COMBC(_1675087, tc_fun(_1675087, tc_HOL_Obool), tc_HOL_Obool), c_member(_1675087)), hAPP(c_List_Oset(_1675087), _1675091)))), _1675089)))], (44572 ^ _777081) ^ [_1675170, _1675172, _1675174, _1675176, _1675178] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675170)), hAPP(c_List_Ofilter(_1675170, _1675172), hAPP(hAPP(c_List_Omap(_1675174, _1675170), _1675176), _1675178))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675174)), hAPP(c_List_Ofilter(_1675174, hAPP(c_Fun_Ocomp(_1675170, tc_HOL_Obool, _1675174, _1675172), _1675176)), _1675178)))], (44574 ^ _777081) ^ [_1675244, _1675246, _1675248, _1675250] : [hBOOL(hAPP(hAPP(c_member(_1675244), _1675246), hAPP(c_List_Oset(_1675244), _1675248))), -(hBOOL(hAPP(_1675250, _1675246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675244)), hAPP(c_List_Ofilter(_1675244, _1675250), _1675248))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675244)), _1675248))))], (44584 ^ _777081) ^ [_1675418, _1675420, _1675422] : [-(c_List_Opartition(_1675418, _1675420, _1675422) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1675418), tc_List_Olist(_1675418)), hAPP(c_List_Ofilter(_1675418, _1675420), _1675422)), hAPP(c_List_Ofilter(_1675418, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1675418, c_fNot), _1675420)), _1675422)))], (44586 ^ _777081) ^ [_1675482, _1675484, _1675486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1675482, tc_HOL_Obool)), _1675484), _1675486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1675482), tc_HOL_Obool)), c_List_Olistsp(_1675482, _1675484)), c_List_Olistsp(_1675482, _1675486))))], (44592 ^ _777081) ^ [_1675617, _1675619, _1675621] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1675617, tc_HOL_Obool)), hAPP(c_List_Oset(_1675617), _1675619)), hAPP(hAPP(c_Set_Oinsert(_1675617), _1675621), c_Orderings_Obot__class_Obot(tc_fun(_1675617, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1675617), hAPP(c_List_Ofilter(_1675617, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1675617), c_fNot), hAPP(hAPP(c_COMBC(_1675617, _1675617, tc_HOL_Obool), c_fequal), _1675621))), _1675619)))], (44594 ^ _777081) ^ [_1675704, _1675706, _1675708] : [hBOOL(hAPP(c_List_Odistinct(_1675704), _1675706)), -(hAPP(c_List_Ofilter(_1675704, hAPP(hAPP(c_COMBC(_1675704, tc_fun(_1675704, tc_HOL_Obool), tc_HOL_Obool), c_member(_1675704)), hAPP(c_List_Oset(_1675704), c_List_Osublist(_1675704, _1675706, _1675708)))), _1675706) = c_List_Osublist(_1675704, _1675706, _1675708))], (44600 ^ _777081) ^ [_1675877, _1675879, _1675881] : [hBOOL(hAPP(c_List_Olistsp(_1675877, hAPP(hAPP(c_COMBC(_1675877, tc_fun(_1675877, tc_HOL_Obool), tc_HOL_Obool), c_member(_1675877)), _1675879)), _1675881)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1675877)), _1675881), c_List_Olists(_1675877, _1675879))))], (44606 ^ _777081) ^ [_1676016, _1676018, _1676020] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1676016)), _1676020), c_List_Olists(_1676016, _1676018))), -(hBOOL(hAPP(c_List_Olistsp(_1676016, hAPP(hAPP(c_COMBC(_1676016, tc_fun(_1676016, tc_HOL_Obool), tc_HOL_Obool), c_member(_1676016)), _1676018)), _1676020)))], (44612 ^ _777081) ^ [_1676161, _1676163, _1676165] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676161)), hAPP(c_List_Ofilter(_1676161, _1676163), _1676165)) = 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(_1676161)), _1676165)))), hAPP(hAPP(c_COMBB(_1676161, tc_HOL_Obool, tc_Nat_Onat), _1676163), hAPP(c_List_Onth(_1676161), _1676165))))))], (44614 ^ _777081) ^ [_1676241, _1676243, _1676245, _1676247] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1676241)), _1676243), c_List_Olists(_1676241, _1676245))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1676241)), _1676243), c_List_Olists(_1676241, _1676247))), -(hBOOL(hAPP(c_List_Olistsp(_1676241, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1676241, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1676241, tc_fun(_1676241, tc_HOL_Obool), tc_HOL_Obool), c_member(_1676241)), _1676245)), hAPP(hAPP(c_COMBC(_1676241, tc_fun(_1676241, tc_HOL_Obool), tc_HOL_Obool), c_member(_1676241)), _1676247))), _1676243)))], (44624 ^ _777081) ^ [_1676518, _1676520, _1676522, _1676524] : [-(c_List_Omap__filter(_1676518, _1676520, _1676522, _1676524) = hAPP(hAPP(c_List_Omap(_1676518, _1676520), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1676520), _1676520, _1676518, c_Option_Othe(_1676520)), _1676522)), hAPP(c_List_Ofilter(_1676518, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1676518), c_fNot), hAPP(hAPP(c_COMBC(_1676518, tc_Option_Ooption(_1676520), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1676520), tc_fun(tc_Option_Ooption(_1676520), tc_HOL_Obool), _1676518), c_fequal), _1676522)), c_Option_Ooption_ONone(_1676520)))), _1676524)))], (44626 ^ _777081) ^ [_1676620, _1676622] : [-(c_List_Ofoldr(tc_List_Olist(_1676620), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1676620)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1676620))), c_List_Otranspose(_1676620, _1676622), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1676620))), hAPP(c_List_Ofilter(tc_List_Olist(_1676620), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1676620)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1676620), tc_List_Olist(_1676620), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1676620)))), _1676622)))], (44628 ^ _777081) ^ [_1676717, _1676719] : [-(c_List_Otranspose(_1676717, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1676717)), c_List_Olist_ONil(_1676717)), _1676719)) = c_List_Otranspose(_1676717, _1676719))], (44630 ^ _777081) ^ [_1676760, _1676762, _1676764, _1676766] : [-(c_List_Otranspose(_1676760, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1676762), tc_List_Olist(_1676760)), hAPP(c_List_Omap(_1676762, _1676760), _1676764)), _1676766)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1676762), tc_List_Olist(_1676760)), hAPP(c_List_Omap(_1676762, _1676760), _1676764)), c_List_Otranspose(_1676762, _1676766)))], (44632 ^ _777081) ^ [_1676833, _1676835, _1676837] : [-(c_List_Omap__filter(_1676833, _1676835, _1676837, c_List_Olist_ONil(_1676833)) = c_List_Olist_ONil(_1676835))], (44644 ^ _777081) ^ [_1677094, _1677096] : [44646 ^ _777081 : [(44647 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1677094)), 44645 ^ [_1677094, _1677096]), hAPP(c_List_Oset(tc_List_Olist(_1677094)), _1677096))))], (44649 ^ _777081) ^ [] : [44645 ^ [_1677094, _1677096] = c_List_Olist_ONil(_1677094)]], -(c_List_Otranspose(_1677094, _1677096) = c_List_Olist_ONil(tc_List_Olist(_1677094)))], (44634 ^ _777081) ^ [_1676884, _1676886] : [c_List_Otranspose(_1676884, _1676886) = c_List_Olist_ONil(tc_List_Olist(_1676884)), 44637 ^ _777081 : [(44638 ^ _777081) ^ [_1676979] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1676884)), _1676979), hAPP(c_List_Oset(tc_List_Olist(_1676884)), _1676886))), -(_1676979 = c_List_Olist_ONil(_1676884))]]], (44653 ^ _777081) ^ [_1677289] : [-(c_List_Otranspose(_1677289, c_List_Olist_ONil(tc_List_Olist(_1677289))) = c_List_Olist_ONil(tc_List_Olist(_1677289)))], (44655 ^ _777081) ^ [_1677323, _1677325, _1677327, _1677329, _1677331, _1677333] : [hAPP(hAPP(c_Map_Omap__of(_1677323, _1677325), _1677327), _1677329) = hAPP(c_Option_Ooption_OSome(_1677325), _1677331), hBOOL(hAPP(hAPP(_1677333, _1677329), _1677331)), -(hAPP(hAPP(c_Map_Omap__of(_1677323, _1677325), hAPP(c_List_Ofilter(tc_prod(_1677323, _1677325), hAPP(c_Product__Type_Oprod_Oprod__case(_1677323, _1677325, tc_HOL_Obool), _1677333)), _1677327)), _1677329) = hAPP(c_Option_Ooption_OSome(_1677325), _1677331))], (44665 ^ _777081) ^ [_1677566, _1677568, _1677570, _1677572, _1677574] : [-(c_List_Omap__filter(_1677566, _1677568, _1677570, hAPP(hAPP(c_List_Olist_OCons(_1677566), _1677572), _1677574)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1677568), _1677568, c_List_Omap__filter(_1677566, _1677568, _1677570, _1677574), hAPP(hAPP(c_COMBC(_1677568, tc_List_Olist(_1677568), tc_List_Olist(_1677568)), c_List_Olist_OCons(_1677568)), c_List_Omap__filter(_1677566, _1677568, _1677570, _1677574))), hAPP(_1677570, _1677572)))], (44667 ^ _777081) ^ [_1677649, _1677651, _1677653, _1677655] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1677649, tc_Nat_Onat), _1677649), c_Product__Type_Ofst(_1677649, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1677649, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1677649, tc_Nat_Onat)), _1677651), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1677649, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1677649, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1677649, tc_Nat_Onat), _1677653), _1677655))) = hAPP(hAPP(c_List_Omap(tc_prod(_1677649, tc_Nat_Onat), _1677649), c_Product__Type_Ofst(_1677649, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1677649, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1677649, tc_Nat_Onat)), _1677651), c_Product__Type_Osnd(_1677649, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1677649, tc_Nat_Onat), _1677653), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1677655)))))], (44669 ^ _777081) ^ [_1677792, _1677794, _1677796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1677792), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1677794))), c_List_Otranspose(_1677794, _1677796)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1677794)), c_List_Otranspose(_1677794, _1677796)), _1677792) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1677794), _1677794), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677794), tc_Nat_Onat, _1677794), c_List_Onth(_1677794)), _1677792)), hAPP(c_List_Ofilter(tc_List_Olist(_1677794), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1677794)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1677792)), c_Nat_Osize__class_Osize(tc_List_Olist(_1677794)))), _1677796)))], (44675 ^ _777081) ^ [_1678035, _1678037] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1678035))), c_List_Otranspose(_1678035, _1678037)) = c_List_Ofoldr(tc_List_Olist(_1678035), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1678035)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1678035))), _1678037, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (44677 ^ _777081) ^ [_1678096, _1678098, _1678100, _1678102, _1678104] : [-(hAPP(hAPP(c_List_Omap(_1678096, _1678098), _1678100), hAPP(c_List_Ofilter(_1678096, _1678102), _1678104)) = c_List_Omap__filter(_1678096, _1678098, hAPP(hAPP(c_COMBC(_1678096, tc_Option_Ooption(_1678098), tc_Option_Ooption(_1678098)), hAPP(hAPP(c_COMBS(_1678096, tc_Option_Ooption(_1678098), tc_fun(tc_Option_Ooption(_1678098), tc_Option_Ooption(_1678098))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1678098), tc_fun(tc_Option_Ooption(_1678098), tc_Option_Ooption(_1678098))), _1678096), c_If(tc_Option_Ooption(_1678098))), _1678102)), hAPP(hAPP(c_COMBB(_1678098, tc_Option_Ooption(_1678098), _1678096), c_Option_Ooption_OSome(_1678098)), _1678100))), c_Option_Ooption_ONone(_1678098)), _1678104))], (44679 ^ _777081) ^ [_1678222, _1678224, _1678226, _1678228, _1678230] : [class_Orderings_Olinorder(_1678222), hBOOL(hAPP(hAPP(c_member(_1678224), _1678226), hAPP(c_List_Oset(_1678224), _1678228))), c_List_Olinorder__class_Osorted(_1678222, hAPP(hAPP(c_List_Omap(_1678224, _1678222), _1678230), _1678228)), hAPP(c_List_Ohd(_1678224), hAPP(c_List_Ofilter(_1678224, hAPP(hAPP(c_COMBB(_1678222, tc_HOL_Obool, _1678224), hAPP(c_fequal, hAPP(_1678230, _1678226))), _1678230)), _1678228)) = _1678226, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1678224, _1678222, _1678230), _1678226), c_List_Oremove1(_1678224, _1678226, _1678228)) = _1678228)], (44697 ^ _777081) ^ [_1678601, _1678603, _1678605] : [-(c_List_Osublist(_1678601, _1678603, _1678605) = hAPP(hAPP(c_List_Omap(tc_prod(_1678601, tc_Nat_Onat), _1678601), c_Product__Type_Ofst(_1678601, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1678601, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1678601, 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(_1678601, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1678601, tc_Nat_Onat))), _1678605)), hAPP(hAPP(c_List_Ozip(_1678601, tc_Nat_Onat), _1678603), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678601)), _1678603))))))], (44699 ^ _777081) ^ [_1678704] : [class_Orderings_Olinorder(_1678704), -(c_List_Olinorder__class_Osorted(_1678704, c_List_Olist_ONil(_1678704)))], (44705 ^ _777081) ^ [_1678781, _1678783] : [class_Orderings_Olinorder(_1678781), -(c_List_Olinorder__class_Osorted(_1678781, hAPP(hAPP(c_List_Olist_OCons(_1678781), _1678783), c_List_Olist_ONil(_1678781))))], (44711 ^ _777081) ^ [_1678876, _1678878, _1678880, _1678882, _1678884] : [class_Orderings_Olinorder(_1678876), c_List_Olinorder__class_Osorted(_1678876, hAPP(hAPP(c_List_Omap(_1678878, _1678876), _1678880), _1678882)), -(c_List_Olinorder__class_Osorted(_1678876, hAPP(hAPP(c_List_Omap(_1678878, _1678876), _1678880), hAPP(c_List_Ofilter(_1678878, _1678884), _1678882))))], (44721 ^ _777081) ^ [_1679063, _1679065, _1679067, _1679069, _1679071] : [class_Orderings_Olinorder(_1679063), -(c_List_Olinorder__class_Osorted(_1679063, hAPP(hAPP(c_List_Omap(_1679065, _1679063), _1679067), hAPP(c_List_Ofilter(_1679065, hAPP(hAPP(c_COMBC(_1679065, _1679063, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1679063, tc_fun(_1679063, tc_HOL_Obool), _1679065), c_fequal), _1679067)), hAPP(_1679069, _1679071))), _1679071))))], (44727 ^ _777081) ^ [_1679226, _1679228, _1679230] : [class_Orderings_Olinorder(_1679226), -(c_List_Olinorder__class_Osorted(_1679226, hAPP(c_List_Ofilter(_1679226, hAPP(hAPP(c_COMBC(_1679226, _1679226, tc_HOL_Obool), c_fequal), hAPP(_1679228, _1679230))), _1679230)))], (44733 ^ _777081) ^ [_1679341, _1679343, _1679345, _1679347, _1679349] : [class_Orderings_Olinorder(_1679341), c_List_Olinorder__class_Osorted(_1679341, hAPP(hAPP(c_List_Omap(_1679343, _1679341), _1679345), _1679347)), -(c_List_Olinorder__class_Osorted(_1679341, hAPP(hAPP(c_List_Omap(_1679343, _1679341), _1679345), c_List_Olinorder__class_Oinsort__insert__key(_1679343, _1679341, _1679345, _1679349, _1679347))))], (44743 ^ _777081) ^ [_1679528, _1679530, _1679532] : [class_Orderings_Olinorder(_1679528), c_List_Olinorder__class_Osorted(_1679528, _1679530), -(c_List_Olinorder__class_Osorted(_1679528, hAPP(hAPP(c_List_Odrop(_1679528), _1679532), _1679530)))], (44753 ^ _777081) ^ [_1679675, _1679677, _1679679] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1679675), c_List_Oupt(_1679677, _1679679)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1679677), _1679675), _1679679))], (44755 ^ _777081) ^ [_1679720, _1679722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679720), _1679722)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1679720, _1679722)) = _1679720)], (44761 ^ _777081) ^ [_1679819, _1679821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1679819), _1679821)), -(c_List_Oupt(_1679819, hAPP(c_Nat_OSuc, _1679821)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1679819, _1679821)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1679821), c_List_Olist_ONil(tc_Nat_Onat))))], (44767 ^ _777081) ^ [_1679957, _1679959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1679957), _1679959)), -(c_List_Oupt(_1679957, hAPP(c_Nat_OSuc, _1679959)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1679957, _1679959)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1679959), c_List_Olist_ONil(tc_Nat_Onat))))], (44773 ^ _777081) ^ [_1680080, _1680082] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1680080), _1680082))), -(c_List_Oupt(_1680080, hAPP(c_Nat_OSuc, _1680082)) = c_List_Olist_ONil(tc_Nat_Onat))], (44779 ^ _777081) ^ [_1680129, _1680131, _1680133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1680129), _1680131)), -(c_List_Oupt(_1680129, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1680131), _1680133)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1680129, _1680131)), c_List_Oupt(_1680131, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1680131), _1680133))))], (44795 ^ _777081) ^ [_1680389, _1680391] : [44796 ^ _777081 : [(44797 ^ _777081) ^ [] : [_1680391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44799 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1680391), _1680389))]], -(c_List_Oupt(_1680389, _1680391) = c_List_Olist_ONil(tc_Nat_Onat))], (44785 ^ _777081) ^ [_1680287, _1680289] : [c_List_Oupt(_1680287, _1680289) = c_List_Olist_ONil(tc_Nat_Onat), -(_1680289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1680289), _1680287)))], (44803 ^ _777081) ^ [_1680522, _1680524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1680522), _1680524)), -(c_List_Oupt(_1680524, _1680522) = c_List_Olist_ONil(tc_Nat_Onat))], (44809 ^ _777081) ^ [_1680615] : [class_Orderings_Olinorder(_1680615), -(c_List_Olinorder__class_Osorted(_1680615, c_List_Olist_ONil(_1680615)))], (44815 ^ _777081) ^ [_1680692] : [-(c_List_Oupt(_1680692, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (44817 ^ _777081) ^ [_1680718, _1680720] : [class_Orderings_Olinorder(_1680718), -(_1680720 = c_List_Olist_ONil(_1680718)), c_List_Olinorder__class_Osorted(_1680718, _1680720), -(c_List_Olinorder__class_Osorted(_1680718, c_List_Obutlast(_1680718, _1680720)))], (44831 ^ _777081) ^ [_1680910, _1680912] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1680910, _1680912)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1680910), hAPP(c_Nat_OSuc, _1680912)))], (44833 ^ _777081) ^ [_1680950, _1680952, _1680954] : [class_Orderings_Olinorder(_1680950), c_List_Olinorder__class_Osorted(_1680950, _1680952), hBOOL(hAPP(c_List_Odistinct(_1680950), _1680952)), c_List_Olinorder__class_Osorted(_1680950, _1680954), hBOOL(hAPP(c_List_Odistinct(_1680950), _1680954)), hAPP(c_List_Oset(_1680950), _1680952) = hAPP(c_List_Oset(_1680950), _1680954), -(_1680952 = _1680954)], (44859 ^ _777081) ^ [_1681333, _1681335, _1681337, _1681339, _1681341] : [class_Orderings_Olinorder(_1681333), c_List_Olinorder__class_Osorted(_1681333, hAPP(hAPP(c_List_Omap(_1681335, _1681333), _1681337), _1681339)), -(c_List_Olinorder__class_Osorted(_1681333, hAPP(hAPP(c_List_Omap(_1681335, _1681333), _1681337), c_List_Oremove1(_1681335, _1681341, _1681339))))], (44869 ^ _777081) ^ [_1681516, _1681518, _1681520, _1681522, _1681524] : [class_Orderings_Olinorder(_1681516), 44872 ^ _777081 : [(44873 ^ _777081) ^ [] : [c_List_Olinorder__class_Osorted(_1681516, hAPP(hAPP(c_List_Omap(_1681518, _1681516), _1681520), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681518, _1681516, _1681520), _1681522), _1681524))), -(c_List_Olinorder__class_Osorted(_1681516, hAPP(hAPP(c_List_Omap(_1681518, _1681516), _1681520), _1681524)))], (44879 ^ _777081) ^ [] : [c_List_Olinorder__class_Osorted(_1681516, hAPP(hAPP(c_List_Omap(_1681518, _1681516), _1681520), _1681524)), -(c_List_Olinorder__class_Osorted(_1681516, hAPP(hAPP(c_List_Omap(_1681518, _1681516), _1681520), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681518, _1681516, _1681520), _1681522), _1681524))))]]], (44885 ^ _777081) ^ [_1681823, _1681825, _1681827] : [class_Orderings_Olinorder(_1681823), c_List_Olinorder__class_Osorted(_1681823, _1681825), -(c_List_Olinorder__class_Osorted(_1681823, hAPP(hAPP(c_List_Otake(_1681823), _1681827), _1681825)))], (44895 ^ _777081) ^ [_1681970, _1681972, _1681974] : [class_Orderings_Olinorder(_1681970), 44898 ^ _777081 : [(44899 ^ _777081) ^ [] : [c_List_Olinorder__class_Osorted(_1681970, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681970, _1681970, c_COMBI(_1681970)), _1681972), _1681974)), -(c_List_Olinorder__class_Osorted(_1681970, _1681974))], (44905 ^ _777081) ^ [] : [c_List_Olinorder__class_Osorted(_1681970, _1681974), -(c_List_Olinorder__class_Osorted(_1681970, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1681970, _1681970, c_COMBI(_1681970)), _1681972), _1681974)))]]], (44911 ^ _777081) ^ [_1682217, _1682219] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1682217, _1682219))))], (44913 ^ _777081) ^ [_1682247, _1682249, _1682251] : [class_Orderings_Olinorder(_1682247), c_List_Olinorder__class_Osorted(_1682247, _1682249), -(c_List_Olinorder__class_Osorted(_1682247, c_List_Oremove1(_1682247, _1682251, _1682249)))], (44923 ^ _777081) ^ [_1682386, _1682388] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1682386, _1682388)))], (44925 ^ _777081) ^ [_1682414, _1682416] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1682414, _1682416)))], (44927 ^ _777081) ^ [_1682442, _1682444] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1682442), _1682444)) = c_List_Oupt(_1682442, _1682444))], (44929 ^ _777081) ^ [_1682479, _1682481, _1682483] : [class_Orderings_Olinorder(_1682479), c_List_Olinorder__class_Osorted(_1682479, _1682481), -(c_List_Olinorder__class_Osorted(_1682479, c_List_Olinorder__class_Oinsort__insert__key(_1682479, _1682479, c_COMBI(_1682479), _1682483, _1682481)))], (44939 ^ _777081) ^ [_1682626, _1682628, _1682630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1682626), _1682628)), _1682630)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1682628), c_List_Oupt(_1682626, _1682630)) = c_List_Oupt(_1682626, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1682626), _1682628)))], (44945 ^ _777081) ^ [_1682763, _1682765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682763), _1682765)), -(c_List_Oupt(_1682763, _1682765) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1682763), c_List_Oupt(hAPP(c_Nat_OSuc, _1682763), _1682765)))], (44951 ^ _777081) ^ [_1682880, _1682882, _1682884, _1682886] : [class_Orderings_Olinorder(_1682880), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1682880), _1682882), _1682884)), c_List_Olinorder__class_Osorted(_1682880, hAPP(hAPP(c_List_Olist_OCons(_1682880), _1682884), _1682886)), -(c_List_Olinorder__class_Osorted(_1682880, hAPP(hAPP(c_List_Olist_OCons(_1682880), _1682882), hAPP(hAPP(c_List_Olist_OCons(_1682880), _1682884), _1682886))))], (44965 ^ _777081) ^ [_1683133, _1683135, _1683137, _1683139] : [class_Orderings_Olinorder(_1683133), 44968 ^ _777081 : [(44969 ^ _777081) ^ [] : [c_List_Olinorder__class_Osorted(_1683133, hAPP(hAPP(c_List_Olist_OCons(_1683133), _1683135), hAPP(hAPP(c_List_Olist_OCons(_1683133), _1683137), _1683139))), 44972 ^ _777081 : [(44973 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1683133), _1683135), _1683137)))], (44975 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1683133, hAPP(hAPP(c_List_Olist_OCons(_1683133), _1683137), _1683139)))]]], (44977 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1683133, hAPP(hAPP(c_List_Olist_OCons(_1683133), _1683135), hAPP(hAPP(c_List_Olist_OCons(_1683133), _1683137), _1683139)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1683133), _1683135), _1683137)), c_List_Olinorder__class_Osorted(_1683133, hAPP(hAPP(c_List_Olist_OCons(_1683133), _1683137), _1683139))]]], (44987 ^ _777081) ^ [_1683528, _1683530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1683528), _1683530)), -(c_List_Oupt(_1683528, _1683530) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1683528), c_List_Oupt(hAPP(c_Nat_OSuc, _1683528), _1683530)))], (44993 ^ _777081) ^ [_1683639, _1683641] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1683639), _1683641))), -(c_List_Oupt(_1683639, _1683641) = c_List_Olist_ONil(tc_Nat_Onat))], (44999 ^ _777081) ^ [_1683685, _1683687] : [class_Orderings_Olinorder(_1683685), c_List_Olinorder__class_Osorted(_1683685, _1683687), -(c_List_Olinorder__class_Osorted(_1683685, hAPP(c_List_Otl(_1683685), _1683687)))], (45009 ^ _777081) ^ [_1683822, _1683824] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1683822), _1683824) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1683822, _1683824)))], (45011 ^ _777081) ^ [_1683859, _1683861] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1683859, _1683861)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1683859), _1683861))], (45013 ^ _777081) ^ [_1683896, _1683898] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1683896, _1683898)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1683898), _1683896))], (45015 ^ _777081) ^ [_1683933, _1683935, _1683937] : [class_Orderings_Olinorder(_1683933), 45018 ^ _777081 : [(45019 ^ _777081) ^ [] : [c_List_Olinorder__class_Osorted(_1683933, hAPP(hAPP(c_List_Olist_OCons(_1683933), _1683935), _1683937)), 45022 ^ _777081 : [(45023 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1683933, _1683937))], (45025 ^ _777081) ^ [_1684119] : [hBOOL(hAPP(hAPP(c_member(_1683933), _1684119), hAPP(c_List_Oset(_1683933), _1683937))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1683933), _1683935), _1684119)))]]], (45031 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1683933, hAPP(hAPP(c_List_Olist_OCons(_1683933), _1683935), _1683937))), c_List_Olinorder__class_Osorted(_1683933, _1683937), 45037 ^ _777081 : [(45038 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1683933), 45036 ^ [_1683933, _1683935, _1683937]), hAPP(c_List_Oset(_1683933), _1683937))))], (45040 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1683933), _1683935), 45036 ^ [_1683933, _1683935, _1683937]))]]]]], (45044 ^ _777081) ^ [_1684458, _1684460, _1684462] : [class_Orderings_Olinorder(_1684458), 45047 ^ _777081 : [(45048 ^ _777081) ^ [] : [c_List_Olinorder__class_Osorted(_1684458, hAPP(hAPP(c_List_Oappend(_1684458), _1684460), _1684462)), 45051 ^ _777081 : [(45052 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1684458, _1684460))], (45054 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1684458, _1684462))], (45056 ^ _777081) ^ [_1684694] : [hBOOL(hAPP(hAPP(c_member(_1684458), _1684694), hAPP(c_List_Oset(_1684458), _1684460))), 45059 ^ _777081 : [(45060 ^ _777081) ^ [_1684804] : [hBOOL(hAPP(hAPP(c_member(_1684458), _1684804), hAPP(c_List_Oset(_1684458), _1684462))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1684458), _1684694), _1684804)))]]]]], (45066 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1684458, hAPP(hAPP(c_List_Oappend(_1684458), _1684460), _1684462))), c_List_Olinorder__class_Osorted(_1684458, _1684460), c_List_Olinorder__class_Osorted(_1684458, _1684462), 45076 ^ _777081 : [(45077 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1684458), 45075 ^ [_1684458, _1684460, _1684462]), hAPP(c_List_Oset(_1684458), _1684460))))], (45080 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1684458), 45078 ^ [_1684458, _1684460, _1684462]), hAPP(c_List_Oset(_1684458), _1684462))))], (45082 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1684458), 45075 ^ [_1684458, _1684460, _1684462]), 45078 ^ [_1684458, _1684460, _1684462]))]]]]], (45086 ^ _777081) ^ [_1685315, _1685317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685315)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685317))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685315), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685317)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685315)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685315)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685317))))], (45092 ^ _777081) ^ [_1685468, _1685470] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685468)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685470)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685468), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1685470)) = c_List_Olist_ONil(tc_Nat_Onat))], (45098 ^ _777081) ^ [_1685547, _1685549, _1685551, _1685553] : [c_List_Oupt(_1685547, _1685549) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1685551), _1685553), 45101 ^ _777081 : [(45102 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685547), _1685549)))], (45104 ^ _777081) ^ [] : [-(_1685547 = _1685551)], (45106 ^ _777081) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1685547), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1685549) = _1685553)]]], (45108 ^ _777081) ^ [_1685720, _1685722, _1685724, _1685726] : [-(c_List_Oupt(_1685720, _1685722) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1685724), _1685726)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685720), _1685722)), _1685720 = _1685724, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1685720), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1685722) = _1685726], (45122 ^ _777081) ^ [_1685961, _1685963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685961), _1685963)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1685961, _1685963)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1685963), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45128 ^ _777081) ^ [_1686072, _1686074, _1686076, _1686078, _1686080, _1686082] : [class_Orderings_Olinorder(_1686072), c_List_Olinorder__class_Osorted(_1686072, hAPP(hAPP(c_List_Omap(_1686074, _1686072), _1686076), _1686078)), hBOOL(hAPP(_1686080, _1686082)), -(hAPP(c_List_Ofilter(_1686074, _1686080), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1686074, _1686072, _1686076), _1686082), _1686078)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1686074, _1686072, _1686076), _1686082), hAPP(c_List_Ofilter(_1686074, _1686080), _1686078)))], (45142 ^ _777081) ^ [_1686361, _1686363] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1686361), hAPP(c_List_Onth(_1686361), _1686363)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686361)), _1686363))) = _1686363)], (45144 ^ _777081) ^ [_1686410, _1686412] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1686410, _1686412) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1686410, hAPP(c_Nat_OSuc, _1686412))))], (45146 ^ _777081) ^ [_1686448] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1686448) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1686448)))], (45148 ^ _777081) ^ [_1686480, _1686482, _1686484, _1686486] : [class_Groups_Ocomm__monoid__add(_1686480), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1686480), _1686482), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1686484, _1686486))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1686480), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1686480), _1686482), c_List_Oupt(_1686484, _1686486))))], (45154 ^ _777081) ^ [_1686623, _1686625, _1686627, _1686629] : [class_Groups_Ocomm__monoid__add(_1686623), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1686623), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1686623), _1686625), c_List_Oupt(_1686627, _1686629))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1686623), _1686625), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1686627, _1686629))))], (45160 ^ _777081) ^ [_1686766, _1686768, _1686770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1686766), _1686768)), _1686770)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1686766, _1686770)), _1686768) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1686766), _1686768))], (45166 ^ _777081) ^ [_1686897, _1686899] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1686897, _1686899) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1686897), hAPP(c_Nat_OSuc, _1686899))))], (45168 ^ _777081) ^ [_1686938, _1686940, _1686942] : [class_Orderings_Olinorder(_1686938), 45171 ^ _777081 : [(45172 ^ _777081) ^ [] : [c_List_Olinorder__class_Osorted(_1686938, hAPP(hAPP(c_List_Olist_OCons(_1686938), _1686940), _1686942)), 45175 ^ _777081 : [(45182 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1686938, _1686942))], (45176 ^ _777081) ^ [_1687106] : [hBOOL(hAPP(hAPP(c_member(_1686938), _1687106), hAPP(c_List_Oset(_1686938), _1686942))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1686938), _1686940), _1687106)))]]], (45184 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1686938, hAPP(hAPP(c_List_Olist_OCons(_1686938), _1686940), _1686942))), 45188 ^ _777081 : [(45189 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1686938), 45187 ^ [_1686938, _1686940, _1686942]), hAPP(c_List_Oset(_1686938), _1686942))))], (45191 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1686938), _1686940), 45187 ^ [_1686938, _1686940, _1686942]))]], c_List_Olinorder__class_Osorted(_1686938, _1686942)]]], (45197 ^ _777081) ^ [_1687464, _1687466] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1687464, _1687466) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1687464), _1687466)))], (45199 ^ _777081) ^ [_1687502, _1687504, _1687506, _1687508, _1687510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1687502), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1687504), _1687506))), -(hAPP(hAPP(c_List_Onth(_1687508), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1687508), _1687510), c_List_Oupt(_1687506, _1687504))), _1687502) = hAPP(_1687510, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1687506), _1687502)))], (45205 ^ _777081) ^ [_1687665, _1687667] : [class_Orderings_Olinorder(_1687665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1687665), _1687667)), 45212 ^ _777081 : [(45213 ^ _777081) ^ [] : [-(hAPP(c_List_Oset(_1687665), c_List_Olinorder__class_Osorted__list__of__set(_1687665, _1687667)) = _1687667)], (45215 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1687665, c_List_Olinorder__class_Osorted__list__of__set(_1687665, _1687667)))], (45217 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1687665), c_List_Olinorder__class_Osorted__list__of__set(_1687665, _1687667))))]]], (45219 ^ _777081) ^ [_1687886] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1687886) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1687886))))], (45221 ^ _777081) ^ [_1687921, _1687923, _1687925] : [class_Orderings_Olinorder(_1687921), hBOOL(hAPP(hAPP(c_member(_1687921), _1687923), hAPP(c_List_Oset(_1687921), _1687925))), c_List_Olinorder__class_Osorted(_1687921, _1687925), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1687921, _1687921, c_COMBI(_1687921)), _1687923), c_List_Oremove1(_1687921, _1687923, _1687925)) = _1687925)], (45235 ^ _777081) ^ [_1688162, _1688164] : [class_Orderings_Olinorder(_1688162), 45238 ^ _777081 : [(45253 ^ _777081) ^ [] : [45255 ^ _777081 : [(45256 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45254 ^ [_1688162, _1688164]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688162)), _1688164))))], (45259 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 45257 ^ [_1688162, _1688164]), 45254 ^ [_1688162, _1688164])))], (45261 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1688162), hAPP(hAPP(c_List_Onth(_1688162), _1688164), 45257 ^ [_1688162, _1688164])), hAPP(hAPP(c_List_Onth(_1688162), _1688164), 45254 ^ [_1688162, _1688164])))]], -(c_List_Olinorder__class_Osorted(_1688162, _1688164))], (45239 ^ _777081) ^ [] : [c_List_Olinorder__class_Osorted(_1688162, _1688164), 45242 ^ _777081 : [(45243 ^ _777081) ^ [_1688333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688333), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688162)), _1688164))), 45246 ^ _777081 : [(45247 ^ _777081) ^ [_1688450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1688450), _1688333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1688162), hAPP(hAPP(c_List_Onth(_1688162), _1688164), _1688450)), hAPP(hAPP(c_List_Onth(_1688162), _1688164), _1688333))))]]]]]]], (45265 ^ _777081) ^ [_1688886, _1688888, _1688890, _1688892] : [class_Orderings_Olinorder(_1688886), c_List_Olinorder__class_Osorted(_1688886, _1688888), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1688890), _1688892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688892), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688886)), _1688888))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1688886), hAPP(hAPP(c_List_Onth(_1688886), _1688888), _1688890)), hAPP(hAPP(c_List_Onth(_1688886), _1688888), _1688892))))], (45283 ^ _777081) ^ [_1689213, _1689215, _1689217, _1689219, _1689221] : [class_Orderings_Olinorder(_1689213), c_Fun_Oinj__on(_1689215, _1689213, _1689217, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1689215, tc_HOL_Obool)), hAPP(c_List_Oset(_1689215), _1689219)), hAPP(c_List_Oset(_1689215), _1689221))), c_List_Olinorder__class_Osorted(_1689213, hAPP(hAPP(c_List_Omap(_1689215, _1689213), _1689217), _1689219)), hBOOL(hAPP(c_List_Odistinct(_1689213), hAPP(hAPP(c_List_Omap(_1689215, _1689213), _1689217), _1689219))), c_List_Olinorder__class_Osorted(_1689213, hAPP(hAPP(c_List_Omap(_1689215, _1689213), _1689217), _1689221)), hBOOL(hAPP(c_List_Odistinct(_1689213), hAPP(hAPP(c_List_Omap(_1689215, _1689213), _1689217), _1689221))), hAPP(c_List_Oset(_1689215), _1689219) = hAPP(c_List_Oset(_1689215), _1689221), -(_1689219 = _1689221)], (45313 ^ _777081) ^ [_1689796, _1689798, _1689800, _1689802] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1689796, tc_Nat_Onat), _1689796), c_Product__Type_Ofst(_1689796, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1689796, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1689796, 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(_1689796, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1689796, tc_Nat_Onat))), _1689798)), hAPP(hAPP(c_List_Ozip(_1689796, tc_Nat_Onat), _1689800), c_List_Oupt(_1689802, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1689802), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689796)), _1689800)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1689796, tc_Nat_Onat), _1689796), c_Product__Type_Ofst(_1689796, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1689796, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1689796, 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(_1689796, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1689796, 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(_1689796, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1689796, tc_Nat_Onat))), _1689802))), _1689798)), hAPP(hAPP(c_List_Ozip(_1689796, tc_Nat_Onat), _1689800), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689796)), _1689800))))))], (45315 ^ _777081) ^ [_1690001, _1690003, _1690005] : [45316 ^ _777081 : [(45317 ^ _777081) ^ [] : [-(_1690001 = c_List_Olist_ONil(tc_List_Olist(_1690003)))], (45319 ^ _777081) ^ [] : [_1690005 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 45323 ^ _777081 : [(45324 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45322 ^ [_1690001, _1690003, _1690005]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1690003))), _1690001))))], (45326 ^ _777081) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690003)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1690003)), _1690001), 45322 ^ [_1690001, _1690003, _1690005])) = _1690005]], -(c_List_Otranspose(_1690003, _1690001) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1690003)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1690003)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1690003), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1690003)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1690003)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1690003), hAPP(hAPP(c_COMBB(tc_List_Olist(_1690003), tc_fun(tc_Nat_Onat, _1690003), tc_Nat_Onat), c_List_Onth(_1690003)), hAPP(c_List_Onth(tc_List_Olist(_1690003)), _1690001))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1690003))), _1690001)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1690005)))], (45330 ^ _777081) ^ [_1690511, _1690513] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1690511)), c_List_Otranspose__rel(_1690511)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1690511)), c_List_Olist_ONil(_1690511)), _1690513))), -(c_List_Otranspose(_1690511, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1690511)), c_List_Olist_ONil(_1690511)), _1690513)) = c_List_Otranspose(_1690511, _1690513))], (45336 ^ _777081) ^ [_1690670] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1690670)), c_List_Otranspose__rel(_1690670)), c_List_Olist_ONil(tc_List_Olist(_1690670)))), -(c_List_Otranspose(_1690670, c_List_Olist_ONil(tc_List_Olist(_1690670))) = c_List_Olist_ONil(tc_List_Olist(_1690670)))], (45342 ^ _777081) ^ [_1690797, _1690799, _1690801] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1690797), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1690797))), _1690799))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690801), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1690797))), _1690799))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1690797), _1690797), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690797), tc_Nat_Onat, _1690797), c_List_Onth(_1690797)), _1690801)), hAPP(c_List_Ofilter(tc_List_Olist(_1690797), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1690797)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1690801)), c_Nat_Osize__class_Osize(tc_List_Olist(_1690797)))), c_List_Otranspose(_1690797, _1690799))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1690797)), _1690799), _1690801))], (45352 ^ _777081) ^ [_1691124, _1691126] : [-(c_List_Oconcat(_1691124, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1691124), tc_List_Olist(_1691124)), c_List_Olist_Olist__case(tc_List_Olist(_1691124), _1691124, c_List_Olist_ONil(_1691124), hAPP(hAPP(c_COMBB(tc_List_Olist(_1691124), tc_fun(tc_List_Olist(_1691124), tc_List_Olist(_1691124)), _1691124), c_COMBK(tc_List_Olist(_1691124), tc_List_Olist(_1691124))), hAPP(hAPP(c_COMBC(_1691124, tc_List_Olist(_1691124), tc_List_Olist(_1691124)), c_List_Olist_OCons(_1691124)), c_List_Olist_ONil(_1691124))))), _1691126)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1691124), _1691124), c_List_Ohd(_1691124)), hAPP(c_List_Ofilter(tc_List_Olist(_1691124), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1691124)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1691124), tc_List_Olist(_1691124), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1691124)))), _1691126)))], (45354 ^ _777081) ^ [_1691267, _1691269] : [-(c_Fun_Oinj__on(tc_List_Olist(_1691267), tc_List_Olist(_1691267), c_List_Orev(_1691267), _1691269))], (45356 ^ _777081) ^ [_1691315, _1691317] : [hAPP(c_List_Orev(_1691315), _1691317) = c_List_Olist_ONil(_1691315), -(_1691317 = c_List_Olist_ONil(_1691315))], (45362 ^ _777081) ^ [_1691406, _1691408] : [_1691408 = c_List_Olist_ONil(_1691406), -(hAPP(c_List_Orev(_1691406), _1691408) = c_List_Olist_ONil(_1691406))], (45368 ^ _777081) ^ [_1691518, _1691520] : [c_List_Olist_ONil(_1691518) = hAPP(c_List_Orev(_1691518), _1691520), -(_1691520 = c_List_Olist_ONil(_1691518))], (45374 ^ _777081) ^ [_1691609, _1691611] : [_1691611 = c_List_Olist_ONil(_1691609), -(c_List_Olist_ONil(_1691609) = hAPP(c_List_Orev(_1691609), _1691611))], (45380 ^ _777081) ^ [_1691706] : [-(hAPP(c_List_Orev(_1691706), c_List_Olist_ONil(_1691706)) = c_List_Olist_ONil(_1691706))], (45382 ^ _777081) ^ [_1691738, _1691740] : [-(hAPP(c_List_Orev(_1691738), c_List_Oconcat(_1691738, _1691740)) = c_List_Oconcat(_1691738, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1691738), tc_List_Olist(_1691738)), c_List_Orev(_1691738)), hAPP(c_List_Orev(tc_List_Olist(_1691738)), _1691740))))], (45384 ^ _777081) ^ [_1691796, _1691798, _1691800, _1691802] : [-(hAPP(c_List_Orev(_1691796), hAPP(hAPP(c_List_Omap(_1691798, _1691796), _1691800), _1691802)) = hAPP(hAPP(c_List_Omap(_1691798, _1691796), _1691800), hAPP(c_List_Orev(_1691798), _1691802)))], (45386 ^ _777081) ^ [_1691871, _1691873, _1691875] : [hAPP(c_List_Orev(_1691871), _1691873) = hAPP(hAPP(c_List_Olist_OCons(_1691871), _1691875), c_List_Olist_ONil(_1691871)), -(_1691873 = hAPP(hAPP(c_List_Olist_OCons(_1691871), _1691875), c_List_Olist_ONil(_1691871)))], (45392 ^ _777081) ^ [_1691996, _1691998, _1692000] : [_1691998 = hAPP(hAPP(c_List_Olist_OCons(_1691996), _1692000), c_List_Olist_ONil(_1691996)), -(hAPP(c_List_Orev(_1691996), _1691998) = hAPP(hAPP(c_List_Olist_OCons(_1691996), _1692000), c_List_Olist_ONil(_1691996)))], (45398 ^ _777081) ^ [_1692145, _1692147, _1692149] : [hAPP(hAPP(c_List_Olist_OCons(_1692145), _1692147), c_List_Olist_ONil(_1692145)) = hAPP(c_List_Orev(_1692145), _1692149), -(_1692149 = hAPP(hAPP(c_List_Olist_OCons(_1692145), _1692147), c_List_Olist_ONil(_1692145)))], (45404 ^ _777081) ^ [_1692270, _1692272, _1692274] : [_1692274 = hAPP(hAPP(c_List_Olist_OCons(_1692270), _1692272), c_List_Olist_ONil(_1692270)), -(hAPP(hAPP(c_List_Olist_OCons(_1692270), _1692272), c_List_Olist_ONil(_1692270)) = hAPP(c_List_Orev(_1692270), _1692274))], (45410 ^ _777081) ^ [_1692401, _1692403] : [-(c_List_Oconcat(_1692401, _1692403) = hAPP(c_List_Ofoldl(tc_List_Olist(_1692401), tc_List_Olist(_1692401), c_List_Oappend(_1692401), c_List_Olist_ONil(_1692401)), _1692403))], (45412 ^ _777081) ^ [_1692445, _1692447] : [-(hAPP(c_List_Orev(_1692445), _1692447) = hAPP(c_List_Ofoldl(tc_List_Olist(_1692445), _1692445, hAPP(c_COMBC(_1692445, tc_List_Olist(_1692445), tc_List_Olist(_1692445)), c_List_Olist_OCons(_1692445)), c_List_Olist_ONil(_1692445)), _1692447))], (45414 ^ _777081) ^ [_1692500, _1692502, _1692504] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1692500), tc_List_Olist(_1692500), c_List_Oappend(_1692500), _1692502), _1692504) = hAPP(hAPP(c_List_Oappend(_1692500), _1692502), c_List_Oconcat(_1692500, _1692504)))], (45416 ^ _777081) ^ [_1692567, _1692569] : [hBOOL(hAPP(c_List_Odistinct(_1692567), hAPP(c_List_Orev(_1692567), _1692569))), -(hBOOL(hAPP(c_List_Odistinct(_1692567), _1692569)))], (45422 ^ _777081) ^ [_1692666, _1692668] : [hBOOL(hAPP(c_List_Odistinct(_1692666), _1692668)), -(hBOOL(hAPP(c_List_Odistinct(_1692666), hAPP(c_List_Orev(_1692666), _1692668))))], (45428 ^ _777081) ^ [_1692771, _1692773, _1692775] : [-(c_List_Oconcat(_1692771, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1692771)), _1692773), _1692775)) = hAPP(hAPP(c_List_Oappend(_1692771), c_List_Oconcat(_1692771, _1692773)), c_List_Oconcat(_1692771, _1692775)))], (45430 ^ _777081) ^ [_1692825, _1692827, _1692829] : [-(hAPP(c_List_Orev(_1692825), hAPP(hAPP(c_List_Oappend(_1692825), _1692827), _1692829)) = hAPP(hAPP(c_List_Oappend(_1692825), hAPP(c_List_Orev(_1692825), _1692829)), hAPP(c_List_Orev(_1692825), _1692827)))], (45432 ^ _777081) ^ [_1692883, _1692885, _1692887, _1692889, _1692891] : [-(hAPP(c_List_Ofoldl(_1692883, _1692885, _1692887, _1692889), _1692891) = c_List_Ofoldr(_1692885, _1692883, hAPP(c_COMBC(_1692883, _1692885, _1692883), _1692887), hAPP(c_List_Orev(_1692885), _1692891), _1692889))], (45434 ^ _777081) ^ [_1692940, _1692942, _1692944, _1692946, _1692948] : [-(c_List_Ofoldr(_1692940, _1692942, _1692944, _1692946, _1692948) = hAPP(c_List_Ofoldl(_1692942, _1692940, hAPP(c_COMBC(_1692940, _1692942, _1692942), _1692944), _1692948), hAPP(c_List_Orev(_1692940), _1692946)))], (45436 ^ _777081) ^ [_1692997] : [-(c_List_Oconcat(_1692997, c_List_Olist_ONil(tc_List_Olist(_1692997))) = c_List_Olist_ONil(_1692997))], (45438 ^ _777081) ^ [_1693029, _1693031] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693029)), hAPP(c_List_Orev(_1693029), _1693031)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693029)), _1693031))], (45440 ^ _777081) ^ [_1693073, _1693075] : [class_Groups_Ocomm__monoid__add(_1693073), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1693073), hAPP(c_List_Orev(_1693073), _1693075)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1693073), _1693075))], (45446 ^ _777081) ^ [_1693178, _1693180] : [-(hAPP(c_List_Orev(_1693178), hAPP(c_List_Orev(_1693178), _1693180)) = _1693180)], (45448 ^ _777081) ^ [_1693231, _1693233, _1693235] : [hAPP(c_List_Orev(_1693231), _1693233) = _1693235, -(_1693233 = hAPP(c_List_Orev(_1693231), _1693235))], (45454 ^ _777081) ^ [_1693326, _1693328, _1693330] : [_1693328 = hAPP(c_List_Orev(_1693326), _1693330), -(hAPP(c_List_Orev(_1693326), _1693328) = _1693330)], (45460 ^ _777081) ^ [_1693445, _1693447, _1693449] : [hAPP(c_List_Orev(_1693445), _1693447) = hAPP(c_List_Orev(_1693445), _1693449), -(_1693447 = _1693449)], (45466 ^ _777081) ^ [_1693540, _1693542, _1693544] : [_1693542 = _1693544, -(hAPP(c_List_Orev(_1693540), _1693542) = hAPP(c_List_Orev(_1693540), _1693544))], (45472 ^ _777081) ^ [_1693641, _1693643] : [-(hAPP(c_List_Oset(_1693641), hAPP(c_List_Orev(_1693641), _1693643)) = hAPP(c_List_Oset(_1693641), _1693643))], (45474 ^ _777081) ^ [_1693681, _1693683, _1693685, _1693687] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693681)), _1693683) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693685)), _1693687), -(hAPP(hAPP(c_List_Ozip(_1693681, _1693685), hAPP(c_List_Orev(_1693681), _1693683)), hAPP(c_List_Orev(_1693685), _1693687)) = hAPP(c_List_Orev(tc_prod(_1693681, _1693685)), hAPP(hAPP(c_List_Ozip(_1693681, _1693685), _1693683), _1693687)))], (45480 ^ _777081) ^ [_1693862, _1693864, _1693866] : [-(hAPP(c_List_Orev(_1693862), hAPP(c_List_Ofilter(_1693862, _1693864), _1693866)) = hAPP(c_List_Ofilter(_1693862, _1693864), hAPP(c_List_Orev(_1693862), _1693866)))], (45482 ^ _777081) ^ [_1693911, _1693913, _1693915] : [-(c_List_Oconcat(_1693911, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1693911)), _1693913), _1693915)) = hAPP(hAPP(c_List_Oappend(_1693911), _1693913), c_List_Oconcat(_1693911, _1693915)))], (45494 ^ _777081) ^ [_1694183, _1694185] : [45496 ^ _777081 : [(45497 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1694183)), 45495 ^ [_1694183, _1694185]), hAPP(c_List_Oset(tc_List_Olist(_1694183)), _1694185))))], (45499 ^ _777081) ^ [] : [45495 ^ [_1694183, _1694185] = c_List_Olist_ONil(_1694183)]], -(c_List_Oconcat(_1694183, _1694185) = c_List_Olist_ONil(_1694183))], (45484 ^ _777081) ^ [_1693977, _1693979] : [c_List_Oconcat(_1693977, _1693979) = c_List_Olist_ONil(_1693977), 45487 ^ _777081 : [(45488 ^ _777081) ^ [_1694068] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1693977)), _1694068), hAPP(c_List_Oset(tc_List_Olist(_1693977)), _1693979))), -(_1694068 = c_List_Olist_ONil(_1693977))]]], (45513 ^ _777081) ^ [_1694595, _1694597] : [45515 ^ _777081 : [(45516 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1694595)), 45514 ^ [_1694595, _1694597]), hAPP(c_List_Oset(tc_List_Olist(_1694595)), _1694597))))], (45518 ^ _777081) ^ [] : [45514 ^ [_1694595, _1694597] = c_List_Olist_ONil(_1694595)]], -(c_List_Olist_ONil(_1694595) = c_List_Oconcat(_1694595, _1694597))], (45503 ^ _777081) ^ [_1694389, _1694391] : [c_List_Olist_ONil(_1694389) = c_List_Oconcat(_1694389, _1694391), 45506 ^ _777081 : [(45507 ^ _777081) ^ [_1694480] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1694389)), _1694480), hAPP(c_List_Oset(tc_List_Olist(_1694389)), _1694391))), -(_1694480 = c_List_Olist_ONil(_1694389))]]], (45522 ^ _777081) ^ [_1694786, _1694788, _1694790, _1694792] : [-(hAPP(hAPP(c_List_Omap(_1694786, _1694788), _1694790), c_List_Oconcat(_1694786, _1694792)) = c_List_Oconcat(_1694788, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694786), tc_List_Olist(_1694788)), hAPP(c_List_Omap(_1694786, _1694788), _1694790)), _1694792)))], (45524 ^ _777081) ^ [_1694849, _1694851, _1694853] : [-(hAPP(c_List_Ofilter(_1694849, _1694851), c_List_Oconcat(_1694849, _1694853)) = c_List_Oconcat(_1694849, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1694849), tc_List_Olist(_1694849)), c_List_Ofilter(_1694849, _1694851)), _1694853)))], (45526 ^ _777081) ^ [_1694925, _1694927, _1694929, _1694931] : [hAPP(c_List_Orev(_1694925), _1694927) = hAPP(hAPP(c_List_Olist_OCons(_1694925), _1694929), _1694931), -(_1694927 = hAPP(hAPP(c_List_Oappend(_1694925), hAPP(c_List_Orev(_1694925), _1694931)), hAPP(hAPP(c_List_Olist_OCons(_1694925), _1694929), c_List_Olist_ONil(_1694925))))], (45532 ^ _777081) ^ [_1695074, _1695076, _1695078, _1695080] : [_1695076 = hAPP(hAPP(c_List_Oappend(_1695074), hAPP(c_List_Orev(_1695074), _1695080)), hAPP(hAPP(c_List_Olist_OCons(_1695074), _1695078), c_List_Olist_ONil(_1695074))), -(hAPP(c_List_Orev(_1695074), _1695076) = hAPP(hAPP(c_List_Olist_OCons(_1695074), _1695078), _1695080))], (45538 ^ _777081) ^ [_1695229, _1695231, _1695233] : [-(hAPP(c_List_Orev(_1695229), hAPP(hAPP(c_List_Olist_OCons(_1695229), _1695231), _1695233)) = hAPP(hAPP(c_List_Oappend(_1695229), hAPP(c_List_Orev(_1695229), _1695233)), hAPP(hAPP(c_List_Olist_OCons(_1695229), _1695231), c_List_Olist_ONil(_1695229))))], (45540 ^ _777081) ^ [_1695292, _1695294] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695292)), c_List_Oconcat(_1695292, _1695294)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695292), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1695292))), _1695294)))], (45542 ^ _777081) ^ [_1695345, _1695347] : [-(hAPP(c_List_Oset(_1695345), c_List_Oconcat(_1695345, _1695347)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1695345), tc_fun(_1695345, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1695345)), _1695347)), c_List_Oset(_1695345)))], (45544 ^ _777081) ^ [_1695397, _1695399] : [-(_1695397 = c_List_Olist_ONil(_1695399)), -(hAPP(c_List_Ohd(_1695399), hAPP(c_List_Orev(_1695399), _1695397)) = c_List_Olast(_1695399, _1695397))], (45550 ^ _777081) ^ [_1695444, _1695446] : [-(_1695444 = c_List_Olist_ONil(_1695446)), -(c_List_Olast(_1695446, hAPP(c_List_Orev(_1695446), _1695444)) = hAPP(c_List_Ohd(_1695446), _1695444))], (45556 ^ _777081) ^ [_1695495, _1695497] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695495), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1695495))), c_List_Otranspose(_1695495, _1695497)))))], (45558 ^ _777081) ^ [_1695541, _1695543, _1695545] : [-(hAPP(c_List_Orev(_1695541), hAPP(hAPP(c_List_Otake(_1695541), _1695543), _1695545)) = hAPP(hAPP(c_List_Odrop(_1695541), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695541)), _1695545)), _1695543)), hAPP(c_List_Orev(_1695541), _1695545)))], (45560 ^ _777081) ^ [_1695607, _1695609, _1695611] : [-(hAPP(c_List_Orev(_1695607), hAPP(hAPP(c_List_Odrop(_1695607), _1695609), _1695611)) = hAPP(hAPP(c_List_Otake(_1695607), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695607)), _1695611)), _1695609)), hAPP(c_List_Orev(_1695607), _1695611)))], (45562 ^ _777081) ^ [_1695673, _1695675, _1695677] : [-(hAPP(c_List_Orotate(_1695673, _1695675), hAPP(c_List_Orev(_1695673), _1695677)) = hAPP(c_List_Orev(_1695673), hAPP(c_List_Orotate(_1695673, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695673)), _1695677)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1695675, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695673)), _1695677)))), _1695677)))], (45564 ^ _777081) ^ [_1695746, _1695748, _1695750, _1695752] : [-(c_List_Otranspose(_1695746, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695746)), hAPP(hAPP(c_List_Olist_OCons(_1695746), _1695748), _1695750)), _1695752)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695746)), hAPP(hAPP(c_List_Olist_OCons(_1695746), _1695748), c_List_Oconcat(_1695746, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695746), tc_List_Olist(_1695746)), c_List_Olist_Olist__case(tc_List_Olist(_1695746), _1695746, c_List_Olist_ONil(_1695746), hAPP(hAPP(c_COMBB(tc_List_Olist(_1695746), tc_fun(tc_List_Olist(_1695746), tc_List_Olist(_1695746)), _1695746), c_COMBK(tc_List_Olist(_1695746), tc_List_Olist(_1695746))), hAPP(hAPP(c_COMBC(_1695746, tc_List_Olist(_1695746), tc_List_Olist(_1695746)), c_List_Olist_OCons(_1695746)), c_List_Olist_ONil(_1695746))))), _1695752)))), c_List_Otranspose(_1695746, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695746)), _1695750), c_List_Oconcat(tc_List_Olist(_1695746), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695746), tc_List_Olist(tc_List_Olist(_1695746))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1695746)), _1695746, c_List_Olist_ONil(tc_List_Olist(_1695746)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1695746), tc_List_Olist(tc_List_Olist(_1695746))), _1695746), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695746), tc_List_Olist(tc_List_Olist(_1695746)), tc_List_Olist(tc_List_Olist(_1695746))), c_List_Olist_OCons(tc_List_Olist(_1695746))), c_List_Olist_ONil(tc_List_Olist(_1695746)))))), _1695752))))))], (45566 ^ _777081) ^ [_1695972, _1695974, _1695976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695972), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695974)), _1695976))), -(hAPP(hAPP(c_List_Onth(_1695974), hAPP(c_List_Orev(_1695974), _1695976)), _1695972) = hAPP(hAPP(c_List_Onth(_1695974), _1695976), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695974)), _1695976)), hAPP(c_Nat_OSuc, _1695972))))], (45572 ^ _777081) ^ [_1696149, _1696151, _1696153] : [c_List_Oconcat(_1696149, _1696151) = c_List_Oconcat(_1696149, _1696153), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1696149))), _1696151) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1696149))), _1696153), 45582 ^ _777081 : [(45583 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1696149), tc_List_Olist(_1696149))), 45581 ^ [_1696149, _1696151, _1696153]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1696149), tc_List_Olist(_1696149))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1696149), tc_List_Olist(_1696149)), _1696151), _1696153)))))], (45585 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1696149), tc_List_Olist(_1696149), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1696149), tc_fun(tc_List_Olist(_1696149), tc_Nat_Onat), tc_fun(tc_List_Olist(_1696149), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1696149), tc_Nat_Onat), tc_fun(tc_List_Olist(_1696149), tc_HOL_Obool)), tc_List_Olist(_1696149)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1696149))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1696149)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1696149))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1696149)))), 45581 ^ [_1696149, _1696151, _1696153]))]], -(_1696151 = _1696153)], (45589 ^ _777081) ^ [_1696790, _1696792, _1696794] : [45591 ^ _777081 : [(45592 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1696790), tc_List_Olist(_1696790))), 45590 ^ [_1696790, _1696792, _1696794]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1696790), tc_List_Olist(_1696790))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1696790), tc_List_Olist(_1696790)), _1696792), _1696794)))))], (45594 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1696790), tc_List_Olist(_1696790), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1696790), tc_fun(tc_List_Olist(_1696790), tc_Nat_Onat), tc_fun(tc_List_Olist(_1696790), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1696790), tc_Nat_Onat), tc_fun(tc_List_Olist(_1696790), tc_HOL_Obool)), tc_List_Olist(_1696790)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1696790))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1696790)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1696790))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1696790)))), 45590 ^ [_1696790, _1696792, _1696794]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1696790))), _1696792) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1696790))), _1696794), 45599 ^ _777081 : [(45600 ^ _777081) ^ [] : [c_List_Oconcat(_1696790, _1696792) = c_List_Oconcat(_1696790, _1696794), -(_1696792 = _1696794)], (45606 ^ _777081) ^ [] : [_1696792 = _1696794, -(c_List_Oconcat(_1696790, _1696792) = c_List_Oconcat(_1696790, _1696794))]]], (45612 ^ _777081) ^ [_1697517, _1697519, _1697521, _1697523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697517), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697519)), _1697521))), -(hAPP(c_List_Orev(_1697519), hAPP(hAPP(c_List_Olist__update(_1697519, _1697521), _1697517), _1697523)) = hAPP(hAPP(c_List_Olist__update(_1697519, hAPP(c_List_Orev(_1697519), _1697521)), 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(_1697519)), _1697521)), _1697517)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1697523))], (45618 ^ _777081) ^ [_1697716, _1697718, _1697720, _1697722] : [-(c_List_Oconcat(_1697716, hAPP(hAPP(c_List_Omap(_1697718, tc_List_Olist(_1697716)), hAPP(hAPP(c_COMBC(_1697718, tc_List_Olist(_1697716), tc_List_Olist(_1697716)), hAPP(hAPP(c_COMBB(_1697716, tc_fun(tc_List_Olist(_1697716), tc_List_Olist(_1697716)), _1697718), c_List_Olist_OCons(_1697716)), _1697720)), c_List_Olist_ONil(_1697716))), _1697722)) = hAPP(hAPP(c_List_Omap(_1697718, _1697716), _1697720), _1697722))], (45620 ^ _777081) ^ [_1697803, _1697805, _1697807, _1697809] : [class_Orderings_Olinorder(_1697803), c_List_Olinorder__class_Osorted(_1697803, hAPP(c_List_Orev(_1697803), _1697805)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1697807), _1697809)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1697809), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697803)), _1697805))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1697803), hAPP(hAPP(c_List_Onth(_1697803), _1697805), _1697809)), hAPP(hAPP(c_List_Onth(_1697803), _1697805), _1697807))))], (45638 ^ _777081) ^ [_1698140, _1698142, _1698144] : [class_Orderings_Olinorder(_1698140), c_List_Olinorder__class_Osorted(_1698140, hAPP(c_List_Orev(_1698140), _1698142)), 45645 ^ _777081 : [(45646 ^ _777081) ^ [] : [_1698142 = c_List_Olist_ONil(_1698140), -(c_List_Ofoldr(_1698140, _1698140, c_Orderings_Oord__class_Omax(_1698140), _1698142, _1698144) = _1698144)], (45652 ^ _777081) ^ [] : [-(_1698142 = c_List_Olist_ONil(_1698140)), -(c_List_Ofoldr(_1698140, _1698140, c_Orderings_Oord__class_Omax(_1698140), _1698142, _1698144) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1698140), hAPP(hAPP(c_List_Onth(_1698140), _1698142), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1698144))]]], (45658 ^ _777081) ^ [_1698454, _1698456, _1698458, _1698460] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1698454)), c_List_Otranspose__rel(_1698454)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698454)), hAPP(hAPP(c_List_Olist_OCons(_1698454), _1698456), _1698458)), _1698460))), -(c_List_Otranspose(_1698454, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698454)), hAPP(hAPP(c_List_Olist_OCons(_1698454), _1698456), _1698458)), _1698460)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698454)), hAPP(hAPP(c_List_Olist_OCons(_1698454), _1698456), c_List_Oconcat(_1698454, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698454), tc_List_Olist(_1698454)), c_List_Olist_Olist__case(tc_List_Olist(_1698454), _1698454, c_List_Olist_ONil(_1698454), hAPP(hAPP(c_COMBB(tc_List_Olist(_1698454), tc_fun(tc_List_Olist(_1698454), tc_List_Olist(_1698454)), _1698454), c_COMBK(tc_List_Olist(_1698454), tc_List_Olist(_1698454))), hAPP(hAPP(c_COMBC(_1698454, tc_List_Olist(_1698454), tc_List_Olist(_1698454)), c_List_Olist_OCons(_1698454)), c_List_Olist_ONil(_1698454))))), _1698460)))), c_List_Otranspose(_1698454, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698454)), _1698458), c_List_Oconcat(tc_List_Olist(_1698454), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698454), tc_List_Olist(tc_List_Olist(_1698454))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1698454)), _1698454, c_List_Olist_ONil(tc_List_Olist(_1698454)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1698454), tc_List_Olist(tc_List_Olist(_1698454))), _1698454), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698454), tc_List_Olist(tc_List_Olist(_1698454)), tc_List_Olist(tc_List_Olist(_1698454))), c_List_Olist_OCons(tc_List_Olist(_1698454))), c_List_Olist_ONil(tc_List_Olist(_1698454)))))), _1698460))))))], (45664 ^ _777081) ^ [_1698987, _1698989] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698987), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1698987))), _1698989))), 45667 ^ _777081 : [(45668 ^ _777081) ^ [] : [_1698989 = c_List_Olist_ONil(tc_List_Olist(_1698987)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1698987))), c_List_Otranspose(_1698987, _1698989)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45674 ^ _777081) ^ [] : [-(_1698989 = c_List_Olist_ONil(tc_List_Olist(_1698987))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1698987))), c_List_Otranspose(_1698987, _1698989)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698987)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1698987)), _1698989), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (45680 ^ _777081) ^ [_1699297, _1699299, _1699301] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699297), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1699297))), _1699299))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1699301), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699297))), _1699299))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699297))), hAPP(c_List_Ofilter(tc_List_Olist(_1699297), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1699297)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1699301)), c_Nat_Osize__class_Osize(tc_List_Olist(_1699297)))), c_List_Otranspose(_1699297, _1699299))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699297)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1699297)), _1699299), _1699301)))], (45690 ^ _777081) ^ [_1699606, _1699608] : [-(c_List_Oconcat(tc_List_Olist(_1699606), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699606), tc_List_Olist(tc_List_Olist(_1699606))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1699606)), _1699606, c_List_Olist_ONil(tc_List_Olist(_1699606)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1699606), tc_List_Olist(tc_List_Olist(_1699606))), _1699606), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699606), tc_List_Olist(tc_List_Olist(_1699606)), tc_List_Olist(tc_List_Olist(_1699606))), c_List_Olist_OCons(tc_List_Olist(_1699606))), c_List_Olist_ONil(tc_List_Olist(_1699606)))))), _1699608)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699606), tc_List_Olist(_1699606)), c_List_Otl(_1699606)), hAPP(c_List_Ofilter(tc_List_Olist(_1699606), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1699606)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699606), tc_List_Olist(_1699606), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1699606)))), _1699608)))], (45692 ^ _777081) ^ [_1699758, _1699760, _1699762, _1699764] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699758), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1699758))), _1699760))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1699762), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699758))), c_List_Otranspose(_1699758, _1699760)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1699764), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1699758))), hAPP(c_List_Ofilter(tc_List_Olist(_1699758), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1699758)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1699762)), c_Nat_Osize__class_Osize(tc_List_Olist(_1699758)))), _1699760)))), -(hAPP(hAPP(c_List_Onth(_1699758), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1699758)), c_List_Otranspose(_1699758, _1699760)), _1699762)), _1699764) = hAPP(hAPP(c_List_Onth(_1699758), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1699758)), _1699760), _1699764)), _1699762))], (45706 ^ _777081) ^ [_1700181, _1700183] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1700181), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1700181))), _1700183))), -(c_List_Otranspose(_1700181, c_List_Otranspose(_1700181, _1700183)) = c_List_OtakeWhile(tc_List_Olist(_1700181), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700181)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700181), tc_List_Olist(_1700181), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700181))), _1700183))], (45712 ^ _777081) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (45714 ^ _777081) ^ [_1700392, _1700394, _1700396, _1700398, _1700400] : [-(c_List_OtakeWhile(_1700392, _1700394, hAPP(hAPP(c_List_Omap(_1700396, _1700392), _1700398), _1700400)) = hAPP(hAPP(c_List_Omap(_1700396, _1700392), _1700398), c_List_OtakeWhile(_1700396, hAPP(c_Fun_Ocomp(_1700392, tc_HOL_Obool, _1700396, _1700394), _1700398), _1700400)))], (45716 ^ _777081) ^ [_1700457, _1700459, _1700461, _1700463, _1700465] : [-(hAPP(hAPP(c_List_Ozip(_1700457, _1700459), c_List_OtakeWhile(_1700457, _1700461, _1700463)), _1700465) = c_List_OtakeWhile(tc_prod(_1700457, _1700459), hAPP(c_Fun_Ocomp(_1700457, tc_HOL_Obool, tc_prod(_1700457, _1700459), _1700461), c_Product__Type_Ofst(_1700457, _1700459)), hAPP(hAPP(c_List_Ozip(_1700457, _1700459), _1700463), _1700465)))], (45718 ^ _777081) ^ [_1700531, _1700533, _1700535, _1700537, _1700539] : [-(hAPP(hAPP(c_List_Ozip(_1700531, _1700533), _1700535), c_List_OtakeWhile(_1700533, _1700537, _1700539)) = c_List_OtakeWhile(tc_prod(_1700531, _1700533), hAPP(c_Fun_Ocomp(_1700533, tc_HOL_Obool, tc_prod(_1700531, _1700533), _1700537), c_Product__Type_Osnd(_1700531, _1700533)), hAPP(hAPP(c_List_Ozip(_1700531, _1700533), _1700535), _1700539)))], (45730 ^ _777081) ^ [_1700819, _1700821, _1700823] : [45732 ^ _777081 : [(45733 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1700819), 45731 ^ [_1700819, _1700821, _1700823]), hAPP(c_List_Oset(_1700819), _1700823))))], (45735 ^ _777081) ^ [] : [hBOOL(hAPP(_1700821, 45731 ^ [_1700819, _1700821, _1700823]))]], -(c_List_OtakeWhile(_1700819, _1700821, _1700823) = _1700823)], (45720 ^ _777081) ^ [_1700623, _1700625, _1700627] : [c_List_OtakeWhile(_1700623, _1700625, _1700627) = _1700627, 45723 ^ _777081 : [(45724 ^ _777081) ^ [_1700710] : [hBOOL(hAPP(hAPP(c_member(_1700623), _1700710), hAPP(c_List_Oset(_1700623), _1700627))), -(hBOOL(hAPP(_1700625, _1700710)))]]], (45739 ^ _777081) ^ [_1701007, _1701009, _1701011, _1701013] : [hBOOL(hAPP(hAPP(c_member(_1701007), _1701009), hAPP(c_List_Oset(_1701007), c_List_OtakeWhile(_1701007, _1701011, _1701013)))), 45742 ^ _777081 : [(45743 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1701007), _1701009), hAPP(c_List_Oset(_1701007), _1701013))))], (45745 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1701011, _1701009)))]]], (45747 ^ _777081) ^ [_1701174, _1701176, _1701178] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701174)), c_List_OtakeWhile(_1701174, _1701176, _1701178))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701174)), _1701178))))], (45749 ^ _777081) ^ [_1701224, _1701226, _1701228] : [-(c_List_OtakeWhile(_1701224, _1701226, _1701228) = hAPP(hAPP(c_List_Otake(_1701224), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701224)), c_List_OtakeWhile(_1701224, _1701226, _1701228))), _1701228))], (45751 ^ _777081) ^ [_1701274, _1701276, _1701278] : [hBOOL(hAPP(c_List_Odistinct(_1701274), _1701276)), -(hBOOL(hAPP(c_List_Odistinct(_1701274), c_List_OtakeWhile(_1701274, _1701278, _1701276))))], (45757 ^ _777081) ^ [_1701392, _1701394, _1701396, _1701398] : [hBOOL(hAPP(_1701392, _1701394)), -(c_List_OtakeWhile(_1701396, _1701392, hAPP(hAPP(c_List_Olist_OCons(_1701396), _1701394), _1701398)) = hAPP(hAPP(c_List_Olist_OCons(_1701396), _1701394), c_List_OtakeWhile(_1701396, _1701392, _1701398)))], (45763 ^ _777081) ^ [_1701519, _1701521, _1701523, _1701525] : [-(hBOOL(hAPP(_1701519, _1701521))), -(c_List_OtakeWhile(_1701523, _1701519, hAPP(hAPP(c_List_Olist_OCons(_1701523), _1701521), _1701525)) = c_List_Olist_ONil(_1701523))], (45769 ^ _777081) ^ [_1701577, _1701579, _1701581] : [class_Orderings_Olinorder(_1701577), c_List_Olinorder__class_Osorted(_1701577, _1701579), -(c_List_Olinorder__class_Osorted(_1701577, c_List_OtakeWhile(_1701577, _1701581, _1701579)))], (45779 ^ _777081) ^ [_1701716, _1701718] : [-(c_List_OtakeWhile(_1701716, _1701718, c_List_Olist_ONil(_1701716)) = c_List_Olist_ONil(_1701716))], (45781 ^ _777081) ^ [_1701745, _1701747, _1701749, _1701751, _1701753] : [-(hBOOL(hAPP(_1701745, _1701747))), -(c_List_OtakeWhile(_1701749, _1701745, hAPP(hAPP(c_List_Oappend(_1701749), _1701751), hAPP(hAPP(c_List_Olist_OCons(_1701749), _1701747), _1701753))) = c_List_OtakeWhile(_1701749, _1701745, _1701751))], (45787 ^ _777081) ^ [_1701813] : [-(c_List_Oreturn__list(_1701813) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1701813))], (45789 ^ _777081) ^ [_1701841, _1701843, _1701845, _1701847, _1701849] : [hBOOL(hAPP(hAPP(c_member(_1701841), _1701843), hAPP(c_List_Oset(_1701841), _1701845))), -(hBOOL(hAPP(_1701847, _1701843))), -(c_List_OtakeWhile(_1701841, _1701847, hAPP(hAPP(c_List_Oappend(_1701841), _1701845), _1701849)) = c_List_OtakeWhile(_1701841, _1701847, _1701845))], (45799 ^ _777081) ^ [_1701999, _1702001, _1702003, _1702005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1701999), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702001)), c_List_OtakeWhile(_1702001, _1702003, _1702005)))), -(hAPP(hAPP(c_List_Onth(_1702001), c_List_OtakeWhile(_1702001, _1702003, _1702005)), _1701999) = hAPP(hAPP(c_List_Onth(_1702001), _1702005), _1701999))], (45805 ^ _777081) ^ [_1702152, _1702154, _1702156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702152)), c_List_OtakeWhile(_1702152, _1702154, _1702156))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702152)), _1702156))), hBOOL(hAPP(_1702154, hAPP(hAPP(c_List_Onth(_1702152), _1702156), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702152)), c_List_OtakeWhile(_1702152, _1702154, _1702156)))))], (45811 ^ _777081) ^ [_1702320, _1702322, _1702324, _1702326, _1702328] : [-(c_Map_Omap__upds(_1702320, _1702322, _1702324, _1702326, _1702328) = c_Map_Omap__add(_1702320, _1702322, _1702324, hAPP(c_Map_Omap__of(_1702320, _1702322), hAPP(c_List_Orev(tc_prod(_1702320, _1702322)), hAPP(hAPP(c_List_Ozip(_1702320, _1702322), _1702326), _1702328)))))], (45813 ^ _777081) ^ [_1702384, _1702386] : [-(_1702384 = c_List_Olist_ONil(_1702386)), hBOOL(hAPP(c_List_Odistinct(_1702386), _1702384)), -(c_List_OtakeWhile(_1702386, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1702386), c_fNot), hAPP(hAPP(c_COMBC(_1702386, _1702386, tc_HOL_Obool), c_fequal), c_List_Olast(_1702386, _1702384))), _1702384) = c_List_Obutlast(_1702386, _1702384))], (45823 ^ _777081) ^ [_1702581, _1702583, _1702585, _1702587, _1702589] : [class_Orderings_Olinorder(_1702581), c_List_Olinorder__class_Osorted(_1702581, hAPP(c_List_Orev(_1702581), hAPP(hAPP(c_List_Omap(_1702583, _1702581), _1702585), _1702587))), -(hAPP(c_List_Ofilter(_1702583, hAPP(hAPP(c_COMBB(_1702581, tc_HOL_Obool, _1702583), hAPP(c_Orderings_Oord__class_Oless(_1702581), _1702589)), _1702585)), _1702587) = c_List_OtakeWhile(_1702583, hAPP(hAPP(c_COMBB(_1702581, tc_HOL_Obool, _1702583), hAPP(c_Orderings_Oord__class_Oless(_1702581), _1702589)), _1702585), _1702587))], (45833 ^ _777081) ^ [_1702828] : [c_List_Onat__list(_1702828), -(c_List_Oembed__list(c_List_Oreturn__list(_1702828)) = _1702828)], (45839 ^ _777081) ^ [_1702909, _1702911] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702909)), c_List_Oremdups(_1702909, c_List_Oconcat(_1702909, _1702911))) = hAPP(c_Finite__Set_Ocard(_1702909), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1702909), tc_fun(_1702909, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1702909)), _1702911)), c_List_Oset(_1702909))))], (45841 ^ _777081) ^ [_1702975, _1702977] : [-(hBOOL(hAPP(c_List_Odistinct(_1702975), c_List_Oremdups(_1702975, _1702977))))], (45843 ^ _777081) ^ [_1703007, _1703009] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703007)), c_List_Oremdups(_1703007, _1703009))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703007)), _1703009))))], (45845 ^ _777081) ^ [_1703054, _1703056, _1703058, _1703060] : [-(c_List_Oremdups(_1703054, hAPP(hAPP(c_List_Omap(_1703056, _1703054), _1703058), c_List_Oremdups(_1703056, _1703060))) = c_List_Oremdups(_1703054, hAPP(hAPP(c_List_Omap(_1703056, _1703054), _1703058), _1703060)))], (45847 ^ _777081) ^ [_1703110, _1703112] : [-(hAPP(c_List_Oset(_1703110), c_List_Oremdups(_1703110, _1703112)) = hAPP(c_List_Oset(_1703110), _1703112))], (45849 ^ _777081) ^ [_1703148, _1703150, _1703152] : [hBOOL(hAPP(c_List_Odistinct(_1703148), _1703150)), -(c_List_Oremove1(_1703148, _1703152, c_List_Oremdups(_1703148, _1703150)) = c_List_Oremdups(_1703148, c_List_Oremove1(_1703148, _1703152, _1703150)))], (45855 ^ _777081) ^ [_1703278, _1703280] : [c_List_Oremdups(_1703278, _1703280) = c_List_Olist_ONil(_1703278), -(_1703280 = c_List_Olist_ONil(_1703278))], (45861 ^ _777081) ^ [_1703365, _1703367] : [_1703367 = c_List_Olist_ONil(_1703365), -(c_List_Oremdups(_1703365, _1703367) = c_List_Olist_ONil(_1703365))], (45867 ^ _777081) ^ [_1703473, _1703475] : [c_List_Olist_ONil(_1703473) = c_List_Oremdups(_1703473, _1703475), -(_1703475 = c_List_Olist_ONil(_1703473))], (45873 ^ _777081) ^ [_1703560, _1703562] : [_1703562 = c_List_Olist_ONil(_1703560), -(c_List_Olist_ONil(_1703560) = c_List_Oremdups(_1703560, _1703562))], (45879 ^ _777081) ^ [_1703653] : [-(c_List_Oremdups(_1703653, c_List_Olist_ONil(_1703653)) = c_List_Olist_ONil(_1703653))], (45881 ^ _777081) ^ [_1703683, _1703685] : [class_Orderings_Olinorder(_1703683), c_List_Olinorder__class_Osorted(_1703683, _1703685), -(c_List_Olinorder__class_Osorted(_1703683, c_List_Oremdups(_1703683, _1703685)))], (45891 ^ _777081) ^ [_1703831, _1703833] : [c_List_Oremdups(_1703831, _1703833) = _1703833, -(hBOOL(hAPP(c_List_Odistinct(_1703831), _1703833)))], (45897 ^ _777081) ^ [_1703918, _1703920] : [hBOOL(hAPP(c_List_Odistinct(_1703918), _1703920)), -(c_List_Oremdups(_1703918, _1703920) = _1703920)], (45903 ^ _777081) ^ [_1704011, _1704013] : [hBOOL(hAPP(c_List_Odistinct(_1704011), _1704013)), -(c_List_Oremdups(_1704011, _1704013) = _1704013)], (45909 ^ _777081) ^ [_1704117, _1704119] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704117)), c_List_Oremdups(_1704117, _1704119)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704117)), _1704119), -(c_List_Oremdups(_1704117, _1704119) = _1704119)], (45915 ^ _777081) ^ [_1704230, _1704232] : [c_List_Oremdups(_1704230, _1704232) = _1704232, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704230)), c_List_Oremdups(_1704230, _1704232)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704230)), _1704232))], (45921 ^ _777081) ^ [_1704349, _1704351] : [-(c_List_Oremdups(_1704349, c_List_Oremdups(_1704349, _1704351)) = c_List_Oremdups(_1704349, _1704351))], (45923 ^ _777081) ^ [_1704383, _1704385, _1704387] : [-(c_List_Oremdups(_1704383, hAPP(c_List_Ofilter(_1704383, _1704385), _1704387)) = hAPP(c_List_Ofilter(_1704383, _1704385), c_List_Oremdups(_1704383, _1704387)))], (45925 ^ _777081) ^ [_1704428] : [-(c_List_Oembed__list(_1704428) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1704428))], (45927 ^ _777081) ^ [_1704468, _1704470, _1704472] : [hBOOL(hAPP(hAPP(c_member(_1704468), _1704470), hAPP(c_List_Oset(_1704468), _1704472))), -(c_List_Oremdups(_1704468, hAPP(hAPP(c_List_Olist_OCons(_1704468), _1704470), _1704472)) = c_List_Oremdups(_1704468, _1704472))], (45933 ^ _777081) ^ [_1704593, _1704595, _1704597] : [-(hBOOL(hAPP(hAPP(c_member(_1704593), _1704595), hAPP(c_List_Oset(_1704593), _1704597)))), -(c_List_Oremdups(_1704593, hAPP(hAPP(c_List_Olist_OCons(_1704593), _1704595), _1704597)) = hAPP(hAPP(c_List_Olist_OCons(_1704593), _1704595), c_List_Oremdups(_1704593, _1704597)))], (45939 ^ _777081) ^ [_1704667, _1704669] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704667)), c_List_Oremdups(_1704667, _1704669)) = hAPP(c_Finite__Set_Ocard(_1704667), hAPP(c_List_Oset(_1704667), _1704669)))], (45941 ^ _777081) ^ [_1704712, _1704714] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1704712), _1704714) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1704712)), c_List_Oembed__list(_1704714))))], (45943 ^ _777081) ^ [_1704755, _1704757, _1704759] : [hBOOL(hAPP(c_List_Odistinct(_1704755), _1704757)), hBOOL(hAPP(hAPP(c_member(_1704755), _1704759), hAPP(c_List_Oset(_1704755), _1704757))), -(c_List_OtakeWhile(_1704755, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1704755), c_fNot), hAPP(hAPP(c_COMBC(_1704755, _1704755, tc_HOL_Obool), c_fequal), _1704759)), hAPP(c_List_Orev(_1704755), _1704757)) = hAPP(c_List_Orev(_1704755), hAPP(c_List_Otl(_1704755), c_List_OdropWhile(_1704755, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1704755), c_fNot), hAPP(hAPP(c_COMBC(_1704755, _1704755, tc_HOL_Obool), c_fequal), _1704759)), _1704757))))], (45953 ^ _777081) ^ [_1705046, _1705048, _1705050] : [hBOOL(hAPP(c_List_Odistinct(_1705046), _1705048)), hBOOL(hAPP(hAPP(c_member(_1705046), _1705050), hAPP(c_List_Oset(_1705046), _1705048))), -(c_List_OdropWhile(_1705046, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1705046), c_fNot), hAPP(hAPP(c_COMBC(_1705046, _1705046, tc_HOL_Obool), c_fequal), _1705050)), hAPP(c_List_Orev(_1705046), _1705048)) = hAPP(hAPP(c_List_Olist_OCons(_1705046), _1705050), hAPP(c_List_Orev(_1705046), c_List_OtakeWhile(_1705046, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1705046), c_fNot), hAPP(hAPP(c_COMBC(_1705046, _1705046, tc_HOL_Obool), c_fequal), _1705050)), _1705048))))], (45963 ^ _777081) ^ [_1705343, _1705345, _1705347] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705343)), c_List_OdropWhile(_1705343, _1705345, _1705347))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705343)), _1705347))))], (45965 ^ _777081) ^ [_1705393, _1705395, _1705397] : [hBOOL(hAPP(c_List_Odistinct(_1705393), _1705395)), -(hBOOL(hAPP(c_List_Odistinct(_1705393), c_List_OdropWhile(_1705393, _1705397, _1705395))))], (45971 ^ _777081) ^ [_1705511, _1705513, _1705515, _1705517] : [hBOOL(hAPP(_1705511, _1705513)), -(c_List_OdropWhile(_1705515, _1705511, hAPP(hAPP(c_List_Olist_OCons(_1705515), _1705513), _1705517)) = c_List_OdropWhile(_1705515, _1705511, _1705517))], (45977 ^ _777081) ^ [_1705622, _1705624, _1705626, _1705628] : [-(hBOOL(hAPP(_1705622, _1705624))), -(c_List_OdropWhile(_1705626, _1705622, hAPP(hAPP(c_List_Olist_OCons(_1705626), _1705624), _1705628)) = hAPP(hAPP(c_List_Olist_OCons(_1705626), _1705624), _1705628))], (45983 ^ _777081) ^ [_1705686, _1705688, _1705690] : [class_Orderings_Olinorder(_1705686), c_List_Olinorder__class_Osorted(_1705686, _1705688), -(c_List_Olinorder__class_Osorted(_1705686, c_List_OdropWhile(_1705686, _1705690, _1705688)))], (45993 ^ _777081) ^ [_1705825, _1705827] : [-(c_List_OdropWhile(_1705825, _1705827, c_List_Olist_ONil(_1705825)) = c_List_Olist_ONil(_1705825))], (46005 ^ _777081) ^ [_1706076, _1706078, _1706080] : [46007 ^ _777081 : [(46008 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1706076), 46006 ^ [_1706076, _1706078, _1706080]), hAPP(c_List_Oset(_1706076), _1706080))))], (46010 ^ _777081) ^ [] : [hBOOL(hAPP(_1706078, 46006 ^ [_1706076, _1706078, _1706080]))]], -(c_List_OdropWhile(_1706076, _1706078, _1706080) = c_List_Olist_ONil(_1706076))], (45995 ^ _777081) ^ [_1705876, _1705878, _1705880] : [c_List_OdropWhile(_1705876, _1705878, _1705880) = c_List_Olist_ONil(_1705876), 45998 ^ _777081 : [(45999 ^ _777081) ^ [_1705967] : [hBOOL(hAPP(hAPP(c_member(_1705876), _1705967), hAPP(c_List_Oset(_1705876), _1705880))), -(hBOOL(hAPP(_1705878, _1705967)))]]], (46014 ^ _777081) ^ [_1706268, _1706270, _1706272] : [-(hAPP(hAPP(c_List_Oappend(_1706268), c_List_OtakeWhile(_1706268, _1706270, _1706272)), c_List_OdropWhile(_1706268, _1706270, _1706272)) = _1706272)], (46016 ^ _777081) ^ [_1706310, _1706312, _1706314] : [-(c_List_OdropWhile(_1706310, _1706312, _1706314) = c_List_Olist_ONil(_1706310)), hBOOL(hAPP(_1706312, hAPP(c_List_Ohd(_1706310), c_List_OdropWhile(_1706310, _1706312, _1706314))))], (46022 ^ _777081) ^ [_1706416, _1706418, _1706420, _1706422, _1706424] : [-(c_List_OdropWhile(_1706416, _1706418, hAPP(hAPP(c_List_Omap(_1706420, _1706416), _1706422), _1706424)) = hAPP(hAPP(c_List_Omap(_1706420, _1706416), _1706422), c_List_OdropWhile(_1706420, hAPP(c_Fun_Ocomp(_1706416, tc_HOL_Obool, _1706420, _1706418), _1706422), _1706424)))], (46024 ^ _777081) ^ [_1706481, _1706483, _1706485, _1706487, _1706489] : [hBOOL(hAPP(hAPP(c_member(_1706481), _1706483), hAPP(c_List_Oset(_1706481), _1706485))), -(hBOOL(hAPP(_1706487, _1706483))), -(c_List_OdropWhile(_1706481, _1706487, hAPP(hAPP(c_List_Oappend(_1706481), _1706485), _1706489)) = hAPP(hAPP(c_List_Oappend(_1706481), c_List_OdropWhile(_1706481, _1706487, _1706485)), _1706489))], (46034 ^ _777081) ^ [_1706679, _1706681, _1706683, _1706685, _1706687] : [c_List_OdropWhile(_1706679, _1706681, _1706683) = hAPP(hAPP(c_List_Olist_OCons(_1706679), _1706685), _1706687), 46037 ^ _777081 : [(46038 ^ _777081) ^ [] : [-(_1706683 = hAPP(hAPP(c_List_Oappend(_1706679), c_List_OtakeWhile(_1706679, _1706681, _1706683)), hAPP(hAPP(c_List_Olist_OCons(_1706679), _1706685), _1706687)))], (46040 ^ _777081) ^ [] : [hBOOL(hAPP(_1706681, _1706685))]]], (46042 ^ _777081) ^ [_1706860, _1706862, _1706864, _1706866, _1706868] : [-(c_List_OdropWhile(_1706860, _1706862, _1706864) = hAPP(hAPP(c_List_Olist_OCons(_1706860), _1706866), _1706868)), _1706864 = hAPP(hAPP(c_List_Oappend(_1706860), c_List_OtakeWhile(_1706860, _1706862, _1706864)), hAPP(hAPP(c_List_Olist_OCons(_1706860), _1706866), _1706868)), -(hBOOL(hAPP(_1706862, _1706866)))], (46052 ^ _777081) ^ [_1707074, _1707076, _1707078] : [-(c_List_OdropWhile(_1707074, _1707076, _1707078) = hAPP(hAPP(c_List_Odrop(_1707074), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707074)), c_List_OtakeWhile(_1707074, _1707076, _1707078))), _1707078))], (46054 ^ _777081) ^ [_1707124, _1707126, _1707128, _1707130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707124), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707126)), c_List_OdropWhile(_1707126, _1707128, _1707130)))), -(hAPP(hAPP(c_List_Onth(_1707126), c_List_OdropWhile(_1707126, _1707128, _1707130)), _1707124) = hAPP(hAPP(c_List_Onth(_1707126), _1707130), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1707124), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707126)), c_List_OtakeWhile(_1707126, _1707128, _1707130)))))], (46060 ^ _777081) ^ [_1707311, _1707313, _1707315, _1707317, _1707319] : [class_Groups_Omonoid__add(_1707311), 46066 ^ _777081 : [(46067 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1707313), 46065 ^ [_1707311, _1707313, _1707315, _1707317, _1707319]), hAPP(c_List_Oset(_1707313), _1707315))))], (46069 ^ _777081) ^ [] : [hBOOL(hAPP(_1707317, 46065 ^ [_1707311, _1707313, _1707315, _1707317, _1707319]))], (46071 ^ _777081) ^ [] : [hAPP(_1707319, 46065 ^ [_1707311, _1707313, _1707315, _1707317, _1707319]) = c_Groups_Ozero__class_Ozero(_1707311)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1707311), hAPP(hAPP(c_List_Omap(_1707313, _1707311), _1707319), hAPP(c_List_Ofilter(_1707313, _1707317), _1707315))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1707311), hAPP(hAPP(c_List_Omap(_1707313, _1707311), _1707319), _1707315)))], (46075 ^ _777081) ^ [_1707702, _1707704] : [class_Orderings_Olinorder(_1707702), 46082 ^ _777081 : [(46083 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46080 ^ [_1707702, _1707704]), 46081 ^ [_1707702, _1707704])))], (46085 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46081 ^ [_1707702, _1707704]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707702)), _1707704))))], (46087 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707702), hAPP(hAPP(c_List_Onth(_1707702), _1707704), 46080 ^ [_1707702, _1707704])), hAPP(hAPP(c_List_Onth(_1707702), _1707704), 46081 ^ [_1707702, _1707704])))]], -(c_List_Olinorder__class_Osorted(_1707702, _1707704))], (46091 ^ _777081) ^ [_1708077, _1708079, _1708081] : [-(c_Enum_On__lists(_1708077, hAPP(c_Nat_OSuc, _1708079), _1708081) = c_List_Oconcat(tc_List_Olist(_1708077), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1708077), tc_List_Olist(tc_List_Olist(_1708077))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708077), tc_List_Olist(_1708077), tc_List_Olist(tc_List_Olist(_1708077))), hAPP(hAPP(c_COMBB(tc_fun(_1708077, tc_List_Olist(_1708077)), tc_fun(tc_List_Olist(_1708077), tc_List_Olist(tc_List_Olist(_1708077))), tc_List_Olist(_1708077)), c_List_Omap(_1708077, tc_List_Olist(_1708077))), hAPP(c_COMBC(_1708077, tc_List_Olist(_1708077), tc_List_Olist(_1708077)), c_List_Olist_OCons(_1708077)))), _1708081)), c_Enum_On__lists(_1708077, _1708079, _1708081))))], (46093 ^ _777081) ^ [_1708197, _1708199] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1708197))), c_Enum_Osublists(_1708197, _1708199)) = 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(_1708197)), _1708199)))], (46095 ^ _777081) ^ [_1708244, _1708246, _1708248] : [hBOOL(hAPP(c_List_Odistinct(_1708244), _1708246)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1708244)), c_Enum_On__lists(_1708244, _1708248, _1708246))))], (46101 ^ _777081) ^ [_1708351, _1708353] : [hBOOL(hAPP(c_List_Odistinct(_1708351), _1708353)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1708351, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1708351), tc_fun(_1708351, tc_HOL_Obool)), c_List_Oset(_1708351)), c_Enum_Osublists(_1708351, _1708353)))))], (46107 ^ _777081) ^ [_1708488, _1708490, _1708492] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1708488))), c_Enum_On__lists(_1708488, _1708490, _1708492)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708488)), _1708492)), _1708490))], (46109 ^ _777081) ^ [_1708541, _1708543, _1708545, _1708547] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1708541)), _1708543), hAPP(c_List_Oset(tc_List_Olist(_1708541)), c_Enum_On__lists(_1708541, _1708545, _1708547)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708541)), _1708543) = _1708545)], (46115 ^ _777081) ^ [_1708676, _1708678] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1708676), tc_fun(_1708676, tc_HOL_Obool), c_List_Oset(_1708676)), hAPP(c_List_Oset(tc_List_Olist(_1708676)), c_Enum_Osublists(_1708676, _1708678))) = hAPP(c_Set_OPow(_1708676), hAPP(c_List_Oset(_1708676), _1708678)))], (46117 ^ _777081) ^ [_1708735] : [-(c_Enum_Osublists(_1708735, c_List_Olist_ONil(_1708735)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708735)), c_List_Olist_ONil(_1708735)), c_List_Olist_ONil(tc_List_Olist(_1708735))))], (46119 ^ _777081) ^ [_1708779, _1708781] : [-(c_Enum_On__lists(_1708779, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1708781) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708779)), c_List_Olist_ONil(_1708779)), c_List_Olist_ONil(tc_List_Olist(_1708779))))], (46121 ^ _777081) ^ [_1708833, _1708835] : [_1708833 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1708835, _1708833, c_List_Olist_ONil(_1708835)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708835)), c_List_Olist_ONil(_1708835)), c_List_Olist_ONil(tc_List_Olist(_1708835))))], (46127 ^ _777081) ^ [_1708948, _1708950] : [-(_1708948 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1708950, _1708948, c_List_Olist_ONil(_1708950)) = c_List_Olist_ONil(tc_List_Olist(_1708950)))], (46133 ^ _777081) ^ [_1708996, _1708998, _1709000] : [-(c_Enum_Osublists(_1708996, hAPP(hAPP(c_List_Olist_OCons(_1708996), _1708998), _1709000)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1708996)), tc_List_Olist(tc_List_Olist(_1708996))), c_Enum_Osublists(_1708996, _1709000)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1708996)), tc_List_Olist(tc_List_Olist(_1708996)), tc_List_Olist(tc_List_Olist(_1708996))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1708996)), tc_fun(tc_List_Olist(tc_List_Olist(_1708996)), tc_List_Olist(tc_List_Olist(_1708996))), tc_List_Olist(tc_List_Olist(_1708996))), c_List_Oappend(tc_List_Olist(_1708996))), hAPP(c_List_Omap(tc_List_Olist(_1708996), tc_List_Olist(_1708996)), hAPP(c_List_Olist_OCons(_1708996), _1708998)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1708996))))))], (46135 ^ _777081) ^ [_1709130, _1709132, _1709134] : [-(hAPP(c_List_Oset(tc_List_Olist(_1709130)), c_Enum_On__lists(_1709130, _1709132, _1709134)) = hAPP(c_Set_OCollect(tc_List_Olist(_1709130)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1709130), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1709130)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1709130), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1709130)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1709130)))), _1709132))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1709130), tc_fun(_1709130, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1709130, tc_HOL_Obool), tc_fun(tc_fun(_1709130, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1709130)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1709130, tc_HOL_Obool))), c_List_Oset(_1709130))), hAPP(c_List_Oset(_1709130), _1709134)))))], (46137 ^ _777081) ^ [_1709275, _1709277, _1709279, _1709281, _1709283] : [-(c_Enum_Oproduct(_1709275, _1709277, hAPP(hAPP(c_List_Olist_OCons(_1709275), _1709279), _1709281), _1709283) = hAPP(hAPP(c_List_Oappend(tc_prod(_1709275, _1709277)), hAPP(hAPP(c_List_Omap(_1709277, tc_prod(_1709275, _1709277)), hAPP(c_Product__Type_OPair(_1709275, _1709277), _1709279)), _1709283)), c_Enum_Oproduct(_1709275, _1709277, _1709281, _1709283)))], (46139 ^ _777081) ^ [_1709353, _1709355] : [-(c_Enum_Oenum__the(_1709353, _1709355) = c_HOL_OThe(_1709353, _1709355))], (46141 ^ _777081) ^ [_1709384, _1709386, _1709388] : [-(c_Enum_Oproduct(_1709384, _1709386, c_List_Olist_ONil(_1709384), _1709388) = c_List_Olist_ONil(tc_prod(_1709384, _1709386)))], (46143 ^ _777081) ^ [_1709423, _1709425, _1709427, _1709429] : [hBOOL(hAPP(c_List_Odistinct(_1709423), _1709425)), hBOOL(hAPP(c_List_Odistinct(_1709427), _1709429)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1709423, _1709427)), c_Enum_Oproduct(_1709423, _1709427, _1709425, _1709429))))], (46153 ^ _777081) ^ [_1709600, _1709602, _1709604, _1709606] : [-(hAPP(c_List_Oset(tc_prod(_1709600, _1709602)), c_Enum_Oproduct(_1709600, _1709602, _1709604, _1709606)) = hAPP(hAPP(c_Product__Type_OSigma(_1709600, _1709602), hAPP(c_List_Oset(_1709600), _1709604)), hAPP(c_COMBK(tc_fun(_1709602, tc_HOL_Obool), _1709600), hAPP(c_List_Oset(_1709602), _1709606))))], (46155 ^ _777081) ^ [_1709670, _1709672, _1709674, _1709676] : [class_Enum_Oenum(_1709670), class_Enum_Oenum(_1709672), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709672)), _1709674) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709670)), c_Enum_Oenum__class_Oenum(_1709670)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709672)), _1709676) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709670)), c_Enum_Oenum__class_Oenum(_1709670)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1709672), _1709672, _1709670, c_Option_Othe(_1709672)), hAPP(c_Map_Omap__of(_1709670, _1709672), hAPP(hAPP(c_List_Ozip(_1709670, _1709672), c_Enum_Oenum__class_Oenum(_1709670)), _1709674))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1709672), _1709672, _1709670, c_Option_Othe(_1709672)), hAPP(c_Map_Omap__of(_1709670, _1709672), hAPP(hAPP(c_List_Ozip(_1709670, _1709672), c_Enum_Oenum__class_Oenum(_1709670)), _1709676))), -(_1709674 = _1709676)], (46177 ^ _777081) ^ [_1710153, _1710155] : [class_Orderings_Olinorder(_1710153), -(c_List_Olinorder__class_Osort__key(_1710153, _1710153, c_COMBI(_1710153), _1710155) = hAPP(c_List_Ofoldl(tc_List_Olist(_1710153), _1710153, hAPP(c_COMBC(_1710153, tc_List_Olist(_1710153), tc_List_Olist(_1710153)), c_List_Olinorder__class_Oinsort__key(_1710153, _1710153, c_COMBI(_1710153))), c_List_Olist_ONil(_1710153)), _1710155))], (46183 ^ _777081) ^ [_1710300, _1710302] : [-(c_Enum_Oenum__class_Oenum(tc_prod(_1710300, _1710302)) = c_Enum_Oproduct(_1710300, _1710302, c_Enum_Oenum__class_Oenum(_1710300), c_Enum_Oenum__class_Oenum(_1710302))), class_Enum_Oenum(_1710300), class_Enum_Oenum(_1710302)], (46193 ^ _777081) ^ [_1710453] : [class_Enum_Oenum(_1710453), -(hBOOL(hAPP(c_List_Odistinct(_1710453), c_Enum_Oenum__class_Oenum(_1710453))))], (46199 ^ _777081) ^ [_1710538] : [class_Enum_Oenum(_1710538), -(c_Enum_Oenum__class_Oenum(tc_Option_Ooption(_1710538)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(_1710538)), c_Option_Ooption_ONone(_1710538)), hAPP(hAPP(c_List_Omap(_1710538, tc_Option_Ooption(_1710538)), c_Option_Ooption_OSome(_1710538)), c_Enum_Oenum__class_Oenum(_1710538))))], (46205 ^ _777081) ^ [_1710673, _1710675] : [-(c_Enum_Oenum__class_Oenum(tc_sum(_1710673, _1710675)) = hAPP(hAPP(c_List_Oappend(tc_sum(_1710673, _1710675)), hAPP(hAPP(c_List_Omap(_1710673, tc_sum(_1710673, _1710675)), c_Sum__Type_OInl(_1710673, _1710675)), c_Enum_Oenum__class_Oenum(_1710673))), hAPP(hAPP(c_List_Omap(_1710675, tc_sum(_1710673, _1710675)), c_Sum__Type_OInr(_1710675, _1710673)), c_Enum_Oenum__class_Oenum(_1710675)))), class_Enum_Oenum(_1710673), class_Enum_Oenum(_1710675)], (46215 ^ _777081) ^ [_1710898, _1710900, _1710902, _1710904] : [class_Orderings_Olinorder(_1710898), 46218 ^ _777081 : [(46219 ^ _777081) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1710900), c_List_Olinorder__class_Osort__key(_1710900, _1710898, _1710902, _1710904))), -(hBOOL(hAPP(c_List_Odistinct(_1710900), _1710904)))], (46225 ^ _777081) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1710900), _1710904)), -(hBOOL(hAPP(c_List_Odistinct(_1710900), c_List_Olinorder__class_Osort__key(_1710900, _1710898, _1710902, _1710904))))]]], (46231 ^ _777081) ^ [_1711154, _1711156, _1711158, _1711160, _1711162] : [class_Orderings_Olinorder(_1711154), -(hAPP(c_List_Ofilter(_1711156, _1711158), c_List_Olinorder__class_Osort__key(_1711156, _1711154, _1711160, _1711162)) = c_List_Olinorder__class_Osort__key(_1711156, _1711154, _1711160, hAPP(c_List_Ofilter(_1711156, _1711158), _1711162)))], (46237 ^ _777081) ^ [_1711279, _1711281, _1711283, _1711285] : [class_Orderings_Olinorder(_1711279), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711281)), c_List_Olinorder__class_Osort__key(_1711281, _1711279, _1711283, _1711285)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711281)), _1711285))], (46243 ^ _777081) ^ [_1711396, _1711398] : [class_Orderings_Olinorder(_1711396), -(c_List_Olinorder__class_Osorted(_1711396, c_List_Olinorder__class_Osort__key(_1711396, _1711396, c_COMBI(_1711396), _1711398)))], (46249 ^ _777081) ^ [_1711485, _1711487, _1711489] : [class_Orderings_Olinorder(_1711485), -(c_List_Olinorder__class_Osort__key(_1711487, _1711485, _1711489, c_List_Olist_ONil(_1711487)) = c_List_Olist_ONil(_1711487))], (46255 ^ _777081) ^ [_1711580, _1711582, _1711584, _1711586] : [class_Orderings_Olinorder(_1711580), -(hAPP(c_List_Oset(_1711582), c_List_Olinorder__class_Osort__key(_1711582, _1711580, _1711584, _1711586)) = hAPP(c_List_Oset(_1711582), _1711586))], (46261 ^ _777081) ^ [_1711689, _1711691] : [class_Enum_Oenum(_1711689), -(hBOOL(hAPP(hAPP(c_member(_1711689), _1711691), hAPP(c_List_Oset(_1711689), c_Enum_Oenum__class_Oenum(_1711689)))))], (46267 ^ _777081) ^ [_1711792] : [class_Enum_Oenum(_1711792), -(c_Orderings_Otop__class_Otop(tc_fun(_1711792, tc_HOL_Obool)) = hAPP(c_List_Oset(_1711792), c_Enum_Oenum__class_Oenum(_1711792)))], (46273 ^ _777081) ^ [_1711889] : [class_Enum_Oenum(_1711889), -(hAPP(c_List_Oset(_1711889), c_Enum_Oenum__class_Oenum(_1711889)) = c_Orderings_Otop__class_Otop(tc_fun(_1711889, tc_HOL_Obool)))], (46279 ^ _777081) ^ [_1711986, _1711988, _1711990, _1711992] : [class_Orderings_Olinorder(_1711986), -(c_List_Olinorder__class_Osorted(_1711986, hAPP(hAPP(c_List_Omap(_1711988, _1711986), _1711990), c_List_Olinorder__class_Osort__key(_1711988, _1711986, _1711990, _1711992))))], (46285 ^ _777081) ^ [_1712093, _1712095, _1712097, _1712099, _1712101] : [class_Orderings_Olinorder(_1712093), -(c_List_Olinorder__class_Osort__key(_1712095, _1712093, _1712097, hAPP(hAPP(c_List_Olist_OCons(_1712095), _1712099), _1712101)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712095, _1712093, _1712097), _1712099), c_List_Olinorder__class_Osort__key(_1712095, _1712093, _1712097, _1712101)))], (46291 ^ _777081) ^ [_1712230, _1712232] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1712230, _1712232)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1712232), tc_fun(_1712230, _1712232)), hAPP(hAPP(c_COMBB(tc_fun(_1712230, tc_Option_Ooption(_1712232)), tc_fun(_1712230, _1712232), tc_List_Olist(_1712232)), c_Fun_Ocomp(tc_Option_Ooption(_1712232), _1712232, _1712230, c_Option_Othe(_1712232))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1712230, _1712232)), tc_fun(_1712230, tc_Option_Ooption(_1712232)), tc_List_Olist(_1712232)), c_Map_Omap__of(_1712230, _1712232)), hAPP(c_List_Ozip(_1712230, _1712232), c_Enum_Oenum__class_Oenum(_1712230))))), c_Enum_On__lists(_1712232, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712230)), c_Enum_Oenum__class_Oenum(_1712230)), c_Enum_Oenum__class_Oenum(_1712232)))), class_Enum_Oenum(_1712230), class_HOL_Oequal(_1712230), class_Enum_Oenum(_1712232)], (46305 ^ _777081) ^ [_1712597, _1712599] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1712597, _1712599)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1712599), tc_fun(_1712597, _1712599)), hAPP(hAPP(c_COMBB(tc_fun(_1712597, tc_Option_Ooption(_1712599)), tc_fun(_1712597, _1712599), tc_List_Olist(_1712599)), c_Fun_Ocomp(tc_Option_Ooption(_1712599), _1712599, _1712597, c_Option_Othe(_1712599))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1712597, _1712599)), tc_fun(_1712597, tc_Option_Ooption(_1712599)), tc_List_Olist(_1712599)), c_Map_Omap__of(_1712597, _1712599)), hAPP(c_List_Ozip(_1712597, _1712599), c_Enum_Oenum__class_Oenum(_1712597))))), c_Enum_On__lists(_1712599, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712597)), c_Enum_Oenum__class_Oenum(_1712597)), c_Enum_Oenum__class_Oenum(_1712599)))), class_Enum_Oenum(_1712597), class_Enum_Oenum(_1712599)], (46315 ^ _777081) ^ [_1712914, _1712916] : [class_Orderings_Olinorder(_1712914), -(c_List_Olinorder__class_Osorted__list__of__set(_1712914, hAPP(c_List_Oset(_1712914), _1712916)) = c_List_Olinorder__class_Osort__key(_1712914, _1712914, c_COMBI(_1712914), c_List_Oremdups(_1712914, _1712916)))], (46321 ^ _777081) ^ [_1713025, _1713027, _1713029] : [class_Enum_Oenum(_1713025), 46324 ^ _777081 : [(46335 ^ _777081) ^ [] : [46337 ^ _777081 : [(46338 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1713025)), 46336 ^ [_1713025, _1713027, _1713029]), hAPP(c_List_Oset(tc_List_Olist(_1713025)), c_Enum_On__lists(_1713025, _1713029, c_Enum_Oenum__class_Oenum(_1713025))))))], (46340 ^ _777081) ^ [] : [hBOOL(hAPP(_1713027, 46336 ^ [_1713025, _1713027, _1713029]))]], -(c_Enum_Oall__n__lists(_1713025, _1713027, _1713029))], (46325 ^ _777081) ^ [] : [c_Enum_Oall__n__lists(_1713025, _1713027, _1713029), 46328 ^ _777081 : [(46329 ^ _777081) ^ [_1713175] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1713025)), _1713175), hAPP(c_List_Oset(tc_List_Olist(_1713025)), c_Enum_On__lists(_1713025, _1713029, c_Enum_Oenum__class_Oenum(_1713025))))), -(hBOOL(hAPP(_1713027, _1713175)))]]]]], (46344 ^ _777081) ^ [_1713466, _1713468, _1713470] : [class_Enum_Oenum(_1713466), 46347 ^ _777081 : [(46348 ^ _777081) ^ [] : [c_Enum_Oex__n__lists(_1713466, _1713468, _1713470), 46352 ^ _777081 : [(46353 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1713466)), 46351 ^ [_1713466, _1713468, _1713470]), hAPP(c_List_Oset(tc_List_Olist(_1713466)), c_Enum_On__lists(_1713466, _1713470, c_Enum_Oenum__class_Oenum(_1713466))))))], (46355 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1713468, 46351 ^ [_1713466, _1713468, _1713470])))]]], (46357 ^ _777081) ^ [] : [-(c_Enum_Oex__n__lists(_1713466, _1713468, _1713470)), 46358 ^ _777081 : [(46359 ^ _777081) ^ [_1713722] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1713466)), _1713722), hAPP(c_List_Oset(tc_List_Olist(_1713466)), c_Enum_On__lists(_1713466, _1713470, c_Enum_Oenum__class_Oenum(_1713466))))), hBOOL(hAPP(_1713468, _1713722))]]]]], (46367 ^ _777081) ^ [_1713885, _1713887, _1713889] : [class_Enum_Oenum(_1713885), class_Enum_Oenum(_1713887), 46374 ^ _777081 : [(46375 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1713887, _1713885)), _1713889)), -(c_Enum_Oall__n__lists(_1713885, hAPP(hAPP(c_COMBB(tc_fun(_1713887, _1713885), tc_HOL_Obool, tc_List_Olist(_1713885)), _1713889), hAPP(hAPP(c_COMBB(tc_fun(_1713887, tc_Option_Ooption(_1713885)), tc_fun(_1713887, _1713885), tc_List_Olist(_1713885)), c_Fun_Ocomp(tc_Option_Ooption(_1713885), _1713885, _1713887, c_Option_Othe(_1713885))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1713887, _1713885)), tc_fun(_1713887, tc_Option_Ooption(_1713885)), tc_List_Olist(_1713885)), c_Map_Omap__of(_1713887, _1713885)), hAPP(c_List_Ozip(_1713887, _1713885), c_Enum_Oenum__class_Oenum(_1713887))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713887)), c_Enum_Oenum__class_Oenum(_1713887))))], (46381 ^ _777081) ^ [] : [c_Enum_Oall__n__lists(_1713885, hAPP(hAPP(c_COMBB(tc_fun(_1713887, _1713885), tc_HOL_Obool, tc_List_Olist(_1713885)), _1713889), hAPP(hAPP(c_COMBB(tc_fun(_1713887, tc_Option_Ooption(_1713885)), tc_fun(_1713887, _1713885), tc_List_Olist(_1713885)), c_Fun_Ocomp(tc_Option_Ooption(_1713885), _1713885, _1713887, c_Option_Othe(_1713885))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1713887, _1713885)), tc_fun(_1713887, tc_Option_Ooption(_1713885)), tc_List_Olist(_1713885)), c_Map_Omap__of(_1713887, _1713885)), hAPP(c_List_Ozip(_1713887, _1713885), c_Enum_Oenum__class_Oenum(_1713887))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713887)), c_Enum_Oenum__class_Oenum(_1713887))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1713887, _1713885)), _1713889)))]]], (46387 ^ _777081) ^ [_1714432, _1714434, _1714436] : [class_Enum_Oenum(_1714432), class_Enum_Oenum(_1714434), 46394 ^ _777081 : [(46395 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1714434, _1714432)), _1714436)), -(c_Enum_Oex__n__lists(_1714432, hAPP(hAPP(c_COMBB(tc_fun(_1714434, _1714432), tc_HOL_Obool, tc_List_Olist(_1714432)), _1714436), hAPP(hAPP(c_COMBB(tc_fun(_1714434, tc_Option_Ooption(_1714432)), tc_fun(_1714434, _1714432), tc_List_Olist(_1714432)), c_Fun_Ocomp(tc_Option_Ooption(_1714432), _1714432, _1714434, c_Option_Othe(_1714432))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1714434, _1714432)), tc_fun(_1714434, tc_Option_Ooption(_1714432)), tc_List_Olist(_1714432)), c_Map_Omap__of(_1714434, _1714432)), hAPP(c_List_Ozip(_1714434, _1714432), c_Enum_Oenum__class_Oenum(_1714434))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714434)), c_Enum_Oenum__class_Oenum(_1714434))))], (46401 ^ _777081) ^ [] : [c_Enum_Oex__n__lists(_1714432, hAPP(hAPP(c_COMBB(tc_fun(_1714434, _1714432), tc_HOL_Obool, tc_List_Olist(_1714432)), _1714436), hAPP(hAPP(c_COMBB(tc_fun(_1714434, tc_Option_Ooption(_1714432)), tc_fun(_1714434, _1714432), tc_List_Olist(_1714432)), c_Fun_Ocomp(tc_Option_Ooption(_1714432), _1714432, _1714434, c_Option_Othe(_1714432))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1714434, _1714432)), tc_fun(_1714434, tc_Option_Ooption(_1714432)), tc_List_Olist(_1714432)), c_Map_Omap__of(_1714434, _1714432)), hAPP(c_List_Ozip(_1714434, _1714432), c_Enum_Oenum__class_Oenum(_1714434))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714434)), c_Enum_Oenum__class_Oenum(_1714434))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1714434, _1714432)), _1714436)))]]], (46407 ^ _777081) ^ [_1714979, _1714981] : [class_Enum_Oenum(_1714979), 46410 ^ _777081 : [(46411 ^ _777081) ^ [] : [hBOOL(hAPP(_1714981, 46412 ^ [_1714979, _1714981])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1714979), _1714981)))], (46418 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1714979), _1714981)), 46421 ^ _777081 : [(46422 ^ _777081) ^ [_1715197] : [-(hBOOL(hAPP(_1714981, _1715197)))]]]]], (46424 ^ _777081) ^ [_1715232, _1715234] : [class_Enum_Oenum(_1715232), 46427 ^ _777081 : [(46428 ^ _777081) ^ [] : [46429 ^ _777081 : [(46430 ^ _777081) ^ [_1715334] : [hBOOL(hAPP(_1715234, _1715334))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1715232), _1715234)))], (46434 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1715232), _1715234)), -(hBOOL(hAPP(_1715234, 46437 ^ [_1715232, _1715234])))]]], (46441 ^ _777081) ^ [_1715475, _1715477] : [class_Enum_Oenum(_1715475), 46444 ^ _777081 : [(46445 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1715475), _1715477)), 46448 ^ _777081 : [(46449 ^ _777081) ^ [_1715601] : [-(hBOOL(hAPP(_1715477, _1715601)))]]], (46451 ^ _777081) ^ [] : [hBOOL(hAPP(_1715477, 46452 ^ [_1715475, _1715477])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1715475), _1715477)))]]], (46458 ^ _777081) ^ [_1715728, _1715730] : [class_Enum_Oenum(_1715728), 46461 ^ _777081 : [(46462 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1715728), _1715730)), -(hBOOL(hAPP(_1715730, 46465 ^ [_1715728, _1715730])))], (46469 ^ _777081) ^ [] : [46470 ^ _777081 : [(46471 ^ _777081) ^ [_1715908] : [hBOOL(hAPP(_1715730, _1715908))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1715728), _1715730)))]]], (46475 ^ _777081) ^ [_1715971, _1715973] : [class_Enum_Oenum(_1715971), 46478 ^ _777081 : [(46489 ^ _777081) ^ [] : [46490 ^ _777081 : [(46491 ^ _777081) ^ [] : [hBOOL(hAPP(_1715973, c_Option_Ooption_ONone(_1715971)))], (46493 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1715971), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1715971), tc_HOL_Obool, _1715971), _1715973), c_Option_Ooption_OSome(_1715971))))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1715971)), _1715973)))], (46479 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1715971)), _1715973)), -(hBOOL(hAPP(_1715973, c_Option_Ooption_ONone(_1715971)))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1715971), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1715971), tc_HOL_Obool, _1715971), _1715973), c_Option_Ooption_OSome(_1715971)))))]]], (46497 ^ _777081) ^ [_1716305, _1716307] : [class_Enum_Oenum(_1716305), 46500 ^ _777081 : [(46501 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1716305)), _1716307)), 46504 ^ _777081 : [(46505 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1716307, c_Option_Ooption_ONone(_1716305))))], (46507 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1716305), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1716305), tc_HOL_Obool, _1716305), _1716307), c_Option_Ooption_OSome(_1716305)))))]]], (46509 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1716305)), _1716307))), hBOOL(hAPP(_1716307, c_Option_Ooption_ONone(_1716305))), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1716305), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1716305), tc_HOL_Obool, _1716305), _1716307), c_Option_Ooption_OSome(_1716305))))]]], (46519 ^ _777081) ^ [_1716666, _1716668, _1716670] : [class_Enum_Oenum(_1716666), class_Enum_Oenum(_1716668), 46526 ^ _777081 : [(46537 ^ _777081) ^ [] : [46538 ^ _777081 : [(46539 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1716666), hAPP(hAPP(c_COMBB(tc_sum(_1716666, _1716668), tc_HOL_Obool, _1716666), _1716670), c_Sum__Type_OInl(_1716666, _1716668))))], (46541 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1716668), hAPP(hAPP(c_COMBB(tc_sum(_1716666, _1716668), tc_HOL_Obool, _1716668), _1716670), c_Sum__Type_OInr(_1716668, _1716666))))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_sum(_1716666, _1716668)), _1716670)))], (46527 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_sum(_1716666, _1716668)), _1716670)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1716666), hAPP(hAPP(c_COMBB(tc_sum(_1716666, _1716668), tc_HOL_Obool, _1716666), _1716670), c_Sum__Type_OInl(_1716666, _1716668))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1716668), hAPP(hAPP(c_COMBB(tc_sum(_1716666, _1716668), tc_HOL_Obool, _1716668), _1716670), c_Sum__Type_OInr(_1716668, _1716666)))))]]], (46545 ^ _777081) ^ [_1717117, _1717119, _1717121] : [class_Enum_Oenum(_1717117), class_Enum_Oenum(_1717119), 46552 ^ _777081 : [(46553 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_sum(_1717117, _1717119)), _1717121)), 46556 ^ _777081 : [(46557 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1717117), hAPP(hAPP(c_COMBB(tc_sum(_1717117, _1717119), tc_HOL_Obool, _1717117), _1717121), c_Sum__Type_OInl(_1717117, _1717119)))))], (46559 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1717119), hAPP(hAPP(c_COMBB(tc_sum(_1717117, _1717119), tc_HOL_Obool, _1717119), _1717121), c_Sum__Type_OInr(_1717119, _1717117)))))]]], (46561 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_sum(_1717117, _1717119)), _1717121))), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1717117), hAPP(hAPP(c_COMBB(tc_sum(_1717117, _1717119), tc_HOL_Obool, _1717117), _1717121), c_Sum__Type_OInl(_1717117, _1717119)))), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1717119), hAPP(hAPP(c_COMBB(tc_sum(_1717117, _1717119), tc_HOL_Obool, _1717119), _1717121), c_Sum__Type_OInr(_1717119, _1717117))))]]], (46571 ^ _777081) ^ [_1717597, _1717599, _1717601] : [class_Enum_Oenum(_1717597), class_Enum_Oenum(_1717599), 46578 ^ _777081 : [(46579 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1717599, _1717597)), _1717601)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1717599), hAPP(hAPP(c_COMBB(tc_fun(_1717597, tc_HOL_Obool), tc_HOL_Obool, _1717599), c_Enum_Oenum__class_Oenum__ex(_1717597)), hAPP(hAPP(c_COMBB(tc_fun(_1717597, tc_prod(_1717599, _1717597)), tc_fun(_1717597, tc_HOL_Obool), _1717599), hAPP(c_COMBB(tc_prod(_1717599, _1717597), tc_HOL_Obool, _1717597), _1717601)), c_Product__Type_OPair(_1717599, _1717597))))))], (46585 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1717599), hAPP(hAPP(c_COMBB(tc_fun(_1717597, tc_HOL_Obool), tc_HOL_Obool, _1717599), c_Enum_Oenum__class_Oenum__ex(_1717597)), hAPP(hAPP(c_COMBB(tc_fun(_1717597, tc_prod(_1717599, _1717597)), tc_fun(_1717597, tc_HOL_Obool), _1717599), hAPP(c_COMBB(tc_prod(_1717599, _1717597), tc_HOL_Obool, _1717597), _1717601)), c_Product__Type_OPair(_1717599, _1717597))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1717599, _1717597)), _1717601)))]]], (46591 ^ _777081) ^ [_1718036, _1718038, _1718040] : [class_Enum_Oenum(_1718036), class_Enum_Oenum(_1718038), 46598 ^ _777081 : [(46599 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1718038, _1718036)), _1718040)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1718038), hAPP(hAPP(c_COMBB(tc_fun(_1718036, tc_HOL_Obool), tc_HOL_Obool, _1718038), c_Enum_Oenum__class_Oenum__all(_1718036)), hAPP(hAPP(c_COMBB(tc_fun(_1718036, tc_prod(_1718038, _1718036)), tc_fun(_1718036, tc_HOL_Obool), _1718038), hAPP(c_COMBB(tc_prod(_1718038, _1718036), tc_HOL_Obool, _1718036), _1718040)), c_Product__Type_OPair(_1718038, _1718036))))))], (46605 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1718038), hAPP(hAPP(c_COMBB(tc_fun(_1718036, tc_HOL_Obool), tc_HOL_Obool, _1718038), c_Enum_Oenum__class_Oenum__all(_1718036)), hAPP(hAPP(c_COMBB(tc_fun(_1718036, tc_prod(_1718038, _1718036)), tc_fun(_1718036, tc_HOL_Obool), _1718038), hAPP(c_COMBB(tc_prod(_1718038, _1718036), tc_HOL_Obool, _1718036), _1718040)), c_Product__Type_OPair(_1718038, _1718036))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1718038, _1718036)), _1718040)))]]], (46611 ^ _777081) ^ [_1718475, _1718477, _1718479, _1718481] : [class_Orderings_Oorder(_1718475), class_Enum_Oenum(_1718477), 46618 ^ _777081 : [(46619 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1718477, _1718475)), _1718479), _1718481)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1718477), hAPP(hAPP(c_COMBS(_1718477, _1718475, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1718475, tc_fun(_1718475, tc_HOL_Obool), _1718477), c_Orderings_Oord__class_Oless__eq(_1718475)), _1718479)), _1718481))))], (46625 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1718477), hAPP(hAPP(c_COMBS(_1718477, _1718475, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1718475, tc_fun(_1718475, tc_HOL_Obool), _1718477), c_Orderings_Oord__class_Oless__eq(_1718475)), _1718479)), _1718481))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1718477, _1718475)), _1718479), _1718481)))]]], (46631 ^ _777081) ^ [_1718865, _1718867, _1718869, _1718871] : [class_Orderings_Oorder(_1718865), class_Enum_Oenum(_1718867), 46638 ^ _777081 : [(46639 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1718867, _1718865)), _1718869), _1718871)), 46642 ^ _777081 : [(46643 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1718867, _1718865)), _1718869), _1718871)))], (46645 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1718867), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1718867), c_fNot), hAPP(hAPP(c_COMBS(_1718867, _1718865, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1718865, tc_fun(_1718865, tc_HOL_Obool), _1718867), c_fequal), _1718869)), _1718871)))))]]], (46647 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1718867, _1718865)), _1718869), _1718871))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1718867, _1718865)), _1718869), _1718871)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1718867), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1718867), c_fNot), hAPP(hAPP(c_COMBS(_1718867, _1718865, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1718865, tc_fun(_1718865, tc_HOL_Obool), _1718867), c_fequal), _1718869)), _1718871))))]]], (46657 ^ _777081) ^ [_1719385, _1719387, _1719389] : [class_Enum_Oenum(_1719385), class_Enum_Oenum(_1719387), class_HOL_Oequal(_1719387), 46668 ^ _777081 : [(46669 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1719387, _1719385)), _1719389)), -(c_Enum_Oex__n__lists(_1719385, hAPP(hAPP(c_COMBB(tc_fun(_1719387, _1719385), tc_HOL_Obool, tc_List_Olist(_1719385)), _1719389), hAPP(hAPP(c_COMBB(tc_fun(_1719387, tc_Option_Ooption(_1719385)), tc_fun(_1719387, _1719385), tc_List_Olist(_1719385)), c_Fun_Ocomp(tc_Option_Ooption(_1719385), _1719385, _1719387, c_Option_Othe(_1719385))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1719387, _1719385)), tc_fun(_1719387, tc_Option_Ooption(_1719385)), tc_List_Olist(_1719385)), c_Map_Omap__of(_1719387, _1719385)), hAPP(c_List_Ozip(_1719387, _1719385), c_Enum_Oenum__class_Oenum(_1719387))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719387)), c_Enum_Oenum__class_Oenum(_1719387))))], (46675 ^ _777081) ^ [] : [c_Enum_Oex__n__lists(_1719385, hAPP(hAPP(c_COMBB(tc_fun(_1719387, _1719385), tc_HOL_Obool, tc_List_Olist(_1719385)), _1719389), hAPP(hAPP(c_COMBB(tc_fun(_1719387, tc_Option_Ooption(_1719385)), tc_fun(_1719387, _1719385), tc_List_Olist(_1719385)), c_Fun_Ocomp(tc_Option_Ooption(_1719385), _1719385, _1719387, c_Option_Othe(_1719385))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1719387, _1719385)), tc_fun(_1719387, tc_Option_Ooption(_1719385)), tc_List_Olist(_1719385)), c_Map_Omap__of(_1719387, _1719385)), hAPP(c_List_Ozip(_1719387, _1719385), c_Enum_Oenum__class_Oenum(_1719387))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719387)), c_Enum_Oenum__class_Oenum(_1719387))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1719387, _1719385)), _1719389)))]]], (46681 ^ _777081) ^ [_1719986, _1719988, _1719990] : [class_Enum_Oenum(_1719986), class_Enum_Oenum(_1719988), class_HOL_Oequal(_1719988), 46692 ^ _777081 : [(46693 ^ _777081) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1719988, _1719986)), _1719990)), -(c_Enum_Oall__n__lists(_1719986, hAPP(hAPP(c_COMBB(tc_fun(_1719988, _1719986), tc_HOL_Obool, tc_List_Olist(_1719986)), _1719990), hAPP(hAPP(c_COMBB(tc_fun(_1719988, tc_Option_Ooption(_1719986)), tc_fun(_1719988, _1719986), tc_List_Olist(_1719986)), c_Fun_Ocomp(tc_Option_Ooption(_1719986), _1719986, _1719988, c_Option_Othe(_1719986))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1719988, _1719986)), tc_fun(_1719988, tc_Option_Ooption(_1719986)), tc_List_Olist(_1719986)), c_Map_Omap__of(_1719988, _1719986)), hAPP(c_List_Ozip(_1719988, _1719986), c_Enum_Oenum__class_Oenum(_1719988))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719988)), c_Enum_Oenum__class_Oenum(_1719988))))], (46699 ^ _777081) ^ [] : [c_Enum_Oall__n__lists(_1719986, hAPP(hAPP(c_COMBB(tc_fun(_1719988, _1719986), tc_HOL_Obool, tc_List_Olist(_1719986)), _1719990), hAPP(hAPP(c_COMBB(tc_fun(_1719988, tc_Option_Ooption(_1719986)), tc_fun(_1719988, _1719986), tc_List_Olist(_1719986)), c_Fun_Ocomp(tc_Option_Ooption(_1719986), _1719986, _1719988, c_Option_Othe(_1719986))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1719988, _1719986)), tc_fun(_1719988, tc_Option_Ooption(_1719986)), tc_List_Olist(_1719986)), c_Map_Omap__of(_1719988, _1719986)), hAPP(c_List_Ozip(_1719988, _1719986), c_Enum_Oenum__class_Oenum(_1719988))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719988)), c_Enum_Oenum__class_Oenum(_1719988))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1719988, _1719986)), _1719990)))]]], (46705 ^ _777081) ^ [_1720587, _1720589, _1720591, _1720593, _1720595, _1720597, _1720599, _1720601] : [c_Fun_Oinj__on(_1720587, _1720589, _1720591, _1720593), 46711 ^ _777081 : [(46712 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720595), 46710 ^ [_1720587, _1720589, _1720591, _1720593, _1720595, _1720597, _1720599, _1720601]), _1720597)))], (46714 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1720587, tc_HOL_Obool)), hAPP(_1720599, 46710 ^ [_1720587, _1720589, _1720591, _1720593, _1720595, _1720597, _1720599, _1720601])), _1720593))]], hBOOL(hAPP(hAPP(c_member(_1720595), _1720601), _1720597)), -(hAPP(c_Set_Oimage(_1720587, _1720589, _1720591), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1720595, tc_fun(_1720587, tc_HOL_Obool)), _1720597), _1720599)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1720595, tc_fun(_1720589, tc_HOL_Obool)), _1720597), hAPP(hAPP(c_COMBB(tc_fun(_1720587, tc_HOL_Obool), tc_fun(_1720589, tc_HOL_Obool), _1720595), c_Set_Oimage(_1720587, _1720589, _1720591)), _1720599)))], (46722 ^ _777081) ^ [_1721076, _1721078, _1721080, _1721082] : [class_Enum_Oenum(_1721076), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721078)), _1721080) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721076)), c_Enum_Oenum__class_Oenum(_1721076)), -(hAPP(hAPP(c_Map_Omap__of(_1721076, _1721078), hAPP(hAPP(c_List_Ozip(_1721076, _1721078), c_Enum_Oenum__class_Oenum(_1721076)), _1721080)), _1721082) = hAPP(c_Option_Ooption_OSome(_1721078), 46729 ^ [_1721076, _1721078, _1721080, _1721082]))], (46733 ^ _777081) ^ [_1721305, _1721307, _1721309] : [46735 ^ _777081 : [(46736 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1721305), 46734 ^ [_1721305, _1721307, _1721309]), hAPP(c_List_Oset(_1721305), c_List_OdropWhile(_1721305, _1721307, _1721309)))))], (46738 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1721307, 46734 ^ [_1721305, _1721307, _1721309])))]], -(c_List_OtakeWhile(_1721305, _1721307, _1721309) = hAPP(c_List_Ofilter(_1721305, _1721307), _1721309))], (46742 ^ _777081) ^ [_1721426, _1721428, _1721430, _1721432] : [c_Fun_Oinj__on(_1721426, _1721428, _1721430, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1721426, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1721426), tc_fun(_1721426, tc_HOL_Obool), c_List_Oset(_1721426)), _1721432))), -(c_Fun_Oinj__on(tc_List_Olist(_1721426), tc_List_Olist(_1721428), hAPP(c_List_Omap(_1721426, _1721428), _1721430), _1721432))], (46748 ^ _777081) ^ [_1721575, _1721577, _1721579, _1721581] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1721575, tc_HOL_Obool)), _1721577), _1721579)), hBOOL(hAPP(hAPP(c_member(_1721575), _1721581), _1721577)), -(hBOOL(hAPP(hAPP(c_member(_1721575), _1721581), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1721575, tc_HOL_Obool), _1721579))))], (46758 ^ _777081) ^ [_1721772, _1721774, _1721776, _1721778] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1721772, tc_fun(_1721774, tc_HOL_Obool)), _1721776), _1721778) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1721774, tc_HOL_Obool), hAPP(c_Set_Oimage(_1721772, tc_fun(_1721774, tc_HOL_Obool), _1721778), _1721776)))], (46760 ^ _777081) ^ [_1721829, _1721831, _1721833, _1721835] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1721829, tc_HOL_Obool), hAPP(c_Set_Oimage(_1721831, tc_fun(_1721829, tc_HOL_Obool), _1721833), _1721835)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1721831, tc_fun(_1721829, tc_HOL_Obool)), _1721835), _1721833))], (46762 ^ _777081) ^ [_1721886, _1721888, _1721890, _1721892] : [-(hAPP(c_Set_Oimage(_1721886, _1721888, _1721890), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1721886, tc_HOL_Obool), _1721892)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1721886, tc_HOL_Obool), tc_fun(_1721888, tc_HOL_Obool)), _1721892), c_Set_Oimage(_1721886, _1721888, _1721890)))], (46764 ^ _777081) ^ [_1721947, _1721949] : [-(hAPP(c_Relation_OField(_1721947), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1721947, _1721947), tc_HOL_Obool), _1721949)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1721947, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1721947, _1721947), tc_HOL_Obool), tc_fun(_1721947, tc_HOL_Obool), c_Relation_OField(_1721947)), _1721949)))], (46766 ^ _777081) ^ [_1722010, _1722012, _1722014, _1722016] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1722010, tc_fun(_1722012, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1722010, tc_HOL_Obool), _1722014)), _1722016) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1722010, tc_HOL_Obool), tc_fun(_1722012, tc_HOL_Obool)), _1722014), hAPP(hAPP(c_COMBC(tc_fun(_1722010, tc_HOL_Obool), tc_fun(_1722010, tc_fun(_1722012, tc_HOL_Obool)), tc_fun(_1722012, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1722010, tc_fun(_1722012, tc_HOL_Obool))), _1722016)))], (46768 ^ _777081) ^ [_1722100, _1722102, _1722104, _1722106] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1722100, tc_HOL_Obool), tc_fun(_1722102, tc_HOL_Obool)), _1722104), hAPP(hAPP(c_COMBC(tc_fun(_1722100, tc_HOL_Obool), tc_fun(_1722100, tc_fun(_1722102, tc_HOL_Obool)), tc_fun(_1722102, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1722100, tc_fun(_1722102, tc_HOL_Obool))), _1722106)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1722100, tc_fun(_1722102, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1722100, tc_HOL_Obool), _1722104)), _1722106))], (46780 ^ _777081) ^ [_1722476, _1722478, _1722480] : [46782 ^ _777081 : [(46783 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1722476, tc_HOL_Obool)), 46781 ^ [_1722476, _1722478, _1722480]), _1722478)))], (46785 ^ _777081) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1722476, tc_HOL_Obool)), 46781 ^ [_1722476, _1722478, _1722480]), _1722480) = c_Orderings_Obot__class_Obot(tc_fun(_1722476, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1722476, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1722476, tc_HOL_Obool), _1722478)), _1722480) = c_Orderings_Obot__class_Obot(tc_fun(_1722476, tc_HOL_Obool)))], (46770 ^ _777081) ^ [_1722208, _1722210, _1722212] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1722208, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1722208, tc_HOL_Obool), _1722210)), _1722212) = c_Orderings_Obot__class_Obot(tc_fun(_1722208, tc_HOL_Obool)), 46773 ^ _777081 : [(46774 ^ _777081) ^ [_1722343] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1722208, tc_HOL_Obool)), _1722343), _1722210)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1722208, tc_HOL_Obool)), _1722343), _1722212) = c_Orderings_Obot__class_Obot(tc_fun(_1722208, tc_HOL_Obool)))]]], (46789 ^ _777081) ^ [_1722739, _1722741, _1722743] : [class_Complete__Lattice_Ocomplete__lattice(_1722739), hBOOL(hAPP(hAPP(c_member(_1722739), _1722741), _1722743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1722739), _1722741), c_Complete__Lattice_OSup__class_OSup(_1722739, _1722743))))], (46799 ^ _777081) ^ [_1722904, _1722906, _1722908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1722904, tc_HOL_Obool), tc_HOL_Obool)), _1722906), _1722908)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1722904, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1722904, tc_HOL_Obool), _1722906)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1722904, tc_HOL_Obool), _1722908))))], (46805 ^ _777081) ^ [_1723053, _1723055, _1723057] : [class_Complete__Lattice_Ocomplete__lattice(_1723053), 46808 ^ _777081 : [(46819 ^ _777081) ^ [] : [46821 ^ _777081 : [(46822 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1723053), 46820 ^ [_1723053, _1723055, _1723057]), _1723055)))], (46824 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1723053), 46820 ^ [_1723053, _1723055, _1723057]), _1723057))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1723053), c_Complete__Lattice_OSup__class_OSup(_1723053, _1723055)), _1723057)))], (46809 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1723053), c_Complete__Lattice_OSup__class_OSup(_1723053, _1723055)), _1723057)), 46812 ^ _777081 : [(46813 ^ _777081) ^ [_1723211] : [hBOOL(hAPP(hAPP(c_member(_1723053), _1723211), _1723055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1723053), _1723211), _1723057)))]]]]], (46828 ^ _777081) ^ [_1723487, _1723489, _1723491] : [c_Equiv__Relations_Oequiv(_1723487, _1723489, _1723491), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1723487, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1723487), _1723489), _1723491)) = _1723489)], (46834 ^ _777081) ^ [_1723596, _1723598, _1723600] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1723596, tc_HOL_Obool)), _1723598), _1723600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1723596, tc_HOL_Obool)), _1723598), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1723596, tc_HOL_Obool), _1723600))))], (46840 ^ _777081) ^ [_1723727, _1723729] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1723727), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1723727, tc_HOL_Obool), _1723729))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1723727, tc_HOL_Obool)), _1723729)))], (46846 ^ _777081) ^ [_1723838] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1723838, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1723838, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1723838, tc_HOL_Obool)))], (46848 ^ _777081) ^ [_1723880, _1723882, _1723884] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1723880, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1723880, tc_HOL_Obool)), _1723882), _1723884)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1723880, tc_HOL_Obool)), _1723882), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1723880, tc_HOL_Obool), _1723884)))], (46850 ^ _777081) ^ [_1723941, _1723943] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1723941, tc_HOL_Obool), hAPP(c_Set_OPow(_1723941), _1723943)) = _1723943)], (46852 ^ _777081) ^ [_1723977, _1723979, _1723981] : [class_Complete__Lattice_Ocomplete__lattice(_1723977), class_Orderings_Olinorder(_1723977), 46859 ^ _777081 : [(46860 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1723977), _1723979), c_Complete__Lattice_OSup__class_OSup(_1723977, _1723981))), 46864 ^ _777081 : [(46865 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1723977), 46863 ^ [_1723977, _1723979, _1723981]), _1723981)))], (46867 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1723977), _1723979), 46863 ^ [_1723977, _1723979, _1723981])))]]], (46869 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1723977), _1723979), c_Complete__Lattice_OSup__class_OSup(_1723977, _1723981)))), 46870 ^ _777081 : [(46871 ^ _777081) ^ [_1724283] : [hBOOL(hAPP(hAPP(c_member(_1723977), _1724283), _1723981)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1723977), _1723979), _1724283))]]]]], (46879 ^ _777081) ^ [_1724437, _1724439] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1724437, tc_HOL_Obool), tc_HOL_Obool)), _1724439), hAPP(c_Set_OPow(_1724437), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1724437, tc_HOL_Obool), _1724439)))))], (46881 ^ _777081) ^ [_1724486, _1724488, _1724490] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1724486, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1724486, tc_HOL_Obool), tc_HOL_Obool)), _1724488), _1724490)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1724486, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1724486, tc_HOL_Obool), _1724488)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1724486, tc_HOL_Obool), _1724490)))], (46883 ^ _777081) ^ [_1724556] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1724556, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1724556, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1724556, tc_HOL_Obool)))], (46885 ^ _777081) ^ [_1724598, _1724600, _1724602] : [class_Complete__Lattice_Ocomplete__lattice(_1724598), -(c_Complete__Lattice_OSup__class_OSup(_1724598, hAPP(hAPP(c_Set_Oinsert(_1724598), _1724600), _1724602)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1724598), _1724600), c_Complete__Lattice_OSup__class_OSup(_1724598, _1724602)))], (46891 ^ _777081) ^ [_1724719, _1724721] : [class_Complete__Lattice_Ocomplete__lattice(_1724719), -(c_Complete__Lattice_OSup__class_OSup(_1724719, hAPP(hAPP(c_Set_Oinsert(_1724719), _1724721), c_Orderings_Obot__class_Obot(tc_fun(_1724719, tc_HOL_Obool)))) = _1724721)], (46897 ^ _777081) ^ [_1724826] : [class_Complete__Lattice_Ocomplete__lattice(_1724826), -(c_Complete__Lattice_OSup__class_OSup(_1724826, c_Orderings_Obot__class_Obot(tc_fun(_1724826, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1724826))], (46903 ^ _777081) ^ [_1724919] : [class_Complete__Lattice_Ocomplete__lattice(_1724919), -(c_Complete__Lattice_OSup__class_OSup(_1724919, c_Orderings_Otop__class_Otop(tc_fun(_1724919, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1724919))], (46909 ^ _777081) ^ [_1725012, _1725014, _1725016, _1725018] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1725012, _1725014), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725012, tc_HOL_Obool), _1725016)), _1725018) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1725012, tc_HOL_Obool), tc_fun(tc_prod(_1725012, _1725014), tc_HOL_Obool)), _1725016), hAPP(hAPP(c_COMBC(tc_fun(_1725012, tc_HOL_Obool), tc_fun(_1725012, tc_fun(_1725014, tc_HOL_Obool)), tc_fun(tc_prod(_1725012, _1725014), tc_HOL_Obool)), c_Product__Type_OSigma(_1725012, _1725014)), _1725018)))], (46911 ^ _777081) ^ [_1725102, _1725104, _1725106] : [-(hAPP(c_Relation_ODomain(_1725102, _1725104), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1725102, _1725104), tc_HOL_Obool), _1725106)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1725102, _1725104), tc_HOL_Obool), tc_fun(_1725102, tc_HOL_Obool)), _1725106), c_Relation_ODomain(_1725102, _1725104)))], (46913 ^ _777081) ^ [_1725165, _1725167, _1725169, _1725171] : [-(hAPP(c_Set_Ovimage(_1725165, _1725167, _1725169), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725167, tc_HOL_Obool), _1725171)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1725167, tc_HOL_Obool), tc_fun(_1725165, tc_HOL_Obool)), _1725171), c_Set_Ovimage(_1725165, _1725167, _1725169)))], (46915 ^ _777081) ^ [_1725226, _1725228, _1725230, _1725232] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1725226, tc_fun(_1725228, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725226, tc_HOL_Obool), _1725230)), _1725232) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1725226, tc_HOL_Obool), tc_fun(_1725228, tc_HOL_Obool)), _1725230), hAPP(hAPP(c_COMBC(tc_fun(_1725226, tc_HOL_Obool), tc_fun(_1725226, tc_fun(_1725228, tc_HOL_Obool)), tc_fun(_1725228, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1725226, tc_fun(_1725228, tc_HOL_Obool))), _1725232)))], (46917 ^ _777081) ^ [_1725316, _1725318, _1725320, _1725322] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1725316, tc_HOL_Obool), tc_fun(_1725318, tc_HOL_Obool)), _1725320), hAPP(hAPP(c_COMBC(tc_fun(_1725316, tc_HOL_Obool), tc_fun(_1725316, tc_fun(_1725318, tc_HOL_Obool)), tc_fun(_1725318, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1725316, tc_fun(_1725318, tc_HOL_Obool))), _1725322)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1725316, tc_fun(_1725318, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725316, tc_HOL_Obool), _1725320)), _1725322))], (46919 ^ _777081) ^ [_1725406, _1725408] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725406, tc_HOL_Obool), _1725408) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1725406, tc_HOL_Obool), tc_fun(_1725406, tc_HOL_Obool)), _1725408), c_COMBI(tc_fun(_1725406, tc_HOL_Obool))))], (46921 ^ _777081) ^ [_1725457, _1725459, _1725461] : [-(hAPP(c_Relation_ORange(_1725457, _1725459), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1725457, _1725459), tc_HOL_Obool), _1725461)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1725457, _1725459), tc_HOL_Obool), tc_fun(_1725459, tc_HOL_Obool)), _1725461), c_Relation_ORange(_1725457, _1725459)))], (46923 ^ _777081) ^ [_1725520, _1725522, _1725524] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1725520, tc_HOL_Obool)), _1725522), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725520, tc_HOL_Obool), _1725524)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1725520, tc_HOL_Obool), tc_fun(_1725520, tc_HOL_Obool)), _1725524), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1725520, tc_HOL_Obool)), _1725522)))], (46925 ^ _777081) ^ [_1725587, _1725589, _1725591] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1725587, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725587, tc_HOL_Obool), _1725589)), _1725591) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1725587, tc_HOL_Obool), tc_fun(_1725587, tc_HOL_Obool)), _1725589), hAPP(hAPP(c_COMBC(tc_fun(_1725587, tc_HOL_Obool), tc_fun(_1725587, tc_HOL_Obool), tc_fun(_1725587, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1725587, tc_HOL_Obool))), _1725591)))], (46927 ^ _777081) ^ [_1725670, _1725672, _1725674] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1725670, tc_HOL_Obool)), _1725672), _1725674) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725670, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1725670, tc_HOL_Obool)), _1725672), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1725670, tc_HOL_Obool)), _1725674), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1725670, tc_HOL_Obool), tc_HOL_Obool))))))], (46929 ^ _777081) ^ [_1725744, _1725746, _1725748, _1725750, _1725752] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1725744, tc_fun(_1725746, tc_HOL_Obool)), _1725748), hAPP(hAPP(c_COMBS(_1725744, tc_fun(_1725746, tc_HOL_Obool), tc_fun(_1725746, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1725746, tc_HOL_Obool), tc_fun(tc_fun(_1725746, tc_HOL_Obool), tc_fun(_1725746, tc_HOL_Obool)), _1725744), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1725746, tc_HOL_Obool))), _1725750)), _1725752)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1725746, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725746, tc_HOL_Obool), hAPP(c_Set_Oimage(_1725744, tc_fun(_1725746, tc_HOL_Obool), _1725750), _1725748))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725746, tc_HOL_Obool), hAPP(c_Set_Oimage(_1725744, tc_fun(_1725746, tc_HOL_Obool), _1725752), _1725748))))], (46931 ^ _777081) ^ [_1725873, _1725875, _1725877] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1725873, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725873, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1725873, tc_HOL_Obool), tc_HOL_Obool)), _1725875), _1725877))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1725873, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725873, tc_HOL_Obool), _1725875)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1725873, tc_HOL_Obool), _1725877)))))], (46933 ^ _777081) ^ [_1725953, _1725955, _1725957] : [class_Complete__Lattice_Ocomplete__lattice(_1725953), -(c_Complete__Lattice_OSup__class_OSup(_1725953, hAPP(hAPP(c_Set_Oinsert(_1725953), _1725955), hAPP(hAPP(c_Set_Oinsert(_1725953), _1725957), c_Orderings_Obot__class_Obot(tc_fun(_1725953, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1725953), _1725955), _1725957))], (46939 ^ _777081) ^ [_1726094, _1726096] : [class_Complete__Lattice_Ocomplete__lattice(_1726094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1726094), _1726096)), -(_1726096 = c_Orderings_Obot__class_Obot(tc_fun(_1726094, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1726094, _1726096) = c_Complete__Lattice_OSup__class_OSup(_1726094, _1726096))], (46953 ^ _777081) ^ [_1726266, _1726268] : [class_Complete__Lattice_Ocomplete__lattice(_1726266), -(c_Complete__Lattice_OSup__class_OSup(_1726266, hAPP(c_List_Oset(_1726266), _1726268)) = hAPP(c_List_Ofoldl(_1726266, _1726266, c_Lattices_Osemilattice__sup__class_Osup(_1726266), c_Orderings_Obot__class_Obot(_1726266)), _1726268))], (46959 ^ _777081) ^ [_1726381, _1726383] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1726381, tc_HOL_Obool)), _1726383)), 46965 ^ _777081 : [(46966 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1726381, tc_HOL_Obool)), 46964 ^ [_1726381, _1726383]), _1726383)))], (46968 ^ _777081) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1726381), 46964 ^ [_1726381, _1726383]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1726381), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1726381, tc_HOL_Obool), _1726383))))], (46972 ^ _777081) ^ [_1726639, _1726641, _1726643] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1726639, tc_HOL_Obool)), _1726641), _1726643))), 46978 ^ _777081 : [(46979 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1726639, tc_HOL_Obool)), 46977 ^ [_1726639, _1726641, _1726643]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1726639, tc_HOL_Obool)), _1726641), _1726643))))], (46982 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1726639, tc_HOL_Obool)), 46980 ^ [_1726639, _1726641, _1726643]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1726639, tc_HOL_Obool)), _1726641), _1726643))))], (46984 ^ _777081) ^ [] : [46977 ^ [_1726639, _1726641, _1726643] = 46980 ^ [_1726639, _1726641, _1726643]], (46986 ^ _777081) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1726639, tc_HOL_Obool)), 46977 ^ [_1726639, _1726641, _1726643]), 46980 ^ [_1726639, _1726641, _1726643]) = c_Orderings_Obot__class_Obot(tc_fun(_1726639, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1726639, tc_HOL_Obool)), _1726641), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1726639, tc_HOL_Obool), _1726643)) = c_Orderings_Obot__class_Obot(tc_fun(_1726639, tc_HOL_Obool)))], (46990 ^ _777081) ^ [_1727233, _1727235, _1727237, _1727239] : [46992 ^ _777081 : [(46993 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46991 ^ [_1727233, _1727235, _1727237, _1727239]), _1727233)))], (46995 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46991 ^ [_1727233, _1727235, _1727237, _1727239]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727235)), _1727237))))], (46997 ^ _777081) ^ [] : [hBOOL(hAPP(_1727239, hAPP(hAPP(c_List_Onth(_1727235), _1727237), 46991 ^ [_1727233, _1727235, _1727237, _1727239])))]], 47000 ^ _777081 : [(47001 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1727233), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727235)), _1727237))))], (47003 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1727239, hAPP(hAPP(c_List_Onth(_1727235), _1727237), _1727233))))]], -(c_List_OtakeWhile(_1727235, _1727239, _1727237) = hAPP(hAPP(c_List_Otake(_1727235), _1727233), _1727237))], (47007 ^ _777081) ^ [_1727637, _1727639, _1727641, _1727643] : [47009 ^ _777081 : [(47010 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47008 ^ [_1727637, _1727639, _1727641, _1727643]), _1727637)))], (47012 ^ _777081) ^ [] : [hBOOL(hAPP(_1727639, hAPP(hAPP(c_List_Onth(_1727641), _1727643), 47008 ^ [_1727637, _1727639, _1727641, _1727643])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1727637), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727641)), _1727643))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1727637), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727641)), c_List_OtakeWhile(_1727641, _1727639, _1727643)))))], (47020 ^ _777081) ^ [_1727945, _1727947] : [class_Complete__Lattice_Ocomplete__lattice(_1727945), -(c_Complete__Lattice_OSup__class_OSup(_1727945, _1727947) = c_Complete__Lattice_OInf__class_OInf(_1727945, hAPP(c_Set_OCollect(_1727945), hAPP(hAPP(c_COMBB(tc_fun(_1727945, tc_HOL_Obool), tc_HOL_Obool, _1727945), c_HOL_OAll(_1727945)), hAPP(hAPP(c_COMBB(tc_fun(_1727945, tc_HOL_Obool), tc_fun(_1727945, tc_HOL_Obool), _1727945), hAPP(c_COMBS(_1727945, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1727945), c_fimplies), hAPP(hAPP(c_COMBC(_1727945, tc_fun(_1727945, tc_HOL_Obool), tc_HOL_Obool), c_member(_1727945)), _1727947)))), hAPP(c_COMBC(_1727945, _1727945, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1727945)))))))], (47026 ^ _777081) ^ [_1728186, _1728188] : [class_Complete__Lattice_Ocomplete__lattice(_1728186), -(c_Complete__Lattice_OInf__class_OInf(_1728186, _1728188) = c_Complete__Lattice_OSup__class_OSup(_1728186, hAPP(c_Set_OCollect(_1728186), hAPP(hAPP(c_COMBB(tc_fun(_1728186, tc_HOL_Obool), tc_HOL_Obool, _1728186), c_HOL_OAll(_1728186)), hAPP(hAPP(c_COMBB(tc_fun(_1728186, tc_HOL_Obool), tc_fun(_1728186, tc_HOL_Obool), _1728186), hAPP(c_COMBS(_1728186, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1728186), c_fimplies), hAPP(hAPP(c_COMBC(_1728186, tc_fun(_1728186, tc_HOL_Obool), tc_HOL_Obool), c_member(_1728186)), _1728188)))), c_Orderings_Oord__class_Oless__eq(_1728186))))))], (47032 ^ _777081) ^ [_1728413, _1728415] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1728413), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1728413, tc_HOL_Obool), _1728415)))), 47033 ^ _777081 : [(47034 ^ _777081) ^ [_1728477] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1728413, tc_HOL_Obool)), _1728477), _1728415)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1728413), _1728477))]]], (47042 ^ _777081) ^ [_1728621, _1728623, _1728625, _1728627] : [hBOOL(hAPP(hAPP(c_member(_1728621), _1728623), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1728621, tc_HOL_Obool), _1728625))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1728621, tc_HOL_Obool)), _1728627), _1728625)), -(hBOOL(hAPP(hAPP(c_member(_1728621), _1728623), _1728627)))], (47052 ^ _777081) ^ [_1728818, _1728820, _1728822, _1728824] : [hBOOL(hAPP(hAPP(c_member(_1728818), _1728820), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1728818, tc_HOL_Obool), _1728822))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1728818, tc_HOL_Obool)), _1728824), _1728822)), -(hBOOL(hAPP(hAPP(c_member(_1728818), _1728820), _1728824)))], (47062 ^ _777081) ^ [_1729015, _1729017] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1729015, tc_HOL_Obool), _1729017) = hAPP(c_Set_OCollect(_1729015), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1729015, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1729015), c_HOL_OAll(tc_fun(_1729015, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1729015, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1729015, tc_HOL_Obool), tc_HOL_Obool), _1729015), hAPP(c_COMBS(tc_fun(_1729015, 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(_1729015, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1729015, tc_HOL_Obool), tc_fun(tc_fun(_1729015, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1729015, tc_HOL_Obool))), _1729017)))), c_member(_1729015)))))], (47064 ^ _777081) ^ [_1729143, _1729145] : [class_Complete__Lattice_Ocomplete__lattice(_1729143), -(c_Complete__Lattice_OInf__class_OInf(_1729143, hAPP(hAPP(c_Set_Oinsert(_1729143), _1729145), c_Orderings_Obot__class_Obot(tc_fun(_1729143, tc_HOL_Obool)))) = _1729145)], (47070 ^ _777081) ^ [_1729250] : [class_Complete__Lattice_Ocomplete__lattice(_1729250), -(c_Complete__Lattice_OInf__class_OInf(_1729250, c_Orderings_Obot__class_Obot(tc_fun(_1729250, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1729250))], (47076 ^ _777081) ^ [_1729343] : [class_Complete__Lattice_Ocomplete__lattice(_1729343), -(c_Complete__Lattice_OInf__class_OInf(_1729343, c_Orderings_Otop__class_Otop(tc_fun(_1729343, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1729343))], (47082 ^ _777081) ^ [_1729436, _1729438, _1729440] : [class_Complete__Lattice_Ocomplete__lattice(_1729436), -(c_Complete__Lattice_OInf__class_OInf(_1729436, hAPP(hAPP(c_Set_Oinsert(_1729436), _1729438), _1729440)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1729436), _1729438), c_Complete__Lattice_OInf__class_OInf(_1729436, _1729440)))], (47088 ^ _777081) ^ [_1729557, _1729559, _1729561] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1729557, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1729557, tc_HOL_Obool), tc_HOL_Obool)), _1729559), _1729561)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1729557, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1729557, tc_HOL_Obool), _1729559)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1729557, tc_HOL_Obool), _1729561)))], (47090 ^ _777081) ^ [_1729627] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1729627, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1729627, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1729627, tc_HOL_Obool)))], (47092 ^ _777081) ^ [_1729669, _1729671, _1729673] : [class_Complete__Lattice_Ocomplete__lattice(_1729669), class_Orderings_Olinorder(_1729669), 47099 ^ _777081 : [(47100 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1729669), c_Complete__Lattice_OInf__class_OInf(_1729669, _1729671)), _1729673)), 47104 ^ _777081 : [(47105 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1729669), 47103 ^ [_1729669, _1729671, _1729673]), _1729671)))], (47107 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1729669), 47103 ^ [_1729669, _1729671, _1729673]), _1729673)))]]], (47109 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1729669), c_Complete__Lattice_OInf__class_OInf(_1729669, _1729671)), _1729673))), 47110 ^ _777081 : [(47111 ^ _777081) ^ [_1729975] : [hBOOL(hAPP(hAPP(c_member(_1729669), _1729975), _1729671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1729669), _1729975), _1729673))]]]]], (47119 ^ _777081) ^ [_1730129, _1730131, _1730133] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1730129, tc_HOL_Obool)), _1730131), _1730133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730129, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1730129, tc_HOL_Obool), _1730133)), _1730131)))], (47125 ^ _777081) ^ [_1730260, _1730262, _1730264] : [class_Complete__Lattice_Ocomplete__lattice(_1730260), 47128 ^ _777081 : [(47139 ^ _777081) ^ [] : [47141 ^ _777081 : [(47142 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730260), 47140 ^ [_1730260, _1730262, _1730264]), _1730264)))], (47144 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1730260), _1730262), 47140 ^ [_1730260, _1730262, _1730264]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1730260), _1730262), c_Complete__Lattice_OInf__class_OInf(_1730260, _1730264))))], (47129 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1730260), _1730262), c_Complete__Lattice_OInf__class_OInf(_1730260, _1730264))), 47132 ^ _777081 : [(47133 ^ _777081) ^ [_1730418] : [hBOOL(hAPP(hAPP(c_member(_1730260), _1730418), _1730264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1730260), _1730262), _1730418)))]]]]], (47148 ^ _777081) ^ [_1730694] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1730694, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1730694, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1730694, tc_HOL_Obool)))], (47150 ^ _777081) ^ [_1730736, _1730738, _1730740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1730736, tc_HOL_Obool), tc_HOL_Obool)), _1730738), _1730740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730736, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1730736, tc_HOL_Obool), _1730740)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1730736, tc_HOL_Obool), _1730738))))], (47156 ^ _777081) ^ [_1730885, _1730887, _1730889] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1730885, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1730885, tc_HOL_Obool)), _1730887), _1730889)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1730885, tc_HOL_Obool)), _1730887), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1730885, tc_HOL_Obool), _1730889)))], (47158 ^ _777081) ^ [_1730946, _1730948, _1730950] : [class_Complete__Lattice_Ocomplete__lattice(_1730946), hBOOL(hAPP(hAPP(c_member(_1730946), _1730948), _1730950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1730946), c_Complete__Lattice_OInf__class_OInf(_1730946, _1730950)), _1730948)))], (47168 ^ _777081) ^ [_1731111, _1731113, _1731115, _1731117] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1731111, tc_HOL_Obool), hAPP(c_Set_Oimage(_1731113, tc_fun(_1731111, tc_HOL_Obool), _1731115), _1731117)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1731113, tc_fun(_1731111, tc_HOL_Obool)), _1731117), _1731115))], (47170 ^ _777081) ^ [_1731168, _1731170, _1731172, _1731174] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1731168, tc_fun(_1731170, tc_HOL_Obool)), _1731172), _1731174) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1731170, tc_HOL_Obool), hAPP(c_Set_Oimage(_1731168, tc_fun(_1731170, tc_HOL_Obool), _1731174), _1731172)))], (47172 ^ _777081) ^ [_1731225, _1731227] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1731225, tc_HOL_Obool), _1731227) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1731225, tc_HOL_Obool), tc_fun(_1731225, tc_HOL_Obool)), _1731227), c_COMBI(tc_fun(_1731225, tc_HOL_Obool))))], (47174 ^ _777081) ^ [_1731276, _1731278, _1731280] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1731276, tc_HOL_Obool)), _1731278), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1731276, tc_HOL_Obool), _1731280)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1731276, tc_HOL_Obool), tc_fun(_1731276, tc_HOL_Obool)), _1731280), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1731276, tc_HOL_Obool)), _1731278)))], (47176 ^ _777081) ^ [_1731343, _1731345, _1731347] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1731343, tc_HOL_Obool)), _1731345), _1731347) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1731343, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1731343, tc_HOL_Obool)), _1731345), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1731343, tc_HOL_Obool)), _1731347), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1731343, tc_HOL_Obool), tc_HOL_Obool))))))], (47178 ^ _777081) ^ [_1731417, _1731419, _1731421, _1731423, _1731425] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1731417, tc_fun(_1731419, tc_HOL_Obool)), _1731421), hAPP(hAPP(c_COMBS(_1731417, tc_fun(_1731419, tc_HOL_Obool), tc_fun(_1731419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1731419, tc_HOL_Obool), tc_fun(tc_fun(_1731419, tc_HOL_Obool), tc_fun(_1731419, tc_HOL_Obool)), _1731417), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1731419, tc_HOL_Obool))), _1731423)), _1731425)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1731419, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1731419, tc_HOL_Obool), hAPP(c_Set_Oimage(_1731417, tc_fun(_1731419, tc_HOL_Obool), _1731423), _1731421))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1731419, tc_HOL_Obool), hAPP(c_Set_Oimage(_1731417, tc_fun(_1731419, tc_HOL_Obool), _1731425), _1731421))))], (47180 ^ _777081) ^ [_1731546, _1731548, _1731550] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731546, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1731546, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1731546, tc_HOL_Obool), _1731548)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1731546, tc_HOL_Obool), _1731550))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1731546, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1731546, tc_HOL_Obool), tc_HOL_Obool)), _1731548), _1731550)))))], (47182 ^ _777081) ^ [_1731626, _1731628, _1731630] : [class_Complete__Lattice_Ocomplete__lattice(_1731626), -(c_Complete__Lattice_OInf__class_OInf(_1731626, hAPP(hAPP(c_Set_Oinsert(_1731626), _1731628), hAPP(hAPP(c_Set_Oinsert(_1731626), _1731630), c_Orderings_Obot__class_Obot(tc_fun(_1731626, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1731626), _1731628), _1731630))], (47188 ^ _777081) ^ [_1731767, _1731769] : [class_Complete__Lattice_Ocomplete__lattice(_1731767), hBOOL(hAPP(c_Finite__Set_Ofinite(_1731767), _1731769)), -(_1731769 = c_Orderings_Obot__class_Obot(tc_fun(_1731767, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1731767, _1731769) = c_Complete__Lattice_OInf__class_OInf(_1731767, _1731769))], (47202 ^ _777081) ^ [_1731939, _1731941] : [class_Complete__Lattice_Ocomplete__lattice(_1731939), -(c_Complete__Lattice_OInf__class_OInf(_1731939, hAPP(c_List_Oset(_1731939), _1731941)) = hAPP(c_List_Ofoldl(_1731939, _1731939, c_Lattices_Osemilattice__inf__class_Oinf(_1731939), c_Orderings_Otop__class_Otop(_1731939)), _1731941))], (47208 ^ _777081) ^ [_1732078, _1732080, _1732082, _1732084, _1732086] : [c_List_Olist__all2(_1732078, _1732080, _1732082, _1732084, _1732086), 47211 ^ _777081 : [(47212 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732078)), _1732084) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732080)), _1732086))], (47214 ^ _777081) ^ [_1732244] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1732078, _1732080)), _1732244), hAPP(c_List_Oset(tc_prod(_1732078, _1732080)), hAPP(hAPP(c_List_Ozip(_1732078, _1732080), _1732084), _1732086)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1732078, _1732080, tc_HOL_Obool), _1732082), _1732244)))]]], (47220 ^ _777081) ^ [_1732403, _1732405, _1732407, _1732409, _1732411] : [-(c_List_Olist__all2(_1732403, _1732405, _1732407, _1732409, _1732411)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732403)), _1732409) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732405)), _1732411), 47226 ^ _777081 : [(47227 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1732403, _1732405)), 47225 ^ [_1732403, _1732405, _1732407, _1732409, _1732411]), hAPP(c_List_Oset(tc_prod(_1732403, _1732405)), hAPP(hAPP(c_List_Ozip(_1732403, _1732405), _1732409), _1732411)))))], (47229 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1732403, _1732405, tc_HOL_Obool), _1732407), 47225 ^ [_1732403, _1732405, _1732407, _1732409, _1732411]))]]], (47233 ^ _777081) ^ [_1732744, _1732746] : [class_Orderings_Olinorder(_1732744), 47236 ^ _777081 : [(47237 ^ _777081) ^ [] : [c_List_Olinorder__class_Osorted(_1732744, _1732746), -(_1732746 = c_List_Olist_ONil(_1732744)), 47246 ^ _777081 : [(47247 ^ _777081) ^ [] : [-(_1732746 = hAPP(hAPP(c_List_Olist_OCons(_1732744), 47245 ^ [_1732744, _1732746]), 47244 ^ [_1732744, _1732746]))], (47255 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1732744, 47244 ^ [_1732744, _1732746]))], (47249 ^ _777081) ^ [_1733078] : [hBOOL(hAPP(hAPP(c_member(_1732744), _1733078), hAPP(c_List_Oset(_1732744), 47244 ^ [_1732744, _1732746]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732744), 47245 ^ [_1732744, _1732746]), _1733078)))]]], (47257 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1732744, _1732746)), 47258 ^ _777081 : [(47259 ^ _777081) ^ [] : [_1732746 = c_List_Olist_ONil(_1732744)], (47261 ^ _777081) ^ [_1733304, _1733306] : [_1732746 = hAPP(hAPP(c_List_Olist_OCons(_1732744), _1733304), _1733306), 47267 ^ _777081 : [(47268 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1732744), 47266 ^ [_1732744, _1732746, _1733304, _1733306]), hAPP(c_List_Oset(_1732744), _1733306))))], (47270 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1732744), _1733304), 47266 ^ [_1732744, _1732746, _1733304, _1733306]))]], c_List_Olinorder__class_Osorted(_1732744, _1733306)]]]]], (47276 ^ _777081) ^ [_1733613, _1733615, _1733617, _1733619, _1733621, _1733623, _1733625] : [c_List_Olist__all2(_1733613, _1733615, _1733617, _1733619, _1733621), c_List_Olist__all2(_1733613, _1733615, _1733617, _1733623, _1733625), -(c_List_Olist__all2(_1733613, _1733615, _1733617, hAPP(hAPP(c_List_Oappend(_1733613), _1733619), _1733623), hAPP(hAPP(c_List_Oappend(_1733615), _1733621), _1733625)))], (47286 ^ _777081) ^ [_1733812, _1733814, _1733816, _1733818, _1733820, _1733822, _1733824] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733812)), _1733814) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733816)), _1733818), 47289 ^ _777081 : [(47290 ^ _777081) ^ [] : [c_List_Olist__all2(_1733812, _1733816, _1733820, hAPP(hAPP(c_List_Oappend(_1733812), _1733814), _1733822), hAPP(hAPP(c_List_Oappend(_1733816), _1733818), _1733824)), 47293 ^ _777081 : [(47294 ^ _777081) ^ [] : [-(c_List_Olist__all2(_1733812, _1733816, _1733820, _1733814, _1733818))], (47296 ^ _777081) ^ [] : [-(c_List_Olist__all2(_1733812, _1733816, _1733820, _1733822, _1733824))]]], (47298 ^ _777081) ^ [] : [-(c_List_Olist__all2(_1733812, _1733816, _1733820, hAPP(hAPP(c_List_Oappend(_1733812), _1733814), _1733822), hAPP(hAPP(c_List_Oappend(_1733816), _1733818), _1733824))), c_List_Olist__all2(_1733812, _1733816, _1733820, _1733814, _1733818), c_List_Olist__all2(_1733812, _1733816, _1733820, _1733822, _1733824)]]], (47308 ^ _777081) ^ [_1734264, _1734266, _1734268, _1734270, _1734272, _1734274, _1734276] : [c_List_Olist__all2(_1734264, _1734266, _1734268, hAPP(hAPP(c_List_Olist_OCons(_1734264), _1734270), _1734272), hAPP(hAPP(c_List_Olist_OCons(_1734266), _1734274), _1734276)), 47311 ^ _777081 : [(47312 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(_1734268, _1734270), _1734274)))], (47314 ^ _777081) ^ [] : [-(c_List_Olist__all2(_1734264, _1734266, _1734268, _1734272, _1734276))]]], (47316 ^ _777081) ^ [_1734427, _1734429, _1734431, _1734433, _1734435, _1734437, _1734439] : [-(c_List_Olist__all2(_1734427, _1734429, _1734431, hAPP(hAPP(c_List_Olist_OCons(_1734427), _1734433), _1734435), hAPP(hAPP(c_List_Olist_OCons(_1734429), _1734437), _1734439))), hBOOL(hAPP(hAPP(_1734431, _1734433), _1734437)), c_List_Olist__all2(_1734427, _1734429, _1734431, _1734435, _1734439)], (47326 ^ _777081) ^ [_1734662, _1734664, _1734666, _1734668, _1734670, _1734672, _1734674] : [c_List_Olist__all2(_1734662, _1734664, _1734666, hAPP(hAPP(c_List_Omap(_1734668, _1734662), _1734670), _1734672), _1734674), -(c_List_Olist__all2(_1734668, _1734664, hAPP(hAPP(c_COMBB(_1734662, tc_fun(_1734664, tc_HOL_Obool), _1734668), _1734666), _1734670), _1734672, _1734674))], (47332 ^ _777081) ^ [_1734801, _1734803, _1734805, _1734807, _1734809, _1734811, _1734813] : [c_List_Olist__all2(_1734807, _1734803, hAPP(hAPP(c_COMBB(_1734801, tc_fun(_1734803, tc_HOL_Obool), _1734807), _1734805), _1734809), _1734811, _1734813), -(c_List_Olist__all2(_1734801, _1734803, _1734805, hAPP(hAPP(c_List_Omap(_1734807, _1734801), _1734809), _1734811), _1734813))], (47338 ^ _777081) ^ [_1734976, _1734978, _1734980, _1734982, _1734984, _1734986, _1734988] : [c_List_Olist__all2(_1734976, _1734978, _1734980, _1734982, hAPP(hAPP(c_List_Omap(_1734984, _1734978), _1734986), _1734988)), -(c_List_Olist__all2(_1734976, _1734984, hAPP(hAPP(c_COMBC(_1734976, tc_fun(_1734984, _1734978), tc_fun(_1734984, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1734978, tc_HOL_Obool), tc_fun(tc_fun(_1734984, _1734978), tc_fun(_1734984, tc_HOL_Obool)), _1734976), c_COMBB(_1734978, tc_HOL_Obool, _1734984)), _1734980)), _1734986), _1734982, _1734988))], (47344 ^ _777081) ^ [_1735173, _1735175, _1735177, _1735179, _1735181, _1735183, _1735185] : [c_List_Olist__all2(_1735173, _1735181, hAPP(hAPP(c_COMBC(_1735173, tc_fun(_1735181, _1735175), tc_fun(_1735181, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1735175, tc_HOL_Obool), tc_fun(tc_fun(_1735181, _1735175), tc_fun(_1735181, tc_HOL_Obool)), _1735173), c_COMBB(_1735175, tc_HOL_Obool, _1735181)), _1735177)), _1735183), _1735179, _1735185), -(c_List_Olist__all2(_1735173, _1735175, _1735177, _1735179, hAPP(hAPP(c_List_Omap(_1735181, _1735175), _1735183), _1735185)))], (47350 ^ _777081) ^ [_1735394, _1735396, _1735398] : [_1735394 = _1735396, -(c_List_Olist__all2(_1735398, _1735398, c_fequal, _1735394, _1735396))], (47356 ^ _777081) ^ [_1735475, _1735477, _1735479] : [c_List_Olist__all2(_1735479, _1735479, c_fequal, _1735475, _1735477), -(_1735475 = _1735477)], (47362 ^ _777081) ^ [_1735562, _1735564, _1735566, _1735568, _1735570] : [c_List_Olist__all2(_1735562, _1735564, _1735566, _1735568, _1735570), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735562)), _1735568) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735564)), _1735570))], (47368 ^ _777081) ^ [_1735679, _1735681, _1735683, _1735685, _1735687, _1735689] : [c_List_Olist__all2(_1735679, _1735681, _1735683, _1735685, _1735687), -(c_List_Olist__all2(_1735679, _1735681, _1735683, hAPP(hAPP(c_List_Odrop(_1735679), _1735689), _1735685), hAPP(hAPP(c_List_Odrop(_1735681), _1735689), _1735687)))], (47374 ^ _777081) ^ [_1735808, _1735810, _1735812, _1735814, _1735816, _1735818] : [c_List_Olist__all2(_1735808, _1735810, _1735812, _1735814, _1735816), -(c_List_Olist__all2(_1735808, _1735810, _1735812, hAPP(hAPP(c_List_Otake(_1735808), _1735818), _1735814), hAPP(hAPP(c_List_Otake(_1735810), _1735818), _1735816)))], (47380 ^ _777081) ^ [_1735958, _1735960, _1735962, _1735964] : [c_List_Olist__all2(_1735958, _1735960, _1735962, c_List_Olist_ONil(_1735958), _1735964), -(_1735964 = c_List_Olist_ONil(_1735960))], (47386 ^ _777081) ^ [_1736049, _1736051, _1736053, _1736055] : [_1736055 = c_List_Olist_ONil(_1736051), -(c_List_Olist__all2(_1736049, _1736051, _1736053, c_List_Olist_ONil(_1736049), _1736055))], (47392 ^ _777081) ^ [_1736167, _1736169, _1736171, _1736173] : [c_List_Olist__all2(_1736167, _1736169, _1736171, _1736173, c_List_Olist_ONil(_1736169)), -(_1736173 = c_List_Olist_ONil(_1736167))], (47398 ^ _777081) ^ [_1736258, _1736260, _1736262, _1736264] : [_1736264 = c_List_Olist_ONil(_1736258), -(c_List_Olist__all2(_1736258, _1736260, _1736262, _1736264, c_List_Olist_ONil(_1736260)))], (47404 ^ _777081) ^ [_1736379, _1736381, _1736383, _1736385, _1736387] : [c_List_Olist__all2(_1736379, _1736381, _1736383, hAPP(c_List_Orev(_1736379), _1736385), hAPP(c_List_Orev(_1736381), _1736387)), -(c_List_Olist__all2(_1736379, _1736381, _1736383, _1736385, _1736387))], (47410 ^ _777081) ^ [_1736490, _1736492, _1736494, _1736496, _1736498] : [c_List_Olist__all2(_1736490, _1736492, _1736494, _1736496, _1736498), -(c_List_Olist__all2(_1736490, _1736492, _1736494, hAPP(c_List_Orev(_1736490), _1736496), hAPP(c_List_Orev(_1736492), _1736498)))], (47416 ^ _777081) ^ [_1736631, _1736633, _1736635, _1736637, _1736639] : [c_List_Olist__all2(_1736631, _1736633, _1736635, hAPP(c_List_Orev(_1736631), _1736637), _1736639), -(c_List_Olist__all2(_1736631, _1736633, _1736635, _1736637, hAPP(c_List_Orev(_1736633), _1736639)))], (47422 ^ _777081) ^ [_1736742, _1736744, _1736746, _1736748, _1736750] : [c_List_Olist__all2(_1736742, _1736744, _1736746, _1736748, hAPP(c_List_Orev(_1736744), _1736750)), -(c_List_Olist__all2(_1736742, _1736744, _1736746, hAPP(c_List_Orev(_1736742), _1736748), _1736750))], (47428 ^ _777081) ^ [_1736883, _1736885, _1736887, _1736889, _1736891] : [c_List_Olist__all2(_1736883, _1736885, _1736887, _1736889, _1736891), 47431 ^ _777081 : [(47432 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736883)), _1736889) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736885)), _1736891))], (47434 ^ _777081) ^ [_1737046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737046), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736883)), _1736889))), -(hBOOL(hAPP(hAPP(_1736887, hAPP(hAPP(c_List_Onth(_1736883), _1736889), _1737046)), hAPP(hAPP(c_List_Onth(_1736885), _1736891), _1737046))))]]], (47440 ^ _777081) ^ [_1737199, _1737201, _1737203, _1737205, _1737207] : [-(c_List_Olist__all2(_1737199, _1737201, _1737203, _1737205, _1737207)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737199)), _1737205) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737201)), _1737207), 47446 ^ _777081 : [(47447 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47445 ^ [_1737199, _1737201, _1737203, _1737205, _1737207]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737199)), _1737205))))], (47449 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1737203, hAPP(hAPP(c_List_Onth(_1737199), _1737205), 47445 ^ [_1737199, _1737201, _1737203, _1737205, _1737207])), hAPP(hAPP(c_List_Onth(_1737201), _1737207), 47445 ^ [_1737199, _1737201, _1737203, _1737205, _1737207])))]]], (47453 ^ _777081) ^ [_1737559, _1737561, _1737563, _1737565, _1737567, _1737569] : [c_List_Olist__all2(_1737559, _1737561, _1737563, _1737565, _1737567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737569), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737559)), _1737565))), -(hBOOL(hAPP(hAPP(_1737563, hAPP(hAPP(c_List_Onth(_1737559), _1737565), _1737569)), hAPP(hAPP(c_List_Onth(_1737561), _1737567), _1737569))))], (47463 ^ _777081) ^ [_1737776, _1737778, _1737780, _1737782, _1737784, _1737786] : [c_List_Olist__all2(_1737776, _1737778, _1737780, _1737782, _1737784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737786), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737778)), _1737784))), -(hBOOL(hAPP(hAPP(_1737780, hAPP(hAPP(c_List_Onth(_1737776), _1737782), _1737786)), hAPP(hAPP(c_List_Onth(_1737778), _1737784), _1737786))))], (47473 ^ _777081) ^ [_1737993, _1737995, _1737997, _1737999, _1738001, _1738003, _1738005, _1738007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737993), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1737995)), _1737997))), c_List_Olist__all2(_1737995, _1737999, _1738001, _1737997, _1738003), hBOOL(hAPP(hAPP(_1738001, _1738005), _1738007)), -(c_List_Olist__all2(_1737995, _1737999, _1738001, hAPP(hAPP(c_List_Olist__update(_1737995, _1737997), _1737993), _1738005), hAPP(hAPP(c_List_Olist__update(_1737999, _1738003), _1737993), _1738007)))], (47487 ^ _777081) ^ [_1738292, _1738294, _1738296, _1738298, _1738300, _1738302, _1738304, _1738306] : [c_List_Olist__all2(_1738292, _1738294, _1738296, _1738298, _1738300), hBOOL(hAPP(hAPP(_1738296, _1738302), _1738304)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738306), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738294)), _1738300))), -(c_List_Olist__all2(_1738292, _1738294, _1738296, hAPP(hAPP(c_List_Olist__update(_1738292, _1738298), _1738306), _1738302), hAPP(hAPP(c_List_Olist__update(_1738294, _1738300), _1738306), _1738304)))], (47501 ^ _777081) ^ [_1738591, _1738593, _1738595, _1738597, _1738599] : [47503 ^ _777081 : [(47504 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1738591, _1738593)), 47502 ^ [_1738591, _1738593, _1738595, _1738597, _1738599]), hAPP(c_List_Oset(tc_prod(_1738591, _1738593)), hAPP(hAPP(c_List_Ozip(_1738591, _1738593), _1738595), _1738597)))))], (47506 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1738591, _1738593, tc_HOL_Obool), _1738599), 47502 ^ [_1738591, _1738593, _1738595, _1738597, _1738599]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738591)), _1738595) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738593)), _1738597), -(c_List_Olist__all2(_1738591, _1738593, _1738599, _1738595, _1738597))], (47514 ^ _777081) ^ [_1738930, _1738932, _1738934] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1738930, tc_HOL_Obool)), _1738932)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1738930), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1738930, tc_HOL_Obool), _1738932))), 47524 ^ _777081 : [(47525 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1738930, tc_HOL_Obool)), 47523 ^ [_1738930, _1738932, _1738934]), _1738932)))], (47527 ^ _777081) ^ [] : [hAPP(c_Finite__Set_Ocard(_1738930), 47523 ^ [_1738930, _1738932, _1738934]) = _1738934]], 47531 ^ _777081 : [(47532 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1738930, tc_HOL_Obool)), 47530 ^ [_1738930, _1738932, _1738934]), _1738932)))], (47535 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1738930, tc_HOL_Obool)), 47533 ^ [_1738930, _1738932, _1738934]), _1738932)))], (47537 ^ _777081) ^ [] : [47530 ^ [_1738930, _1738932, _1738934] = 47533 ^ [_1738930, _1738932, _1738934]], (47539 ^ _777081) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1738930, tc_HOL_Obool)), 47530 ^ [_1738930, _1738932, _1738934]), 47533 ^ [_1738930, _1738932, _1738934]) = c_Orderings_Obot__class_Obot(tc_fun(_1738930, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1738934), hAPP(c_Finite__Set_Ocard(tc_fun(_1738930, tc_HOL_Obool)), _1738932)) = hAPP(c_Finite__Set_Ocard(_1738930), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1738930, tc_HOL_Obool), _1738932)))], (47543 ^ _777081) ^ [_1739712, _1739714, _1739716, _1739718] : [47545 ^ _777081 : [(47546 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47544 ^ [_1739712, _1739714, _1739716, _1739718]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739712)), _1739714))))], (47548 ^ _777081) ^ [] : [hBOOL(hAPP(_1739716, hAPP(hAPP(c_List_Onth(_1739712), _1739714), 47544 ^ [_1739712, _1739714, _1739716, _1739718])))]], hBOOL(hAPP(hAPP(c_member(_1739712), _1739718), hAPP(c_List_Oset(_1739712), _1739714))), -(hBOOL(hAPP(_1739716, _1739718)))], (47556 ^ _777081) ^ [_1740008, _1740010, _1740012, _1740014, _1740016] : [c_Fun_Oinj__on(_1740008, _1740010, _1740012, hAPP(hAPP(c_Set_Oinsert(_1740008), _1740014), hAPP(c_List_Oset(_1740008), _1740016))), -(hAPP(hAPP(c_List_Omap(_1740008, _1740010), _1740012), hAPP(c_List_OremoveAll(_1740008, _1740014), _1740016)) = hAPP(c_List_OremoveAll(_1740010, hAPP(_1740012, _1740014)), hAPP(hAPP(c_List_Omap(_1740008, _1740010), _1740012), _1740016)))], (47562 ^ _777081) ^ [_1740187, _1740189, _1740191, _1740193] : [-(hAPP(c_List_OremoveAll(_1740187, _1740189), hAPP(hAPP(c_List_Oappend(_1740187), _1740191), _1740193)) = hAPP(hAPP(c_List_Oappend(_1740187), hAPP(c_List_OremoveAll(_1740187, _1740189), _1740191)), hAPP(c_List_OremoveAll(_1740187, _1740189), _1740193)))], (47564 ^ _777081) ^ [_1740265, _1740267, _1740269, _1740271] : [_1740265 = _1740267, -(hAPP(c_List_OremoveAll(_1740269, _1740265), hAPP(hAPP(c_List_Olist_OCons(_1740269), _1740267), _1740271)) = hAPP(c_List_OremoveAll(_1740269, _1740265), _1740271))], (47570 ^ _777081) ^ [_1740380, _1740382, _1740384, _1740386] : [-(_1740380 = _1740382), -(hAPP(c_List_OremoveAll(_1740384, _1740380), hAPP(hAPP(c_List_Olist_OCons(_1740384), _1740382), _1740386)) = hAPP(hAPP(c_List_Olist_OCons(_1740384), _1740382), hAPP(c_List_OremoveAll(_1740384, _1740380), _1740386)))], (47576 ^ _777081) ^ [_1740450, _1740452, _1740454] : [hBOOL(hAPP(c_List_Odistinct(_1740450), _1740452)), -(hBOOL(hAPP(c_List_Odistinct(_1740450), hAPP(c_List_OremoveAll(_1740450, _1740454), _1740452))))], (47582 ^ _777081) ^ [_1740553, _1740555, _1740557, _1740559] : [-(hBOOL(hAPP(_1740553, _1740555))), -(hAPP(c_List_OremoveAll(_1740557, _1740555), hAPP(c_List_Ofilter(_1740557, _1740553), _1740559)) = hAPP(c_List_Ofilter(_1740557, _1740553), _1740559))], (47588 ^ _777081) ^ [_1740613, _1740615] : [-(c_List_OremoveAll(_1740613, _1740615) = c_List_Ofilter(_1740613, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1740613), c_fNot), hAPP(c_fequal, _1740615))))], (47590 ^ _777081) ^ [_1740657, _1740659] : [-(hAPP(c_List_OremoveAll(_1740657, _1740659), c_List_Olist_ONil(_1740657)) = c_List_Olist_ONil(_1740657))], (47592 ^ _777081) ^ [_1740688, _1740690, _1740692] : [-(hBOOL(hAPP(hAPP(c_member(_1740688), _1740690), hAPP(c_List_Oset(_1740688), _1740692)))), -(hAPP(c_List_OremoveAll(_1740688, _1740690), _1740692) = _1740692)], (47598 ^ _777081) ^ [_1740744, _1740746, _1740748] : [hBOOL(hAPP(c_List_Odistinct(_1740744), _1740746)), -(c_List_Oremove1(_1740744, _1740748, _1740746) = hAPP(c_List_OremoveAll(_1740744, _1740748), _1740746))], (47604 ^ _777081) ^ [_1740851, _1740853, _1740855, _1740857, _1740859] : [c_Fun_Oinj__on(_1740851, _1740853, _1740855, c_Orderings_Otop__class_Otop(tc_fun(_1740851, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1740851, _1740853), _1740855), hAPP(c_List_OremoveAll(_1740851, _1740857), _1740859)) = hAPP(c_List_OremoveAll(_1740853, hAPP(_1740855, _1740857)), hAPP(hAPP(c_List_Omap(_1740851, _1740853), _1740855), _1740859)))], (47610 ^ _777081) ^ [_1741014, _1741016, _1741018] : [-(hAPP(c_List_Oset(_1741014), hAPP(c_List_OremoveAll(_1741014, _1741016), _1741018)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1741014, tc_HOL_Obool)), hAPP(c_List_Oset(_1741014), _1741018)), hAPP(hAPP(c_Set_Oinsert(_1741014), _1741016), c_Orderings_Obot__class_Obot(tc_fun(_1741014, tc_HOL_Obool)))))], (47612 ^ _777081) ^ [_1741093, _1741095, _1741097] : [hBOOL(hAPP(hAPP(c_member(_1741093), _1741095), hAPP(c_List_Oset(_1741093), _1741097))), -(c_List_Oinsert(_1741093, _1741095, _1741097) = _1741097)], (47618 ^ _777081) ^ [_1741198, _1741200, _1741202] : [-(hBOOL(hAPP(hAPP(c_member(_1741198), _1741200), hAPP(c_List_Oset(_1741198), _1741202)))), -(c_List_Oinsert(_1741198, _1741200, _1741202) = hAPP(hAPP(c_List_Olist_OCons(_1741198), _1741200), _1741202))], (47624 ^ _777081) ^ [_1741258, _1741260, _1741262] : [-(hBOOL(hAPP(hAPP(c_member(_1741258), _1741260), hAPP(c_List_Oset(_1741258), _1741262)))), -(c_List_Oinsert(_1741258, _1741260, _1741262) = hAPP(hAPP(c_List_Olist_OCons(_1741258), _1741260), _1741262))], (47630 ^ _777081) ^ [_1741320, _1741322, _1741324] : [-(c_List_Oinsert(_1741320, _1741322, c_List_Oremdups(_1741320, _1741324)) = c_List_Oremdups(_1741320, c_List_Oinsert(_1741320, _1741322, _1741324)))], (47632 ^ _777081) ^ [_1741361, _1741363, _1741365] : [hBOOL(hAPP(c_List_Odistinct(_1741361), _1741363)), -(hBOOL(hAPP(c_List_Odistinct(_1741361), c_List_Oinsert(_1741361, _1741365, _1741363))))], (47638 ^ _777081) ^ [_1741464, _1741466, _1741468] : [hBOOL(hAPP(hAPP(c_member(_1741464), _1741466), hAPP(c_List_Oset(_1741464), _1741468))), -(c_List_Oinsert(_1741464, _1741466, _1741468) = _1741468)], (47644 ^ _777081) ^ [_1741575, _1741577, _1741579] : [-(hAPP(c_List_Oset(_1741575), c_List_Oinsert(_1741575, _1741577, _1741579)) = hAPP(hAPP(c_Set_Oinsert(_1741575), _1741577), hAPP(c_List_Oset(_1741575), _1741579)))], (47646 ^ _777081) ^ [_1741624, _1741626] : [-(c_List_Oinsert(_1741624, _1741626, c_List_Olist_ONil(_1741624)) = hAPP(hAPP(c_List_Olist_OCons(_1741624), _1741626), c_List_Olist_ONil(_1741624)))], (47648 ^ _777081) ^ [_1741665, _1741667, _1741669, _1741671] : [-(c_List_Oconcat(_1741665, hAPP(hAPP(c_List_Omap(_1741667, tc_List_Olist(_1741665)), _1741669), _1741671)) = c_List_Omaps(_1741667, _1741665, _1741669, _1741671))], (47650 ^ _777081) ^ [_1741713, _1741715, _1741717, _1741719] : [-(c_List_Omaps(_1741713, _1741715, _1741717, _1741719) = c_List_Oconcat(_1741715, hAPP(hAPP(c_List_Omap(_1741713, tc_List_Olist(_1741715)), _1741717), _1741719)))], (47652 ^ _777081) ^ [_1741761, _1741763, _1741765] : [-(c_List_Omaps(_1741761, _1741763, _1741765, c_List_Olist_ONil(_1741761)) = c_List_Olist_ONil(_1741763))], (47654 ^ _777081) ^ [_1741797, _1741799, _1741801, _1741803, _1741805] : [-(c_List_Omaps(_1741797, _1741799, _1741801, hAPP(hAPP(c_List_Olist_OCons(_1741797), _1741803), _1741805)) = hAPP(hAPP(c_List_Oappend(_1741799), hAPP(_1741801, _1741803)), c_List_Omaps(_1741797, _1741799, _1741801, _1741805)))], (47656 ^ _777081) ^ [_1741857, _1741859] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1741857)), _1741859)), 47662 ^ _777081 : [(47663 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1741857)), 47661 ^ [_1741857, _1741859]), hAPP(c_List_Oset(tc_List_Olist(_1741857)), _1741859))))], (47665 ^ _777081) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1741857), 47661 ^ [_1741857, _1741859]))]], 47669 ^ _777081 : [(47670 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1741857)), 47668 ^ [_1741857, _1741859]), hAPP(c_List_Oset(tc_List_Olist(_1741857)), _1741859))))], (47673 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1741857)), 47671 ^ [_1741857, _1741859]), hAPP(c_List_Oset(tc_List_Olist(_1741857)), _1741859))))], (47675 ^ _777081) ^ [] : [47668 ^ [_1741857, _1741859] = 47671 ^ [_1741857, _1741859]], (47677 ^ _777081) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1741857, tc_HOL_Obool)), hAPP(c_List_Oset(_1741857), 47668 ^ [_1741857, _1741859])), hAPP(c_List_Oset(_1741857), 47671 ^ [_1741857, _1741859])) = c_Orderings_Obot__class_Obot(tc_fun(_1741857, tc_HOL_Obool))]], -(hBOOL(hAPP(c_List_Odistinct(_1741857), c_List_Oconcat(_1741857, _1741859))))], (47681 ^ _777081) ^ [_1742574, _1742576, _1742578, _1742580, _1742582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1742574, _1742576)), hAPP(_1742574, _1742578))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1742580, _1742580)), hAPP(hAPP(c_Product__Type_OPair(_1742580, _1742580), _1742576), _1742578)), c_List_Omeasures(_1742580, _1742582))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1742580, _1742580)), hAPP(hAPP(c_Product__Type_OPair(_1742580, _1742580), _1742576), _1742578)), c_List_Omeasures(_1742580, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1742580, tc_Nat_Onat)), _1742574), _1742582)))))], (47691 ^ _777081) ^ [_1742847, _1742849] : [-(c_Wellfounded_Owf(_1742847, c_List_Omeasures(_1742847, _1742849)))], (47693 ^ _777081) ^ [_1742890, _1742892, _1742894] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1742890, _1742890)), hAPP(hAPP(c_Product__Type_OPair(_1742890, _1742890), _1742892), _1742894)), c_List_Omeasures(_1742890, c_List_Olist_ONil(tc_fun(_1742890, tc_Nat_Onat)))))], (47695 ^ _777081) ^ [_1742944, _1742946] : [-(c_List_Omeasures(_1742944, _1742946) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1742944), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1742944, tc_List_Olist(tc_fun(_1742944, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1742944, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1742944, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1742944), c_List_Omap(tc_fun(_1742944, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1742944, tc_Nat_Onat), _1742944, tc_Nat_Onat), c_COMBI(tc_fun(_1742944, tc_Nat_Onat))))), _1742946)))], (47697 ^ _777081) ^ [_1743065, _1743067, _1743069, _1743071, _1743073] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1743065, _1743065)), hAPP(hAPP(c_Product__Type_OPair(_1743065, _1743065), _1743067), _1743069)), c_List_Omeasures(_1743065, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1743065, tc_Nat_Onat)), _1743071), _1743073)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1743071, _1743067)), hAPP(_1743071, _1743069)))), 47704 ^ _777081 : [(47705 ^ _777081) ^ [] : [-(hAPP(_1743071, _1743067) = hAPP(_1743071, _1743069))], (47707 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1743065, _1743065)), hAPP(hAPP(c_Product__Type_OPair(_1743065, _1743065), _1743067), _1743069)), c_List_Omeasures(_1743065, _1743073))))]]], (47709 ^ _777081) ^ [_1743344, _1743346, _1743348, _1743350, _1743352] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1743344, _1743344)), hAPP(hAPP(c_Product__Type_OPair(_1743344, _1743344), _1743346), _1743348)), c_List_Omeasures(_1743344, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1743344, tc_Nat_Onat)), _1743350), _1743352))))), 47710 ^ _777081 : [(47711 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1743350, _1743346)), hAPP(_1743350, _1743348)))], (47713 ^ _777081) ^ [] : [hAPP(_1743350, _1743346) = hAPP(_1743350, _1743348), hBOOL(hAPP(hAPP(c_member(tc_prod(_1743344, _1743344)), hAPP(hAPP(c_Product__Type_OPair(_1743344, _1743344), _1743346), _1743348)), c_List_Omeasures(_1743344, _1743352)))]]], (47721 ^ _777081) ^ [_1743667, _1743669, _1743671, _1743673, _1743675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1743667, _1743669)), hAPP(_1743667, _1743671))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1743673, _1743673)), hAPP(hAPP(c_Product__Type_OPair(_1743673, _1743673), _1743669), _1743671)), c_List_Omeasures(_1743673, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1743673, tc_Nat_Onat)), _1743667), _1743675)))))], (47727 ^ _777081) ^ [_1743837, _1743839, _1743841, _1743843] : [-(_1743837 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1743839, tc_HOL_Obool), tc_HOL_Obool))), 47733 ^ _777081 : [(47734 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1743839, tc_HOL_Obool)), 47732 ^ [_1743837, _1743839, _1743841, _1743843]), _1743837)))], (47736 ^ _777081) ^ [] : [c_Fun_Oinj__on(_1743839, _1743841, _1743843, 47732 ^ [_1743837, _1743839, _1743841, _1743843])]], -(c_Fun_Oinj__on(_1743839, _1743841, _1743843, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1743839, tc_HOL_Obool), _1743837)))], (47740 ^ _777081) ^ [_1744098, _1744100, _1744102] : [47742 ^ _777081 : [(47743 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1744098, tc_HOL_Obool)), 47741 ^ [_1744098, _1744100, _1744102]), _1744100)))], (47745 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1744098, tc_HOL_Obool)), 47741 ^ [_1744098, _1744100, _1744102]), _1744102))]], -(_1744100 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1744098, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1744098, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1744098, tc_HOL_Obool), _1744100)), _1744102)))], (47753 ^ _777081) ^ [_1744360, _1744362, _1744364, _1744366, _1744368, _1744370, _1744372, _1744374] : [47755 ^ _777081 : [(47756 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744360), 47754 ^ [_1744360, _1744362, _1744364, _1744366, _1744368, _1744370, _1744372, _1744374]), hAPP(c_List_Oset(_1744360), _1744362))))], (47758 ^ _777081) ^ [] : [hAPP(c_Fun_Ocomp(_1744364, _1744364, _1744366, hAPP(_1744368, 47754 ^ [_1744360, _1744362, _1744364, _1744366, _1744368, _1744370, _1744372, _1744374])), _1744370) = hAPP(c_Fun_Ocomp(_1744366, _1744364, _1744366, _1744370), hAPP(_1744372, 47754 ^ [_1744360, _1744362, _1744364, _1744366, _1744368, _1744370, _1744372, _1744374]))]], -(hAPP(c_List_Ofoldl(_1744364, _1744360, hAPP(c_COMBC(_1744360, _1744364, _1744364), _1744368), hAPP(_1744370, _1744374)), _1744362) = hAPP(_1744370, hAPP(c_List_Ofoldl(_1744366, _1744360, hAPP(c_COMBC(_1744360, _1744366, _1744366), _1744372), _1744374), _1744362)))], (47762 ^ _777081) ^ [_1744728, _1744730, _1744732, _1744734, _1744736, _1744738] : [-(_1744728 = c_Orderings_Obot__class_Obot(tc_fun(_1744730, tc_HOL_Obool))), 47768 ^ _777081 : [(47769 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744730), 47767 ^ [_1744728, _1744730, _1744732, _1744734, _1744736, _1744738]), _1744728)))], (47771 ^ _777081) ^ [] : [c_Fun_Oinj__on(_1744732, _1744734, _1744736, hAPP(_1744738, 47767 ^ [_1744728, _1744730, _1744732, _1744734, _1744736, _1744738]))]], -(c_Fun_Oinj__on(_1744732, _1744734, _1744736, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1744730, tc_fun(_1744732, tc_HOL_Obool)), _1744728), _1744738)))], (47775 ^ _777081) ^ [_1745020, _1745022, _1745024, _1745026, _1745028] : [47776 ^ _777081 : [(47777 ^ _777081) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745020)), hAPP(hAPP(c_List_Otake(_1745020), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745020)), _1745022)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745024)), _1745026))), _1745022)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745024)), hAPP(hAPP(c_List_Otake(_1745024), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745020)), _1745022)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745024)), _1745026))), _1745026)))], (47779 ^ _777081) ^ [] : [hBOOL(hAPP(_1745028, hAPP(hAPP(c_List_Ozip(_1745020, _1745024), hAPP(hAPP(c_List_Otake(_1745020), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745020)), _1745022)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745024)), _1745026))), _1745022)), hAPP(hAPP(c_List_Otake(_1745024), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745020)), _1745022)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1745024)), _1745026))), _1745026))))]], -(hBOOL(hAPP(_1745028, hAPP(hAPP(c_List_Ozip(_1745020, _1745024), _1745022), _1745026))))], (47783 ^ _777081) ^ [_1745432, _1745434, _1745436, _1745438] : [hAPP(c_List_Oset(_1745432), hAPP(hAPP(c_List_Omap(tc_prod(_1745432, _1745434), _1745432), c_Product__Type_Ofst(_1745432, _1745434)), _1745436)) = hAPP(c_List_Oset(_1745432), hAPP(hAPP(c_List_Omap(tc_prod(_1745432, _1745434), _1745432), c_Product__Type_Ofst(_1745432, _1745434)), _1745438)), 47789 ^ _777081 : [(47790 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745432), 47788 ^ [_1745432, _1745434, _1745436, _1745438]), hAPP(c_List_Oset(_1745432), hAPP(hAPP(c_List_Omap(tc_prod(_1745432, _1745434), _1745432), c_Product__Type_Ofst(_1745432, _1745434)), _1745436)))))], (47792 ^ _777081) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1745432, _1745434), _1745436), 47788 ^ [_1745432, _1745434, _1745436, _1745438]) = hAPP(hAPP(c_Map_Omap__of(_1745432, _1745434), _1745438), 47788 ^ [_1745432, _1745434, _1745436, _1745438])]], -(hAPP(c_Map_Omap__of(_1745432, _1745434), _1745436) = hAPP(c_Map_Omap__of(_1745432, _1745434), _1745438))], (47796 ^ _777081) ^ [_1745870, _1745872, _1745874] : [c_Wellfounded_OwfP(_1745870, hAPP(_1745872, 47797 ^ [_1745870, _1745872, _1745874])), 47804 ^ _777081 : [(47805 ^ _777081) ^ [] : [hAPP(_1745872, 47802 ^ [_1745870, _1745872, _1745874]) = hAPP(_1745872, 47803 ^ [_1745870, _1745872, _1745874])], (47807 ^ _777081) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1745870, tc_HOL_Obool)), c_Predicate_ODomainP(_1745870, _1745870, hAPP(_1745872, 47802 ^ [_1745870, _1745872, _1745874]))), c_Predicate_ORangeP(_1745870, _1745870, hAPP(_1745872, 47803 ^ [_1745870, _1745872, _1745874]))) = c_Orderings_Obot__class_Obot(tc_fun(_1745870, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1745870, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1745874, tc_fun(_1745870, tc_fun(_1745870, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1745874, tc_HOL_Obool))), _1745872)))], (47811 ^ _777081) ^ [_1746310, _1746312, _1746314, _1746316] : [47813 ^ _777081 : [(47814 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1746310), 47812 ^ [_1746310, _1746312, _1746314, _1746316]), hAPP(c_List_Oset(_1746310), _1746312))))], (47816 ^ _777081) ^ [] : [hBOOL(hAPP(_1746314, 47812 ^ [_1746310, _1746312, _1746314, _1746316]))]], -(c_List_OdropWhile(_1746310, _1746314, hAPP(hAPP(c_List_Oappend(_1746310), _1746312), _1746316)) = c_List_OdropWhile(_1746310, _1746314, _1746316))], (47820 ^ _777081) ^ [_1746528, _1746530, _1746532, _1746534, _1746536] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746528)), _1746530) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746532)), _1746534), 47826 ^ _777081 : [(47827 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47825 ^ [_1746528, _1746530, _1746532, _1746534, _1746536]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746528)), _1746530))))], (47829 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(_1746536, hAPP(hAPP(c_List_Onth(_1746528), _1746530), 47825 ^ [_1746528, _1746530, _1746532, _1746534, _1746536])), hAPP(hAPP(c_List_Onth(_1746532), _1746534), 47825 ^ [_1746528, _1746530, _1746532, _1746534, _1746536])))]], -(c_List_Olist__all2(_1746528, _1746532, _1746536, _1746530, _1746534))], (47833 ^ _777081) ^ [_1746886, _1746888, _1746890] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1746886), c_Map_Odom(_1746886, _1746888, _1746890))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1746886), c_Orderings_Otop__class_Otop(tc_fun(_1746886, tc_HOL_Obool))))), -(hAPP(_1746890, 47840 ^ [_1746886, _1746888, _1746890]) = c_Option_Ooption_ONone(_1746888))], (47844 ^ _777081) ^ [_1747038, _1747040, _1747042, _1747044, _1747046, _1747048] : [hBOOL(hAPP(hAPP(c_member(_1747038), _1747040), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1747042, _1747044, tc_fun(_1747038, tc_HOL_Obool)), _1747046), _1747048))), 47849 ^ _777081 : [(47850 ^ _777081) ^ [] : [-(_1747048 = hAPP(hAPP(c_Product__Type_OPair(_1747042, _1747044), 47847 ^ [_1747038, _1747040, _1747042, _1747044, _1747046, _1747048]), 47848 ^ [_1747038, _1747040, _1747042, _1747044, _1747046, _1747048]))], (47852 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747038), _1747040), hAPP(hAPP(_1747046, 47847 ^ [_1747038, _1747040, _1747042, _1747044, _1747046, _1747048]), 47848 ^ [_1747038, _1747040, _1747042, _1747044, _1747046, _1747048]))))]]], (47854 ^ _777081) ^ [_1747307, _1747309, _1747311, _1747313, _1747315, _1747317] : [47857 ^ _777081 : [(47858 ^ _777081) ^ [] : [-(_1747307 = hAPP(hAPP(c_Product__Type_OPair(_1747309, _1747311), 47855 ^ [_1747307, _1747309, _1747311, _1747313, _1747315, _1747317]), 47856 ^ [_1747307, _1747309, _1747311, _1747313, _1747315, _1747317]))], (47860 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1747313), _1747315), hAPP(hAPP(_1747317, 47855 ^ [_1747307, _1747309, _1747311, _1747313, _1747315, _1747317]), 47856 ^ [_1747307, _1747309, _1747311, _1747313, _1747315, _1747317])))]], -(hBOOL(hAPP(hAPP(c_member(_1747313), _1747315), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1747309, _1747311, tc_fun(_1747313, tc_HOL_Obool)), _1747317), _1747307))))], (47864 ^ _777081) ^ [_1747632, _1747634] : [class_Orderings_Olinorder(_1747632), hBOOL(hAPP(c_Finite__Set_Ofinite(_1747632), _1747634)), 47872 ^ _777081 : [(47873 ^ _777081) ^ [] : [-(hAPP(c_List_Oset(_1747632), 47871 ^ [_1747632, _1747634]) = _1747634)], (47875 ^ _777081) ^ [] : [-(c_List_Olinorder__class_Osorted(_1747632, 47871 ^ [_1747632, _1747634]))], (47877 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1747632), 47871 ^ [_1747632, _1747634])))], (47879 ^ _777081) ^ [_1747958] : [-(_1747958 = 47871 ^ [_1747632, _1747634]), hAPP(c_List_Oset(_1747632), _1747958) = _1747634, c_List_Olinorder__class_Osorted(_1747632, _1747958), hBOOL(hAPP(c_List_Odistinct(_1747632), _1747958))]]], (47893 ^ _777081) ^ [_1748189, _1748191, _1748193, _1748195] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1748189, tc_Nat_Onat), _1748191), _1748193) = hAPP(c_Nat_OSuc, _1748195), 47897 ^ _777081 : [(47898 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748189), 47896 ^ [_1748189, _1748191, _1748193, _1748195]), _1748193)))], (47900 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1748191, 47896 ^ [_1748189, _1748191, _1748193, _1748195]))))]]], (47902 ^ _777081) ^ [_1748371, _1748373, _1748375] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1748371, _1748373) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1748375, _1748373), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1748375), _1748371)), -(_1748371 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1748375), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1748373), 47909 ^ [_1748371, _1748373, _1748375])))], (47913 ^ _777081) ^ [_1748568, _1748570, _1748572, _1748574] : [47915 ^ _777081 : [(47916 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748568), 47914 ^ [_1748568, _1748570, _1748572, _1748574]), hAPP(c_List_Oset(_1748568), _1748570))))], (47918 ^ _777081) ^ [] : [hBOOL(hAPP(_1748572, 47914 ^ [_1748568, _1748570, _1748572, _1748574]))]], -(c_List_OtakeWhile(_1748568, _1748572, hAPP(hAPP(c_List_Oappend(_1748568), _1748570), _1748574)) = hAPP(hAPP(c_List_Oappend(_1748568), _1748570), c_List_OtakeWhile(_1748568, _1748572, _1748574)))], (47922 ^ _777081) ^ [_1748802, _1748804, _1748806, _1748808, _1748810] : [class_Orderings_Olinorder(_1748802), 47928 ^ _777081 : [(47929 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1748804), 47927 ^ [_1748802, _1748804, _1748806, _1748808, _1748810]), hAPP(c_List_Oset(_1748804), _1748806))))], (47931 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1748802), hAPP(_1748808, _1748810)), hAPP(_1748808, 47927 ^ [_1748802, _1748804, _1748806, _1748808, _1748810])))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1748804, _1748802, _1748808), _1748810), _1748806) = hAPP(hAPP(c_List_Olist_OCons(_1748804), _1748810), _1748806))], (47935 ^ _777081) ^ [_1749121, _1749123] : [47937 ^ _777081 : [(47938 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1749121, tc_HOL_Obool)), 47936 ^ [_1749121, _1749123]), hAPP(c_Relation_OImage(_1749121, _1749121, _1749123), 47936 ^ [_1749121, _1749123]))))], (47940 ^ _777081) ^ [] : [47936 ^ [_1749121, _1749123] = c_Orderings_Obot__class_Obot(tc_fun(_1749121, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1749121, _1749123))], (47944 ^ _777081) ^ [_1749342, _1749344, _1749346, _1749348, _1749350] : [hAPP(c_List_Ofilter(_1749342, _1749344), _1749346) = hAPP(hAPP(c_List_Olist_OCons(_1749342), _1749348), _1749350), 47949 ^ _777081 : [(47950 ^ _777081) ^ [] : [-(_1749346 = hAPP(hAPP(c_List_Oappend(_1749342), 47947 ^ [_1749342, _1749344, _1749346, _1749348, _1749350]), hAPP(hAPP(c_List_Olist_OCons(_1749342), _1749348), 47948 ^ [_1749342, _1749344, _1749346, _1749348, _1749350])))], (47958 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1749344, _1749348)))], (47960 ^ _777081) ^ [] : [-(_1749350 = hAPP(c_List_Ofilter(_1749342, _1749344), 47948 ^ [_1749342, _1749344, _1749346, _1749348, _1749350]))], (47952 ^ _777081) ^ [_1749656] : [hBOOL(hAPP(hAPP(c_member(_1749342), _1749656), hAPP(c_List_Oset(_1749342), 47947 ^ [_1749342, _1749344, _1749346, _1749348, _1749350]))), hBOOL(hAPP(_1749344, _1749656))]]], (47962 ^ _777081) ^ [_1749860, _1749862, _1749864, _1749866, _1749868] : [-(hAPP(c_List_Ofilter(_1749860, _1749862), _1749864) = hAPP(hAPP(c_List_Olist_OCons(_1749860), _1749866), _1749868)), 47963 ^ _777081 : [(47964 ^ _777081) ^ [_1749988, _1749990] : [_1749864 = hAPP(hAPP(c_List_Oappend(_1749860), _1749990), hAPP(hAPP(c_List_Olist_OCons(_1749860), _1749866), _1749988)), 47970 ^ _777081 : [(47971 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1749860), 47969 ^ [_1749860, _1749862, _1749864, _1749866, _1749868, _1749988, _1749990]), hAPP(c_List_Oset(_1749860), _1749990))))], (47973 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1749862, 47969 ^ [_1749860, _1749862, _1749864, _1749866, _1749868, _1749988, _1749990])))]], hBOOL(hAPP(_1749862, _1749866)), _1749868 = hAPP(c_List_Ofilter(_1749860, _1749862), _1749988)]]], (47983 ^ _777081) ^ [_1750410, _1750412, _1750414, _1750416, _1750418] : [hAPP(hAPP(c_List_Olist_OCons(_1750410), _1750412), _1750414) = hAPP(c_List_Ofilter(_1750410, _1750416), _1750418), 47988 ^ _777081 : [(47989 ^ _777081) ^ [] : [-(_1750418 = hAPP(hAPP(c_List_Oappend(_1750410), 47986 ^ [_1750410, _1750412, _1750414, _1750416, _1750418]), hAPP(hAPP(c_List_Olist_OCons(_1750410), _1750412), 47987 ^ [_1750410, _1750412, _1750414, _1750416, _1750418])))], (47997 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1750416, _1750412)))], (47999 ^ _777081) ^ [] : [-(_1750414 = hAPP(c_List_Ofilter(_1750410, _1750416), 47987 ^ [_1750410, _1750412, _1750414, _1750416, _1750418]))], (47991 ^ _777081) ^ [_1750724] : [hBOOL(hAPP(hAPP(c_member(_1750410), _1750724), hAPP(c_List_Oset(_1750410), 47986 ^ [_1750410, _1750412, _1750414, _1750416, _1750418]))), hBOOL(hAPP(_1750416, _1750724))]]], (48001 ^ _777081) ^ [_1750928, _1750930, _1750932, _1750934, _1750936] : [-(hAPP(hAPP(c_List_Olist_OCons(_1750928), _1750930), _1750932) = hAPP(c_List_Ofilter(_1750928, _1750934), _1750936)), 48002 ^ _777081 : [(48003 ^ _777081) ^ [_1751056, _1751058] : [_1750936 = hAPP(hAPP(c_List_Oappend(_1750928), _1751058), hAPP(hAPP(c_List_Olist_OCons(_1750928), _1750930), _1751056)), 48009 ^ _777081 : [(48010 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1750928), 48008 ^ [_1750928, _1750930, _1750932, _1750934, _1750936, _1751056, _1751058]), hAPP(c_List_Oset(_1750928), _1751058))))], (48012 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1750934, 48008 ^ [_1750928, _1750930, _1750932, _1750934, _1750936, _1751056, _1751058])))]], hBOOL(hAPP(_1750934, _1750930)), _1750932 = hAPP(c_List_Ofilter(_1750928, _1750934), _1751056)]]], (48022 ^ _777081) ^ [_1751454, _1751456, _1751458, _1751460, _1751462, _1751464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1751454, tc_HOL_Obool)), _1751456), _1751458)), 48028 ^ _777081 : [(48029 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751454), 48027 ^ [_1751454, _1751456, _1751458, _1751460, _1751462, _1751464]), _1751456)))], (48031 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1751460, tc_HOL_Obool)), hAPP(_1751462, 48027 ^ [_1751454, _1751456, _1751458, _1751460, _1751462, _1751464])), hAPP(_1751464, 48027 ^ [_1751454, _1751456, _1751458, _1751460, _1751462, _1751464])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1751454, _1751460), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1751454, _1751460), _1751456), _1751462)), hAPP(hAPP(c_Product__Type_OSigma(_1751454, _1751460), _1751458), _1751464))))], (48035 ^ _777081) ^ [_1751844, _1751846, _1751848] : [-(hBOOL(hAPP(hAPP(c_member(_1751844), _1751846), c_Wellfounded_Oacc(_1751844, _1751848)))), 48039 ^ _777081 : [(48040 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1751844, _1751844)), hAPP(hAPP(c_Product__Type_OPair(_1751844, _1751844), 48038 ^ [_1751844, _1751846, _1751848]), _1751846)), _1751848)))], (48042 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1751844), 48038 ^ [_1751844, _1751846, _1751848]), c_Wellfounded_Oacc(_1751844, _1751848)))]]], (48044 ^ _777081) ^ [_1752071, _1752073, _1752075] : [48046 ^ _777081 : [(48047 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1752071, _1752071)), hAPP(hAPP(c_Product__Type_OPair(_1752071, _1752071), 48045 ^ [_1752071, _1752073, _1752075]), _1752073)), _1752075)))], (48049 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1752071), 48045 ^ [_1752071, _1752073, _1752075]), c_Wellfounded_Oacc(_1752071, _1752075)))]], -(hBOOL(hAPP(hAPP(c_member(_1752071), _1752073), c_Wellfounded_Oacc(_1752071, _1752075))))], (48053 ^ _777081) ^ [_1752309, _1752311, _1752313, _1752315] : [class_Groups_Ocomm__monoid__mult(_1752309), hBOOL(hAPP(c_Finite__Set_Ofinite(_1752311), _1752313)), 48063 ^ _777081 : [(48064 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752311), 48062 ^ [_1752309, _1752311, _1752313, _1752315]), _1752313)))], (48066 ^ _777081) ^ [] : [hAPP(_1752315, 48062 ^ [_1752309, _1752311, _1752313, _1752315]) = c_Groups_Oone__class_Oone(_1752309)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1752309, _1752311, c_Groups_Otimes__class_Otimes(_1752309)), _1752315), c_Groups_Oone__class_Oone(_1752309)), _1752313) = c_Groups_Oone__class_Oone(_1752309))], (48070 ^ _777081) ^ [_1752650, _1752652] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1752650), _1752652)), 48076 ^ _777081 : [(48077 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752650), 48075 ^ [_1752650, _1752652]), _1752652)))], (48079 ^ _777081) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1752650), _1752652) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48083 ^ _777081) ^ [_1752850, _1752852, _1752854, _1752856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752850), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752852)), _1752854))), 48089 ^ _777081 : [(48090 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752852), 48088 ^ [_1752850, _1752852, _1752854, _1752856]), hAPP(c_List_Oset(_1752852), _1752854))))], (48092 ^ _777081) ^ [] : [hBOOL(hAPP(_1752856, 48088 ^ [_1752850, _1752852, _1752854, _1752856]))]], -(hBOOL(hAPP(_1752856, hAPP(hAPP(c_List_Onth(_1752852), _1752854), _1752850))))], (48096 ^ _777081) ^ [_1753157, _1753159, _1753161, _1753163] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1753157, tc_HOL_Obool), tc_fun(_1753157, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1753157, tc_HOL_Obool), tc_fun(_1753157, tc_HOL_Obool)), _1753159), _1753161)), c_Wellfounded_Omax__ext(_1753157, _1753163))), 48099 ^ _777081 : [(48100 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1753157), _1753159)))], (48102 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1753157), _1753161)))], (48104 ^ _777081) ^ [] : [_1753161 = c_Orderings_Obot__class_Obot(tc_fun(_1753157, tc_HOL_Obool))], (48106 ^ _777081) ^ [_1753451] : [hBOOL(hAPP(hAPP(c_member(_1753157), _1753451), _1753159)), 48110 ^ _777081 : [(48111 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753157), 48109 ^ [_1753157, _1753159, _1753161, _1753163, _1753451]), _1753161)))], (48113 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1753157, _1753157)), hAPP(hAPP(c_Product__Type_OPair(_1753157, _1753157), _1753451), 48109 ^ [_1753157, _1753159, _1753161, _1753163, _1753451])), _1753163)))]]]]], (48115 ^ _777081) ^ [_1753663, _1753665, _1753667, _1753669] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1753663, tc_HOL_Obool), tc_fun(_1753663, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1753663, tc_HOL_Obool), tc_fun(_1753663, tc_HOL_Obool)), _1753665), _1753667)), c_Wellfounded_Omax__ext(_1753663, _1753669)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1753663), _1753665)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1753663), _1753667)), -(_1753667 = c_Orderings_Obot__class_Obot(tc_fun(_1753663, tc_HOL_Obool))), 48129 ^ _777081 : [(48130 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753663), 48128 ^ [_1753663, _1753665, _1753667, _1753669]), _1753665)))], (48132 ^ _777081) ^ [_1754068] : [hBOOL(hAPP(hAPP(c_member(_1753663), _1754068), _1753667)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1753663, _1753663)), hAPP(hAPP(c_Product__Type_OPair(_1753663, _1753663), 48128 ^ [_1753663, _1753665, _1753667, _1753669]), _1754068)), _1753669))]]], (48140 ^ _777081) ^ [_1754296, _1754298, _1754300] : [48142 ^ _777081 : [(48143 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48141 ^ [_1754296, _1754298, _1754300]), _1754296)))], (48145 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1754298, 48141 ^ [_1754296, _1754298, _1754300])))], (48147 ^ _777081) ^ [] : [hBOOL(hAPP(_1754298, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 48141 ^ [_1754296, _1754298, _1754300]), _1754296)))]], hBOOL(hAPP(_1754298, _1754300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1754300), _1754296)), -(hBOOL(hAPP(_1754298, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48159 ^ _777081) ^ [_1754658, _1754660, _1754662] : [class_Orderings_Olinorder(_1754658), 48165 ^ _777081 : [(48166 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754658), 48164 ^ [_1754658, _1754660, _1754662]), hAPP(c_List_Oset(_1754658), _1754660))))], (48168 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1754658), _1754662), 48164 ^ [_1754658, _1754660, _1754662]))]], c_List_Olinorder__class_Osorted(_1754658, _1754660), -(c_List_Olinorder__class_Osorted(_1754658, hAPP(hAPP(c_List_Olist_OCons(_1754658), _1754662), _1754660)))], (48176 ^ _777081) ^ [_1754974, _1754976, _1754978] : [48178 ^ _777081 : [(48179 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1754974, tc_HOL_Obool)), 48177 ^ [_1754974, _1754976, _1754978]), _1754976)))], (48181 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1754974), _1754978), 48177 ^ [_1754974, _1754976, _1754978]))]], -(hBOOL(hAPP(hAPP(c_member(_1754974), _1754978), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1754974, tc_HOL_Obool), _1754976))))], (48185 ^ _777081) ^ [_1755190, _1755192, _1755194, _1755196, _1755198, _1755200] : [class_Groups_Oab__semigroup__mult(_1755190), hBOOL(hAPP(c_Finite__Set_Ofinite(_1755192), _1755194)), 48195 ^ _777081 : [(48196 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1755192), 48194 ^ [_1755190, _1755192, _1755194, _1755196, _1755198, _1755200]), _1755194)))], (48198 ^ _777081) ^ [] : [hAPP(_1755196, 48194 ^ [_1755190, _1755192, _1755194, _1755196, _1755198, _1755200]) = hAPP(_1755198, 48194 ^ [_1755190, _1755192, _1755194, _1755196, _1755198, _1755200])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1755190, _1755192, c_Groups_Otimes__class_Otimes(_1755190)), _1755196), _1755200), _1755194) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1755190, _1755192, c_Groups_Otimes__class_Otimes(_1755190)), _1755198), _1755200), _1755194))], (48202 ^ _777081) ^ [_1755595, _1755597, _1755599] : [class_Orderings_Olinorder(_1755595), hBOOL(hAPP(c_Finite__Set_Ofinite(_1755595), _1755597)), 48212 ^ _777081 : [(48213 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1755595), 48211 ^ [_1755595, _1755597, _1755599]), _1755597)))], (48215 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1755595), 48211 ^ [_1755595, _1755597, _1755599]), _1755599))]], hBOOL(hAPP(hAPP(c_member(_1755595), _1755599), _1755597)), -(c_Big__Operators_Olinorder__class_OMax(_1755595, _1755597) = _1755599)], (48223 ^ _777081) ^ [_1755967, _1755969, _1755971] : [class_Orderings_Olinorder(_1755967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1755967), _1755969)), 48233 ^ _777081 : [(48234 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1755967), 48232 ^ [_1755967, _1755969, _1755971]), _1755969)))], (48236 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1755967), _1755971), 48232 ^ [_1755967, _1755969, _1755971]))]], hBOOL(hAPP(hAPP(c_member(_1755967), _1755971), _1755969)), -(c_Big__Operators_Olinorder__class_OMin(_1755967, _1755969) = _1755971)], (48244 ^ _777081) ^ [_1756339, _1756341, _1756343] : [c_Wellfounded_Owf(_1756339, _1756341), hBOOL(hAPP(hAPP(c_member(tc_prod(_1756339, _1756339)), hAPP(hAPP(c_Product__Type_OPair(_1756339, _1756339), hAPP(_1756343, hAPP(c_Nat_OSuc, 48247 ^ [_1756339, _1756341, _1756343]))), hAPP(_1756343, 48247 ^ [_1756339, _1756341, _1756343]))), _1756341))], (48251 ^ _777081) ^ [_1756558, _1756560, _1756562] : [c_List_Olist__ex(_1756558, _1756560, _1756562), 48255 ^ _777081 : [(48256 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48254 ^ [_1756558, _1756560, _1756562]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756558)), _1756562))))], (48258 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1756560, hAPP(hAPP(c_List_Onth(_1756558), _1756562), 48254 ^ [_1756558, _1756560, _1756562]))))]]], (48260 ^ _777081) ^ [_1756728, _1756730, _1756732] : [-(c_List_Olist__ex(_1756728, _1756730, _1756732)), 48261 ^ _777081 : [(48262 ^ _777081) ^ [_1756793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1756793), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756728)), _1756732))), hBOOL(hAPP(_1756730, hAPP(hAPP(c_List_Onth(_1756728), _1756732), _1756793)))]]], (48270 ^ _777081) ^ [_1756948, _1756950, _1756952, _1756954, _1756956, _1756958, _1756960, _1756962] : [class_Groups_Ocomm__monoid__add(_1756948), c_Fun_Oinj__on(_1756950, _1756952, _1756954, _1756956), _1756958 = hAPP(c_Set_Oimage(_1756950, _1756952, _1756954), _1756956), 48284 ^ _777081 : [(48285 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756950), 48283 ^ [_1756948, _1756950, _1756952, _1756954, _1756956, _1756958, _1756960, _1756962]), _1756956)))], (48287 ^ _777081) ^ [] : [hAPP(_1756960, 48283 ^ [_1756948, _1756950, _1756952, _1756954, _1756956, _1756958, _1756960, _1756962]) = hAPP(_1756962, hAPP(_1756954, 48283 ^ [_1756948, _1756950, _1756952, _1756954, _1756956, _1756958, _1756960, _1756962]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1756952, _1756948), _1756962), _1756958) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1756950, _1756948), _1756960), _1756956))], (48291 ^ _777081) ^ [_1757452, _1757454] : [c_List_Olist__ex(_1757452, _1757454, c_List_Olist_ONil(_1757452))], (48293 ^ _777081) ^ [_1757498, _1757500, _1757502] : [c_List_Olist__ex(_1757498, _1757500, hAPP(c_List_Orev(_1757498), _1757502)), -(c_List_Olist__ex(_1757498, _1757500, _1757502))], (48299 ^ _777081) ^ [_1757587, _1757589, _1757591] : [c_List_Olist__ex(_1757587, _1757589, _1757591), -(c_List_Olist__ex(_1757587, _1757589, hAPP(c_List_Orev(_1757587), _1757591)))], (48305 ^ _777081) ^ [_1757700, _1757702, _1757704] : [c_List_Olist__ex(_1757700, _1757702, _1757704), 48309 ^ _777081 : [(48310 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757700), 48308 ^ [_1757700, _1757702, _1757704]), hAPP(c_List_Oset(_1757700), _1757704))))], (48312 ^ _777081) ^ [] : [-(hBOOL(hAPP(_1757702, 48308 ^ [_1757700, _1757702, _1757704])))]]], (48314 ^ _777081) ^ [_1757854, _1757856, _1757858] : [-(c_List_Olist__ex(_1757854, _1757856, _1757858)), 48315 ^ _777081 : [(48316 ^ _777081) ^ [_1757911] : [hBOOL(hAPP(hAPP(c_member(_1757854), _1757911), hAPP(c_List_Oset(_1757854), _1757858))), hBOOL(hAPP(_1757856, _1757911))]]], (48334 ^ _777081) ^ [_1758183, _1758185, _1758187, _1758189] : [48335 ^ _777081 : [(48336 ^ _777081) ^ [] : [c_List_Olist__ex(_1758183, _1758185, _1758187)], (48338 ^ _777081) ^ [] : [c_List_Olist__ex(_1758183, _1758185, _1758189)]], -(c_List_Olist__ex(_1758183, _1758185, hAPP(hAPP(c_List_Oappend(_1758183), _1758187), _1758189)))], (48324 ^ _777081) ^ [_1758071, _1758073, _1758075, _1758077] : [c_List_Olist__ex(_1758071, _1758073, hAPP(hAPP(c_List_Oappend(_1758071), _1758075), _1758077)), -(c_List_Olist__ex(_1758071, _1758073, _1758075)), -(c_List_Olist__ex(_1758071, _1758073, _1758077))], (48352 ^ _777081) ^ [_1758572, _1758574, _1758576, _1758578] : [48353 ^ _777081 : [(48354 ^ _777081) ^ [] : [hBOOL(hAPP(_1758574, _1758576))], (48356 ^ _777081) ^ [] : [c_List_Olist__ex(_1758572, _1758574, _1758578)]], -(c_List_Olist__ex(_1758572, _1758574, hAPP(hAPP(c_List_Olist_OCons(_1758572), _1758576), _1758578)))], (48342 ^ _777081) ^ [_1758347, _1758349, _1758351, _1758353] : [c_List_Olist__ex(_1758347, _1758349, hAPP(hAPP(c_List_Olist_OCons(_1758347), _1758351), _1758353)), -(hBOOL(hAPP(_1758349, _1758351))), -(c_List_Olist__ex(_1758347, _1758349, _1758353))], (48360 ^ _777081) ^ [_1758953, _1758955, _1758957, _1758959, _1758961, _1758963, _1758965] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1758953, _1758955, _1758957, _1758959), _1758961), _1758963), _1758965) = hAPP(hAPP(_1758963, hAPP(c_Product__Type_Ofst(_1758955, _1758957), hAPP(_1758961, _1758965))), hAPP(c_Product__Type_Osnd(_1758955, _1758957), hAPP(_1758961, _1758965))))], (48362 ^ _777081) ^ [_1759194, _1759196, _1759198, _1759200, _1759202, _1759204, _1759206, _1759208] : [class_Groups_Ocomm__monoid__add(_1759194), class_Orderings_Oord(_1759196), _1759198 = _1759200, _1759202 = _1759204, 48380 ^ _777081 : [(48381 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1759196), _1759200), 48379 ^ [_1759194, _1759196, _1759198, _1759200, _1759202, _1759204, _1759206, _1759208])))], (48383 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1759196), 48379 ^ [_1759194, _1759196, _1759198, _1759200, _1759202, _1759204, _1759206, _1759208]), _1759204)))], (48385 ^ _777081) ^ [] : [hAPP(_1759206, 48379 ^ [_1759194, _1759196, _1759198, _1759200, _1759202, _1759204, _1759206, _1759208]) = hAPP(_1759208, 48379 ^ [_1759194, _1759196, _1759198, _1759200, _1759202, _1759204, _1759206, _1759208])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1759196, _1759194), _1759206), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1759196, _1759198), _1759202)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1759196, _1759194), _1759208), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1759196, _1759200), _1759204)))], (48389 ^ _777081) ^ [_1760400, _1760402, _1760404, _1760406, _1760408, _1760410, _1760412] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1760400, _1760402, _1760404, _1760406), _1760408), _1760410), _1760412) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1760402, _1760404, _1760406), _1760410), hAPP(_1760408, _1760412)))], (48391 ^ _777081) ^ [_1760601, _1760603, _1760605, _1760607, _1760609, _1760611, _1760613] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1760601, _1760603, _1760605, _1760607), _1760609), _1760611), _1760613) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1760603, _1760605, _1760607), _1760611), hAPP(_1760609, _1760613)))], (48393 ^ _777081) ^ [_1760760, _1760762, _1760764, _1760766] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1760760, _1760762, _1760764, tc_prod(_1760762, _1760764)), _1760766), c_Product__Type_OPair(_1760762, _1760764)) = _1760766)], (48395 ^ _777081) ^ [_1760917, _1760919, _1760921, _1760923, _1760925] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1760917, _1760919, _1760917, _1760921), hAPP(c_Product__Type_OPair(_1760919, _1760917), _1760923)), _1760925) = hAPP(_1760925, _1760923))], (48397 ^ _777081) ^ [_1761135, _1761137, _1761139, _1761141, _1761143, _1761145, _1761147, _1761149, _1761151] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1761135, _1761137, _1761139, _1761141), hAPP(hAPP(c_Product__Type_Oscomp(_1761135, _1761143, _1761145, tc_prod(_1761137, _1761139)), _1761147), _1761149)), _1761151) = hAPP(hAPP(c_Product__Type_Oscomp(_1761135, _1761143, _1761145, _1761141), _1761147), hAPP(hAPP(c_COMBC(_1761143, tc_fun(_1761137, tc_fun(_1761139, _1761141)), tc_fun(_1761145, _1761141)), hAPP(hAPP(c_COMBB(tc_fun(_1761145, tc_prod(_1761137, _1761139)), tc_fun(tc_fun(_1761137, tc_fun(_1761139, _1761141)), tc_fun(_1761145, _1761141)), _1761143), c_Product__Type_Oscomp(_1761145, _1761137, _1761139, _1761141)), _1761149)), _1761151)))], (48399 ^ _777081) ^ [_1761408, _1761410, _1761412, _1761414, _1761416] : [_1761408 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1761410, _1761412, _1761408, _1761414), _1761416) = hAPP(c_Product__Type_OPair(_1761410, _1761412), _1761416))], (48405 ^ _777081) ^ [_1761616, _1761618, _1761620, _1761622, _1761624] : [-(_1761616 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1761618, _1761620, _1761616, _1761622), _1761624) = hAPP(hAPP(c_Product__Type_Oscomp(_1761620, _1761618, _1761620, tc_prod(_1761618, _1761620)), hAPP(_1761622, _1761624)), c_Random_Oiterate(_1761618, _1761620, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1761616), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1761622)))], (48411 ^ _777081) ^ [_1761950, _1761952] : [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), _1761950), _1761952)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761950), _1761952)))], (48417 ^ _777081) ^ [_1762144, _1762146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1762144), _1762146)), -(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), _1762144), _1762146)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (48423 ^ _777081) ^ [_1762417, _1762419] : [c_Wellfounded_Oacyclic(_1762417, _1762419), 48426 ^ _777081 : [(48427 ^ _777081) ^ [_1762556] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1762417, _1762417)), hAPP(hAPP(c_Product__Type_OPair(_1762417, _1762417), _1762556), _1762556)), c_Transitive__Closure_Otrancl(_1762417, _1762419)))]]], (48429 ^ _777081) ^ [_1762646, _1762648] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1762646, _1762646)), hAPP(hAPP(c_Product__Type_OPair(_1762646, _1762646), 48430 ^ [_1762646, _1762648]), 48430 ^ [_1762646, _1762648])), c_Transitive__Closure_Otrancl(_1762646, _1762648)))), -(c_Wellfounded_Oacyclic(_1762646, _1762648))], (48436 ^ _777081) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (48438 ^ _777081) ^ [_1763046, _1763048] : [c_Wellfounded_Owf(_1763046, _1763048), -(c_Wellfounded_Owf(_1763046, c_Transitive__Closure_Otrancl(_1763046, _1763048)))], (48444 ^ _777081) ^ [_1763290, _1763292, _1763294, _1763296] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763290, _1763290)), hAPP(hAPP(c_Product__Type_OPair(_1763290, _1763290), _1763292), _1763294)), _1763296)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763290, _1763290)), hAPP(hAPP(c_Product__Type_OPair(_1763290, _1763290), _1763292), _1763294)), c_Transitive__Closure_Otrancl(_1763290, _1763296))))], (48450 ^ _777081) ^ [_1763579, _1763581] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1763579, _1763579), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1763579, _1763581)), hAPP(hAPP(c_Product__Type_OSigma(_1763579, _1763579), hAPP(c_Relation_OField(_1763579), _1763581)), hAPP(c_COMBK(tc_fun(_1763579, tc_HOL_Obool), _1763579), hAPP(c_Relation_OField(_1763579), _1763581))))))], (48452 ^ _777081) ^ [_1763746, _1763748, _1763750] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763746, _1763746)), _1763748), _1763750)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763746, _1763746)), _1763748), c_Transitive__Closure_Otrancl(_1763746, _1763750))))], (48458 ^ _777081) ^ [_1763979] : [-(c_Transitive__Closure_Otrancl(_1763979, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1763979, _1763979), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1763979, _1763979), tc_HOL_Obool)))], (48460 ^ _777081) ^ [_1764090, _1764092] : [-(hAPP(c_Relation_ODomain(_1764090, _1764090), c_Transitive__Closure_Otrancl(_1764090, _1764092)) = hAPP(c_Relation_ODomain(_1764090, _1764090), _1764092))], (48462 ^ _777081) ^ [_1764199, _1764201] : [-(hAPP(c_Relation_ORange(_1764199, _1764199), c_Transitive__Closure_Otrancl(_1764199, _1764201)) = hAPP(c_Relation_ORange(_1764199, _1764199), _1764201))], (48464 ^ _777081) ^ [_1764352, _1764354] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1764352, _1764352)), c_Transitive__Closure_Otrancl(_1764352, _1764354))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1764352, _1764352)), _1764354)))], (48470 ^ _777081) ^ [_1764548, _1764550] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1764548, _1764548)), _1764550)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1764548, _1764548)), c_Transitive__Closure_Otrancl(_1764548, _1764550))))], (48476 ^ _777081) ^ [_1764836, _1764838, _1764840, _1764842, _1764844] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764836, _1764836)), hAPP(hAPP(c_Product__Type_OPair(_1764836, _1764836), _1764838), _1764840)), _1764842)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764836, _1764836)), hAPP(hAPP(c_Product__Type_OPair(_1764836, _1764836), _1764840), _1764844)), _1764842)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764836, _1764836)), hAPP(hAPP(c_Product__Type_OPair(_1764836, _1764836), _1764838), _1764844)), c_Transitive__Closure_Otrancl(_1764836, _1764842))))], (48486 ^ _777081) ^ [_1765327, _1765329, _1765331, _1765333, _1765335] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1765327, _1765327)), hAPP(hAPP(c_Product__Type_OPair(_1765327, _1765327), _1765329), _1765331)), _1765333)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1765327, _1765327)), hAPP(hAPP(c_Product__Type_OPair(_1765327, _1765327), _1765331), _1765335)), c_Transitive__Closure_Otrancl(_1765327, _1765333))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765327, _1765327)), hAPP(hAPP(c_Product__Type_OPair(_1765327, _1765327), _1765329), _1765335)), c_Transitive__Closure_Otrancl(_1765327, _1765333))))], (48496 ^ _777081) ^ [_1765824, _1765826, _1765828, _1765830, _1765832] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1765824, _1765824)), hAPP(hAPP(c_Product__Type_OPair(_1765824, _1765824), _1765826), _1765828)), c_Transitive__Closure_Otrancl(_1765824, _1765830))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1765824, _1765824)), hAPP(hAPP(c_Product__Type_OPair(_1765824, _1765824), _1765828), _1765832)), _1765830)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765824, _1765824)), hAPP(hAPP(c_Product__Type_OPair(_1765824, _1765824), _1765826), _1765832)), c_Transitive__Closure_Otrancl(_1765824, _1765830))))], (48506 ^ _777081) ^ [_1766321, _1766323, _1766325, _1766327, _1766329] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1766321, _1766321)), hAPP(hAPP(c_Product__Type_OPair(_1766321, _1766321), _1766323), _1766325)), c_Transitive__Closure_Otrancl(_1766321, _1766327))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1766321, _1766321)), hAPP(hAPP(c_Product__Type_OPair(_1766321, _1766321), _1766325), _1766329)), c_Transitive__Closure_Otrancl(_1766321, _1766327))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1766321, _1766321)), hAPP(hAPP(c_Product__Type_OPair(_1766321, _1766321), _1766323), _1766329)), c_Transitive__Closure_Otrancl(_1766321, _1766327))))], (48516 ^ _777081) ^ [_1766810, _1766812, _1766814, _1766816] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1766810, _1766810)), _1766812), c_Transitive__Closure_Otrancl(_1766810, _1766814))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1766810, _1766810), tc_HOL_Obool)), _1766814), _1766816)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1766810, _1766810)), _1766812), c_Transitive__Closure_Otrancl(_1766810, _1766816))))], (48526 ^ _777081) ^ [_1767192, _1767194] : [-(c_Transitive__Closure_Otrancl(_1767192, _1767194) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1767192, _1767192), tc_HOL_Obool)), _1767194), hAPP(hAPP(c_Relation_Orel__comp(_1767192, _1767192, _1767192), c_Transitive__Closure_Otrancl(_1767192, _1767194)), _1767194)))], (48528 ^ _777081) ^ [_1767345, _1767347, _1767349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767345, _1767345), tc_HOL_Obool)), _1767347), hAPP(hAPP(c_Product__Type_OSigma(_1767345, _1767345), _1767349), hAPP(c_COMBK(tc_fun(_1767345, tc_HOL_Obool), _1767345), _1767349)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767345, _1767345), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1767345, _1767347)), hAPP(hAPP(c_Product__Type_OSigma(_1767345, _1767345), _1767349), hAPP(c_COMBK(tc_fun(_1767345, tc_HOL_Obool), _1767345), _1767349)))))], (48534 ^ _777081) ^ [_1767705, _1767707, _1767709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767705, _1767705), tc_HOL_Obool)), _1767707), _1767709)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767705, _1767705), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1767705, _1767705, _1767705), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1767705, _1767705), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1767705, _1767707)), _1767709)), _1767707)), _1767709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1767705, _1767705), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1767705, _1767707)), _1767709)))], (48544 ^ _777081) ^ [_1768172, _1768174] : [48545 ^ _777081 : [(48546 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1768172), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (48548 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1768174), _1768172))]], -(c_Random_Olog(_1768172, _1768174) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (48552 ^ _777081) ^ [_1768434, _1768436] : [-(c_Random_Olog(_1768434, _1768436) = 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(_1768434, hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral, _1768436), _1768434)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1768434), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1768436), _1768434)))], (48562 ^ _777081) ^ [_1768823, _1768825, _1768827] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1768823), _1768825)), -(c_Random_Ominus__shift(_1768827, _1768823, _1768825) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1768827), _1768823)), _1768825))], (48568 ^ _777081) ^ [_1769033, _1769035, _1769037] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1769033), _1769035))), -(c_Random_Ominus__shift(_1769037, _1769033, _1769035) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1769033), _1769035))], (48574 ^ _777081) ^ [_1769304, _1769306] : [_1769304 = _1769306, -(c_Random_Oinc__shift(_1769304, _1769306) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (48580 ^ _777081) ^ [_1769472, _1769474] : [-(_1769472 = _1769474), -(c_Random_Oinc__shift(_1769472, _1769474) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1769474), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (48586 ^ _777081) ^ [_1769719, _1769721, _1769723] : [-(_1769719 = c_List_Olist_ONil(_1769721)), -(hBOOL(hAPP(hAPP(c_member(_1769721), hAPP(c_Product__Type_Ofst(_1769721, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1769721, _1769719), _1769723))), hAPP(c_List_Oset(_1769721), _1769719))))], (48592 ^ _777081) ^ [_1770004, _1770006, _1770008] : [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, _1770004), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1770004)), _1770006)))), -(hBOOL(hAPP(hAPP(c_member(_1770004), hAPP(c_Product__Type_Ofst(_1770004, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1770004, _1770006), _1770008))), hAPP(c_List_Oset(_1770004), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1770004), _1770004), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1770004)), _1770006)))))], (48598 ^ _777081) ^ [_1770338, _1770340] : [-(_1770338 = c_List_Olist_ONil(_1770340)), -(c_Random_Oselect__weight(_1770340, hAPP(hAPP(c_List_Omap(_1770340, tc_prod(tc_Code__Numeral_Ocode__numeral, _1770340)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1770340), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1770338)) = c_Random_Oselect(_1770340, _1770338))], (48604 ^ _777081) ^ [_1770602, _1770604, _1770606] : [-(c_Random_Oselect__weight(_1770602, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1770602)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1770602), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1770604)), _1770606)) = c_Random_Oselect__weight(_1770602, _1770606))], (48606 ^ _777081) ^ [_1770724, _1770726] : [-(c_Random_Oselect__weight(_1770724, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1770724), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1770724, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1770724, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1770724)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1770726)) = c_Random_Oselect__weight(_1770724, _1770726))], (48608 ^ _777081) ^ [_1770885, _1770887, _1770889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1770885), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1770887), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1770887)), _1770889)))), -(hBOOL(hAPP(hAPP(c_member(_1770887), hAPP(c_Random_Opick(_1770887, _1770889), _1770885)), hAPP(c_List_Oset(_1770887), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1770887), _1770887), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1770887)), _1770889)))))], (48614 ^ _777081) ^ [_1771261, _1771263, _1771265, _1771267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1771261), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1771263), _1771265))), -(hAPP(c_Random_Opick(_1771263, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1771263)), _1771265), _1771267)), _1771261) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1771263), _1771265))], (48620 ^ _777081) ^ [_1771503, _1771505, _1771507, _1771509] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1771503), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1771505), _1771507)))), -(hAPP(c_Random_Opick(_1771505, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1771505)), _1771507), _1771509)), _1771503) = hAPP(c_Random_Opick(_1771505, _1771509), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1771503), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1771505), _1771507))))], (48626 ^ _777081) ^ [_1771807, _1771809] : [-(c_Random_Opick(_1771807, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1771807), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1771807, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1771807, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1771807)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1771809)) = c_Random_Opick(_1771807, _1771809))], (48628 ^ _777081) ^ [_1771939, _1771941] : [-(c_Random_Oselect__weight(_1771939, _1771941) = 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(_1771939, 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, _1771939), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1771939)), _1771941)))), hAPP(hAPP(c_COMBB(_1771939, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1771939, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1771939, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1771939, _1771941))))], (48630 ^ _777081) ^ [_1772121, _1772123, _1772125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1772121), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1772123)), _1772125))), -(hAPP(c_Random_Opick(_1772123, hAPP(hAPP(c_List_Omap(_1772123, tc_prod(tc_Code__Numeral_Ocode__numeral, _1772123)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1772123), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1772125)), hAPP(c_Code__Numeral_Oof__nat, _1772121)) = hAPP(hAPP(c_List_Onth(_1772123), _1772125), _1772121))], (48636 ^ _777081) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (48638 ^ _777081) ^ [_1772469, _1772471] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1772469)), hAPP(c_Code__Numeral_Oof__nat, _1772471)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1772469), _1772471)))], (48640 ^ _777081) ^ [_1772628, _1772630] : [hAPP(c_Code__Numeral_Oof__nat, _1772628) = hAPP(c_Code__Numeral_Oof__nat, _1772630), -(_1772628 = _1772630)], (48646 ^ _777081) ^ [_1772802, _1772804] : [_1772802 = _1772804, -(hAPP(c_Code__Numeral_Oof__nat, _1772802) = hAPP(c_Code__Numeral_Oof__nat, _1772804))], (48652 ^ _777081) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (48654 ^ _777081) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48656 ^ _777081) ^ [_1773132, _1773134] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1773132), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1773134), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 48663 ^ _777081 : [(48664 ^ _777081) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1773132) = hAPP(c_Code__Numeral_Oof__nat, _1773134), -(_1773132 = _1773134)], (48670 ^ _777081) ^ [] : [_1773132 = _1773134, -(hAPP(c_Code__Numeral_Oof__nat, _1773132) = hAPP(c_Code__Numeral_Oof__nat, _1773134))]]], (48676 ^ _777081) ^ [] : [-(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))], (48678 ^ _777081) ^ [_1773801, _1773803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1773801)), hAPP(c_Code__Numeral_Oof__nat, _1773803))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1773801), _1773803)))], (48684 ^ _777081) ^ [_1773995, _1773997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1773995), _1773997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1773995)), hAPP(c_Code__Numeral_Oof__nat, _1773997))))], (48690 ^ _777081) ^ [_1774224, _1774226] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1774224)), hAPP(c_Code__Numeral_Oof__nat, _1774226)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1774224), _1774226)))], (48692 ^ _777081) ^ [_1774383, _1774385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1774383)), hAPP(c_Code__Numeral_Oof__nat, _1774385))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1774383), _1774385)))], (48698 ^ _777081) ^ [_1774577, _1774579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1774577), _1774579)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1774577)), hAPP(c_Code__Numeral_Oof__nat, _1774579))))], (48704 ^ _777081) ^ [_1774836] : [-(_1774836 = 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)), _1774836)))], (48710 ^ _777081) ^ [_1774999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1774999)), _1774999 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48716 ^ _777081) ^ [_1775210, _1775212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1775210)), -(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(_1775210), _1775212))), _1775210)))], (48722 ^ _777081) ^ [_1775435, _1775437] : [-(c_Random_Oselect(_1775435, _1775437) = 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(_1775435, 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(_1775435)), _1775437)))), hAPP(hAPP(c_COMBB(_1775435, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1775435, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1775435, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1775435, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1775435), _1775437)), c_Code__Numeral_Onat__of))))], (48724 ^ _777081) ^ [_1775620, _1775622, _1775624, _1775626] : [-(c_Transitive__Closure_Otrancl(_1775620, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1775620, _1775620)), hAPP(hAPP(c_Product__Type_OPair(_1775620, _1775620), _1775622), _1775624)), _1775626)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1775620, _1775620), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1775620, _1775626)), hAPP(c_Set_OCollect(tc_prod(_1775620, _1775620)), hAPP(c_Product__Type_Oprod_Oprod__case(_1775620, _1775620, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1775620, tc_fun(_1775620, tc_HOL_Obool), tc_fun(_1775620, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1775620, tc_HOL_Obool), tc_fun(_1775620, tc_HOL_Obool)), _1775620), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1775620)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1775620), c_fconj), hAPP(hAPP(c_COMBC(_1775620, tc_fun(tc_prod(_1775620, _1775620), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1775620, _1775620), tc_fun(tc_fun(tc_prod(_1775620, _1775620), tc_HOL_Obool), tc_HOL_Obool), _1775620), c_member(tc_prod(_1775620, _1775620))), hAPP(hAPP(c_COMBC(_1775620, _1775620, tc_prod(_1775620, _1775620)), c_Product__Type_OPair(_1775620, _1775620)), _1775622))), c_Transitive__Closure_Ortrancl(_1775620, _1775626))))), hAPP(hAPP(c_COMBC(_1775620, tc_fun(tc_prod(_1775620, _1775620), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1775620, _1775620), tc_fun(tc_fun(tc_prod(_1775620, _1775620), tc_HOL_Obool), tc_HOL_Obool), _1775620), c_member(tc_prod(_1775620, _1775620))), hAPP(c_Product__Type_OPair(_1775620, _1775620), _1775624))), c_Transitive__Closure_Ortrancl(_1775620, _1775626)))))))], (48726 ^ _777081) ^ [_1775965, _1775967, _1775969] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775965, _1775965)), _1775967), _1775969)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775965, _1775965)), _1775967), c_Transitive__Closure_Ortrancl(_1775965, _1775969))))], (48732 ^ _777081) ^ [_1776226, _1776228, _1776230] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776226, _1776226)), hAPP(hAPP(c_Product__Type_OPair(_1776226, _1776226), _1776228), _1776228)), c_Transitive__Closure_Ortrancl(_1776226, _1776230))))], (48734 ^ _777081) ^ [_1776387, _1776389, _1776391, _1776393] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776387, _1776387)), hAPP(hAPP(c_Product__Type_OPair(_1776387, _1776387), _1776389), _1776391)), c_Transitive__Closure_Otrancl(_1776387, _1776393))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776387, _1776387)), hAPP(hAPP(c_Product__Type_OPair(_1776387, _1776387), _1776389), _1776391)), c_Transitive__Closure_Ortrancl(_1776387, _1776393))))], (48740 ^ _777081) ^ [_1776696, _1776698, _1776700] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1776696), tc_List_Olist(_1776696))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1776696), tc_List_Olist(_1776696)), _1776698), _1776698)), c_List_Olistrel(_1776696, c_Transitive__Closure_Ortrancl(_1776696, _1776700)))))], (48742 ^ _777081) ^ [_1776896, _1776898, _1776900, _1776902, _1776904, _1776906] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776896, _1776896)), hAPP(hAPP(c_Product__Type_OPair(_1776896, _1776896), _1776898), _1776900)), c_Transitive__Closure_Ortrancl(_1776896, _1776902))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1776896), tc_List_Olist(_1776896))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1776896), tc_List_Olist(_1776896)), _1776904), _1776906)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1776896), c_List_Olistrel1(_1776896, _1776902)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1776896), tc_List_Olist(_1776896))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1776896), tc_List_Olist(_1776896)), hAPP(hAPP(c_List_Olist_OCons(_1776896), _1776898), _1776904)), hAPP(hAPP(c_List_Olist_OCons(_1776896), _1776900), _1776906))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1776896), c_List_Olistrel1(_1776896, _1776902)))))], (48752 ^ _777081) ^ [_1777422] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1777422)) = _1777422)], (48754 ^ _777081) ^ [_1777506] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1777506)) = _1777506)], (48756 ^ _777081) ^ [_1777590] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1777590)) = _1777590)], (48758 ^ _777081) ^ [_1777688, _1777690] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1777688), _1777690) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1777688)), hAPP(c_Code__Numeral_Onat__of, _1777690))))], (48760 ^ _777081) ^ [] : [-(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))))], (48762 ^ _777081) ^ [_1777913, _1777915, _1777917, _1777919, _1777921] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1777913), tc_List_Olist(_1777913))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1777913), tc_List_Olist(_1777913)), _1777915), _1777917)), c_List_Olistrel(_1777913, c_Transitive__Closure_Ortrancl(_1777913, _1777919)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1777913), tc_List_Olist(_1777913))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1777913), tc_List_Olist(_1777913)), _1777917), _1777921)), c_List_Olistrel(_1777913, c_Transitive__Closure_Ortrancl(_1777913, _1777919)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1777913), tc_List_Olist(_1777913))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1777913), tc_List_Olist(_1777913)), _1777915), _1777921)), c_List_Olistrel(_1777913, c_Transitive__Closure_Ortrancl(_1777913, _1777919)))))], (48772 ^ _777081) ^ [_1778482, _1778484, _1778486, _1778488, _1778490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1778482, _1778482)), hAPP(hAPP(c_Product__Type_OPair(_1778482, _1778482), _1778484), _1778486)), c_Transitive__Closure_Ortrancl(_1778482, _1778488))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1778482, _1778482)), hAPP(hAPP(c_Product__Type_OPair(_1778482, _1778482), _1778486), _1778490)), c_Transitive__Closure_Ortrancl(_1778482, _1778488))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778482, _1778482)), hAPP(hAPP(c_Product__Type_OPair(_1778482, _1778482), _1778484), _1778490)), c_Transitive__Closure_Ortrancl(_1778482, _1778488))))], (48782 ^ _777081) ^ [_1778985, _1778987, _1778989, _1778991, _1778993] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1778985, _1778985)), hAPP(hAPP(c_Product__Type_OPair(_1778985, _1778985), _1778987), _1778989)), c_Transitive__Closure_Ortrancl(_1778985, _1778991))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1778985, _1778985)), hAPP(hAPP(c_Product__Type_OPair(_1778985, _1778985), _1778989), _1778993)), _1778991)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778985, _1778985)), hAPP(hAPP(c_Product__Type_OPair(_1778985, _1778985), _1778987), _1778993)), c_Transitive__Closure_Ortrancl(_1778985, _1778991))))], (48792 ^ _777081) ^ [_1779482, _1779484, _1779486, _1779488, _1779490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779482, _1779482)), hAPP(hAPP(c_Product__Type_OPair(_1779482, _1779482), _1779484), _1779486)), _1779488)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1779482, _1779482)), hAPP(hAPP(c_Product__Type_OPair(_1779482, _1779482), _1779486), _1779490)), c_Transitive__Closure_Ortrancl(_1779482, _1779488))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779482, _1779482)), hAPP(hAPP(c_Product__Type_OPair(_1779482, _1779482), _1779484), _1779490)), c_Transitive__Closure_Ortrancl(_1779482, _1779488))))], (48802 ^ _777081) ^ [_1779994, _1779996, _1779998, _1780000] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779994, _1779994)), hAPP(hAPP(c_Product__Type_OPair(_1779994, _1779994), _1779996), _1779998)), c_Transitive__Closure_Ortrancl(_1779994, _1780000))), -(_1779996 = _1779998), 48809 ^ _777081 : [(48810 ^ _777081) ^ [] : [_1779996 = _1779998], (48812 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779994, _1779994)), hAPP(hAPP(c_Product__Type_OPair(_1779994, _1779994), _1779996), _1779998)), c_Transitive__Closure_Otrancl(_1779994, _1780000))))]]], (48814 ^ _777081) ^ [_1780434, _1780436, _1780438, _1780440] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780434, _1780434)), hAPP(hAPP(c_Product__Type_OPair(_1780434, _1780434), _1780436), _1780438)), c_Transitive__Closure_Ortrancl(_1780434, _1780440)))), 48815 ^ _777081 : [(48816 ^ _777081) ^ [] : [_1780436 = _1780438], (48818 ^ _777081) ^ [] : [-(_1780436 = _1780438), hBOOL(hAPP(hAPP(c_member(tc_prod(_1780434, _1780434)), hAPP(hAPP(c_Product__Type_OPair(_1780434, _1780434), _1780436), _1780438)), c_Transitive__Closure_Otrancl(_1780434, _1780440)))]]], (48826 ^ _777081) ^ [_1780966, _1780968, _1780970, _1780972, _1780974] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780966, _1780966)), hAPP(hAPP(c_Product__Type_OPair(_1780966, _1780966), _1780968), _1780970)), _1780972)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1780966, _1780966)), hAPP(hAPP(c_Product__Type_OPair(_1780966, _1780966), _1780970), _1780974)), c_Transitive__Closure_Ortrancl(_1780966, _1780972))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780966, _1780966)), hAPP(hAPP(c_Product__Type_OPair(_1780966, _1780966), _1780968), _1780974)), c_Transitive__Closure_Otrancl(_1780966, _1780972))))], (48836 ^ _777081) ^ [_1781449, _1781451, _1781453, _1781455] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1781449, _1781449)), hAPP(hAPP(c_Product__Type_OPair(_1781449, _1781449), _1781451), _1781453)), c_Transitive__Closure_Ortrancl(_1781449, _1781455))), -(_1781451 = _1781453), 48843 ^ _777081 : [(48844 ^ _777081) ^ [] : [_1781451 = _1781453], (48846 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1781449, _1781449)), hAPP(hAPP(c_Product__Type_OPair(_1781449, _1781449), _1781451), _1781453)), c_Transitive__Closure_Otrancl(_1781449, _1781455))))]]], (48848 ^ _777081) ^ [_1781979, _1781981, _1781983, _1781985, _1781987] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1781979, _1781979)), hAPP(hAPP(c_Product__Type_OPair(_1781979, _1781979), _1781981), _1781983)), c_Transitive__Closure_Ortrancl(_1781979, _1781985))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1781979, _1781979)), hAPP(hAPP(c_Product__Type_OPair(_1781979, _1781979), _1781983), _1781987)), _1781985)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1781979, _1781979)), hAPP(hAPP(c_Product__Type_OPair(_1781979, _1781979), _1781981), _1781987)), c_Transitive__Closure_Otrancl(_1781979, _1781985))))], (48858 ^ _777081) ^ [_1782476, _1782478, _1782480, _1782482, _1782484] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1782476, _1782476)), hAPP(hAPP(c_Product__Type_OPair(_1782476, _1782476), _1782478), _1782480)), c_Transitive__Closure_Otrancl(_1782476, _1782482))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1782476, _1782476)), hAPP(hAPP(c_Product__Type_OPair(_1782476, _1782476), _1782480), _1782484)), c_Transitive__Closure_Ortrancl(_1782476, _1782482))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782476, _1782476)), hAPP(hAPP(c_Product__Type_OPair(_1782476, _1782476), _1782478), _1782484)), c_Transitive__Closure_Otrancl(_1782476, _1782482))))], (48868 ^ _777081) ^ [_1782979, _1782981, _1782983, _1782985, _1782987] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1782979, _1782979)), hAPP(hAPP(c_Product__Type_OPair(_1782979, _1782979), _1782981), _1782983)), c_Transitive__Closure_Ortrancl(_1782979, _1782985))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1782979, _1782979)), hAPP(hAPP(c_Product__Type_OPair(_1782979, _1782979), _1782983), _1782987)), c_Transitive__Closure_Otrancl(_1782979, _1782985))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1782979, _1782979)), hAPP(hAPP(c_Product__Type_OPair(_1782979, _1782979), _1782981), _1782987)), c_Transitive__Closure_Otrancl(_1782979, _1782985))))], (48878 ^ _777081) ^ [_1783454, _1783456, _1783458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1783454, _1783454), tc_HOL_Obool)), _1783456), _1783458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1783454, _1783454), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1783454, _1783456)), c_Transitive__Closure_Ortrancl(_1783454, _1783458))))], (48884 ^ _777081) ^ [_1783748, _1783750, _1783752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1783748, _1783748), tc_HOL_Obool)), _1783750), _1783752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1783748, _1783748), tc_HOL_Obool)), _1783752), c_Transitive__Closure_Ortrancl(_1783748, _1783750))), -(c_Transitive__Closure_Ortrancl(_1783748, _1783752) = c_Transitive__Closure_Ortrancl(_1783748, _1783750))], (48894 ^ _777081) ^ [_1784141, _1784143, _1784145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1784141, _1784141), tc_HOL_Obool)), _1784143), c_Transitive__Closure_Ortrancl(_1784141, _1784145))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1784141, _1784141), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1784141, _1784143)), c_Transitive__Closure_Ortrancl(_1784141, _1784145))))], (48900 ^ _777081) ^ [_1784426, _1784428, _1784430] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1784426, _1784426), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1784426, _1784426), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1784426, _1784428)), c_Transitive__Closure_Ortrancl(_1784426, _1784430))), c_Transitive__Closure_Ortrancl(_1784426, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1784426, _1784426), tc_HOL_Obool)), _1784428), _1784430)))))], (48902 ^ _777081) ^ [_1784601, _1784603, _1784605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1784601, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1784601, _1784601, _1784603), _1784605)), _1784605)), -(hAPP(c_Relation_OImage(_1784601, _1784601, c_Transitive__Closure_Ortrancl(_1784601, _1784603)), _1784605) = _1784605)], (48908 ^ _777081) ^ [_1784900, _1784902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1784900), _1784902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1784900)), hAPP(c_Code__Numeral_Onat__of, _1784902))))], (48914 ^ _777081) ^ [_1785094, _1785096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1785094)), hAPP(c_Code__Numeral_Onat__of, _1785096))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1785094), _1785096)))], (48920 ^ _777081) ^ [_1785367, _1785369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1785367), _1785369)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1785367)), hAPP(c_Code__Numeral_Onat__of, _1785369))))], (48926 ^ _777081) ^ [_1785561, _1785563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1785561)), hAPP(c_Code__Numeral_Onat__of, _1785563))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1785561), _1785563)))], (48932 ^ _777081) ^ [_1785790, _1785792] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1785790), tc_List_Olist(_1785790)), tc_HOL_Obool)), c_List_Olistrel1(_1785790, c_Transitive__Closure_Ortrancl(_1785790, _1785792))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1785790), c_List_Olistrel1(_1785790, _1785792)))))], (48934 ^ _777081) ^ [_1785901] : [-(hAPP(c_Code__Numeral_Onat__of, _1785901) = c_Code__Numeral_Onat__of__aux(_1785901, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48936 ^ _777081) ^ [_1785985] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1785985)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1785985))], (48938 ^ _777081) ^ [] : [-(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))], (48940 ^ _777081) ^ [_1786139, _1786141] : [-(c_List_Olistrel(_1786139, c_Transitive__Closure_Ortrancl(_1786139, _1786141)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1786139), c_List_Olistrel1(_1786139, _1786141)))], (48942 ^ _777081) ^ [_1786291, _1786293] : [hAPP(c_Code__Numeral_Onat__of, _1786291) = hAPP(c_Code__Numeral_Onat__of, _1786293), -(_1786291 = _1786293)], (48948 ^ _777081) ^ [_1786465, _1786467] : [_1786465 = _1786467, -(hAPP(c_Code__Numeral_Onat__of, _1786465) = hAPP(c_Code__Numeral_Onat__of, _1786467))], (48954 ^ _777081) ^ [_1786718, _1786720] : [hAPP(c_Code__Numeral_Onat__of, _1786718) = hAPP(c_Code__Numeral_Onat__of, _1786720), -(_1786718 = _1786720)], (48960 ^ _777081) ^ [_1786892, _1786894] : [_1786892 = _1786894, -(hAPP(c_Code__Numeral_Onat__of, _1786892) = hAPP(c_Code__Numeral_Onat__of, _1786894))], (48966 ^ _777081) ^ [_1787087] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1787087)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (48968 ^ _777081) ^ [_1787187, _1787189] : [-(c_Transitive__Closure_Ortrancl(_1787187, c_Transitive__Closure_Ortrancl(_1787187, _1787189)) = c_Transitive__Closure_Ortrancl(_1787187, _1787189))], (48970 ^ _777081) ^ [_1787304, _1787306, _1787308] : [-(c_Transitive__Closure_Ortrancl(_1787304, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1787304, _1787304), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1787304, _1787306)), c_Transitive__Closure_Ortrancl(_1787304, _1787308))) = c_Transitive__Closure_Ortrancl(_1787304, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1787304, _1787304), tc_HOL_Obool)), _1787306), _1787308)))], (48972 ^ _777081) ^ [_1787440, _1787442] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1787440, _1787440, _1787440), c_Transitive__Closure_Ortrancl(_1787440, _1787442)), c_Transitive__Closure_Ortrancl(_1787440, _1787442)) = c_Transitive__Closure_Ortrancl(_1787440, _1787442))], (48974 ^ _777081) ^ [_1787553, _1787555] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1787553, _1787553, _1787553), _1787555), c_Transitive__Closure_Ortrancl(_1787553, _1787555)) = hAPP(hAPP(c_Relation_Orel__comp(_1787553, _1787553, _1787553), c_Transitive__Closure_Ortrancl(_1787553, _1787555)), _1787555))], (48976 ^ _777081) ^ [_1787673, _1787675] : [-(hAPP(c_Relation_ODomain(_1787673, _1787673), c_Transitive__Closure_Ortrancl(_1787673, _1787675)) = c_Orderings_Otop__class_Otop(tc_fun(_1787673, tc_HOL_Obool)))], (48978 ^ _777081) ^ [_1787781, _1787783] : [-(hAPP(c_Relation_ORange(_1787781, _1787781), c_Transitive__Closure_Ortrancl(_1787781, _1787783)) = c_Orderings_Otop__class_Otop(tc_fun(_1787781, tc_HOL_Obool)))], (48980 ^ _777081) ^ [_1787932, _1787934, _1787936, _1787938] : [48981 ^ _777081 : [(48982 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1787932, _1787932)), _1787934), c_Transitive__Closure_Ortrancl(_1787932, _1787936)))], (48984 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1787932, _1787932)), _1787934), c_Transitive__Closure_Ortrancl(_1787932, _1787938)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1787932, _1787932)), _1787934), c_Transitive__Closure_Ortrancl(_1787932, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1787932, _1787932), tc_HOL_Obool)), _1787936), _1787938)))))], (48988 ^ _777081) ^ [_1788323, _1788325] : [-(c_Relation_Orefl__on(_1788323, c_Orderings_Otop__class_Otop(tc_fun(_1788323, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1788323, _1788325)))], (48990 ^ _777081) ^ [_1788426, _1788428] : [-(c_Transitive__Closure_Otrancl(_1788426, _1788428) = hAPP(hAPP(c_Relation_Orel__comp(_1788426, _1788426, _1788426), _1788428), c_Transitive__Closure_Ortrancl(_1788426, _1788428)))], (48992 ^ _777081) ^ [_1788536, _1788538] : [-(c_Transitive__Closure_Otrancl(_1788536, _1788538) = hAPP(hAPP(c_Relation_Orel__comp(_1788536, _1788536, _1788536), c_Transitive__Closure_Ortrancl(_1788536, _1788538)), _1788538))], (48994 ^ _777081) ^ [_1788646, _1788648] : [-(c_Transitive__Closure_Otrancl(_1788646, c_Transitive__Closure_Ortrancl(_1788646, _1788648)) = c_Transitive__Closure_Ortrancl(_1788646, _1788648))], (48996 ^ _777081) ^ [_1788749, _1788751] : [-(c_Transitive__Closure_Ortrancl(_1788749, c_Transitive__Closure_Otrancl(_1788749, _1788751)) = c_Transitive__Closure_Ortrancl(_1788749, _1788751))], (48998 ^ _777081) ^ [_1788852, _1788854] : [-(c_Code__Numeral_Onat__of__aux(_1788852, _1788854) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1788852)), _1788854))], (49000 ^ _777081) ^ [_1788958, _1788960] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1788958), tc_List_Olist(_1788958)), tc_HOL_Obool)), c_List_Olistrel(_1788958, _1788960)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1788958), c_List_Olistrel1(_1788958, _1788960)))))], (49002 ^ _777081) ^ [_1789123, _1789125, _1789127, _1789129] : [-(hBOOL(hAPP(hAPP(c_member(_1789123), _1789125), hAPP(c_Relation_ODomain(_1789123, _1789123), _1789127)))), 49005 ^ _777081 : [(49006 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1789123, _1789123)), hAPP(hAPP(c_Product__Type_OPair(_1789123, _1789123), _1789125), _1789129)), c_Transitive__Closure_Ortrancl(_1789123, _1789127))), -(_1789125 = _1789129)], (49012 ^ _777081) ^ [] : [_1789125 = _1789129, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1789123, _1789123)), hAPP(hAPP(c_Product__Type_OPair(_1789123, _1789123), _1789125), _1789129)), c_Transitive__Closure_Ortrancl(_1789123, _1789127))))]]], (49018 ^ _777081) ^ [_1789738, _1789740, _1789742, _1789744] : [hBOOL(hAPP(hAPP(c_member(_1789738), _1789740), c_Wellfounded_Oacc(_1789738, _1789742))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1789738, _1789738)), hAPP(hAPP(c_Product__Type_OPair(_1789738, _1789738), _1789744), _1789740)), c_Transitive__Closure_Ortrancl(_1789738, _1789742))), -(hBOOL(hAPP(hAPP(c_member(_1789738), _1789744), c_Wellfounded_Oacc(_1789738, _1789742))))], (49028 ^ _777081) ^ [_1790169, _1790171, _1790173, _1790175] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1790169, _1790169)), hAPP(hAPP(c_Product__Type_OPair(_1790169, _1790169), _1790171), _1790173)), c_Transitive__Closure_Ortrancl(_1790169, _1790175))), hBOOL(hAPP(hAPP(c_member(_1790169), _1790173), c_Wellfounded_Oacc(_1790169, _1790175))), -(hBOOL(hAPP(hAPP(c_member(_1790169), _1790171), c_Wellfounded_Oacc(_1790169, _1790175))))], (49038 ^ _777081) ^ [_1790629, _1790631, _1790633, _1790635] : [c_Wellfounded_Owf(_1790629, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1790629, _1790629)), hAPP(hAPP(c_Product__Type_OPair(_1790629, _1790629), _1790631), _1790633)), _1790635)), 49041 ^ _777081 : [(49042 ^ _777081) ^ [] : [-(c_Wellfounded_Owf(_1790629, _1790635))], (49044 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1790629, _1790629)), hAPP(hAPP(c_Product__Type_OPair(_1790629, _1790629), _1790633), _1790631)), c_Transitive__Closure_Ortrancl(_1790629, _1790635)))]]], (49046 ^ _777081) ^ [_1790967, _1790969, _1790971, _1790973] : [-(c_Wellfounded_Owf(_1790967, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1790967, _1790967)), hAPP(hAPP(c_Product__Type_OPair(_1790967, _1790967), _1790969), _1790971)), _1790973))), c_Wellfounded_Owf(_1790967, _1790973), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1790967, _1790967)), hAPP(hAPP(c_Product__Type_OPair(_1790967, _1790967), _1790971), _1790969)), c_Transitive__Closure_Ortrancl(_1790967, _1790973))))], (49056 ^ _777081) ^ [_1791417, _1791419, _1791421, _1791423, _1791425] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1791417), tc_List_Olist(_1791417))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1791417), tc_List_Olist(_1791417)), _1791419), _1791421)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1791417), c_List_Olistrel1(_1791417, _1791423)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1791417), tc_List_Olist(_1791417))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1791417), tc_List_Olist(_1791417)), hAPP(hAPP(c_List_Olist_OCons(_1791417), _1791425), _1791419)), hAPP(hAPP(c_List_Olist_OCons(_1791417), _1791425), _1791421))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1791417), c_List_Olistrel1(_1791417, _1791423)))))], (49062 ^ _777081) ^ [_1791845, _1791847, _1791849, _1791851] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1791845), tc_List_Olist(_1791845))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1791845), tc_List_Olist(_1791845)), _1791847), _1791849)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1791845), c_List_Olistrel1(_1791845, _1791851)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791845)), _1791847) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1791845)), _1791849))], (49068 ^ _777081) ^ [_1792222, _1792224, _1792226, _1792228] : [c_Wellfounded_Oacyclic(_1792222, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1792222, _1792222)), hAPP(hAPP(c_Product__Type_OPair(_1792222, _1792222), _1792224), _1792226)), _1792228)), 49071 ^ _777081 : [(49072 ^ _777081) ^ [] : [-(c_Wellfounded_Oacyclic(_1792222, _1792228))], (49074 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1792222, _1792222)), hAPP(hAPP(c_Product__Type_OPair(_1792222, _1792222), _1792226), _1792224)), c_Transitive__Closure_Ortrancl(_1792222, _1792228)))]]], (49076 ^ _777081) ^ [_1792560, _1792562, _1792564, _1792566] : [-(c_Wellfounded_Oacyclic(_1792560, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1792560, _1792560)), hAPP(hAPP(c_Product__Type_OPair(_1792560, _1792560), _1792562), _1792564)), _1792566))), c_Wellfounded_Oacyclic(_1792560, _1792566), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1792560, _1792560)), hAPP(hAPP(c_Product__Type_OPair(_1792560, _1792560), _1792564), _1792562)), c_Transitive__Closure_Ortrancl(_1792560, _1792566))))], (49086 ^ _777081) ^ [_1792996, _1792998, _1793000, _1793002] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1792996), tc_List_Olist(_1792996))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1792996), tc_List_Olist(_1792996)), _1792998), _1793000)), c_List_Olistrel1(_1792996, _1793002))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1792996), tc_List_Olist(_1792996))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1792996), tc_List_Olist(_1792996)), _1792998), _1793000)), c_List_Olistrel(_1792996, c_Transitive__Closure_Ortrancl(_1792996, _1793002)))))], (49092 ^ _777081) ^ [_1793372, _1793374, _1793376, _1793378] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1793372), tc_List_Olist(_1793372))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1793372), tc_List_Olist(_1793372)), _1793374), _1793376)), c_List_Olistrel(_1793372, _1793378))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1793372), tc_List_Olist(_1793372))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1793372), tc_List_Olist(_1793372)), _1793374), _1793376)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1793372), c_List_Olistrel1(_1793372, _1793378)))))], (49098 ^ _777081) ^ [_1793695] : [-(c_Code__Numeral_OSuc__code__numeral(_1793695) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1793695))))], (49100 ^ _777081) ^ [_1793798, _1793800] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1793798), _1793800) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1793798)), hAPP(c_Code__Numeral_Onat__of, _1793800))))], (49102 ^ _777081) ^ [_1793914] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1793914), 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, _1793914)) = _1793914)], (49108 ^ _777081) ^ [_1794125, _1794127] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1794125), _1794127) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1794125)), hAPP(c_Code__Numeral_Onat__of, _1794127))))], (49110 ^ _777081) ^ [_1794240, _1794242] : [-(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral, _1794240), _1794242) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1794240)), hAPP(c_Code__Numeral_Onat__of, _1794242))))], (49112 ^ _777081) ^ [_1794399, _1794401] : [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), _1794399), _1794401)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1794399), _1794401)))], (49118 ^ _777081) ^ [_1794593, _1794595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1794593), _1794595)), -(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), _1794593), _1794595)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (49124 ^ _777081) ^ [_1794822, _1794824] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1794822, _1794824) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1794822), hAPP(c_Code__Numeral_Onat__of, _1794824))))], (49126 ^ _777081) ^ [_1794990, _1794992, _1794994, _1794996, _1794998] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1794990, _1794990)), hAPP(hAPP(c_Product__Type_OPair(_1794990, _1794990), _1794992), _1794994)), c_Transitive__Closure_Ortrancl(_1794990, _1794996))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1794990, _1794990), tc_HOL_Obool)), _1794996), hAPP(hAPP(c_Product__Type_OSigma(_1794990, _1794990), _1794998), hAPP(c_COMBK(tc_fun(_1794990, tc_HOL_Obool), _1794990), _1794998)))), -(_1794992 = _1794994), -(hBOOL(hAPP(hAPP(c_member(_1794990), _1794992), _1794998)))], (49140 ^ _777081) ^ [_1795527] : [-(_1795527 = 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, _1795527)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1795527))))], (49146 ^ _777081) ^ [_1795753, _1795755] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1795753)), hAPP(c_Code__Numeral_Oof__nat, _1795755)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1795753), _1795755)))], (49148 ^ _777081) ^ [_1795868, _1795870] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1795868), _1795870) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1795868, 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)))), _1795870))))], (49150 ^ _777081) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (49152 ^ _777081) ^ [_1796028, _1796030] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1796028), _1796030) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1796028), _1796030))], (49154 ^ _777081) ^ [_1796163, _1796165, _1796167] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1796163, _1796163), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1796163, _1796163), _1796165)), c_Transitive__Closure_Ortrancl(_1796163, _1796165)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1796163, _1796163), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1796163, _1796163)), hAPP(hAPP(c_Product__Type_OPair(_1796163, _1796163), _1796167), _1796167)), c_Transitive__Closure_Otrancl(_1796163, _1796165)))], (49160 ^ _777081) ^ [_1796528, _1796530, _1796532, _1796534, _1796536] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1796528, _1796528)), hAPP(hAPP(c_Product__Type_OPair(_1796528, _1796528), hAPP(_1796530, hAPP(c_Nat_OSuc, 49161 ^ [_1796528, _1796530, _1796532, _1796534, _1796536]))), hAPP(_1796530, 49161 ^ [_1796528, _1796530, _1796532, _1796534, _1796536]))), c_Transitive__Closure_Ortrancl(_1796528, _1796532))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1796528, _1796528)), hAPP(hAPP(c_Product__Type_OPair(_1796528, _1796528), hAPP(_1796530, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1796534), _1796536))), hAPP(_1796530, _1796534))), c_Transitive__Closure_Ortrancl(_1796528, _1796532))))], (49167 ^ _777081) ^ [_1797033, _1797035, _1797037, _1797039] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1797033, _1797033)), hAPP(hAPP(c_Product__Type_OPair(_1797033, _1797033), _1797035), _1797037)), c_Transitive__Closure_Ortrancl(_1797033, hAPP(c_Relation_Oconverse(_1797033, _1797033), _1797039)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1797033, _1797033)), hAPP(hAPP(c_Product__Type_OPair(_1797033, _1797033), _1797037), _1797035)), c_Transitive__Closure_Ortrancl(_1797033, _1797039))))], (49173 ^ _777081) ^ [_1797383, _1797385, _1797387, _1797389] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1797383, _1797383)), hAPP(hAPP(c_Product__Type_OPair(_1797383, _1797383), _1797385), _1797387)), c_Transitive__Closure_Ortrancl(_1797383, _1797389))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1797383, _1797383)), hAPP(hAPP(c_Product__Type_OPair(_1797383, _1797383), _1797387), _1797385)), c_Transitive__Closure_Ortrancl(_1797383, hAPP(c_Relation_Oconverse(_1797383, _1797383), _1797389)))))], (49179 ^ _777081) ^ [_1797690, _1797692] : [-(c_Transitive__Closure_Ortrancl(_1797690, hAPP(c_Relation_Oconverse(_1797690, _1797690), _1797692)) = hAPP(c_Relation_Oconverse(_1797690, _1797690), c_Transitive__Closure_Ortrancl(_1797690, _1797692)))], (49181 ^ _777081) ^ [_1797888, _1797890, _1797892, _1797894, _1797896] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1797888, _1797890)), hAPP(hAPP(c_Product__Type_OPair(_1797888, _1797890), _1797892), _1797894)), hAPP(c_Relation_Oconverse(_1797890, _1797888), _1797896))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1797890, _1797888)), hAPP(hAPP(c_Product__Type_OPair(_1797890, _1797888), _1797894), _1797892)), _1797896)))], (49187 ^ _777081) ^ [_1798156, _1798158, _1798160, _1798162, _1798164] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1798158, _1798156)), hAPP(hAPP(c_Product__Type_OPair(_1798158, _1798156), _1798162), _1798160)), _1798164)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1798156, _1798158)), hAPP(hAPP(c_Product__Type_OPair(_1798156, _1798158), _1798160), _1798162)), hAPP(c_Relation_Oconverse(_1798158, _1798156), _1798164))))], (49193 ^ _777081) ^ [_1798516, _1798518, _1798520, _1798522, _1798524] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1798516, _1798518)), hAPP(hAPP(c_Product__Type_OPair(_1798516, _1798518), _1798520), _1798522)), _1798524)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1798518, _1798516)), hAPP(hAPP(c_Product__Type_OPair(_1798518, _1798516), _1798522), _1798520)), hAPP(c_Relation_Oconverse(_1798516, _1798518), _1798524))))], (49199 ^ _777081) ^ [_1798874, _1798876, _1798878, _1798880, _1798882] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1798874, _1798876)), hAPP(hAPP(c_Product__Type_OPair(_1798874, _1798876), _1798878), _1798880)), hAPP(c_Relation_Oconverse(_1798876, _1798874), _1798882))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1798876, _1798874)), hAPP(hAPP(c_Product__Type_OPair(_1798876, _1798874), _1798880), _1798878)), _1798882)))], (49205 ^ _777081) ^ [_1799247, _1799249, _1799251, _1799253] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1799247), tc_List_Olist(_1799247))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1799247), tc_List_Olist(_1799247)), _1799249), _1799251)), c_List_Olistrel1(_1799247, hAPP(c_Relation_Oconverse(_1799247, _1799247), _1799253)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1799247), tc_List_Olist(_1799247))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1799247), tc_List_Olist(_1799247)), _1799249), _1799251)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1799247), tc_List_Olist(_1799247)), c_List_Olistrel1(_1799247, _1799253)))))], (49211 ^ _777081) ^ [_1799573, _1799575, _1799577, _1799579] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1799573), tc_List_Olist(_1799573))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1799573), tc_List_Olist(_1799573)), _1799575), _1799577)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1799573), tc_List_Olist(_1799573)), c_List_Olistrel1(_1799573, _1799579)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1799573), tc_List_Olist(_1799573))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1799573), tc_List_Olist(_1799573)), _1799575), _1799577)), c_List_Olistrel1(_1799573, hAPP(c_Relation_Oconverse(_1799573, _1799573), _1799579)))))], (49217 ^ _777081) ^ [_1799977, _1799979, _1799981, _1799983] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1799977, _1799977)), hAPP(hAPP(c_Product__Type_OPair(_1799977, _1799977), _1799979), _1799981)), hAPP(c_Relation_Oconverse(_1799977, _1799977), c_Transitive__Closure_Otrancl(_1799977, _1799983)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1799977, _1799977)), hAPP(hAPP(c_Product__Type_OPair(_1799977, _1799977), _1799979), _1799981)), c_Transitive__Closure_Otrancl(_1799977, hAPP(c_Relation_Oconverse(_1799977, _1799977), _1799983)))))], (49223 ^ _777081) ^ [_1800339, _1800341, _1800343, _1800345] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1800339, _1800339)), hAPP(hAPP(c_Product__Type_OPair(_1800339, _1800339), _1800341), _1800343)), c_Transitive__Closure_Otrancl(_1800339, hAPP(c_Relation_Oconverse(_1800339, _1800339), _1800345)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1800339, _1800339)), hAPP(hAPP(c_Product__Type_OPair(_1800339, _1800339), _1800341), _1800343)), hAPP(c_Relation_Oconverse(_1800339, _1800339), c_Transitive__Closure_Otrancl(_1800339, _1800345)))))], (49229 ^ _777081) ^ [_1800700, _1800702, _1800704, _1800706, _1800708] : [-(hAPP(c_Relation_Oconverse(_1800700, _1800702), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1800704, tc_fun(tc_prod(_1800700, _1800702), tc_HOL_Obool)), _1800706), _1800708)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1800704, tc_fun(tc_prod(_1800702, _1800700), tc_HOL_Obool)), _1800706), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1800700, _1800702), tc_HOL_Obool), tc_fun(tc_prod(_1800702, _1800700), tc_HOL_Obool), _1800704), c_Relation_Oconverse(_1800700, _1800702)), _1800708)))], (49231 ^ _777081) ^ [_1800903, _1800905, _1800907, _1800909, _1800911] : [-(hAPP(c_Relation_Oconverse(_1800903, _1800905), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1800907, tc_fun(tc_prod(_1800903, _1800905), tc_HOL_Obool)), _1800909), _1800911)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1800907, tc_fun(tc_prod(_1800905, _1800903), tc_HOL_Obool)), _1800909), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1800903, _1800905), tc_HOL_Obool), tc_fun(tc_prod(_1800905, _1800903), tc_HOL_Obool), _1800907), c_Relation_Oconverse(_1800903, _1800905)), _1800911)))], (49233 ^ _777081) ^ [_1801092, _1801094, _1801096, _1801098] : [-(hAPP(c_Relation_Oconverse(_1801092, _1801094), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1801092, _1801094), tc_HOL_Obool)), _1801096), _1801098)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1801094, _1801092), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1801092, _1801094), _1801096)), hAPP(c_Relation_Oconverse(_1801092, _1801094), _1801098)))], (49235 ^ _777081) ^ [_1801236, _1801238] : [-(c_List_Olistrel1(_1801236, hAPP(c_Relation_Oconverse(_1801236, _1801236), _1801238)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1801236), tc_List_Olist(_1801236)), c_List_Olistrel1(_1801236, _1801238)))], (49237 ^ _777081) ^ [_1801410, _1801412, _1801414] : [c_Relation_Orefl__on(_1801410, _1801412, hAPP(c_Relation_Oconverse(_1801410, _1801410), _1801414)), -(c_Relation_Orefl__on(_1801410, _1801412, _1801414))], (49243 ^ _777081) ^ [_1801594, _1801596, _1801598] : [c_Relation_Orefl__on(_1801594, _1801596, _1801598), -(c_Relation_Orefl__on(_1801594, _1801596, hAPP(c_Relation_Oconverse(_1801594, _1801594), _1801598)))], (49249 ^ _777081) ^ [_1801842, _1801844, _1801846] : [c_Equiv__Relations_Oequiv(_1801842, _1801844, _1801846), -(hAPP(hAPP(c_Relation_Orel__comp(_1801842, _1801842, _1801842), hAPP(c_Relation_Oconverse(_1801842, _1801842), _1801846)), _1801846) = _1801846)], (49255 ^ _777081) ^ [_1802119, _1802121, _1802123, _1802125, _1802127] : [-(hAPP(c_Relation_Oconverse(_1802119, _1802121), hAPP(hAPP(c_Relation_Orel__comp(_1802119, _1802123, _1802121), _1802125), _1802127)) = hAPP(hAPP(c_Relation_Orel__comp(_1802121, _1802123, _1802119), hAPP(c_Relation_Oconverse(_1802123, _1802121), _1802127)), hAPP(c_Relation_Oconverse(_1802119, _1802123), _1802125)))], (49257 ^ _777081) ^ [_1802285, _1802287, _1802289, _1802291] : [-(hAPP(c_Relation_Oconverse(_1802285, _1802287), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1802285, _1802287), tc_HOL_Obool)), _1802289), _1802291)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1802287, _1802285), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1802285, _1802287), _1802289)), hAPP(c_Relation_Oconverse(_1802285, _1802287), _1802291)))], (49259 ^ _777081) ^ [_1802429, _1802431] : [-(hAPP(c_Relation_Oconverse(_1802429, _1802429), c_Relation_OId__on(_1802429, _1802431)) = c_Relation_OId__on(_1802429, _1802431))], (49261 ^ _777081) ^ [_1802549, _1802551, _1802553] : [-(hAPP(c_Relation_Oconverse(_1802549, _1802551), hAPP(c_Relation_Oconverse(_1802551, _1802549), _1802553)) = _1802553)], (49263 ^ _777081) ^ [_1802657, _1802659] : [-(hAPP(c_Relation_OField(_1802657), hAPP(c_Relation_Oconverse(_1802657, _1802657), _1802659)) = hAPP(c_Relation_OField(_1802657), _1802659))], (49265 ^ _777081) ^ [_1802811, _1802813] : [c_Wellfounded_Oacyclic(_1802811, hAPP(c_Relation_Oconverse(_1802811, _1802811), _1802813)), -(c_Wellfounded_Oacyclic(_1802811, _1802813))], (49271 ^ _777081) ^ [_1802985, _1802987] : [c_Wellfounded_Oacyclic(_1802985, _1802987), -(c_Wellfounded_Oacyclic(_1802985, hAPP(c_Relation_Oconverse(_1802985, _1802985), _1802987)))], (49277 ^ _777081) ^ [_1803252, _1803254, _1803256] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1803252, _1803254)), hAPP(c_Relation_Oconverse(_1803254, _1803252), _1803256))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1803254, _1803252)), _1803256)))], (49283 ^ _777081) ^ [_1803460, _1803462, _1803464] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1803462, _1803460)), _1803464)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1803460, _1803462)), hAPP(c_Relation_Oconverse(_1803462, _1803460), _1803464))))], (49289 ^ _777081) ^ [_1803717, _1803719, _1803721] : [-(hAPP(c_Relation_ORange(_1803717, _1803719), _1803721) = hAPP(c_Relation_ODomain(_1803719, _1803717), hAPP(c_Relation_Oconverse(_1803717, _1803719), _1803721)))], (49291 ^ _777081) ^ [_1803845, _1803847, _1803849] : [-(hAPP(c_Relation_ODomain(_1803845, _1803847), hAPP(c_Relation_Oconverse(_1803847, _1803845), _1803849)) = hAPP(c_Relation_ORange(_1803847, _1803845), _1803849))], (49293 ^ _777081) ^ [_1803973, _1803975, _1803977] : [-(hAPP(c_Relation_ORange(_1803973, _1803975), hAPP(c_Relation_Oconverse(_1803975, _1803973), _1803977)) = hAPP(c_Relation_ODomain(_1803975, _1803973), _1803977))], (49295 ^ _777081) ^ [_1804115, _1804117, _1804119, _1804121] : [-(hAPP(c_Relation_Oconverse(_1804115, _1804115), hAPP(hAPP(c_Relation_Oinv__image(_1804117, _1804115), _1804119), _1804121)) = hAPP(hAPP(c_Relation_Oinv__image(_1804117, _1804115), hAPP(c_Relation_Oconverse(_1804117, _1804117), _1804119)), _1804121))], (49297 ^ _777081) ^ [_1804258, _1804260] : [c_Wellfounded_Owf(_1804258, hAPP(c_Relation_Oconverse(_1804258, _1804258), _1804260)), -(c_Wellfounded_Owf(_1804258, hAPP(c_Relation_Oconverse(_1804258, _1804258), c_Transitive__Closure_Otrancl(_1804258, _1804260))))], (49303 ^ _777081) ^ [_1804483, _1804485] : [-(c_Transitive__Closure_Otrancl(_1804483, hAPP(c_Relation_Oconverse(_1804483, _1804483), _1804485)) = hAPP(c_Relation_Oconverse(_1804483, _1804483), c_Transitive__Closure_Otrancl(_1804483, _1804485)))], (49305 ^ _777081) ^ [_1804681, _1804683, _1804685, _1804687, _1804689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1804681, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1804683, _1804681, _1804685), _1804687)), _1804689)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1804683, tc_HOL_Obool)), _1804687), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1804683, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1804681, _1804683, hAPP(c_Relation_Oconverse(_1804683, _1804681), _1804685)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1804681, tc_HOL_Obool)), _1804689))))))], (49311 ^ _777081) ^ [_1804973, _1804975, _1804977, _1804979, _1804981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1804975, tc_HOL_Obool)), _1804979), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1804975, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1804973, _1804975, hAPP(c_Relation_Oconverse(_1804975, _1804973), _1804977)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1804973, tc_HOL_Obool)), _1804981))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1804973, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1804975, _1804973, _1804977), _1804979)), _1804981)))], (49317 ^ _777081) ^ [_1805329, _1805331, _1805333] : [c_Relation_Orefl__on(_1805329, _1805331, _1805333), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1805329, _1805329), tc_HOL_Obool)), _1805333), hAPP(hAPP(c_Relation_Orel__comp(_1805329, _1805329, _1805329), hAPP(c_Relation_Oconverse(_1805329, _1805329), _1805333)), _1805333))))], (49323 ^ _777081) ^ [_1805619, _1805621, _1805623] : [hAPP(hAPP(c_Relation_Orel__comp(_1805619, _1805619, _1805619), hAPP(c_Relation_Oconverse(_1805619, _1805619), _1805621)), _1805621) = _1805621, hAPP(c_Relation_ODomain(_1805619, _1805619), _1805621) = _1805623, -(c_Equiv__Relations_Oequiv(_1805619, _1805623, _1805621))], (49333 ^ _777081) ^ [_1805974, _1805976] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1805974, _1805974)), _1805976)), c_Wellfounded_Oacyclic(_1805974, _1805976), -(c_Wellfounded_Owf(_1805974, hAPP(c_Relation_Oconverse(_1805974, _1805974), _1805976)))], (49343 ^ _777081) ^ [_1806298, _1806300, _1806302] : [-(hAPP(c_Relation_Oconverse(_1806298, _1806300), _1806302) = hAPP(c_Set_OCollect(tc_prod(_1806300, _1806298)), hAPP(c_Product__Type_Oprod_Oprod__case(_1806300, _1806298, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1806300, tc_fun(tc_prod(_1806298, _1806300), tc_HOL_Obool), tc_fun(_1806298, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1806298, tc_fun(tc_fun(tc_prod(_1806298, _1806300), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1806298, _1806300), tc_HOL_Obool), tc_fun(_1806298, tc_HOL_Obool)), _1806300), c_COMBC(_1806298, tc_fun(tc_prod(_1806298, _1806300), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1806298, tc_prod(_1806298, _1806300)), tc_fun(_1806298, tc_fun(tc_fun(tc_prod(_1806298, _1806300), tc_HOL_Obool), tc_HOL_Obool)), _1806300), hAPP(c_COMBB(tc_prod(_1806298, _1806300), tc_fun(tc_fun(tc_prod(_1806298, _1806300), tc_HOL_Obool), tc_HOL_Obool), _1806298), c_member(tc_prod(_1806298, _1806300)))), hAPP(c_COMBC(_1806298, _1806300, tc_prod(_1806298, _1806300)), c_Product__Type_OPair(_1806298, _1806300))))), _1806302))))], (49345 ^ _777081) ^ [_1806614, _1806616, _1806618, _1806620, _1806622, _1806624] : [c_Relation_Osingle__valued(_1806614, _1806616, hAPP(c_Relation_Oconverse(_1806616, _1806614), _1806618)), -(_1806620 = c_Orderings_Obot__class_Obot(tc_fun(_1806622, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1806616, _1806614, _1806618), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1806622, tc_fun(_1806616, tc_HOL_Obool)), _1806620), _1806624)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1806622, tc_fun(_1806614, tc_HOL_Obool)), _1806620), hAPP(hAPP(c_COMBB(tc_fun(_1806616, tc_HOL_Obool), tc_fun(_1806614, tc_HOL_Obool), _1806622), c_Relation_OImage(_1806616, _1806614, _1806618)), _1806624)))], (49355 ^ _777081) ^ [_1807139, _1807141, _1807143, _1807145] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1807139, tc_fun(_1807139, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1807139, tc_fun(tc_prod(_1807139, _1807139), tc_HOL_Obool), tc_fun(_1807139, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1807139, tc_fun(tc_fun(tc_prod(_1807139, _1807139), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1807139, _1807139), tc_HOL_Obool), tc_fun(_1807139, tc_HOL_Obool)), _1807139), c_COMBC(_1807139, tc_fun(tc_prod(_1807139, _1807139), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1807139, tc_prod(_1807139, _1807139)), tc_fun(_1807139, tc_fun(tc_fun(tc_prod(_1807139, _1807139), tc_HOL_Obool), tc_HOL_Obool)), _1807139), hAPP(c_COMBB(tc_prod(_1807139, _1807139), tc_fun(tc_fun(tc_prod(_1807139, _1807139), tc_HOL_Obool), tc_HOL_Obool), _1807139), c_member(tc_prod(_1807139, _1807139)))), c_Product__Type_OPair(_1807139, _1807139)))), _1807141)), c_fequal), _1807143), _1807145)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1807139, _1807139)), hAPP(hAPP(c_Product__Type_OPair(_1807139, _1807139), _1807143), _1807145)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1807139, _1807139), tc_HOL_Obool)), _1807141), c_Relation_OId(_1807139)))))], (49361 ^ _777081) ^ [_1807657, _1807659, _1807661, _1807663] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1807657, _1807657)), hAPP(hAPP(c_Product__Type_OPair(_1807657, _1807657), _1807661), _1807663)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1807657, _1807657), tc_HOL_Obool)), _1807659), c_Relation_OId(_1807657)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1807657, tc_fun(_1807657, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1807657, tc_fun(tc_prod(_1807657, _1807657), tc_HOL_Obool), tc_fun(_1807657, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1807657, tc_fun(tc_fun(tc_prod(_1807657, _1807657), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1807657, _1807657), tc_HOL_Obool), tc_fun(_1807657, tc_HOL_Obool)), _1807657), c_COMBC(_1807657, tc_fun(tc_prod(_1807657, _1807657), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1807657, tc_prod(_1807657, _1807657)), tc_fun(_1807657, tc_fun(tc_fun(tc_prod(_1807657, _1807657), tc_HOL_Obool), tc_HOL_Obool)), _1807657), hAPP(c_COMBB(tc_prod(_1807657, _1807657), tc_fun(tc_fun(tc_prod(_1807657, _1807657), tc_HOL_Obool), tc_HOL_Obool), _1807657), c_member(tc_prod(_1807657, _1807657)))), c_Product__Type_OPair(_1807657, _1807657)))), _1807659)), c_fequal), _1807661), _1807663)))], (49367 ^ _777081) ^ [_1808210, _1808212] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1808210, _1808210)), hAPP(hAPP(c_Product__Type_OPair(_1808210, _1808210), _1808212), _1808212)), c_Relation_OId(_1808210))))], (49369 ^ _777081) ^ [_1808311] : [-(hAPP(c_Relation_Oconverse(_1808311, _1808311), c_Relation_OId(_1808311)) = c_Relation_OId(_1808311))], (49371 ^ _777081) ^ [_1808399] : [-(hAPP(c_Relation_ORange(_1808399, _1808399), c_Relation_OId(_1808399)) = c_Orderings_Otop__class_Otop(tc_fun(_1808399, tc_HOL_Obool)))], (49373 ^ _777081) ^ [_1808490] : [-(c_Relation_Orefl__on(_1808490, c_Orderings_Otop__class_Otop(tc_fun(_1808490, tc_HOL_Obool)), c_Relation_OId(_1808490)))], (49375 ^ _777081) ^ [_1808576] : [-(hAPP(c_Relation_ODomain(_1808576, _1808576), c_Relation_OId(_1808576)) = c_Orderings_Otop__class_Otop(tc_fun(_1808576, tc_HOL_Obool)))], (49377 ^ _777081) ^ [_1808667] : [-(c_Relation_Osingle__valued(_1808667, _1808667, c_Relation_OId(_1808667)))], (49379 ^ _777081) ^ [_1808776, _1808778, _1808780] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1808776, _1808776, _1808778), c_Relation_OId(_1808776)), _1808780) = _1808780)], (49381 ^ _777081) ^ [_1808898, _1808900, _1808902] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1808898, _1808900, _1808900), _1808902), c_Relation_OId(_1808900)) = _1808902)], (49383 ^ _777081) ^ [_1809063, _1809065, _1809067, _1809069, _1809071] : [c_Relation_Osingle__valued(_1809063, _1809065, _1809067), c_Relation_Osingle__valued(_1809065, _1809069, _1809071), -(c_Relation_Osingle__valued(_1809063, _1809069, hAPP(hAPP(c_Relation_Orel__comp(_1809063, _1809065, _1809069), _1809067), _1809071)))], (49393 ^ _777081) ^ [_1809403, _1809405] : [-(c_Relation_Osingle__valued(_1809403, _1809403, c_Relation_OId__on(_1809403, _1809405)))], (49395 ^ _777081) ^ [_1809501, _1809503] : [-(hAPP(c_Relation_OImage(_1809501, _1809501, c_Relation_OId(_1809501)), _1809503) = _1809503)], (49397 ^ _777081) ^ [_1809647, _1809649, _1809651, _1809653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1809647, _1809649), tc_HOL_Obool)), _1809651), _1809653)), c_Relation_Osingle__valued(_1809647, _1809649, _1809653), -(c_Relation_Osingle__valued(_1809647, _1809649, _1809651))], (49407 ^ _777081) ^ [_1810039, _1810041, _1810043] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1810039, _1810039)), hAPP(hAPP(c_Product__Type_OPair(_1810039, _1810039), _1810041), _1810043)), c_Relation_OId(_1810039))), -(_1810041 = _1810043)], (49413 ^ _777081) ^ [_1810249, _1810251, _1810253] : [_1810251 = _1810253, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1810249, _1810249)), hAPP(hAPP(c_Product__Type_OPair(_1810249, _1810249), _1810251), _1810253)), c_Relation_OId(_1810249))))], (49419 ^ _777081) ^ [_1810565, _1810567, _1810569, _1810571, _1810573, _1810575] : [c_Relation_Osingle__valued(_1810565, _1810567, _1810569), hBOOL(hAPP(hAPP(c_member(tc_prod(_1810565, _1810567)), hAPP(hAPP(c_Product__Type_OPair(_1810565, _1810567), _1810571), _1810573)), _1810569)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1810565, _1810567)), hAPP(hAPP(c_Product__Type_OPair(_1810565, _1810567), _1810571), _1810575)), _1810569)), -(_1810573 = _1810575)], (49447 ^ _777081) ^ [_1811797, _1811799, _1811801] : [49450 ^ _777081 : [(49451 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1811797, _1811799)), hAPP(hAPP(c_Product__Type_OPair(_1811797, _1811799), 49448 ^ [_1811797, _1811799, _1811801]), 49449 ^ [_1811797, _1811799, _1811801])), _1811801)))], (49454 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1811797, _1811799)), hAPP(hAPP(c_Product__Type_OPair(_1811797, _1811799), 49448 ^ [_1811797, _1811799, _1811801]), 49452 ^ [_1811797, _1811799, _1811801])), _1811801)))], (49456 ^ _777081) ^ [] : [49449 ^ [_1811797, _1811799, _1811801] = 49452 ^ [_1811797, _1811799, _1811801]]], -(c_Relation_Osingle__valued(_1811797, _1811799, _1811801))], (49433 ^ _777081) ^ [_1811130, _1811132, _1811134] : [c_Relation_Osingle__valued(_1811130, _1811132, _1811134), 49436 ^ _777081 : [(49437 ^ _777081) ^ [_1811341, _1811343] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1811130, _1811132)), hAPP(hAPP(c_Product__Type_OPair(_1811130, _1811132), _1811343), _1811341)), _1811134)), 49440 ^ _777081 : [(49441 ^ _777081) ^ [_1811553] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1811130, _1811132)), hAPP(hAPP(c_Product__Type_OPair(_1811130, _1811132), _1811343), _1811553)), _1811134)), -(_1811341 = _1811553)]]]]], (49460 ^ _777081) ^ [_1812609] : [-(c_Transitive__Closure_Ortrancl(_1812609, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1812609, _1812609), tc_HOL_Obool))) = c_Relation_OId(_1812609))], (49462 ^ _777081) ^ [_1812714, _1812716] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1812714, _1812714), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1812714, _1812716)), c_Relation_OId(_1812714)) = c_Transitive__Closure_Ortrancl(_1812714, _1812716))], (49464 ^ _777081) ^ [_1812830, _1812832] : [-(c_Transitive__Closure_Ortrancl(_1812830, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1812830, _1812830), tc_HOL_Obool)), _1812832), c_Relation_OId(_1812830))) = c_Transitive__Closure_Ortrancl(_1812830, _1812832))], (49466 ^ _777081) ^ [_1812946, _1812948] : [-(c_Transitive__Closure_Ortrancl(_1812946, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1812946, _1812946), tc_HOL_Obool)), _1812948), c_Relation_OId(_1812946))) = c_Transitive__Closure_Ortrancl(_1812946, _1812948))], (49468 ^ _777081) ^ [] : [-(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))))], (49470 ^ _777081) ^ [_1813115, _1813117] : [-(c_Transitive__Closure_Otrancl(_1813115, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1813115, _1813115), tc_HOL_Obool)), _1813117), c_Relation_OId(_1813115))) = c_Transitive__Closure_Ortrancl(_1813115, _1813117))], (49472 ^ _777081) ^ [_1813231, _1813233] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1813231, _1813231), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1813231, _1813233)), c_Relation_OId(_1813231)) = c_Transitive__Closure_Ortrancl(_1813231, _1813233))], (49474 ^ _777081) ^ [_1813347, _1813349] : [-(c_Transitive__Closure_Ortrancl(_1813347, _1813349) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1813347, _1813347), tc_HOL_Obool)), c_Relation_OId(_1813347)), hAPP(hAPP(c_Relation_Orel__comp(_1813347, _1813347, _1813347), c_Transitive__Closure_Ortrancl(_1813347, _1813349)), _1813349)))], (49476 ^ _777081) ^ [_1813473, _1813475] : [-(c_Relation_Orefl__on(_1813473, c_Orderings_Otop__class_Otop(tc_fun(_1813473, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1813473, _1813473), tc_HOL_Obool)), _1813475), c_Relation_OId(_1813473))))], (49478 ^ _777081) ^ [_1813575] : [-(c_Relation_OId(_1813575) = hAPP(c_Set_OCollect(tc_prod(_1813575, _1813575)), hAPP(hAPP(c_COMBB(tc_fun(_1813575, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1813575, _1813575)), c_HOL_OEx(_1813575)), hAPP(hAPP(c_COMBC(tc_prod(_1813575, _1813575), tc_fun(_1813575, tc_prod(_1813575, _1813575)), tc_fun(_1813575, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1813575, _1813575), tc_HOL_Obool), tc_fun(tc_fun(_1813575, tc_prod(_1813575, _1813575)), tc_fun(_1813575, tc_HOL_Obool)), tc_prod(_1813575, _1813575)), c_COMBB(tc_prod(_1813575, _1813575), tc_HOL_Obool, _1813575)), c_fequal)), hAPP(hAPP(c_COMBS(_1813575, _1813575, tc_prod(_1813575, _1813575)), c_Product__Type_OPair(_1813575, _1813575)), c_COMBI(_1813575))))))], (49480 ^ _777081) ^ [_1813773, _1813775] : [-(c_Relation_Oirrefl(_1813773, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1813773, _1813773), tc_HOL_Obool)), _1813775), c_Relation_OId(_1813773))))], (49482 ^ _777081) ^ [_1813940, _1813942, _1813944, _1813946, _1813948] : [c_Relation_Osingle__valued(_1813940, _1813940, _1813942), hBOOL(hAPP(hAPP(c_member(tc_prod(_1813940, _1813940)), hAPP(hAPP(c_Product__Type_OPair(_1813940, _1813940), _1813944), _1813946)), c_Transitive__Closure_Ortrancl(_1813940, _1813942))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1813940, _1813940)), hAPP(hAPP(c_Product__Type_OPair(_1813940, _1813940), _1813944), _1813948)), c_Transitive__Closure_Ortrancl(_1813940, _1813942))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1813940, _1813940)), hAPP(hAPP(c_Product__Type_OPair(_1813940, _1813940), _1813946), _1813948)), c_Transitive__Closure_Ortrancl(_1813940, _1813942)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1813940, _1813940)), hAPP(hAPP(c_Product__Type_OPair(_1813940, _1813940), _1813948), _1813946)), c_Transitive__Closure_Ortrancl(_1813940, _1813942))))], (49500 ^ _777081) ^ [_1814692, _1814694, _1814696, _1814698, _1814700] : [c_Relation_Osingle__valued(_1814692, _1814694, hAPP(c_Relation_Oconverse(_1814694, _1814692), _1814696)), -(hAPP(c_Relation_OImage(_1814694, _1814692, _1814696), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1814694, tc_HOL_Obool)), _1814698), _1814700)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1814692, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1814694, _1814692, _1814696), _1814698)), hAPP(c_Relation_OImage(_1814694, _1814692, _1814696), _1814700)))], (49506 ^ _777081) ^ [_1815034, _1815036, _1815038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1815034, _1815034), tc_HOL_Obool)), c_Relation_OId(_1815034)), _1815036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1815034, _1815034), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1815034, _1815034, _1815034), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1815034, _1815034), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1815034, _1815038)), _1815036)), _1815038)), _1815036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1815034, _1815034), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1815034, _1815038)), _1815036)))], (49516 ^ _777081) ^ [_1815528, _1815530, _1815532] : [c_Relation_Ototal__on(_1815528, _1815530, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1815528, _1815528), tc_HOL_Obool)), _1815532), c_Relation_OId(_1815528))), -(c_Relation_Ototal__on(_1815528, _1815530, _1815532))], (49522 ^ _777081) ^ [_1815732, _1815734, _1815736] : [c_Relation_Ototal__on(_1815732, _1815734, _1815736), -(c_Relation_Ototal__on(_1815732, _1815734, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1815732, _1815732), tc_HOL_Obool)), _1815736), c_Relation_OId(_1815732))))], (49528 ^ _777081) ^ [_1816000, _1816002, _1816004] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1816000, _1816000)), _1816002), c_Transitive__Closure_Ortrancl(_1816000, _1816004))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1816000, _1816000)), _1816002), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1816000, _1816000), 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(_1816000, _1816000), tc_HOL_Obool), tc_fun(tc_prod(_1816000, _1816000), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1816000, _1816000), tc_HOL_Obool)), _1816004)))))], (49534 ^ _777081) ^ [_1816391, _1816393, _1816395] : [c_Relation_Ototal__on(_1816391, _1816393, hAPP(c_Relation_Oconverse(_1816391, _1816391), _1816395)), -(c_Relation_Ototal__on(_1816391, _1816393, _1816395))], (49540 ^ _777081) ^ [_1816575, _1816577, _1816579] : [c_Relation_Ototal__on(_1816575, _1816577, _1816579), -(c_Relation_Ototal__on(_1816575, _1816577, hAPP(c_Relation_Oconverse(_1816575, _1816575), _1816579)))], (49546 ^ _777081) ^ [_1816794, _1816796] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1816794, _1816794), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1816796) = c_Relation_OId(_1816794))], (49548 ^ _777081) ^ [_1816931, _1816933, _1816935] : [c_Relation_Osingle__valued(_1816931, _1816931, _1816933), -(c_Relation_Osingle__valued(_1816931, _1816931, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1816931, _1816931), tc_HOL_Obool), _1816935), _1816933)))], (49554 ^ _777081) ^ [_1817160, _1817162] : [-(hAPP(hAPP(c_Nat_Ocompow(_1817160, _1817160), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1817162) = c_Fun_Oid(_1817160))], (49556 ^ _777081) ^ [_1817279, _1817281, _1817283] : [-(hAPP(hAPP(c_Nat_Ocompow(_1817279, _1817279), hAPP(c_Nat_OSuc, _1817281)), _1817283) = hAPP(c_Fun_Ocomp(_1817279, _1817279, _1817279, _1817283), hAPP(hAPP(c_Nat_Ocompow(_1817279, _1817279), _1817281), _1817283)))], (49558 ^ _777081) ^ [_1817432, _1817434, _1817436, _1817438] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1817432, _1817434), tc_fun(_1817432, _1817434)), _1817436), c_Fun_Ocomp(_1817434, _1817434, _1817432, _1817438)) = c_Fun_Ocomp(_1817434, _1817434, _1817432, hAPP(hAPP(c_Nat_Ocompow(_1817434, _1817434), _1817436), _1817438)))], (49560 ^ _777081) ^ [_1817622, _1817624, _1817626] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1817622, _1817622)), _1817624), c_Transitive__Closure_Ortrancl(_1817622, _1817626))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1817622, _1817622)), _1817624), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1817622, _1817622), tc_HOL_Obool), 49563 ^ [_1817622, _1817624, _1817626]), _1817626))))], (49567 ^ _777081) ^ [_1817945, _1817947, _1817949] : [49568 ^ _777081 : [(49569 ^ _777081) ^ [_1818052] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1817945, _1817945)), _1817947), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1817945, _1817945), tc_HOL_Obool), _1818052), _1817949)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1817945, _1817945)), _1817947), c_Transitive__Closure_Ortrancl(_1817945, _1817949))))], (49573 ^ _777081) ^ [_1818283, _1818285, _1818287, _1818289] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1818283, _1818283)), _1818285), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1818283, _1818283), tc_HOL_Obool), _1818287), _1818289))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1818283, _1818283)), _1818285), c_Transitive__Closure_Ortrancl(_1818283, _1818289))))], (49579 ^ _777081) ^ [_1818588, _1818590, _1818592, _1818594] : [-(hAPP(hAPP(c_Nat_Ocompow(_1818588, _1818588), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1818590), _1818592)), _1818594) = hAPP(c_Fun_Ocomp(_1818588, _1818588, _1818588, hAPP(hAPP(c_Nat_Ocompow(_1818588, _1818588), _1818590), _1818594)), hAPP(hAPP(c_Nat_Ocompow(_1818588, _1818588), _1818592), _1818594)))], (49581 ^ _777081) ^ [_1818770, _1818772, _1818774, _1818776] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1818770, _1818770)), hAPP(hAPP(c_Product__Type_OPair(_1818770, _1818770), _1818772), _1818774)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1818770, _1818770), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1818776))), -(_1818772 = _1818774)], (49587 ^ _777081) ^ [_1819053, _1819055, _1819057] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1819053, _1819053)), hAPP(hAPP(c_Product__Type_OPair(_1819053, _1819053), _1819055), _1819055)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1819053, _1819053), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1819057))))], (49589 ^ _777081) ^ [_1819251, _1819253, _1819255, _1819257, _1819259, _1819261] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1819251, _1819251)), hAPP(hAPP(c_Product__Type_OPair(_1819251, _1819251), _1819253), _1819255)), _1819257)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1819251, _1819251)), hAPP(hAPP(c_Product__Type_OPair(_1819251, _1819251), _1819255), _1819259)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1819251, _1819251), tc_HOL_Obool), _1819261), _1819257))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1819251, _1819251)), hAPP(hAPP(c_Product__Type_OPair(_1819251, _1819251), _1819253), _1819259)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1819251, _1819251), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1819261)), _1819257))))], (49599 ^ _777081) ^ [_1819814, _1819816, _1819818, _1819820, _1819822, _1819824] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1819814, _1819814)), hAPP(hAPP(c_Product__Type_OPair(_1819814, _1819814), _1819816), _1819818)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1819814, _1819814), tc_HOL_Obool), _1819820), _1819822))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1819814, _1819814)), hAPP(hAPP(c_Product__Type_OPair(_1819814, _1819814), _1819818), _1819824)), _1819822)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1819814, _1819814)), hAPP(hAPP(c_Product__Type_OPair(_1819814, _1819814), _1819816), _1819824)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1819814, _1819814), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1819820)), _1819822))))], (49609 ^ _777081) ^ [_1820334, _1820336, _1820338, _1820340] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1820334, _1820334), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1820336), _1820338)), _1820340) = hAPP(hAPP(c_Relation_Orel__comp(_1820334, _1820334, _1820334), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1820334, _1820334), tc_HOL_Obool), _1820336), _1820340)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1820334, _1820334), tc_HOL_Obool), _1820338), _1820340)))], (49611 ^ _777081) ^ [_1820513, _1820515, _1820517] : [c_Wellfounded_Owf(_1820513, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1820513, _1820513), tc_HOL_Obool), _1820515), _1820517)), -(c_Wellfounded_Owf(_1820513, _1820517))], (49617 ^ _777081) ^ [_1820766, _1820768, _1820770, _1820772] : [-(hAPP(_1820766, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1820768, _1820768), _1820770), _1820766), _1820772)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1820768, _1820768), _1820770), _1820766), hAPP(_1820766, _1820772)))], (49619 ^ _777081) ^ [_1820894, _1820896] : [-(c_Relation_Ototal__on(_1820894, c_Orderings_Obot__class_Obot(tc_fun(_1820894, tc_HOL_Obool)), _1820896))], (49621 ^ _777081) ^ [_1820994, _1820996] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1820994, _1820994), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1820996) = _1820996)], (49623 ^ _777081) ^ [_1821114, _1821116, _1821118] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1821114, _1821114, _1821114), _1821116), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1821114, _1821114), tc_HOL_Obool), _1821118), _1821116)) = hAPP(hAPP(c_Relation_Orel__comp(_1821114, _1821114, _1821114), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1821114, _1821114), tc_HOL_Obool), _1821118), _1821116)), _1821116))], (49625 ^ _777081) ^ [_1821268, _1821270, _1821272] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1821268, _1821268), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1821270)), _1821272) = hAPP(hAPP(c_Relation_Orel__comp(_1821268, _1821268, _1821268), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1821268, _1821268), tc_HOL_Obool), _1821270), _1821272)), _1821272))], (49627 ^ _777081) ^ [_1821429, _1821431, _1821433, _1821435] : [-(hAPP(hAPP(c_Nat_Ocompow(_1821429, _1821429), _1821431), hAPP(hAPP(c_Nat_Ocompow(_1821429, _1821429), _1821433), _1821435)) = hAPP(hAPP(c_Nat_Ocompow(_1821429, _1821429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1821433), _1821431)), _1821435))], (49629 ^ _777081) ^ [_1821618, _1821620, _1821622] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1821618, _1821618)), _1821620), c_Transitive__Closure_Otrancl(_1821618, _1821622))), 49633 ^ _777081 : [(49634 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 49632 ^ [_1821618, _1821620, _1821622])))], (49636 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1821618, _1821618)), _1821620), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1821618, _1821618), tc_HOL_Obool), 49632 ^ [_1821618, _1821620, _1821622]), _1821622))))]]], (49638 ^ _777081) ^ [_1822039, _1822041, _1822043] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1822039, _1822039)), _1822041), c_Transitive__Closure_Otrancl(_1822039, _1822043)))), 49639 ^ _777081 : [(49640 ^ _777081) ^ [_1822170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1822170)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1822039, _1822039)), _1822041), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1822039, _1822039), tc_HOL_Obool), _1822170), _1822043)))]]], (49670 ^ _777081) ^ [_1823494, _1823496, _1823498] : [49672 ^ _777081 : [(49673 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1823494), 49671 ^ [_1823494, _1823496, _1823498]), _1823496)))], (49676 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1823494), 49674 ^ [_1823494, _1823496, _1823498]), _1823496)))], (49678 ^ _777081) ^ [] : [49671 ^ [_1823494, _1823496, _1823498] = 49674 ^ [_1823494, _1823496, _1823498]], (49680 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1823494, _1823494)), hAPP(hAPP(c_Product__Type_OPair(_1823494, _1823494), 49671 ^ [_1823494, _1823496, _1823498]), 49674 ^ [_1823494, _1823496, _1823498])), _1823498))], (49682 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1823494, _1823494)), hAPP(hAPP(c_Product__Type_OPair(_1823494, _1823494), 49674 ^ [_1823494, _1823496, _1823498]), 49671 ^ [_1823494, _1823496, _1823498])), _1823498))]], -(c_Relation_Ototal__on(_1823494, _1823496, _1823498))], (49648 ^ _777081) ^ [_1822556, _1822558, _1822560] : [c_Relation_Ototal__on(_1822556, _1822558, _1822560), 49651 ^ _777081 : [(49652 ^ _777081) ^ [_1822776] : [hBOOL(hAPP(hAPP(c_member(_1822556), _1822776), _1822558)), 49655 ^ _777081 : [(49656 ^ _777081) ^ [_1823000] : [hBOOL(hAPP(hAPP(c_member(_1822556), _1823000), _1822558)), -(_1822776 = _1823000), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1822556, _1822556)), hAPP(hAPP(c_Product__Type_OPair(_1822556, _1822556), _1822776), _1823000)), _1822560))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1822556, _1822556)), hAPP(hAPP(c_Product__Type_OPair(_1822556, _1822556), _1823000), _1822776)), _1822560)))]]]]], (49686 ^ _777081) ^ [_1824463, _1824465] : [-(c_Transitive__Closure_Ortrancl(_1824463, _1824465) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1824463, _1824463), 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(_1824463, _1824463), tc_HOL_Obool), tc_fun(tc_prod(_1824463, _1824463), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1824463, _1824463), tc_HOL_Obool)), _1824465)))], (49688 ^ _777081) ^ [_1824589] : [-(c_Nat_Ofunpow(_1824589) = c_Nat_Ocompow(_1824589, _1824589))], (49690 ^ _777081) ^ [_1824743, _1824745, _1824747, _1824749, _1824751] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1824743, _1824743)), hAPP(hAPP(c_Product__Type_OPair(_1824743, _1824743), _1824745), _1824747)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1824743, _1824743), tc_HOL_Obool), _1824749), _1824751))), 49695 ^ _777081 : [(49696 ^ _777081) ^ [] : [-(_1824749 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49698 ^ _777081) ^ [] : [-(_1824745 = _1824747)]], 49701 ^ _777081 : [(49702 ^ _777081) ^ [] : [-(_1824749 = hAPP(c_Nat_OSuc, 49700 ^ [_1824743, _1824745, _1824747, _1824749, _1824751]))], (49704 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1824743, _1824743)), hAPP(hAPP(c_Product__Type_OPair(_1824743, _1824743), _1824745), 49699 ^ [_1824743, _1824745, _1824747, _1824749, _1824751])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1824743, _1824743), tc_HOL_Obool), 49700 ^ [_1824743, _1824745, _1824747, _1824749, _1824751]), _1824751))))], (49706 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1824743, _1824743)), hAPP(hAPP(c_Product__Type_OPair(_1824743, _1824743), 49699 ^ [_1824743, _1824745, _1824747, _1824749, _1824751]), _1824747)), _1824751)))]]], (49708 ^ _777081) ^ [_1825815, _1825817] : [-(c_List_Orotate(_1825815, _1825817) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1825815), tc_List_Olist(_1825815)), _1825817), c_List_Orotate1(_1825815)))], (49710 ^ _777081) ^ [_1825984, _1825986, _1825988, _1825990, _1825992] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1825984, _1825984)), hAPP(hAPP(c_Product__Type_OPair(_1825984, _1825984), _1825986), _1825988)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1825984, _1825984), tc_HOL_Obool), _1825990), _1825992))), 49715 ^ _777081 : [(49716 ^ _777081) ^ [] : [-(_1825990 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49718 ^ _777081) ^ [] : [-(_1825986 = _1825988)]], 49721 ^ _777081 : [(49722 ^ _777081) ^ [] : [-(_1825990 = hAPP(c_Nat_OSuc, 49720 ^ [_1825984, _1825986, _1825988, _1825990, _1825992]))], (49724 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1825984, _1825984)), hAPP(hAPP(c_Product__Type_OPair(_1825984, _1825984), _1825986), 49719 ^ [_1825984, _1825986, _1825988, _1825990, _1825992])), _1825992)))], (49726 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1825984, _1825984)), hAPP(hAPP(c_Product__Type_OPair(_1825984, _1825984), 49719 ^ [_1825984, _1825986, _1825988, _1825990, _1825992]), _1825988)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1825984, _1825984), tc_HOL_Obool), 49720 ^ [_1825984, _1825986, _1825988, _1825990, _1825992]), _1825992))))]]], (49728 ^ _777081) ^ [_1827071, _1827073] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1827071, _1827071)), hAPP(hAPP(c_Product__Type_OPair(_1827071, _1827071), 49729 ^ [_1827071, _1827073]), 49729 ^ [_1827071, _1827073])), c_Transitive__Closure_Otrancl(_1827071, _1827073)))), -(c_Wellfounded_Oacyclic(_1827071, _1827073))], (49735 ^ _777081) ^ [_1827429, _1827431, _1827433, _1827435] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1827429, _1827431, _1827433, _1827435) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1827429, _1827431), _1827433), _1827435)))], (49737 ^ _777081) ^ [_1827600, _1827602, _1827604, _1827606, _1827608] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1827600, _1827600)), hAPP(hAPP(c_Product__Type_OPair(_1827600, _1827600), _1827602), _1827604)), c_Transitive__Closure_Ortrancl(_1827600, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1827600, _1827600), tc_HOL_Obool)), _1827606), _1827608)))), 49743 ^ _777081 : [(49744 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1827600, _1827600)), hAPP(hAPP(c_Product__Type_OPair(_1827600, _1827600), _1827602), 49742 ^ [_1827600, _1827602, _1827604, _1827606, _1827608])), c_Transitive__Closure_Ortrancl(_1827600, _1827606))))], (49747 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1827600, _1827600)), hAPP(hAPP(c_Product__Type_OPair(_1827600, _1827600), 49742 ^ [_1827600, _1827602, _1827604, _1827606, _1827608]), 49745 ^ [_1827600, _1827602, _1827604, _1827606, _1827608])), _1827608)))], (49749 ^ _777081) ^ [] : [49742 ^ [_1827600, _1827602, _1827604, _1827606, _1827608] = 49745 ^ [_1827600, _1827602, _1827604, _1827606, _1827608]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1827600, _1827600)), hAPP(hAPP(c_Product__Type_OPair(_1827600, _1827600), _1827602), _1827604)), c_Transitive__Closure_Ortrancl(_1827600, _1827606))))], (49753 ^ _777081) ^ [_1828628, _1828630, _1828632, _1828634, _1828636] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1828628, _1828628)), hAPP(hAPP(c_Product__Type_OPair(_1828628, _1828628), _1828630), _1828632)), c_Transitive__Closure_Ortrancl(_1828628, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1828628, _1828628), tc_HOL_Obool)), _1828634), _1828636)))), 49759 ^ _777081 : [(49760 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1828628, _1828628)), hAPP(hAPP(c_Product__Type_OPair(_1828628, _1828628), 49758 ^ [_1828628, _1828630, _1828632, _1828634, _1828636]), _1828632)), c_Transitive__Closure_Ortrancl(_1828628, _1828634))))], (49763 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1828628, _1828628)), hAPP(hAPP(c_Product__Type_OPair(_1828628, _1828628), 49761 ^ [_1828628, _1828630, _1828632, _1828634, _1828636]), 49758 ^ [_1828628, _1828630, _1828632, _1828634, _1828636])), _1828636)))], (49765 ^ _777081) ^ [] : [49761 ^ [_1828628, _1828630, _1828632, _1828634, _1828636] = 49758 ^ [_1828628, _1828630, _1828632, _1828634, _1828636]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1828628, _1828628)), hAPP(hAPP(c_Product__Type_OPair(_1828628, _1828628), _1828630), _1828632)), c_Transitive__Closure_Ortrancl(_1828628, _1828634))))], (49769 ^ _777081) ^ [_1829656, _1829658, _1829660, _1829662, _1829664] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1829656, _1829656)), hAPP(hAPP(c_Product__Type_OPair(_1829656, _1829656), _1829658), _1829660)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1829656, _1829656), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1829662)), _1829664))), 49773 ^ _777081 : [(49774 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1829656, _1829656)), hAPP(hAPP(c_Product__Type_OPair(_1829656, _1829656), _1829658), 49772 ^ [_1829656, _1829658, _1829660, _1829662, _1829664])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1829656, _1829656), tc_HOL_Obool), _1829662), _1829664))))], (49776 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1829656, _1829656)), hAPP(hAPP(c_Product__Type_OPair(_1829656, _1829656), 49772 ^ [_1829656, _1829658, _1829660, _1829662, _1829664]), _1829660)), _1829664)))]]], (49778 ^ _777081) ^ [_1830325, _1830327, _1830329, _1830331, _1830333] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1830325, _1830325)), hAPP(hAPP(c_Product__Type_OPair(_1830325, _1830325), _1830327), _1830329)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1830325, _1830325), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1830331)), _1830333))), 49782 ^ _777081 : [(49783 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1830325, _1830325)), hAPP(hAPP(c_Product__Type_OPair(_1830325, _1830325), _1830327), 49781 ^ [_1830325, _1830327, _1830329, _1830331, _1830333])), _1830333)))], (49785 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1830325, _1830325)), hAPP(hAPP(c_Product__Type_OPair(_1830325, _1830325), 49781 ^ [_1830325, _1830327, _1830329, _1830331, _1830333]), _1830329)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1830325, _1830325), tc_HOL_Obool), _1830331), _1830333))))]]], (49787 ^ _777081) ^ [_1830988, _1830990, _1830992, _1830994, _1830996] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1830988, _1830988)), hAPP(hAPP(c_Product__Type_OPair(_1830988, _1830988), _1830990), _1830992)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1830988, _1830988), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1830994)), _1830996))), 49791 ^ _777081 : [(49792 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1830988, _1830988)), hAPP(hAPP(c_Product__Type_OPair(_1830988, _1830988), _1830990), 49790 ^ [_1830988, _1830990, _1830992, _1830994, _1830996])), _1830996)))], (49794 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1830988, _1830988)), hAPP(hAPP(c_Product__Type_OPair(_1830988, _1830988), 49790 ^ [_1830988, _1830990, _1830992, _1830994, _1830996]), _1830992)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1830988, _1830988), tc_HOL_Obool), _1830994), _1830996))))]]], (49796 ^ _777081) ^ [_1831643, _1831645, _1831647, _1831649] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1831643, _1831643)), hAPP(hAPP(c_Product__Type_OPair(_1831643, _1831643), _1831645), _1831647)), c_Transitive__Closure_Otrancl(_1831643, _1831649))), 49800 ^ _777081 : [(49801 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1831643, _1831643)), hAPP(hAPP(c_Product__Type_OPair(_1831643, _1831643), _1831645), 49799 ^ [_1831643, _1831645, _1831647, _1831649])), c_Transitive__Closure_Ortrancl(_1831643, _1831649))))], (49803 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1831643, _1831643)), hAPP(hAPP(c_Product__Type_OPair(_1831643, _1831643), 49799 ^ [_1831643, _1831645, _1831647, _1831649]), _1831647)), _1831649)))]]], (49805 ^ _777081) ^ [_1832225, _1832227, _1832229, _1832231] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1832225, _1832225)), hAPP(hAPP(c_Product__Type_OPair(_1832225, _1832225), _1832227), _1832229)), c_Transitive__Closure_Otrancl(_1832225, _1832231))), 49809 ^ _777081 : [(49810 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1832225, _1832225)), hAPP(hAPP(c_Product__Type_OPair(_1832225, _1832225), _1832227), 49808 ^ [_1832225, _1832227, _1832229, _1832231])), _1832231)))], (49812 ^ _777081) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1832225, _1832225)), hAPP(hAPP(c_Product__Type_OPair(_1832225, _1832225), 49808 ^ [_1832225, _1832227, _1832229, _1832231]), _1832229)), c_Transitive__Closure_Ortrancl(_1832225, _1832231))))]]], (49814 ^ _777081) ^ [_1832779, _1832781] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1832779, _1832779)), _1832781), c_Relation_OId(_1832779))), -(_1832781 = hAPP(hAPP(c_Product__Type_OPair(_1832779, _1832779), 49817 ^ [_1832779, _1832781]), 49817 ^ [_1832779, _1832781]))], (49821 ^ _777081) ^ [_1833153, _1833155, _1833157] : [hBOOL(hAPP(hAPP(c_member(_1833153), _1833155), hAPP(c_List_Oset(_1833153), _1833157))), -(_1833157 = hAPP(hAPP(c_List_Oappend(_1833153), 49824 ^ [_1833153, _1833155, _1833157]), hAPP(hAPP(c_List_Olist_OCons(_1833153), _1833155), 49825 ^ [_1833153, _1833155, _1833157])))], (49829 ^ _777081) ^ [_1833549, _1833551, _1833553] : [49830 ^ _777081 : [(49831 ^ _777081) ^ [_1833668, _1833670] : [_1833553 = hAPP(hAPP(c_List_Oappend(_1833549), _1833670), hAPP(hAPP(c_List_Olist_OCons(_1833549), _1833551), _1833668))]], -(hBOOL(hAPP(hAPP(c_member(_1833549), _1833551), hAPP(c_List_Oset(_1833549), _1833553))))], (49835 ^ _777081) ^ [_1833909, _1833911, _1833913] : [hBOOL(hAPP(hAPP(c_member(_1833909), _1833911), hAPP(c_List_Oset(_1833909), _1833913))), 49840 ^ _777081 : [(49841 ^ _777081) ^ [] : [-(_1833913 = hAPP(hAPP(c_List_Oappend(_1833909), 49838 ^ [_1833909, _1833911, _1833913]), hAPP(hAPP(c_List_Olist_OCons(_1833909), _1833911), 49839 ^ [_1833909, _1833911, _1833913])))], (49843 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1833909), _1833911), hAPP(c_List_Oset(_1833909), 49838 ^ [_1833909, _1833911, _1833913])))]]], (49845 ^ _777081) ^ [_1834436, _1834438, _1834440] : [-(hBOOL(hAPP(hAPP(c_member(_1834436), _1834438), hAPP(c_List_Oset(_1834436), _1834440)))), 49846 ^ _777081 : [(49847 ^ _777081) ^ [_1834577] : [49848 ^ _777081 : [(49849 ^ _777081) ^ [_1834687] : [_1834440 = hAPP(hAPP(c_List_Oappend(_1834436), _1834577), hAPP(hAPP(c_List_Olist_OCons(_1834436), _1834438), _1834687))]], -(hBOOL(hAPP(hAPP(c_member(_1834436), _1834438), hAPP(c_List_Oset(_1834436), _1834577))))]]], (49855 ^ _777081) ^ [_1834995, _1834997, _1834999] : [hBOOL(hAPP(hAPP(c_member(_1834995), _1834997), hAPP(c_List_Oset(_1834995), _1834999))), 49860 ^ _777081 : [(49861 ^ _777081) ^ [] : [-(_1834999 = hAPP(hAPP(c_List_Oappend(_1834995), 49858 ^ [_1834995, _1834997, _1834999]), hAPP(hAPP(c_List_Olist_OCons(_1834995), _1834997), 49859 ^ [_1834995, _1834997, _1834999])))], (49863 ^ _777081) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1834995), _1834997), hAPP(c_List_Oset(_1834995), 49859 ^ [_1834995, _1834997, _1834999])))]]], (49865 ^ _777081) ^ [_1835542, _1835544, _1835546] : [-(hBOOL(hAPP(hAPP(c_member(_1835542), _1835544), hAPP(c_List_Oset(_1835542), _1835546)))), 49866 ^ _777081 : [(49867 ^ _777081) ^ [_1835697, _1835699] : [_1835546 = hAPP(hAPP(c_List_Oappend(_1835542), _1835699), hAPP(hAPP(c_List_Olist_OCons(_1835542), _1835544), _1835697)), -(hBOOL(hAPP(hAPP(c_member(_1835542), _1835544), hAPP(c_List_Oset(_1835542), _1835697))))]]], (49875 ^ _777081) ^ [_1836070, _1836072, _1836074] : [class_Divides_Osemiring__div(_1836070), -(_1836072 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1836070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1836070), hAPP(c_Divides_Odiv__class_Odiv(_1836070, _1836072), _1836074)), _1836074)), c_Divides_Odiv__class_Omod(_1836070, _1836072, _1836074)))], (49881 ^ _777081) ^ [_1836350, _1836352, _1836354] : [class_Orderings_Olinorder(_1836350), hBOOL(hAPP(c_Finite__Set_Ofinite(_1836350), _1836352)), -(hBOOL(hAPP(hAPP(c_member(_1836350), _1836354), _1836352))), -(c_Big__Operators_Olattice_OSup__fin(_1836350, c_Orderings_Oord__class_Omax(_1836350), hAPP(hAPP(c_Set_Oinsert(_1836350), _1836354), _1836352)) = hAPP(hAPP(c_Finite__Set_Ofold(_1836350, _1836350, c_Orderings_Oord__class_Omax(_1836350)), _1836354), _1836352))], (49895 ^ _777081) ^ [_1836841, _1836843, _1836845] : [class_Complete__Lattice_Ocomplete__lattice(_1836841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1836841), _1836843)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1836841), _1836845), c_Complete__Lattice_OSup__class_OSup(_1836841, _1836843)) = hAPP(hAPP(c_Finite__Set_Ofold(_1836841, _1836841, c_Lattices_Osemilattice__sup__class_Osup(_1836841)), _1836845), _1836843))], (49905 ^ _777081) ^ [_1837230, _1837232, _1837234, _1837236] : [class_Lattices_Osemilattice__sup(_1837230), hBOOL(hAPP(c_Finite__Set_Ofinite(_1837230), _1837232)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1837230, _1837230, c_Lattices_Osemilattice__sup__class_Osup(_1837230)), _1837234), hAPP(hAPP(c_Set_Oinsert(_1837230), _1837236), _1837232)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1837230), _1837236), hAPP(hAPP(c_Finite__Set_Ofold(_1837230, _1837230, c_Lattices_Osemilattice__sup__class_Osup(_1837230)), _1837234), _1837232)))], (49915 ^ _777081) ^ [_1837649, _1837651, _1837653] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1837649), _1837651)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1837649, tc_HOL_Obool)), _1837651), _1837653) = hAPP(hAPP(c_Finite__Set_Ofold(_1837649, tc_fun(_1837649, tc_HOL_Obool), c_Set_Oinsert(_1837649)), _1837653), _1837651))], (49921 ^ _777081) ^ [_1837967, _1837969, _1837971, _1837973, _1837975] : [class_Complete__Lattice_Ocomplete__lattice(_1837967), hBOOL(hAPP(c_Finite__Set_Ofinite(_1837969), _1837971)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1837967), _1837973), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1837969, _1837967), _1837971), _1837975)) = hAPP(hAPP(c_Finite__Set_Ofold(_1837969, _1837967, hAPP(hAPP(c_COMBB(_1837967, tc_fun(_1837967, _1837967), _1837969), c_Lattices_Osemilattice__sup__class_Osup(_1837967)), _1837975)), _1837973), _1837971))], (49931 ^ _777081) ^ [_1838442, _1838444, _1838446, _1838448, _1838450, _1838452] : [c_Finite__Set_Ofun__left__comm__idem(_1838442, _1838444, _1838446), hBOOL(hAPP(c_Finite__Set_Ofinite(_1838442), _1838448)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1838442, _1838444, _1838446), _1838450), hAPP(hAPP(c_Set_Oinsert(_1838442), _1838452), _1838448)) = hAPP(hAPP(c_Finite__Set_Ofold(_1838442, _1838444, _1838446), hAPP(hAPP(_1838446, _1838452), _1838450)), _1838448))], (49941 ^ _777081) ^ [_1838915, _1838917, _1838919, _1838921, _1838923, _1838925] : [c_Finite__Set_Ofun__left__comm__idem(_1838915, _1838917, _1838919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1838915), _1838921)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1838915, _1838917, _1838919), _1838923), hAPP(hAPP(c_Set_Oinsert(_1838915), _1838925), _1838921)) = hAPP(hAPP(_1838919, _1838925), hAPP(hAPP(c_Finite__Set_Ofold(_1838915, _1838917, _1838919), _1838923), _1838921)))], (49951 ^ _777081) ^ [_1839346, _1839348, _1839350] : [class_Complete__Lattice_Ocomplete__lattice(_1839346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1839346), _1839348)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1839346), _1839350), c_Complete__Lattice_OInf__class_OInf(_1839346, _1839348)) = hAPP(hAPP(c_Finite__Set_Ofold(_1839346, _1839346, c_Lattices_Osemilattice__inf__class_Oinf(_1839346)), _1839350), _1839348))], (49961 ^ _777081) ^ [_1839735, _1839737, _1839739, _1839741] : [class_Lattices_Osemilattice__inf(_1839735), hBOOL(hAPP(c_Finite__Set_Ofinite(_1839735), _1839737)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1839735, _1839735, c_Lattices_Osemilattice__inf__class_Oinf(_1839735)), _1839739), hAPP(hAPP(c_Set_Oinsert(_1839735), _1839741), _1839737)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1839735), _1839741), hAPP(hAPP(c_Finite__Set_Ofold(_1839735, _1839735, c_Lattices_Osemilattice__inf__class_Oinf(_1839735)), _1839739), _1839737)))], (49971 ^ _777081) ^ [_1840168, _1840170, _1840172, _1840174] : [class_Orderings_Olinorder(_1840168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1840168), _1840170)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1840168, _1840168, c_Orderings_Oord__class_Omin(_1840168)), _1840172), hAPP(hAPP(c_Set_Oinsert(_1840168), _1840174), _1840170)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1840168), _1840174), hAPP(hAPP(c_Finite__Set_Ofold(_1840168, _1840168, c_Orderings_Oord__class_Omin(_1840168)), _1840172), _1840170)))], (49981 ^ _777081) ^ [_1840601, _1840603, _1840605, _1840607] : [class_Orderings_Olinorder(_1840601), hBOOL(hAPP(c_Finite__Set_Ofinite(_1840601), _1840603)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1840601, _1840601, c_Orderings_Oord__class_Omax(_1840601)), _1840605), hAPP(hAPP(c_Set_Oinsert(_1840601), _1840607), _1840603)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1840601), _1840607), hAPP(hAPP(c_Finite__Set_Ofold(_1840601, _1840601, c_Orderings_Oord__class_Omax(_1840601)), _1840605), _1840603)))], (49991 ^ _777081) ^ [_1841062, _1841064, _1841066, _1841068, _1841070, _1841072] : [c_Finite__Set_Ofolding(_1841062, _1841064, _1841066, _1841068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1841062), _1841070)), -(hAPP(hAPP(_1841068, _1841070), _1841072) = hAPP(hAPP(c_Finite__Set_Ofold(_1841062, _1841064, _1841066), _1841072), _1841070))], (50001 ^ _777081) ^ [_1841458, _1841460, _1841462, _1841464] : [-(hAPP(c_Finite__Set_Ofold__image(_1841458, _1841460, _1841462), _1841464) = c_Finite__Set_Ofold(_1841460, _1841458, hAPP(hAPP(c_COMBB(_1841458, tc_fun(_1841458, _1841458), _1841460), _1841462), _1841464)))], (50003 ^ _777081) ^ [_1841608, _1841610, _1841612, _1841614] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1841608, _1841610, _1841612), _1841614), c_Orderings_Obot__class_Obot(tc_fun(_1841608, tc_HOL_Obool))) = _1841614)], (50005 ^ _777081) ^ [_1841763, _1841765, _1841767, _1841769, _1841771] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1841763, _1841765, _1841767), _1841769), _1841771) = c_HOL_OThe(_1841765, c_Finite__Set_Ofold__graph(_1841763, _1841765, _1841767, _1841769, _1841771)))], (50007 ^ _777081) ^ [_1841939, _1841941, _1841943, _1841945, _1841947] : [c_Finite__Set_Ofolding__one__idem(_1841939, _1841941, _1841943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1841939), _1841945)), -(hAPP(_1841943, hAPP(hAPP(c_Set_Oinsert(_1841939), _1841947), _1841945)) = hAPP(hAPP(c_Finite__Set_Ofold(_1841939, _1841939, _1841941), _1841947), _1841945))], (50017 ^ _777081) ^ [_1842362, _1842364, _1842366, _1842368, _1842370] : [class_Complete__Lattice_Ocomplete__lattice(_1842362), hBOOL(hAPP(c_Finite__Set_Ofinite(_1842364), _1842366)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1842362), _1842368), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1842364, _1842362), _1842366), _1842370)) = hAPP(hAPP(c_Finite__Set_Ofold(_1842364, _1842362, hAPP(hAPP(c_COMBB(_1842362, tc_fun(_1842362, _1842362), _1842364), c_Lattices_Osemilattice__inf__class_Oinf(_1842362)), _1842370)), _1842368), _1842366))], (50027 ^ _777081) ^ [_1842823, _1842825, _1842827, _1842829, _1842831] : [c_Finite__Set_Ofun__left__comm__idem(_1842823, _1842825, _1842827), -(hAPP(hAPP(c_Finite__Set_Ofold(_1842823, _1842825, _1842827), _1842829), hAPP(c_List_Oset(_1842823), _1842831)) = hAPP(c_List_Ofoldl(_1842825, _1842823, hAPP(c_COMBC(_1842823, _1842825, _1842825), _1842827), _1842829), _1842831))], (50033 ^ _777081) ^ [_1843141, _1843143, _1843145, _1843147] : [class_Lattices_Osemilattice__sup(_1843141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1843141), _1843143)), hBOOL(hAPP(hAPP(c_member(_1843141), _1843145), _1843143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1843141), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1843141), _1843145), _1843147)), hAPP(hAPP(c_Finite__Set_Ofold(_1843141, _1843141, c_Lattices_Osemilattice__sup__class_Osup(_1843141)), _1843147), _1843143))))], (50047 ^ _777081) ^ [_1843659, _1843661, _1843663, _1843665] : [class_Lattices_Osemilattice__inf(_1843659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1843659), _1843661)), hBOOL(hAPP(hAPP(c_member(_1843659), _1843663), _1843661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1843659), hAPP(hAPP(c_Finite__Set_Ofold(_1843659, _1843659, c_Lattices_Osemilattice__inf__class_Oinf(_1843659)), _1843665), _1843661)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1843659), _1843663), _1843665))))], (50061 ^ _777081) ^ [_1844177, _1844179, _1844181, _1844183] : [class_Orderings_Olinorder(_1844177), hBOOL(hAPP(c_Finite__Set_Ofinite(_1844177), _1844179)), hBOOL(hAPP(hAPP(c_member(_1844177), _1844181), _1844179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1844177), hAPP(hAPP(c_Finite__Set_Ofold(_1844177, _1844177, c_Orderings_Oord__class_Omin(_1844177)), _1844183), _1844179)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1844177), _1844181), _1844183))))], (50075 ^ _777081) ^ [_1844695, _1844697, _1844699, _1844701] : [class_Orderings_Olinorder(_1844695), hBOOL(hAPP(c_Finite__Set_Ofinite(_1844695), _1844697)), hBOOL(hAPP(hAPP(c_member(_1844695), _1844699), _1844697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1844695), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1844695), _1844699), _1844701)), hAPP(hAPP(c_Finite__Set_Ofold(_1844695, _1844695, c_Orderings_Oord__class_Omax(_1844695)), _1844701), _1844697))))], (50089 ^ _777081) ^ [_1845185, _1845187] : [class_Complete__Lattice_Ocomplete__lattice(_1845185), hBOOL(hAPP(c_Finite__Set_Ofinite(_1845185), _1845187)), -(c_Complete__Lattice_OSup__class_OSup(_1845185, _1845187) = hAPP(hAPP(c_Finite__Set_Ofold(_1845185, _1845185, c_Lattices_Osemilattice__sup__class_Osup(_1845185)), c_Orderings_Obot__class_Obot(_1845185)), _1845187))], (50099 ^ _777081) ^ [_1845524, _1845526] : [class_Complete__Lattice_Ocomplete__lattice(_1845524), hBOOL(hAPP(c_Finite__Set_Ofinite(_1845524), _1845526)), -(c_Complete__Lattice_OInf__class_OInf(_1845524, _1845526) = hAPP(hAPP(c_Finite__Set_Ofold(_1845524, _1845524, c_Lattices_Osemilattice__inf__class_Oinf(_1845524)), c_Orderings_Otop__class_Otop(_1845524)), _1845526))], (50109 ^ _777081) ^ [_1845877, _1845879, _1845881] : [class_Lattices_Oab__semigroup__idem__mult(_1845877), hBOOL(hAPP(c_Finite__Set_Ofinite(_1845877), _1845879)), -(hAPP(c_Finite__Set_Ofold1(_1845877, c_Groups_Otimes__class_Otimes(_1845877)), hAPP(hAPP(c_Set_Oinsert(_1845877), _1845881), _1845879)) = hAPP(hAPP(c_Finite__Set_Ofold(_1845877, _1845877, c_Groups_Otimes__class_Otimes(_1845877)), _1845881), _1845879))], (50119 ^ _777081) ^ [_1846262, _1846264, _1846266] : [class_Lattices_Olattice(_1846262), hBOOL(hAPP(c_Finite__Set_Ofinite(_1846262), _1846264)), -(c_Big__Operators_Olattice__class_OSup__fin(_1846262, hAPP(hAPP(c_Set_Oinsert(_1846262), _1846266), _1846264)) = hAPP(hAPP(c_Finite__Set_Ofold(_1846262, _1846262, c_Lattices_Osemilattice__sup__class_Osup(_1846262)), _1846266), _1846264))], (50129 ^ _777081) ^ [_1846637, _1846639, _1846641] : [class_Lattices_Olattice(_1846637), hBOOL(hAPP(c_Finite__Set_Ofinite(_1846637), _1846639)), -(c_Big__Operators_Olattice__class_OInf__fin(_1846637, hAPP(hAPP(c_Set_Oinsert(_1846637), _1846641), _1846639)) = hAPP(hAPP(c_Finite__Set_Ofold(_1846637, _1846637, c_Lattices_Osemilattice__inf__class_Oinf(_1846637)), _1846641), _1846639))], (50139 ^ _777081) ^ [_1847012, _1847014, _1847016] : [class_Orderings_Olinorder(_1847012), hBOOL(hAPP(c_Finite__Set_Ofinite(_1847012), _1847014)), -(c_Big__Operators_Olinorder__class_OMin(_1847012, hAPP(hAPP(c_Set_Oinsert(_1847012), _1847016), _1847014)) = hAPP(hAPP(c_Finite__Set_Ofold(_1847012, _1847012, c_Orderings_Oord__class_Omin(_1847012)), _1847016), _1847014))], (50149 ^ _777081) ^ [_1847387, _1847389, _1847391] : [class_Orderings_Olinorder(_1847387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1847387), _1847389)), -(c_Big__Operators_Olinorder__class_OMax(_1847387, hAPP(hAPP(c_Set_Oinsert(_1847387), _1847391), _1847389)) = hAPP(hAPP(c_Finite__Set_Ofold(_1847387, _1847387, c_Orderings_Oord__class_Omax(_1847387)), _1847391), _1847389))], (50159 ^ _777081) ^ [_1847762, _1847764, _1847766] : [class_Orderings_Olinorder(_1847762), hBOOL(hAPP(c_Finite__Set_Ofinite(_1847762), _1847764)), -(c_Big__Operators_Olattice_OInf__fin(_1847762, c_Orderings_Oord__class_Omin(_1847762), hAPP(hAPP(c_Set_Oinsert(_1847762), _1847766), _1847764)) = hAPP(hAPP(c_Finite__Set_Ofold(_1847762, _1847762, c_Orderings_Oord__class_Omin(_1847762)), _1847766), _1847764))], (50169 ^ _777081) ^ [_1848143, _1848145, _1848147] : [class_Orderings_Olinorder(_1848143), hBOOL(hAPP(c_Finite__Set_Ofinite(_1848143), _1848145)), -(c_Big__Operators_Olattice_OSup__fin(_1848143, c_Orderings_Oord__class_Omax(_1848143), hAPP(hAPP(c_Set_Oinsert(_1848143), _1848147), _1848145)) = hAPP(hAPP(c_Finite__Set_Ofold(_1848143, _1848143, c_Orderings_Oord__class_Omax(_1848143)), _1848147), _1848145))], (50179 ^ _777081) ^ [_1848524, _1848526, _1848528] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1848524), _1848526)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1848524, tc_HOL_Obool)), _1848528), _1848526) = hAPP(hAPP(c_Finite__Set_Ofold(_1848524, tc_fun(_1848524, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1848524, tc_HOL_Obool), tc_fun(tc_fun(_1848524, tc_HOL_Obool), tc_fun(_1848524, tc_HOL_Obool)), _1848524), hAPP(c_COMBC(tc_fun(_1848524, tc_HOL_Obool), tc_fun(_1848524, tc_HOL_Obool), tc_fun(_1848524, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1848524, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1848524, tc_fun(_1848524, tc_HOL_Obool), tc_fun(_1848524, tc_HOL_Obool)), c_Set_Oinsert(_1848524)), c_Orderings_Obot__class_Obot(tc_fun(_1848524, tc_HOL_Obool))))), _1848528), _1848526))], (50185 ^ _777081) ^ [_1848970, _1848972, _1848974, _1848976, _1848978] : [c_Finite__Set_Ofolding__one(_1848970, _1848972, _1848974), hBOOL(hAPP(c_Finite__Set_Ofinite(_1848970), _1848976)), -(hBOOL(hAPP(hAPP(c_member(_1848970), _1848978), _1848976))), -(hAPP(_1848974, hAPP(hAPP(c_Set_Oinsert(_1848970), _1848978), _1848976)) = hAPP(hAPP(c_Finite__Set_Ofold(_1848970, _1848970, _1848972), _1848978), _1848976))], (50199 ^ _777081) ^ [_1849497, _1849499, _1849501, _1849503] : [class_Complete__Lattice_Ocomplete__lattice(_1849497), hBOOL(hAPP(c_Finite__Set_Ofinite(_1849499), _1849501)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1849499, _1849497), _1849501), _1849503) = hAPP(hAPP(c_Finite__Set_Ofold(_1849499, _1849497, hAPP(hAPP(c_COMBB(_1849497, tc_fun(_1849497, _1849497), _1849499), c_Lattices_Osemilattice__sup__class_Osup(_1849497)), _1849503)), c_Orderings_Obot__class_Obot(_1849497)), _1849501))], (50209 ^ _777081) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (50211 ^ _777081) ^ [_1849947, _1849949] : [class_Lattices_Obounded__lattice(_1849947), -(class_Lattices_Obounded__lattice(tc_fun(_1849949, _1849947)))], (50217 ^ _777081) ^ [_1850159, _1850161] : [class_Complete__Lattice_Ocomplete__lattice(_1850159), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1850161, _1850159)))], (50223 ^ _777081) ^ [_1850371, _1850373] : [class_Lattices_Obounded__lattice(_1850371), -(class_Lattices_Obounded__lattice__top(tc_fun(_1850373, _1850371)))], (50229 ^ _777081) ^ [_1850583, _1850585] : [class_Lattices_Obounded__lattice(_1850583), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1850585, _1850583)))], (50235 ^ _777081) ^ [_1850795, _1850797] : [class_Lattices_Olattice(_1850795), -(class_Lattices_Osemilattice__sup(tc_fun(_1850797, _1850795)))], (50241 ^ _777081) ^ [_1851007, _1851009] : [class_Lattices_Olattice(_1851007), -(class_Lattices_Osemilattice__inf(tc_fun(_1851009, _1851007)))], (50247 ^ _777081) ^ [_1851219, _1851221] : [class_Lattices_Odistrib__lattice(_1851219), -(class_Lattices_Odistrib__lattice(tc_fun(_1851221, _1851219)))], (50253 ^ _777081) ^ [_1851431, _1851433] : [class_Lattices_Oboolean__algebra(_1851431), -(class_Lattices_Oboolean__algebra(tc_fun(_1851433, _1851431)))], (50259 ^ _777081) ^ [_1851643, _1851645] : [class_Orderings_Opreorder(_1851643), -(class_Orderings_Opreorder(tc_fun(_1851645, _1851643)))], (50265 ^ _777081) ^ [_1851855, _1851857] : [-(class_Finite__Set_Ofinite(tc_fun(_1851855, _1851857))), class_Finite__Set_Ofinite(_1851855), class_Finite__Set_Ofinite(_1851857)], (50275 ^ _777081) ^ [_1852154, _1852156] : [class_Lattices_Olattice(_1852154), -(class_Lattices_Olattice(tc_fun(_1852156, _1852154)))], (50281 ^ _777081) ^ [_1852366, _1852368] : [class_Orderings_Oorder(_1852366), -(class_Orderings_Oorder(tc_fun(_1852368, _1852366)))], (50287 ^ _777081) ^ [_1852578, _1852580] : [class_Orderings_Otop(_1852578), -(class_Orderings_Otop(tc_fun(_1852580, _1852578)))], (50293 ^ _777081) ^ [_1852790, _1852792] : [class_Orderings_Oord(_1852790), -(class_Orderings_Oord(tc_fun(_1852792, _1852790)))], (50299 ^ _777081) ^ [_1853002, _1853004] : [class_Orderings_Obot(_1853002), -(class_Orderings_Obot(tc_fun(_1853004, _1853002)))], (50305 ^ _777081) ^ [_1853214, _1853216] : [class_Groups_Ouminus(_1853214), -(class_Groups_Ouminus(tc_fun(_1853216, _1853214)))], (50311 ^ _777081) ^ [_1853426, _1853428] : [class_Groups_Ominus(_1853426), -(class_Groups_Ominus(tc_fun(_1853428, _1853426)))], (50317 ^ _777081) ^ [_1853638, _1853640] : [-(class_HOL_Oequal(tc_fun(_1853638, _1853640))), class_Enum_Oenum(_1853638), class_HOL_Oequal(_1853640)], (50327 ^ _777081) ^ [_1853937, _1853939] : [-(class_Enum_Oenum(tc_fun(_1853937, _1853939))), class_Enum_Oenum(_1853937), class_Enum_Oenum(_1853939)], (50337 ^ _777081) ^ [] : [-(class_HOL_Oequal(tc_Com_Ocom))], (50339 ^ _777081) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (50341 ^ _777081) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (50343 ^ _777081) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (50345 ^ _777081) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (50347 ^ _777081) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (50349 ^ _777081) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (50351 ^ _777081) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (50353 ^ _777081) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (50355 ^ _777081) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (50357 ^ _777081) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (50359 ^ _777081) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (50361 ^ _777081) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (50363 ^ _777081) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (50365 ^ _777081) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (50367 ^ _777081) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (50369 ^ _777081) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (50371 ^ _777081) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (50373 ^ _777081) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (50375 ^ _777081) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (50377 ^ _777081) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (50379 ^ _777081) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (50381 ^ _777081) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (50383 ^ _777081) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (50385 ^ _777081) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (50387 ^ _777081) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (50389 ^ _777081) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (50391 ^ _777081) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (50393 ^ _777081) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (50395 ^ _777081) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (50397 ^ _777081) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (50399 ^ _777081) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (50401 ^ _777081) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (50403 ^ _777081) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (50405 ^ _777081) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (50407 ^ _777081) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (50409 ^ _777081) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (50411 ^ _777081) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (50413 ^ _777081) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (50415 ^ _777081) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (50417 ^ _777081) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (50419 ^ _777081) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (50421 ^ _777081) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (50423 ^ _777081) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (50425 ^ _777081) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (50427 ^ _777081) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (50429 ^ _777081) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (50431 ^ _777081) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (50433 ^ _777081) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (50435 ^ _777081) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (50437 ^ _777081) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (50439 ^ _777081) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (50441 ^ _777081) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (50443 ^ _777081) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (50445 ^ _777081) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (50447 ^ _777081) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (50449 ^ _777081) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (50451 ^ _777081) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (50453 ^ _777081) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (50455 ^ _777081) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (50457 ^ _777081) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (50459 ^ _777081) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (50461 ^ _777081) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (50463 ^ _777081) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (50465 ^ _777081) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (50467 ^ _777081) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (50469 ^ _777081) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (50471 ^ _777081) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (50473 ^ _777081) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (50475 ^ _777081) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (50477 ^ _777081) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (50479 ^ _777081) ^ [] : [-(class_HOL_Oequal(tc_Int_Oint))], (50481 ^ _777081) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (50483 ^ _777081) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (50485 ^ _777081) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (50487 ^ _777081) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (50489 ^ _777081) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (50491 ^ _777081) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (50493 ^ _777081) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (50495 ^ _777081) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (50497 ^ _777081) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (50499 ^ _777081) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (50501 ^ _777081) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (50503 ^ _777081) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (50505 ^ _777081) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (50507 ^ _777081) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (50509 ^ _777081) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (50511 ^ _777081) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (50513 ^ _777081) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (50515 ^ _777081) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (50517 ^ _777081) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (50519 ^ _777081) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (50521 ^ _777081) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (50523 ^ _777081) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (50525 ^ _777081) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (50527 ^ _777081) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (50529 ^ _777081) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (50531 ^ _777081) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (50533 ^ _777081) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (50535 ^ _777081) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (50537 ^ _777081) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (50539 ^ _777081) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (50541 ^ _777081) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (50543 ^ _777081) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (50545 ^ _777081) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (50547 ^ _777081) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (50549 ^ _777081) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (50551 ^ _777081) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (50553 ^ _777081) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (50555 ^ _777081) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (50557 ^ _777081) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (50559 ^ _777081) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (50561 ^ _777081) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (50563 ^ _777081) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (50565 ^ _777081) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (50567 ^ _777081) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (50569 ^ _777081) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (50571 ^ _777081) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (50573 ^ _777081) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (50575 ^ _777081) ^ [] : [-(class_HOL_Oequal(tc_Nat_Onat))], (50577 ^ _777081) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (50579 ^ _777081) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (50581 ^ _777081) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (50583 ^ _777081) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (50585 ^ _777081) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (50587 ^ _777081) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (50589 ^ _777081) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (50591 ^ _777081) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (50593 ^ _777081) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (50595 ^ _777081) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (50597 ^ _777081) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (50599 ^ _777081) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (50601 ^ _777081) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (50603 ^ _777081) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (50605 ^ _777081) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (50607 ^ _777081) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (50609 ^ _777081) ^ [] : [-(class_HOL_Oequal(tc_HOL_Obool))], (50611 ^ _777081) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (50613 ^ _777081) ^ [] : [-(class_HOL_Oequal(tc_Com_Ostate))], (50615 ^ _777081) ^ [] : [-(class_HOL_Oequal(tc_Com_Ovname))], (50617 ^ _777081) ^ [_1861627] : [-(class_HOL_Oequal(tc_List_Olist(_1861627)))], (50619 ^ _777081) ^ [_1861735, _1861737] : [-(class_Finite__Set_Ofinite(tc_sum(_1861735, _1861737))), class_Finite__Set_Ofinite(_1861735), class_Finite__Set_Ofinite(_1861737)], (50629 ^ _777081) ^ [_1862019, _1862021] : [-(class_HOL_Oequal(tc_sum(_1862019, _1862021)))], (50631 ^ _777081) ^ [_1862130, _1862132] : [-(class_Enum_Oenum(tc_sum(_1862130, _1862132))), class_Enum_Oenum(_1862130), class_Enum_Oenum(_1862132)], (50641 ^ _777081) ^ [_1862415] : [class_Finite__Set_Ofinite(_1862415), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1862415)))], (50647 ^ _777081) ^ [_1862590] : [-(class_HOL_Oequal(tc_Option_Ooption(_1862590)))], (50649 ^ _777081) ^ [_1862684] : [class_Enum_Oenum(_1862684), -(class_Enum_Oenum(tc_Option_Ooption(_1862684)))], (50655 ^ _777081) ^ [_1862873, _1862875] : [-(class_HOL_Oequal(tc_Nitpick_Opair__box(_1862873, _1862875)))], (50657 ^ _777081) ^ [_1862984, _1862986] : [-(class_Finite__Set_Ofinite(tc_prod(_1862984, _1862986))), class_Finite__Set_Ofinite(_1862984), class_Finite__Set_Ofinite(_1862986)], (50667 ^ _777081) ^ [_1863283, _1863285] : [-(class_Smallcheck_Osmall(tc_prod(_1863283, _1863285))), class_Smallcheck_Osmall(_1863283), class_Smallcheck_Osmall(_1863285)], (50677 ^ _777081) ^ [_1863567, _1863569] : [-(class_HOL_Oequal(tc_prod(_1863567, _1863569)))], (50679 ^ _777081) ^ [_1863678, _1863680] : [-(class_Enum_Oenum(tc_prod(_1863678, _1863680))), class_Enum_Oenum(_1863678), class_Enum_Oenum(_1863680)], (50689 ^ _777081) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (50691 ^ _777081) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (50693 ^ _777081) ^ [] : [-(class_HOL_Oequal(tc_Product__Type_Ounit))], (50695 ^ _777081) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (50697 ^ _777081) ^ [] : [-(class_HOL_Oequal(tc_Code__Evaluation_Oterm))], (50699 ^ _777081) ^ [_1864213] : [-(class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(_1864213)))], (50701 ^ _777081) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (50703 ^ _777081) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (50705 ^ _777081) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (50707 ^ _777081) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (50709 ^ _777081) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (50711 ^ _777081) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (50713 ^ _777081) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (50715 ^ _777081) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (50717 ^ _777081) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (50719 ^ _777081) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (50721 ^ _777081) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (50723 ^ _777081) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (50725 ^ _777081) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (50727 ^ _777081) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (50729 ^ _777081) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (50731 ^ _777081) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (50733 ^ _777081) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (50735 ^ _777081) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (50737 ^ _777081) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (50739 ^ _777081) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (50741 ^ _777081) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (50743 ^ _777081) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (50745 ^ _777081) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (50747 ^ _777081) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (50749 ^ _777081) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (50751 ^ _777081) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (50753 ^ _777081) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (50755 ^ _777081) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (50757 ^ _777081) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (50759 ^ _777081) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (50761 ^ _777081) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (50763 ^ _777081) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (50765 ^ _777081) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (50767 ^ _777081) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (50769 ^ _777081) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (50771 ^ _777081) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (50773 ^ _777081) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (50775 ^ _777081) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (50777 ^ _777081) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (50779 ^ _777081) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (50781 ^ _777081) ^ [] : [-(class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))], (50783 ^ _777081) ^ [_1866465] : [-(class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(_1866465)))], (50785 ^ _777081) ^ [_1866558, _1866560] : [-(hAPP(c_COMBI(_1866558), _1866560) = _1866560)], (50787 ^ _777081) ^ [_1866685, _1866687, _1866689, _1866691] : [-(hAPP(hAPP(c_COMBK(_1866685, _1866687), _1866689), _1866691) = _1866689)], (50789 ^ _777081) ^ [_1866848, _1866850, _1866852, _1866854, _1866856, _1866858] : [-(hAPP(hAPP(hAPP(c_COMBB(_1866848, _1866850, _1866852), _1866854), _1866856), _1866858) = hAPP(_1866854, hAPP(_1866856, _1866858)))], (50791 ^ _777081) ^ [_1867025, _1867027, _1867029, _1867031, _1867033, _1867035] : [-(hAPP(hAPP(hAPP(c_COMBC(_1867025, _1867027, _1867029), _1867031), _1867033), _1867035) = hAPP(hAPP(_1867031, _1867035), _1867033))], (50793 ^ _777081) ^ [_1867202, _1867204, _1867206, _1867208, _1867210, _1867212] : [-(hAPP(hAPP(hAPP(c_COMBS(_1867202, _1867204, _1867206), _1867208), _1867210), _1867212) = hAPP(hAPP(_1867208, _1867212), hAPP(_1867210, _1867212)))], (50795 ^ _777081) ^ [_1867341, _1867343] : [hBOOL(hAPP(hAPP(c_fequal, _1867341), _1867343)), -(_1867341 = _1867343)], (50801 ^ _777081) ^ [_1867563, _1867565] : [_1867563 = _1867565, -(hBOOL(hAPP(hAPP(c_fequal, _1867563), _1867565)))], (50807 ^ _777081) ^ [] : [hBOOL(c_fFalse)], (50809 ^ _777081) ^ [] : [-(hBOOL(c_fTrue))], (50811 ^ _777081) ^ [_1867876] : [hBOOL(hAPP(c_fNot, _1867876)), hBOOL(_1867876)], (50817 ^ _777081) ^ [_1868071] : [-(hBOOL(_1868071)), -(hBOOL(hAPP(c_fNot, _1868071)))], (50823 ^ _777081) ^ [_1868282, _1868284] : [hBOOL(_1868282), hBOOL(_1868284), -(hBOOL(hAPP(hAPP(c_fconj, _1868282), _1868284)))], (50833 ^ _777081) ^ [_1868591, _1868593] : [hBOOL(hAPP(hAPP(c_fconj, _1868591), _1868593)), -(hBOOL(_1868591))], (50839 ^ _777081) ^ [_1868811, _1868813] : [hBOOL(hAPP(hAPP(c_fconj, _1868811), _1868813)), -(hBOOL(_1868813))], (50845 ^ _777081) ^ [_1869031, _1869033] : [hBOOL(_1869031), -(hBOOL(hAPP(hAPP(c_fdisj, _1869031), _1869033)))], (50851 ^ _777081) ^ [_1869251, _1869253] : [hBOOL(_1869251), -(hBOOL(hAPP(hAPP(c_fdisj, _1869253), _1869251)))], (50857 ^ _777081) ^ [_1869471, _1869473] : [hBOOL(hAPP(hAPP(c_fdisj, _1869471), _1869473)), -(hBOOL(_1869471)), -(hBOOL(_1869473))], (50867 ^ _777081) ^ [_1869779, _1869781] : [-(hBOOL(_1869779)), -(hBOOL(hAPP(hAPP(c_fimplies, _1869779), _1869781)))], (50873 ^ _777081) ^ [_1869998, _1870000] : [hBOOL(_1869998), -(hBOOL(hAPP(hAPP(c_fimplies, _1870000), _1869998)))], (50889 ^ _777081) ^ [] : [-(c_Hoare__Mirabelle_Ostate__not__singleton)], (50891 ^ _777081) ^ [] : [-(c_Com_OWT__bodies)], (50893 ^ _777081) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, v_c)))], (50895 ^ _777081) ^ [] : [-(hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))], (50879 ^ _777081) ^ [_1870218, _1870220] : [hBOOL(hAPP(hAPP(c_fimplies, _1870218), _1870220)), hBOOL(_1870218), -(hBOOL(_1870220))]], input).
% 1.64/2.49  ncf('1',plain,[hBOOL(hAPP(c_Com_OWT, v_y))],start(50897 ^ 0)).
% 1.64/2.49  ncf('1.1',plain,[-(hBOOL(hAPP(c_Com_OWT, v_y))), c_Com_OWT__bodies, hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y)],extension(5299 ^ 1,bind([[_860933, _860935], [v_pn, v_y]]))).
% 1.64/2.49  ncf('1.1.1',plain,[-(c_Com_OWT__bodies)],extension(50891 ^ 2)).
% 1.64/2.49  ncf('1.1.2',plain,[-(hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))],extension(50895 ^ 2)).
% 1.64/2.49  %-----------------------------------------------------
% 1.64/2.49  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------